mental addition problem solving

Mental Math Practice

This page lets you practice mental math for free 🤗

(Want to learn all the tricks? We've broken down everything you need into 14 strategies )

Game Settings

Frequently asked questions, how do i use this page.

First, pick the arithmetic operations you want to practice - addition, subtraction, multiplication, division, squares, and/ or percentages. Then set the number ranges (from single-digit all the way to four-digit numbers) and how many math questions you want. Hit "Play" and you'll be presented with mental math problems one at a time. See how quickly you can solve them! It's great for sharpening your mental math skills (plus it prepares you for situations where quick calculations are necessary, such as case interviews or quant assessments). The key is to practice regularly and push yourself!

Can I use this on my phone?

Finally, the answer is yes! It wasn’t always that way, but it was one of our top requests. So for you, we figured it out. Now you can practice your mental arithmetic whenever you want - waiting in line, on the bus, wherever. Go crazy! Next step for us might be to build an iOS and Android app. Is that something you’d like?

How does this improve problem-solving skills?

By forcing you to think fast and calculate quickly, this trains your brain to process numerical information efficiently. That skill transfers to all kinds of problem-solving, from dissecting a salary negotiation to managing your personal finances. Keep practicing these simple math problems, and you'll develop mental shortcuts that will serve you well in many situations.

Are there ways to track progress or compete?

If you create an account and take our course, you’ll be able to track your best times. As for competing... Not yet, but we're considering it (we’re thinking about adding leaderboards), but not many people seem to care about that. So far our learners are focused on competing against themselves. Even trying to beat your own mental calculation time is hard! 😅

Will you add operators other than addition, subtraction, multiplication, division, squares, and percentages?

Maybe. Right now we're focused on the fundamental arithmetic operations (squares and percentages is a recent addition!). Master these basic operations first - they're the building blocks for all mental math skills (and suitable for all grade levels... You’d be surprised at how many people don’t know their multiplication tables). People have suggested fractions, decimals, and more integers. We want to provide a great math trainer for all learners, without making it too “feature-rich” and complex. So if you have any suggestions let us know!

Want to improve your mental math skills?

Check out our 14 strategies.

* The first 3 strategies are free .

Mental addition strategies: Add in parts; Use an easier problem

I explain two basic strategies for mental addition, using several examples. The first one is that of adding in parts. For example, to add 36 + 47, we can add 30 and 40, and 6 and 7. Since 6 + 7 = 13, this problem becomes 30 + 40 + 13, which is easier than the original.

Another strategy is to use a fact you already know to solve a similar addition problem. For example, if you already know that 6 + 8 = 14, you can use that to solve 76 + 8 or even 60 + 80.

How to quickly add 99 + 37? Compare it to the easy problem 100 + 37. The latter equals 137. The former is just one less, or 136. This strategy of using an easier problem is what we study in this lesson.

In the video below, I solve a PUZZLE CORNER with two unknowns, signified by a triangle and a square. We are given their sum and their difference. Yeah, you could use algebra but here in 3rd grade, we solve this puzzle using guess and check.

More mental addition — with 3-digit numbers

Math Mammoth Grade 3 curriculum

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Try These Mental Math Addition Strategies to Boost Math Fact Fluency

• By Shelley Gray
• October 15, 2011

10 Comments

Math fact fluency is much more than simply speed and accuracy. True fluency also includes flexibility and appropriate strategy use. We can help students become flexible thinkers who are able to build their own understanding by reinforcing mental math addition strategies.

We know that being able to think flexibly is more effective than memorization for math facts. This has been studied in depth by many different math researchers. But sometimes what happens when we begin to teach strategies, is that we “teach” the strategies for memorization. For example, “Whenever you see numbers that differ by 1, you can use the doubles plus one strategy.” Rather than “teaching” the strategies, ideally we want students to discover them and construct their own understanding. The best way to do this is through lots and lots of work with manipulatives. And yes, even if you teach upper grades your students can benefit from manipulatives!

However, sometimes it’s still nice to have a guide for what strategies to steer our students toward.

Seven Different Mental Math Addition Strategies

Below I have outlined seven different different mental math addition strategies that you can model in your classroom to help students build their understanding. I have also included videos and additional resources for some of them.

Counting On – Counting On is a beginning mental math strategy.  Counting on means that you start with the biggest number in an equation, and then count up. For example, in the equation 5+3, you want students to start with the “5” in their heads, and then count up, “6, 7, 8.” This is to discourage students from counting like, “1, 2, 3, 4, 5…..6, 7, 8.” Students also need to understand the commutative property of addition, where if an equation looks like this: “2+6,” they still should start with the bigger number (in this case, 6) and count up “7, 8.”

Here’s a video that will explain this strategy in more depth, or find a unit for teaching the counting on strategy HERE .

Make a Ten – Make a Ten is a mental math strategy where students use the number combinations that make ten to form connections and relationships to other facts. First, students must learn the number combinations that make 10. Then, they can confidently use those combinations. For example, to solve 8+5, a student might think, “I can take two from the 5 and give it to the 8 to make a ten, and then add the leftover 3 to make 13.” Ten frames are a fantastic way to illustrate this strategy.

Here’s a video that explains the make a ten strategy in more depth.

Find a unit for teaching make a ten HERE or find the math mats shown below HERE .

Find a unit for teaching break apart HERE .

I hope this post has helped you make a plan for teaching math strategies in your classroom! I know that if you did not learn this way, it is not an easy transition.

If you’d like more support for teaching addition strategies in the classroom, check out the Mental Math Addition Strategy Bundle that includes units for all of the strategies that were discussed above (photos of contents below).

I love your blog and math strategies. I am trying to improve my math instruction this year and your strategies are great! Thanks for all the ideas.

Hi…My little kid can do addition and subtraction but like you said he still goes back to counting.."1, 2, 3, etc.." Thanks for the counting on strategy, I will try this technique to advance his math skills… 🙂

These strategies are great…they should also be taught to the parents, so parents can better support their children’s learning.

Awesome strategies and I enjoyed reading your blog.

Great! Love me some additional mental math.

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Lovely strategies. Good collection of all the mental strategies. Gonna try in my class.

Thanks for sharing your work so everybody can learn from you. I celebrate innovation Keep up your hard.

Thanks for sharing your work so everybody can learn from you. I celebrate innovation Keep up your hard work.

Glad I found you. Very helpful, Thank you and keep up the good work!

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9 mental math strategies: Tips and Tricks for students

Mental math is an important skill for students of all ages. Applying mental math strategies can help you work faster and more accurately without a calculator.

In this article, we will list 9 strategies that will help you improve your skills. We’ll also include some tips and tricks to make mental math easier and faster!

From my 14+ years of teaching experience, I have observed that there are many students in high school that rely heavily on their calculators instead of using these mental math strategies.

By applying these tips and tricks they can work faster and apply these strategies to other topics such as Algebra and multiplying fractions.

What are mental math strategies?

Mental math strategies are simply methods or techniques that you can use to do math more quickly and accurately using your brain. These strategies can be used for addition, subtraction, multiplication, division, and more!

Here are my favorite mental math strategies that you can use:

1. Bridge to ten

Bridge to ten is when we count on to the next 10 and then add what is left.

Having knowledge of ‘ friends of ten ‘ which is basically recalling number combinations that add to 10, is essential prior knowledge.

The Bridge to ten strategy is great for simple additions such as 8+6.

You can change this to 8+ 2 + 4.

It is also great for questions such as 47 + 8.

Which can be bridged to ten as follows: 47 + 3 + 5.

Number lines are a helpful tool for this strategy.

2. Commutative Property

This mental math strategy can be used with addition and multiplication. It states that you can change the order of the numbers being added or multiplied and get the same answer. For example, 2+3 = 3+2.

Let’s say you’re adding up a list of numbers:

Instead of starting from left to right, try grouping them using ‘friends of ten’.

So you can see the total is 20 + 30 + 4 = 54

This can help you keep track of the numbers more easily and calculate the addition faster using this mental math strategy.

3. Adding 9

This mental math strategy can be used for addition. To use this strategy, you simply need to add 10 and then subtract 1.

For example, let’s say you’re trying to add 56+9

You can add the numbers like this:

Then, it becomes much easier to calculate the addition mentally because it is very easy to add 10 to a number.

4. Near doubles

Near doubles strategy is when you double a number and then adjust.

This is great when adding two consecutive numbers.

For example 7 + 8 is the same as double 7 plus 1, which equals 15.

Or you can adjust by doubling the larger number and subtracting 1.

For example 14+15 is the same as double 15 minus 1 , which equals 29.

5. Compensation strategy

The compensation strategy uses rounding up or down to make it easier to calculate an addition mentally.

First you want to round the second number up to the closest ten.

Then you compensate by subracting.

For example 47+19

This works for subtraction too.

For example, 76- 29

6. Doubling and halving

I LOVE this strategy! It is genius.

Doubling and halving is a mental math strategy for multiplication.

It works by halving one number (the larger one works best) and doubling the other number.

For example 48 x 5

7. Distributive property

The distributive property states that when you are multiplying a number by a certain sum or difference, you can multiply the number by each term in the sum or difference and then add the products together.

For example:

10 x (24 + 16) = 10 x 24 + 10 x 16 = 240 + 160 =400

Algebraically the distributive law looks like this:

This is a great mental math strategy to use for something like 99x 4

8. Using landmark numbers

Landmark numbers, such as multiples of ten or a hundred, are familiar with students so they can be used as a mental math strategy when adding.

For example 97 + 68.

97 is so close to 100. So you could add 3 to 97 and then subtract 3 from 68.

9. Repeated doubling to multiply by 4 and 8

Students often know how to double or multiply by 2 but their number facts for the 4 and 8 times tables are often not as strong.

Repeated doubling is a mental math strategy to help with this.

To multiply a number by four, double it twice.

For example, 12 x 4

To multiply a number by 8, double it three times.

For example 25 x 8

Final thoughts and my experience of using mental math strategies in the classroom

There are many more mental math strategies that I use regularly. These are just a few that I teach my high school mathematics students in our numeracy support sessions.

In my experience students need to be reminded of these strategies and given opportunities to practice them regularly.

As you can see, using mental math strategies can help you work faster and more accurately without a calculator. Try out these strategies the next time you’re doing your math homework.

What are some mental addition strategies?

Some mental addition strategies include bridge to ten, commutative property, using landmark numbers, adding 9, and near doubles. Examples of these mental math strategies are outlined in this article.

Related posts:

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Mental Math Strategies Every Child Should Know From 1st To 5th Grade

Tim Handley

When we think of mental math strategies, we are essentially thinking about those math skills we can do in our heads, without using the formal written methods that we would use for longer questions and standard algorithm methods. 

In this article we introduce you to some of the mental math strategies you can teach your students to help develop their mental math skills throughout elementary school.

What are mental math strategies?

Why are mental math strategies important, developing true fluency in mathematics, rapid recall vs mental calculations with notes, the concept must be understood before introducing the strategy , assessing the mental math strategies that your class is using, building confidence in mental math strategies, the mental math strategies children should know by the end of 5th grade, how to develop the mental math strategies needed for addition and subtraction, mental addition strategies and mental subtraction strategies at upper elementary , how to develop the mental math strategies needed for multiplication and division , mental calculation strategies for fractions, decimals and percentages, top mental math tips: how you can teach mental math strategies.

The Ultimate Guide to Problem Solving Techniques

Download these 9 ready-to-go problem solving techniques that every elementary student should know

Mental math strategies are accepted ways of working math out in your head, that help us take shortcuts, and get to the correct answer in an efficient way.

Mental math strategies are the foundations for most of the areas of mathematics that use numbers. Without efficient mental strategies, children can often struggle to quickly and fluently calculate.

Mental strategies are also the foundation of any written or formal method in mathematics. Referring to it as mental math does not mean you cannot write anything down at all, but any written work would be quick jottings to help remember through multi-step problems.

As children begin to use more formal methods, from around 3rd grade onwards, and as the numbers they are working with increase in value, mental math skills are vital for ensuring fluency and accuracy in math. 

Effective mental strategies are important if children are to develop ‘true’ fluency

True fluency can be best defined as children being able to confidently use and apply their knowledge of number relationships, number facts and our number system in order to calculate and solve problems.

It is worth remembering that fluency in math is not simply restricted to being able to recall known facts. More accurately, it is how children can use and apply these facts, including through a range of mental math strategies, that are important.

“Low achievers are often low achievers not because they know less, but because they don’t use numbers flexibly.” – Jo Boaler

Third Space Learning’s one-to-one online tutoring focuses heavily on building pupils’ confidence and fluency in math. Tailored to each individual child’s needs, our weekly tutoring lessons aim to strengthen pupils’ understanding of number facts and how to apply them across a broad range of questions.

Be careful not to mislabel mental math skills

One important thing to remember when working to develop ‘true’ fluency is that accuracy is not the same as fluency.

For example, consider the following scenarios, which while accurate, may not necessarily be classed as fluent:

• A 1st grader calculating 40 + 8 by counting in ones;
• A 3rd grader calculating 1003 – 998 using a formal written method;
• A 5th grader calculates 41.79 + 25.3 + 25.7 – 41.79 by adding the first three numbers and then subtracting the fourth.

This extract from the research paper, ‘Developing Computational Fluency with Whole Numbers’ published in 2000 by S J Russell, remains one of the best explanations of fluency:

‘Fluency rests on a well-built mathematical foundation with three parts:

• an understanding of the meaning of the operations and their relationships to each other — for example, the inverse relationship between multiplication and division;
• the knowledge of a large repertoire of number relationships, including the addition and multiplication “facts” as well as other relationships, such as how 4 × 5 is related to 4 × 50;
• and a thorough understanding of the base ten number system, how numbers are structured in this system, and how the place value system of numbers behaves in different operations — for example, that 24 + 10 = 34 or 24 × 10 = 240’.

When we discuss mental calculations in math at upper elementary school, we need to be clear about the distinction between facts that children should be able to rapidly recall vs the types of calculations that children should be able to calculate mentally, sometimes with the support of notes.

Retrieval practice and rapid recall of number facts is important because if children are able to recall number facts automatically, it allows them to free up their working memory when faced with more complex questions.

They are also able to more efficiently and accurately solve problems, reason and make connections if they are not having to repeatedly calculate the same ‘basic’ facts.

“In teaching procedural and factual knowledge, ensure the students get to automaticity. Explain to students that automaticity [with key number facts] is important because it frees their minds to think about concepts.” – Daniel Willingham – cognitive scientist, in ‘Is it true that some people just can’t do maths?’

Before we can expect rapid recall and automaticity of number facts with our mental math strategies, we need to teach the underlying math concepts. For example, only when children have a secure conceptual understanding of number bonds to 10, should rapid recall be attempted. 

From this understanding of number bonds to 10, the strategy of partitioning can be used. For example, by 5th grade most children should be able to calculate 34 x 5 mentally (30 x 5 + 4 x 5) using partitioning and their knowledge of the distributive law supported by basic workings.

Although students will be learning more and more math facts which they can recall ‘by rote’, it is vital that they understand the concepts. Working with manipulatives can help with this, moving to virtual manipulatives on the interactive whiteboard when the numbers get too big to physically hold.

One really interesting way to check mental math strategies is to present groups with different written versions of the same math problems.

• Present a single problem

If you present a problem, such as 64 + 17, in a sentence such as this, those children who are confident in their mental math strategies, will work it out in their heads.

They will usually, even subconsciously if they are fluent, partition the numbers and work out 60 + 10 and then 4 + 7, or 60 + 17 then add the 4. Some will do 64 + 10 and then add the 7. 

Some may round the numbers, so say 64 + 20 using their number bonds to 20 knowledge and then minus 3. 

Some may again use their numbers bonds to work out 64 + 17 by adding 63 + 17 to make 80 and then add 1.

You would expect your class to give a range of answers regarding their method, but hopefully all are fluent and can find the correct answer without any more than a quick jot down of some numbers if adding multiple steps.

• Create two versions of the same set of 10 questions

Now put together a sheet of 10 similar questions, with a range of addition and subtraction which you would expect your class to be able to do mentally. Create a second version of this which lays out the same questions, with the same exact numbers and same expected answer, in standard algorithm method format. 

Give half the class the first sheet laid out as a number sentence and the other half the second version where the questions are laid out in a standard algorithm method format. 

Do not tell groups that they have different sheets and hand them out to different tables so they do not see the other format of the same questions. Give them time to individually complete the questions and write down their answers. 

• Ask children to share their methods

Take the first question and ask someone to volunteer to share their method. Then ask someone else to share, then someone else, and so on. Ensure you get a couple of examples from tables who have the horizontal layout of questions, and a couple of examples from the tables who have the vertical column layout. 

You will likely find that the groups who had a horizontal layout were much more likely to have just worked it out mentally, whereas the groups given the vertical layout will have spent time doing the standard algorithm method to find and write down their answers, including every step, even though they could have easily completed those problems mentally. 

This activity is a great reminder that even when we see a formal calculation we should be using our mental math strategies to speed up where we can. 

When any new math concept is introduced – from addition through to percentages and decimals – children will benefit from being shown a physical representation of the numbers (using math manipulatives) and operations before using pictorial representations (such as number lines or bar models) and then finally written methods using the symbols of number and operation. 

Read more: Concrete Pictorial Abstract Method

Along the way there will need to be lots of repetition and practice recalling facts mentally. As children get older, into upper elementary, the move from physical to written will hopefully get quicker for new concepts as they are building on a solid foundation. 

Different children may be able to move to mental strategies at varying points of each unit. Some may jump from physical to mental if they grasp the concept quickly and have a sound understanding already. 

Others may not be able to reach fluency of recall and application until they have had a lot of practice with writing their answers down and building confidence in those new number facts and strategies. 

You may also need to unpack any misconceptions through those stages too, and this may involve going ‘backwards’ to the physical. It is good practice to always have manipulatives available during independent tasks, even in 5th grade and for all abilities. Sometimes a quick comparison using some Base 10 or Cuisenaire rods can help a child to ‘fix’ that strategy in their head. 

It is also important not to teach children to do ‘tricks’ in math such as “add a zero” when multiplying by ten as this can cause issues in later years with their understanding of place value. You would hope, however, that children spot such patterns in their answers and this should lead to discussion and comparison as well as presenting opportunities for children to test their theory, where they have spotted a possible pattern. Even if you know it is wrong/right, they will gain from the chance to test and apply that assumption.

Read more: Math tricks to avoid  

By upper elementary there are some specific mental math calculations that will help children immeasurably when working in both written work and mental work, arithmetic and reasoning. They actually form a progression starting from 3rd grade, so it is important that the groundwork has already been done in Kindergarten – 2nd grade to enable children to carry out the calculations mentally.

These skills are therefore best looked at as a progression, rather than a set of year group expectations.

How to improve mental math year by year

As well as building on children’s range of mental calculations as they progress through elementary, make sure they are also secure in their number facts each year.

In lower elementary, children will learn basic number facts including addition and subtraction. This will include number bonds to 20 by the time they finish 1st grade. They will do a lot of work with physical objects and role play, so it is good practice in these years to not just practice math skills during the math lessons, but also to make opportunities for questioning outside of these lessons. 

Ask children to count up how many students are absent today, counting the pencils on each table to see if they have enough (or too many or too few) and reinforce vocabulary from math lessons.

Once children have grasped the concept of addition facts and subtraction facts, and that they are inverse operations (they may not know that specific word yet though) they will begin to solidify their rapid recall of number bonds and apply them to their work.

It is never too early to introduce different strategies to work out their calculations either, so long as the base understanding is correct. Asking them if there is another way they could have found the answer is a question which can be asked in formal lessons, in role play or in sports. 

Counting forward and backwards

Counting forwards and backwards is first encountered in lower elementary, beginning at one and counting on in ones.

Students’ sense of number is extended by beginning at different numbers and counting forwards and backwards in steps, not only of ones, but also of twos, fives, tens, hundreds, tenths and so on.

Progression in counting forwards and backwards

These are the ways you can help your class to progress with counting forwards and backwards:

• Counting on or back in tens from any number (e.g. working out 27 + 60= ? by counting on in tens from 27)
• Counting on or back in fives from any multiple of 5 (e.g. 35+15=? by counting on in steps of 5 from 35.)
• Counting on or back in hundreds from any number (e.g. 570 + 300= ? by counting on hundreds from 570.)
• Counting on or back in tenths and/or hundredths (e.g. 3.2 + 0.6 = ? by counting on in tenths. 1.7 + 0.55=? by counting on in tenths and hundredths.)

Partitioning for addition and subtraction

Partitioning strategies teach children how to break up larger numbers into smaller ones.

It is important that children are aware that numbers can be partitioned – both along the place value boundaries (canonically) and in other ways (non-canonically).

They can then use their partitioning to help them calculate addition and subtraction calculations. This can be extended as children progress through upper elementary.

Progression in partitioning

These are the ways you can help your class to progress with partitioning:

• Calculations with whole numbers which do not involve crossing place value boundaries. E.g. 23 + 45= ? by 40 + 5 +20 + 3 or 40 + 23 + 5
• Calculations with whole numbers which involves crossing place value boundaries. E.g. 49 – 32= ? by 49 – 9 – 23 or 57 + 34 = ? by 57 + 3 + 31
• Calculations with decimal numbers which do not involve crossing place value boundaries 5.6 + 3.7= ? by 5.6 + 3 +0.7  or 540 + 380= ? by 540 + 300 + 80 or 540 + 360 + 20
• Calculations with decimal numbers which involve crossing place value boundaries. E.g. 1.4 + 1.7= ? by 1.4 + 0.6 + 1.1 and 0.8 + 0.35 = ? by 0.8 + 0.2 + 0.15

Compensating and adjusting

Compensation involves adding more than you need and then subtracting the extra.

This strategy is useful for adding numbers that are close to a multiple of 10, such as numbers that end in 1 or 2, or 8 or 9.

The number to be added is rounded to a multiple of 10 plus or minus a small number.

For example, adding 9 is carried out by adding 10, then subtracting 1. A similar strategy works for adding decimals that are close to whole numbers.

These are the ways you can help your class to progress with compensating and adjusting:

• Compensating and adjusting to 10. (e.g. 34 + 9=? by 34 + 10 – 1 or 34 – 11= ? by 34 – 100 – 1 = ?)
• Compensating and adjusting multiples of 10. (e.g. 38 + 68= ? by 38 + 70 – 2 or 45 – 29 = 45 – 30 + 1)
• Compensating and adjusting multiples of 10 or 100. (e.g. 138 + 69= ? by 138 + 70 – 1 or 299 – 48 = 300 – 48 – 1)
• Compensating and adjusting multiples with decimals. (e.g 2 ½ + 1 ¾ by 2½ + 2 – ¼  or 5.7 + 3.9 by 5.7 + 4.0 – 0.1)

Calculating using near doubles

When children have an automatic recall of basic double facts, they can use this information when adding two numbers that are very close to each other.

These are the ways you can help your class to progress with near doubles:

• Near doubles to numbers under 20. E.g. 18 + 16 is double 18 and subtract 2 or double 16 and add 2.
• Near doubles to multiples of 10. E.g. 60 + 70 is double 60 and add 10 or double 70 and subtract 10 or 75 + 76 is double 76 and subtract 1 or double 75 and add 1.
• Decimal near doubles to whole numbers. E.g. 2.5 + 2.6 is double 2.5 add 0.1 or double 2.6 subtract 0.1.

As students move through elementary school they will learn multiplication facts. They will need fluency in multiplication facts to enable them to recall these fast enough for testing now and in higher education. It is again vital that they understand the concept of multiplication rather than simply parroting the facts, rote style.

Though, practice is crucial as daily recall of known facts is vital to stop new facts pushing out the old where they are not fully embedded.

Children start multiplication understanding with doubling and halving in early elementary. This introduces the concepts of both multiplication and division and they should start noticing the patterns of these and apply this to math questions.

They will also learn multiplication facts for 5 and 10 and this starts with counting forwards and backwards in 5s and 10s, which they should also be doing from any given number not just zero.

By the end of 3rd grade, students should be able to recall all products of two one-digit numbers by memory. And then in 4th grade the 11 and 12 multiplication facts. They should also be applying these to word problems and multi-step problems as confidence increases, to ensure they are able to apply number facts rather than simply repeat them.

These mental arithmetic skills, and the fluency of them, will be vital in test situations. By the time they go to high school, they should have a very firm grasp of the number system along with known facts and patterns.

Place value multiplication strategies

Children should be able to build upon their rapid recall of 1-12 x multiplication and division facts, and multiplication and division facts for multiples of 10 and 100 to calculate an increasing range of multiplication questions mentally.

These are the ways you can help your class progress with place value:

• Multiply a 2-digit number by a single-digit number by partitioning. E.g. 26 x 3 = 20 x 3 + 6 x 3
• Multiply a decimal number with up to 2 decimal places by a single digit by partitioning. E.g. 3.42 x 4 = 3 x 4 + 0.4 x 4 + 0.02 x 4

Doubling and halving strategies

Children should be able to recognize halving as the inverse of doubling and be able to rapidly calculate doubles and halves of numbers.

Some double and half facts are rapid recall rather than ones that children should need to calculate each time, and these are covered in the lists above.

These are the ways you can help your class to progress with doubling and halving:

• Find the doubles and halves of any two-digit number and any multiple of 10 or 100. (e.g. half 680 or double 73)
• Multiply and divide by 4 by doubling/halving twice and 8 by doubling/halving again. (e.g. 34 x 4 = 34 x 2 x 2.)
• Find the doubles and halves of any number up to 10,000 by partitioning. (e.g. half of 32,202 by halving 3,000, 2000, 200 and 2.)
• Multiply by 50 by multiplying by 100 and halving. (e.g. 8 x 50= 8 x 100 divided by 2)
• Divide a multiple of 25 by 25 dividing by 100 then multiplying by 4 (by doubling and doubling again). (e.g. 350 ÷ 25 = 350 ÷ 100 x 2 x 2)
• Divide a multiple of 50 by 50 by dividing by 100 then doubling. (e.g. 450 ÷ 50= 450 ÷ 10 x 2)
• Double and half decimal number with up to one decimal place by portioning. (e.g. half of 8.4 by halving 8 and halving 0.4)

As they progress through elementary school, children should develop their understanding of fractions, decimals and percentages and how they are related to division.

By 5th grade, they should therefore be able to use their rapid recall of multiplication and division facts to calculate some questions involving fractions, decimals and percentages, mentally.

These are the ways you can help your class to progress with fractions, decimals and percentages:

• Mentally find fractions of numbers in the 2,3,4,5 and 10 times table using known multiplication and division facts. (e.g. 3/5 of 45 by 45 ÷ 5 x 3.)
• Recall percentage equivalents to ½, 1/3, ⅕, ⅙, 1/10 and 1/100. (e.g. ¼ = 25%)
• Find 10% or multiples of 10% of whole numbers and quantities. (e.g. 30% of 50 by 50 ÷ 10 x 3)
• Mentally find 50% by halving and 25% by dividing by 4 or 2 of numbers and quantities. (e.g. 25% of 150 by 150 ÷ 4)

Mental math percentages hack 

The tweet below is something that you may have seen going around Twitter in early 2019, but it represents a useful strategy to help work out tricky percentages.

We’ve dealt with the ‘what’ in significant detail, but how do we actually go about teaching mental math strategies? Here is a summary of our top tips:

• Teach mental math strategies and mental calculation techniques, don’t just rely on children ‘picking them up’. It is important that lesson time is devoted to teaching strategies conceptually and supporting children to make connections between their known facts and mental calculations. This is best achieved through modeling and the use of manipulatives etc.
• Engage children in discussion. Children should be encouraged to discuss their mental strategies with each other and as a class, and adults in the classroom should join in this discussion. Children will see and approach calculations mentally in different (and equally as valid) ways and through sharing these, they expose each other to different ways of thinking about and ‘seeing’ a calculation.
• Provide regular mental math practice. Children should have regular mental math practice that focuses on mental calculation strategies. Alongside teaching the strategies in the main math lesson, schools where children have a high level of competency and fluency in mental strategies, often devote 15-20 minutes a day to the practice and development of mental strategies and rapid recall outside of the main math lesson.
• Don’t think that timed testing is the only way to achieve rapid recall. Timed testing has been shown by many research studies to be one of the least effective ways of developing rapid recall. Instead, ensure children have plenty of opportunities to use, apply and recall the facts that you want them to be able to recall rapidly.
• Play games and create opportunities for meaningful activities. If the activities are fun and meaningful children will be supported in developing number sense and fluency in an increasing range of calculations.
• Ensure ‘basic’ number facts are practiced. It’s important that you do not neglect ‘basic’ number facts, for example, number bonds within 10, 20 and 100 and the 1-12x multiplication table. Often facts such as number bonds are only practiced at lower elementary, but it is vital that these are practiced and children are encouraged to use these facts in their mental calculations. Remember, if you don’t provide the opportunity for them to use it, they will lose it!
• How To Teach Multiplication Facts So Pupils Learn Instant Recall
• What Is Fluency In Math?

References:

Russell, Susan Jo (2007). Developing  Computational Fluency with Whole Numbers in the Elementary Grades

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by math consultant and author Tim Handley and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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What is mental math?

What is mental math, and how can we use it to solve the problems in front of us? Let’s take a look!

Author Christina Levandowski

Expert Reviewer Jill Padfield

Published: September 5, 2023

• Key takeaways

Mental calculation is important – While it’s important to learn how to show your work on paper, doing math in your head (or mental math) is a helpful, lifelong skill. 

Practice makes perfect – Don’t be afraid to start your practice with “training wheels” — and don’t be afraid to make mistakes! Use paper, your fingers, and other tools to help nail down concepts before practicing mental math. 

Don’t make it complicated – There are multiple ways to get to the right answer. The “best way” is what is most intuitive for your child. Don’t make the learning process complicated or stressful!

Table of contents

• What is mental math
• Basic strategies for mental math
• Mental math at home
• Tools for mental math

Mental math is a huge part of one’s daily life. In fact, we often find ourselves doing it subconsciously or automatically! 

Many parents and caregivers often wonder how to teach their children mental math skills — and we’re here to show you that with the right techniques, it doesn’t have to be difficult. 

Read on to discover what mental math is, strategies to master core skills (such as calculations), and methods you can use to encourage an attitude of lifelong learning in your child.

Mental math refers to the steps and techniques we use in our daily lives to solve both basic and advanced math problems in our head., From calculating sale prices to balancing our checkbooks, mental math calculations help us make “number sense” of our environment — and the mental processes we use are often much easier than the paper methods we’re taught in the classroom.

Why is mental math so important?​

This form of math helps kids and adults navigate everyday math challenges! Mental math often helps us get faster, more accurate answers, and the techniques used to master a mental math skill can help us improve our ability to reason. 

Basic strategies for successful mental calculations

Everyone’s journey to mastering mental math starts differently. For example: Many might start by focusing instead on fact fluency, mental math exercises (like learning the concepts that go into solving square roots or cube roots), or more complex calculations. 

The concept of mental math usually comes into a child’s life in primary school (or elementary school), and often looks like memorization. Think about the addition facts, multiplication tables, and other basic functions you still remember from childhood; these were all taught to you to help you with mental math later in life. Teachers can inspire this journey for students using games, songs, and other strategies to reinforce the concepts. 

Here are a few common mental math tricks and steps for you to consider as your child begins their learning journey! 

Using multiples of 10​

Basic arithmetical calculations (like using multiples of 10) are part of a core group of skills essential to every learner. 

Using multiples of 10 can help with rounding, pricing, budgeting and more — and they can also help a student learn their multiplication facts. 

Many teachers use cards to teach these math facts, or they might use song or rhythmic beats,  giving students something to remember when it’s time to use the multiplication facts on a test or in real life. 

To do this mental math, simply add 10 to whatever 10s-based multiplication table you’re working with. For example: 

10 x 2 = 20

10 x 3 = 30

10 x 4 = 40

We see that each ascending multiple of 10 is the multiple itself with a 0 at the end. This confirms that 10 x 5 = 50, 10 x 6 = 60 and so on.

Subtracting large numbers

Subtracting larger sums can be difficult for some learners. However, mental math can make this process much easier. 

We can use the power of mental math in two different ways: visualization and estimation. 

Using visualization, we can “see” lines separating each column of a subtraction problem in our mind’s eye. For many, this might look something like the problem below: 

– | 2 | 3 

—————-

We can then solve it as we normally would on paper.

The second method uses estimation. This option relies on logic and a solid grasp on which numbers are “near” other numbers.

We can simplify 109 – 23 in seconds using mental math concepts. Instead of seeing 109 – 23, we can use estimation instead with an easier subtraction problem: such as 100 – 20. 

We know that 100 – 20 = 80. We then subtract 3 from 9, adding the difference to the total answer. This gives us 86. 

You can check your work on paper as you practice — and you’ll see that 109 – 23 does, indeed, equal 86.

Quick trick for multiplying by 5

Multiplying by fives can be helpful for those looking to master telling the time, estimation, and more. It can be done simply using mental math techniques. 

Before we begin, we have to understand a simple rule: Your answers, when counting by 5s, will only ever end in 0 or 5. Using this rule, you can easily determine if you are skip counting correctly (or not!) 

Knowing this, you can then prompt your child to begin multiplying and memorizing the tables. You’ll both find that: 

5 x 2 = 10 

5 x 3 = 15 

…and so on. 

You can then check their work simply, adding “5” to whatever number you leave off with (so long as it ends in 5 or 0). 

You can also have them begin learning this skill on their hands, counting by fives to the next correct integer (i.e., counting five to ten).

Addition by rounding up or down

Addition by rounding works similarly as subtraction by estimation does — as shown above! 

Mental math and estimation skills can be especially helpful if you’re working to add larger numbers. For example: 

While we can solve this using paper, it can be easier, faster, and more convenient to do it in our heads. Using estimation, we can rewrite the equation above as: 200 + 400 — which gives us a sum of 600. 

We can then add 5 + 2 (which equals 7), adding 7 to our total sum of 600. 

This gives us 607. 

We can check our work using paper methods, confirming that 402 + 205 does equal 607. 

Way to encourage mental math at home and in the classroom

Mental math might not be an intuitive skill for some learners — and that’s completely okay! Every student learns at their own pace and in their own ways. However, there are some tips and tricks you can use with your learner to help them take interest in developing these skills, no matter what confidence level they’re operating at. 

Reduce the use of calculators​

Calculators can become a crutch if they’re used too often. While it’s true your learner will eventually have a calculator in their pocket (i.e. their cellphones), it’s not something they should rely on. 

Your student will also be exposed to mathematical concepts and “problems” in their everyday life — such as budgeting, pricing, and estimation) — where a calculator may not be available. Mastering these skills now can give your student the confidence they need to thrive, no matter what situation they might find themselves in. 

The solution to calculator dependency is simple: remove the calculator from the learning experience. 

As you do this, you can offer your student a range of learning strategies and methods to help get them started as they build mental math skills. After your student begins to take interest and master the concepts, you can begin to reintroduce the tool for more complicated computations. 

Use it out in the real world​

A possible barrier to mastering mental math could be determining how and when to use it. You can address this by “striking first,” being purposeful about finding opportunities for mental math when you’re out and about. 

Certain scenarios where mental math might be used/could be talked about include: 

• Counting up 
• Estimating grocery store totals 

Do it with them/model it​

Some students may hesitate to learn mental math due to a fear of failure. Parents and caregivers can address this by jumping into the “deep end” and digging in with the student. 

Modeling can be an ideal way to learn mental math, speaking to a student’s learning style while addressing any fears or insecurities they might have. It also allows the parent, caregiver, or teacher to step in and ensure that the student is getting the right answer(s) as a result of the process they’re using.

Start basic and work from there

It can be easy to dive right in and overwhelm the student with too many advanced concepts. Mental math skills give students the opportunity to go back and master the fundamentals, truly solidifying their mathematical skill and understanding. Don’t be afraid to start (extra) simple, using it as a jumping-off point for future learning. 

Tools to help with mental math

Ready to start your mental math journey?

Here are some tools to consider based on your student’s unique needs: 

• DoodleMath: Our math app offers an engaging, adaptive learning experience tailored to individual needs, helping students sharpen their mental math skills through fun exercises and interactive challenges. With its gamified approach and diverse question formats, it makes mastering mental math both enjoyable and effective.
• Physical math toys, games, and learning supplies: Items created by Lakeshore or similar companies can give students a way to learn on their own terms, in a way that’s the most natural — through play.

Sign up for the DoodleMath app today!

Turn math into an adventure when you sign up for DoodleMath.

Click here to get started for free!

FAQs about mental math

We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!

Practice makes perfect when it comes to improving mental math skills. Some effective ways to enhance mental math abilities include practicing simple arithmetic operations (addition, subtraction, multiplication, and division) daily, memorizing key mathematical facts and tables, breaking down complex problems into smaller, more manageable parts, using visualization techniques, and participating in mental math games or exercises. 

Yes, mental math can be highly beneficial for students of all ages! It not only helps them develop a quicker and more accurate approach to solving math problems, but it also improves their overall math comprehension and confidence. 

Mental math can be especially helpful during exams or timed assessments when a calculator may not be allowed. Furthermore, students who excel in mental math often find it easier to grasp advanced mathematical concepts, and perform better in higher-level math courses.

Yes, there are several online resources available to practice mental math skills. Many websites and mobile applications offer interactive mental math games, quizzes, and exercises suitable for learners of all ages and levels. 

Some popular platforms include Math Playground, Math Games, Khan Academy, and MentalUP. These resources often provide real-time feedback and progress tracking, making it easier for users to measure their improvement over time. Simply search for “online mental math practice” or “mental math games” to find a wide range of options to suit your needs.

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Christina Levandowski

Christina has written for hundreds of clients from small businesses to Indeed.com. She has extensive experience working with marketing strategy and social media marketing, and has her own business creating assets for clients in the space. She enjoys being an entrepreneur and has also started pursuing investment opportunities as time permits.

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12 Mental Math Practices to Improve the Skills of Students of All Ages

Written by Marcus Guido

• Teaching Strategies

• Introduce mnemonic devices
• Read math books
• Provide relevant word problems
• Play estimation games in class
• Play fact fluency games in class
• Encourage the use of math apps and websites
• Round up when multiplying by 9
• Double and halve
• Cover-copy-compare
• Use the Taped-Problem approach
• Building blocks
• Number talks

Mental math isn’t explicitly part of most curricula, but students who can’t answer relatively-simple equations in their heads with speed or automaticity will likely struggle with harder content.

But before answering the question, “How can I improve my mental math?”, it’s helpful to know the definition(s) of mental math.

The Manitoba Association of Mathematics Teachers defines mental math as:

A combination of cognitive strategies that enhances flexible thinking and number sense. It is calculating mentally without the use of external memory aids. It improves computational fluency by developing efficiency, accuracy, and flexibility.

Or, from students’ perspectives, it’s:

• Math done in your head
• Math that is done in the mind, quickly and efficiently
• Warming up your head with math
• To do math instantly, without the effort put into operations and processes
• Math that you understand so well that you don’t need to write anything down to do calculations/find the answer

Prince Edward Island’s Department of Education believes “mental mathematics must be a consistent part of instruction in computation from primary through the elementary and middle grades.”

Wayne Watts, educator and author of numerous math textbooks, once said: “Number sense cannot be taught. It can only be developed.”

The science behind it is convincing, too.

Research-backed benefits of mental math

Credit: Jinx!

For example, an oft-cited study of a 1st grade class found that students who quickly recall addition facts had more cognitive resources to learn other skills and concepts.

In the journal Cogent Education , researchers ran another study with 118 students in 5th grade exploring how mental computation and mathematical reasoning affect each other.

The evidence was fascinating:

[There] is a significant positive correlation between mental computation and mathematical reasoning. It is noteworthy that rather than exposing students to familiar classical problems, students need to be enabled to deal with exceptional/non-routine problems, and especially young children should be encouraged to do mental computing in order for developing both skills.

Duke researchers published a study in Clinical Psychological Science about mental math -- from a health perspective.

After brain-scanning 186 undergraduates, results suggested engaging the brain’s prefrontal cortex during mental math exercises is linked to better emotional health.

Thankfully, you’re already helping students build core mental math skills when you teach rounding, estimating and fact fluency -- developing number sense, as well as how they remember and reproduce steps and solutions.

It's mental math practice time!

To improve how your students build and practice these mental math skills, try the 12 strategies below. Use the ones that best work for you.

1. Introduce mnemonic devices

Students who struggle with basic fact fluency can improve by using mnemonic devices -- cues such as rhymes and acronyms to help recall information.

In her master’s thesis, Teaching Through Mnemonics in Elementary School Classrooms , Arianne Waite-McGough found teachers understand the positive impact this device can have on students within and “beyond the classroom walls.”

Current research shows that singing, moving and overall enjoyment of a subject enhances the learning process and long term recall of material. All of these requirements are present when using mnemonics in the classroom. My research proved similar findings. All of the teachers that I surveyed noted higher levels of learning, engagement and fun while singing songs based on the core content material.

Take this mnemonic device for a multiplication fact as an example: I need to be 16 years old to drive a 4x4 pickup truck.

Because they must be easy to remember, it helps if the cues involve:

• Tangible objects or scenarios
• Quick stories that distill larger chunks of information

Although you can think of mnemonic devices yourself and share them with students, it’s beneficial if you run an activity that gets them to make their own.

They’ll likely find it easier to remember mnemonic devices they create. 

2. Read math books

There are many math books that effectively contextualize the processes behind solving equations, helping students commit them to memory.

Depending on student age, consider:

• Each Orange Had 8 Slices  --  This book focuses on counting and addition, presenting problems in easy-to-process sentences. It sets a new scene, complete with questions, with each turn of the page.
• The Grapes of Math  --  Containing basic multiplication problems, this book is a series of illustrated riddles. Each riddle offers clues and secrets to solving a specific equation, helping students improve reading comprehension along with math skills.
• Sir Cumference  --  Set in medieval times, this book series focuses on measurement and geometry. With occasional help from his son and wife, Radius and Lady Di of Amater, the knight Sir Cumference must solve math-related challenges that pose threats to his family and kingdom.
• Secrets of Mental Math  --  As opposed to a children’s book, this guide promises to “have you thinking like a math genius in no time” with the help of “mathemagician” Arthur Benjamin. Since it’s 200+ pages long, you might find more success in selecting key excerpts and reading -- and applying -- the mental math tricks with your students. There’s also a foreword by Bill Nye the Science Guy!

As you read books out loud, your students can practice their mental math. Alternatively, you may use books as a way to leverage the benefits of peer teaching .

Just pause after identifying an equation, giving them time to work through the problems in their heads. After they share their responses, read on to discover the answer.

3. Provide relevant word problems

Many students will be more receptive to math drills and practice if the material is engaging.

David Kember, a professor in curriculum methods and pedagogy, and his team published an article in Active Learning in Higher Education about the motivators of student learning.

Upon interviewing 36 undergraduate students, Kember concluded:

Teaching abstract theory alone was demotivating.  Relevance could be established through: showing how theory can be applied in practice, establishing relevance to local cases, relating material to everyday applications, or finding applications in current newsworthy issues.

In other words, if students don’t find your math lesson relevant, their motivation to learn will greatly diminish.

A straightforward, yet effective, way of enlivening content is by creating math word problems . This is because you can tailor questions to students.

For example, you can:

• Reference Student Interests --  By framing your word problems with student interests, you should grab attention. If most of your class loves baseball, a measurement problem could involve the throwing distance of a famous outfielder. Using cross-cultural and cross-curricular connections with help strengthen students’ neural loops.
• Make Questions Topical --  Word problems based on current events or issues can engage students by providing clear, tangible ways to apply knowledge. Not only will students find your lessons more interesting, they’ll believe it’s worth knowing.
• Include Student Names --  Naming a question’s characters after your students is an easy way make it relatable, motivating your class to tackle the problem.

By capturing interest, student motivation should increase when practicing skills important for mental math.

Note : If they struggle with world problems, teach the mnemonic, “ STAR ”:

S earch the word problem  T ranslate the words into an equation  A nswer the problem  R eview the solution

4. Play estimation games in class

Estimation games are fun math activities that encourage students to develop skills and techniques they can use to simplify equations in their heads.

Easy to run but challenging to play, a popular estimation game in many classrooms involves only two dice and a sheet of paper that’s divided into two columns. One column lists the values on each dice face, whereas the other contains numbers of your choosing.

For example:

To play, pair students together. Taking turns rolling the dice, they must add the corresponding numbers together in their heads. For example, if a student rolls five and six, the equation is 878 + 777. Without pencil, paper or calculator, the student must solve the equation. If he or she is within a range of five numbers -- verifying the solution with a calculator -- the answer is considered correct.

The first student to answer five questions right wins.

For more advanced classes, you can simplify the numbers but require multiplication instead of addition.

5. Play fact fluency games in class

A fun alternative to flashcards, fact fluency games allow students to build recall and reproduction skills important for mental math.

Engaging options for 1st to 8th grade classes include:

• Math Facts Bingo --  Create bingo cards that contain answers to different equations. Then, hand them out to students. Instead of calling numbers, state equations such as 8 x 7. After determining the product is 56, they can check off the number if it’s on their cards.
• Stand Up, Sit Down --  Pick a number and share it with students. Then, read equations out loud. Sitting in a circle, students must stand if the answer matches the number you picked. If they incorrectly stand or remain seated, eliminate them until one student remains.
• 101 and Out --  As the name implies, the goal is to score as close to 101 points as possible without going over. Start by dividing your class into groups, giving each a die along with paper and a pencil. Groups take turns rolling the die, deciding if it’s best to count the number at face value or multiply it by 10. After each roll, the number is added to the group’s total. The game ends when a group hits 101 points or goes over -- whichever comes first.

As skill-building as they are engaging, your students’ improvement in fact fluency should be clear after playing a few rounds of these math games .

6. Encourage the use of math apps and websites

An alternative or supplement to drills and worksheets, consider using a digital program that features a range of problems aligned with different skills.

Such math apps and websites prompt students to continuously answer questions in an often-engaging environment, building a range of skills important for mental math.

Popular options include:

• Prodigy Math  --  Aligned with math curriculum from across the English-speaking world, Prodigy automatically differentiates content and gives adaptive feedback tailored to each student. Teachers like you can also make in-game assignments to deliver custom content.
• NRICH  --  An ongoing project by the University of Cambridge, this website features math games, articles and problems. It divides resources by United Kingdom key stages and United States grade levels, allowing your students to easily access the right content.
• Math Is Fun  --  This website contains content suitable for younger students, using concise sentences and cartoon characters. On top of exercises that cover essential math skills, there are games and puzzles.

Because all students need is a computer or mobile device to use these programs, it’s likely some will voluntarily practice at home.

Free educational content, aligned to your curriculum

Make mental math practice fun with our safe, standards-aligned math adventure!

7. Round up when multiplying by 9

There are simple ways to alter difficult equations, making them easier to solve with mental math.

Students can use existing rounding and fact fluency skills when multiplying by 9, 99, 999 and any number that follows this pattern.

First, tell students to round up the 9 to 10. Second, after solving the new equation, teach them to subtract the number they just multiplied by 10 from the answer.

For example, 67 x 9 will lead to the same answer as 67 x 10 - 67. Following the order of operations will give a result of 603. Similarly, 67 x 99 is the same as 67 x 100 - 67.

Despite more steps, altering the equation this way is usually faster and allows students complete it in their heads.

8. Double and halve

When mastering multiplication beyond basics, students can quickly use mental math skills to multiply two integers when one is an even number.

They just need to halve the even number and double the other number. They stop this process when the even integer cannot be halved, or when the equation becomes manageable.

Using 33 x 48 as an example, here’s the process:

The only prerequisite to this mental math trick is understanding the 2-times table.

9. Cover-copy-compare

Normally used as an intervention tactic, Cover-Copy-Compare can have a place in most fact fluency lessons.

There are three steps to this mental math practice, which are:

• Creating a Math Fact Sheet --  Divide a sheet into two columns, writing about 10 math facts pertaining the same skill in the left column. Include number-sentences and answers. In the right column, write “Responses.” Distribute copies of the sheet to students.
• Running the Exercise --  The goal for students is to study the math facts in the left column, correctly reproducing them in the “Responses” column. To do so, give them time to study the facts. After, they fold the paper to cover the left column while writing -- from memory -- the first fact in the “Responses” column. If correct, the student can move onto the next fact. If incorrect, the student tries again until he or she has properly reproduced the math fact.
• Recording Mastered Skills --  Once a student has completed a certain number of sheets related to a common skill, you can award him or her a badge that denotes skill mastery. This  gamification strategy  can make the exercise more engaging.

To go beyond basic fact fluency, you can make sheets that focus on rounding, memorizing steps to complex equations and more.

10. Use the Taped-Problem approach

A useful  active learning strategy , the taped-problem approach is one of the most effective ways for students to build fact fluency, indicates a 2004 study that pioneered the strategy.

First, obtain or make an audio recording of basic math problems that has short pauses between stating the problem and revealing the answer. Second, provide each student with a pencil and paper.

As you play the recording, students must write out each equation and try to solve it before the answer is revealed. If the student cannot solve the question, he or she writes down the correct answer. If the student reaches an incorrect answer, he or she crosses it out and writes the right response.

You can lengthen the pauses so students don’t depend on hearing the answers, whereas you can shorten them to encourage automaticity.

11. Building blocks

Wondering how to improve mental math speed across your class? Familiarize students with building blocks such as multiplication tables or fractions, decimal, and percent equivalents.

The more your students become familiar how multiplication tables or equivalents look, the quicker they’ll be able to recognize and solve problems in and outside the classroom.

A study in the Journal of Neuro science titled, “Why mental arithmetic counts: Brain activation during single digit arithmetic predicts high school math scores”, tested 33 high school students on their ability to solve addition and subtraction equations.

All of them performed well, which correlated to their math PSAT scores. Interestingly, as neurobiologist Dr. Susan Barry outlined :

Those students with higher math PSAT scores engaged parts of the brain, the left supramarginal gyrus and bilateral anterior cingulate cortex, which have been associated with arithmetic fact retrieval. In contrast, those students with lower math PSAT scores engaged the right intraparietal sulcus, a region involved with processing numerical quantity. In completing the test in the scanner then,  students with the higher math PSAT scores relied more on their memory of arithmetic facts .

12. Number talks

Ruth Parker, the CEO of the Mathematics Education Collaborative, and Kathy Richardson, one of the nation’s leading educators of elementary mathematics, developed this mental math practice.

To start, pose an abstract math problem. Take 18 x 5 as an example problem and ask your students to try and solve it in their heads.

Naturally, in a class of 20+ students, you’ll likely find they answered correctly -- but differently.

Number talks are a perfect way to illustrate that there’s creativity in math. They’re also a great way to begin your math lesson or encourage parents to do with their kids!

In the article “Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts”, professor of mathematics education and co-founder of Stanford University’s you cubed , Jo Boaler, writes :

Research tells us that the best mathematics classrooms are those in which students learn number facts and number sense through engaging activities that focus on mathematical understanding rather than rote memorization.

So, we trust these activities will help your students’ mental math practice this school year and beyond.

Ready to share these mental math secrets?

Okay, they’re not really secrets. But u

sing these mental math practices should help your students build rounding, estimating and fact fluency skills -- allowing them to solve many equations with ease and automaticity, preparing them to tackle tougher content.

Armed with increased confidence, you may notice an uptick in student engagement and motivation.

These benefits, in and of themselves, make a strong case for practicing mental math.

Create or log in to your teacher account on Prodigy Math , the online math platform designed to help students build mental math skills through an engaging game-based learning environment.

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5 Easy Mental Math Strategies for Addition and How to Teach Them

There are many ways to help your students master mental math strategies for addition. Some strategies are simple, like the counting on strategy , while others are more difficult. In this post, we’ll go over different ways you can help your 1st graders use a mental strategy to solve addition facts.

Mental math is an important skill for students to have, especially in the early grades. Being able to quickly and accurately do basic math calculations in your head can save time and help students feel more confident in their math abilities. You’ll be surprised at how much difference these techniques can make!

Here are five easy mental math strategies and ideas on how to teach and practice them. The ideas are great for small groups , whole group, or partner games!

Counting On

The counting on to add strategy is one of the first mental math strategies for addition that I teach my class. This is when you start with the bigger number and count on. For example, in the problem 3 + 8 you would start with 8 and count on 3 until you get to 11. This strategy does not require anything but the students’ fingers and they catch on really quick to this.

One issue with this strategy is that students tend to want to use it all the time. Once more efficient strategies have been taught, I find I have to require my students to use them throughout the year and not always fall back to counting on.

Make sure when you begin teaching this strategy that you allow students to use manipulatives to slide as they count on. Lots of times teachers will skip this step and go straight to having students solve with just paper and pencil. First graders need to go through the concrete stage to get started with a firm foundation with any math skill.

How To Teach Counting On

To teach this strategy, have students practice counting on from a variety of numbers. You can also play games that involve counting on, such as “Roll and Add” where students roll two dice and then count on from the larger number to find the sum.

Here are a few other easy ideas to use in your classroom.

Number Line Race

Draw a number line on the board or on a large piece of paper. Split the class into pairs and give each pair a marker. Call out an addition problem such as 8 + 6 and ask students to find the sum of the two numbers by counting on from the bigger number. The first pair to reach the correct answer and raise their hand gets to put a mark or their initials on the number line at the answer. Repeat the process with different starting numbers and different sums until all pairs have had a turn.

This activity helps students practice counting on along a number line and reinforces their understanding of addition. By making it a race, students are motivated to find the answer quickly and efficiently.

Addition Dice Game

For this game you’ll need two dice, a whiteboard and marker or paper and pencil.

Player one rolls two dice and adds the numbers together and says the sum out loud. The next player rolls one die and adds that number to the previous sum. Players take turns counting on from the previous sum and adding the next number rolled until they reach a target number.

For example, let’s say player 1 rolls a 4 and a 5, giving them a sum of 9. Player 2 rolls a 3 so they count on from 9 up to 12. Player 1 will now roll one die. If they roll a 5, they would start with 12 (the previous sum) and count up 5 to 17. Whoever reaches the target number set by the teacher wins.

This game helps students practice adding and counting on, and reinforces their understanding of number sequences.

One of the other common mental math strategies for addition are doubles facts. Doubles facts are basic addition facts that involve adding two of the same number together such as 6 + 6 or 8 + 8. To teach doubles facts, flash cards are the best way to start. Simply having students memorize their doubles facts will be extremely beneficial in helping them with basic math down the road.

Try any of these activities to have students review their doubles facts so they don’t forget them.

• Doubles Flashcards: Create flashcards with double facts written on them (e.g. 2 + 2 = 4) and have students practice finding the sum.
• Doubles Fact Bingo: Create bingo cards with double facts and have students play bingo, marking the sums as they are called. Use a bingo card generator to make this easy!
• Roll and Cover: Create a 10×10 grid and write numbers 1 to 10 along the top and also down the side. Give each student a game board and a die. Students take turns rolling the die and adding the number they rolled to its double (if they roll a 4, they find 4 + 4 = 8). Students locate where the sum would go on their game board grid by finding 4 along the side and 4 along the top and write it in that spot like when you play Battleship. The first student to cover all the sums on their game board is the winner.
• Memory Match: Make sets of cards with one half of a double fact on each card (2 on one card, 2 on another). Do this for all numbers 0-10. Lay the cards face down. Students will turn over two cards on their turn. When they turn over 2 of the same number they say the double fact and the answer. If they are correct they keep the cards as a point.
• Doubles Race: Divide students into teams and have them race to write as many double facts as they can within a set time limit. Using a large piece of butcher paper and makers makes this game fun for students!

Doubles Plus 1

This strategy involves adding one more to a doubles fact. For example 5 + 6, if I know 5 + 5 = 10 then 5 + 6 = 11. This strategy cannot be taught until students have mastered their doubles facts. Once they have, try these activities to practice doubles plus 1.

Partner Practice

Have students work in pairs to take turns saying a double fact and the corresponding doubles plus one fact. For example, “2 + 2 = 4 so 2 + 3 = 5. It may be helpful to have doubles facts already written out on cards for students to pick from. Then they must say the doubles plus one fact that goes with the card they draw. This game is great for those times when you have a few extra minutes between lessons.

Doubles Plus One Grid Play

On a grid write all doubles plus one answers (3, 5, 7, 9, 11, 13, 15, 17, 19, 21). Use a 10-sided die or create a spinner with 1-10 on it. This would also be a great oppurtunity to differentiate by using a 6-sided die or a spinner with only 5 sections.

Students will roll or spin and then double that number. Then they will say the doubles plus one fact that goes with it. So if they roll 5 they will say 5 + 5 = 10 so 5 + 6 = 11. If they are correct, they get to cover the number 11 on the grid with their color marker. When all spots are covered the player with the most of their color is the winner.

Fact Families

Fact families are one of the best mental math strategies for addition for 1st graders. They help students understand the relationship between addition and subtraction. One common misconception teachers have when teaching fact families is to give students 3 numbers and have them create 2 addition and 2 subtraction facts that go with those numbers.

By doing this students are not taught the reasoning behind fact families. It is vital for students to understand the relationship between the numbers and why they are related.

To teach fact families, teachers can start by using manipulatives such as number bonds or cuisenaire rods to show the connections between numbers.

For example, using number bonds, the teacher can demonstrate how to add the two smaller numbers to find the larger number, and then how to subtract one of the smaller numbers from the larger number to find the other smaller number. This helps students see the relationship between the numbers in a fact family and understand that the same numbers can be used in different ways in addition and subtraction equations. Using manipulatives can make abstract concepts more concrete and engaging for students, particularly in the early grades.

Here are some ideas to use with your students!

Fact Family Building Blocks

For the “Fact Family Building Blocks” activity, teachers can give each student a set of building blocks in different colors. Students can use the blocks to build the numbers in a fact family, such as the fact family for 4, 2, and 6. To build 4, students can use four blue blocks, for 2 they can use two red blocks, and for 6 they can use two blue and four red blocks, showing the connection between the numbers. Students can then practice solving the addition and subtraction equations using their blocks, such as 2 + 4 = 6 and 6 – 4 = 2. This activity provides a hands-on way for students to understand the relationship between numbers in a fact family and strengthens their understanding of addition and subtraction.

Fact Family Silly Stories

Students can use the numbers in a fact family to create silly stories, reinforcing the connection between the numbers.

For example, using the fact family of 4, 2, and 6:

• A student could create a story about two aliens, each with 4 arms, who find two more arms and now have 6 arms total.
• Their partner could create a story about a cat who loses two of its whiskers, leaving it with 4 whiskers.

This might need to be modeled a few times by the teacher for students to catch on.

By using the numbers in a fact family in their silly stories, students can build their understanding of the relationships between the numbers and practice mental arithmetic.

Making a Ten

Making ten is a crucial mental math strategy for 1st graders to learn. Before students can be held accountable for making a ten to add, they need to know the number partners for ten.

Teachers can make this interactive and fun by using hands-on activities such as building with blocks or using a ten-frame. For example, teachers can ask students to place blocks in a ten-frame to show the number they are working with, then ask them to find another number that, when combined, makes ten.

Another fun activity is to play a game of “What’s missing?” where students are shown a number in the ten-frame and have to figure out what number is missing to make ten. If you want more ideas on teaching your students the partners of ten check out this blog post where I give you 9 Free and Engaging Ways to Make 10 for 1st Graders along with a freebie!

To reinforce this concept, teachers can create a “Ten Club” where students receive a special recognition for being able to quickly recall the partners of ten.

Once students have mastered the partners for ten take this strategy to the next step and have them make a ten while adding.

Making a ten refers to the strategy of manipulating numbers to get a ten which makes adding easier for students. For example, if a student is shown the problem 8 + 6, they can use mental math to make ten by giving 2 to the 8 to make it a 10. The two that was given to the 8 came from the 6 so the six is now a 4. This turns 8 + 6 into 10 + 4 which is so much easier for students to add. This strategy is important for 1st graders to learn as it lays a foundation for more advanced arithmetic skills.

Make a Ten With Students

Use your students to model this strategy. Write the problem 9 + 5 on the board and then have a group of 9 students and group of 5 come up to the front. Let students tell you how many more we need to get from 9 to 10. Students should tell you we need one and you can model moving one student from the group of 5 to the group of 9. Make sure students see that we did not take any students away or add any new students. The numbers 9 and 5 stayed the same but just moved around. Let them count how many are in each group now and decide what the new, easier, addition problem is (10 + 4).

In my experience it takes students lots of practice actually seeing the numbers be moved with manipulatives before they get a sold grasp on this skill. I like to start with only addition problems with a 9 as one addend and then 8.

I will do the activity explained above using different variations such as using toy cars and driving them to make a ten, using goldfish or cheerios, crayons, books from our classroom library. Anything that the students can touch and move.

Mental Math Strategies Conclusion

In conclusion, mental addition is a crucial skill for 1st graders to have and these five mental math strategies can help students achieve that. From counting on, to using a number line, to playing addition games, there are many ways to make mental addition an engaging and fun experience for students. With the right teaching methods, students will develop confidence in their mental math abilities and be able to solve basic math calculations quickly and accurately.

If you’re looking for even more activities to help your students master mental addition, consider using these differentiated lesson plans that include even more activities and strategies to help reinforce these skills plus many other addition and subtraction strategies that every 1st grader needs.

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1. Add in parts , breaking the second number into its tens and ones.

2. Add in parts . Break the number that is not whole tens into its tens and ones in your mind.

3. Add mentally. We already studied these. The first one is the helping problem.

4. Add in parts.

g.  16 + 17 = ______

h.   17 + 15 = ______

5. a. Laura owns 13 cats. Five of her cats live in the house.         How many of her cats live outside?

    b. Laura's cats eat 20 lb of cat food in a week. Laura has two 4-lb         bags at home. How many more pounds of cat food does she         need to have enough for one week?

6. Count by threes.

   42, 45, _______, _______, _______, _______,_______, _______, _______

7. Find the pattern and continue it. This pattern “grows” at each step.

8. Add by adding tens and ones separately.

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3rd Grade Math Worksheets: Addition

Free addition worksheets from k5 learning.

Our 3rd grade addition worksheets include both " mental addition problems" intended for students to solve in their heads and multi-digit column form addition questions giving practice in computational skills.

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Mental Math Strategies – Addition and Subtraction

October 13, 2022

Using Mental Math strategies means solving a math problem mentally using a conceptual understanding of the numbers. We teach mental math strategies like making 10, splitting, and regrouping in grades 1 and 2, however, I think it is important to teach strategies to older students as well. I noticed that once the students learn the algorithms of 2 (and up)-digit addition and subtraction they tend to avoid solving problems mentally, even if the solution is quite obvious. I recently gave my new students the expression 245+57 to solve. Almost all of them wrote the numbers one under the other (some incorrectly) and used the algorithm to solve the problem. Very few students solved it mentally. 245+55+2=302

Teaching Mental math Strategies to students in grades 3 and up is very important as it develops their flexible thinking and boosts their confidence in math. Being able to use the addition and subtraction properties to apply mental math strategies shows a deep conceptual understanding that will, later on, be applied to more advanced concepts.

Some students discover mental math strategies through practice, naturally, however, most of the students need to be taught the strategies and practice applying them to selected problems. There is a special joy in discovering a strategy, a “trick”. We can guide our students to “discover” a strategy by providing appropriate problems and discussing them.

Mental Math strategies come from using the properties of the numbers and operations in our favor, in a way that makes solving the problem “easier”. Make sure that your students understand the properties of addition and subtraction below.

Visuals and Manipulatives

Using visuals and manipulatives reinforces the strategies and helps all students gain a deep understanding. We can solve problems like 35-9, 363+29, and 472-98 using manipulatives to demonstrate a strategy.

Relations and connections

Using number relations and connections enables students to use already-known problems to solve new ones. For example, If 26+4=30 then 26+7 will be? If 14+36=50 then 14+35=? If 382+100= 482 then 382+99=? 14+36=50 then 14+35=?

Mental Math strategies as Math Talks

Mental Math strategies make great math talks. Present a problem and ask students how to solve it. Can we do it mentally? Present a solution and ask them to explain. Discuss the different solutions and find the connections. Introduce strategies through math talks and apply them to more problems. Ask questions like: Which mental math strategy is for this problem? Why? I always include mental math strategies in math talks and I find that it helps the students see beyond the algorithm and look for relations in numbers.

I have created a collection of activity cards to practice mental math strategies for addition and subtraction with visuals, examples, and practice questions for the strategies:

• Compensation 10s 100s addition, subtraction
• Decomposing to create compatible numbers 10s 100s addition subtraction

The collection includes 30 slides or 30 print task cards and you can find them below.

Mental Math strategies for addition and subtraction. Compensation, decomposing, balancing, clustering. Google slides

Mental Math strategies for addition and subtraction. Compensation, decomposing, balancing, clustering. Print task cards

Mental Math strategies for addition and subtraction. Compensation, decomposing, balancing, clustering.worksheets

Bundle of both google slides and print task cards Mental math strategies addition-subtraction

Find the multiplication and division mental math strategies posts below

Mental Math strategies-Multiplication

Mental Math Strategies Division

Bundle of all mental Math strategies, Addition, Subtraction, Multiplication, and Division google slides

Bundle of all mental Math strategies, Addition, Subtraction, Multiplication, Division Print Task Cards

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Addition Worksheets

Welcome to the addition worksheets page at Math-Drills.com where we will add to your learning experience in many positive ways! On this page, you will find Addition worksheets from addition facts and two-digit addition to column addition and addition with games. In the first section, we've included a few addition printables that should help out the beginning student. Teaching addition facts is best done with some interesting teaching strategies.

Some teachers and parents use addition manipulatives to help students understand the basic addition facts. For example, adding groups of "Apple Jacks" (a breakfast cereal) by counting will quickly lead students to understand the concepts of addition. The sooner you can introduce base ten blocks to your students, the better. If you haven't already used them for counting, use them for basic addition and show students how regrouping works.

Most Popular Addition Worksheets this Week

Addition Facts Tables

Disputably not a great way to learn addition facts, but undeniably a great way to summarize, addition facts tables are an invaluable resource in any home or school classroom. Addition works very well as a table since the addends can be sequential. Encourage students to look for patterns and teach them a variety of strategies to learn the addition facts. For students who have not yet memorized their addition facts but need to know them for a more advanced math lesson such as adding two-digit numbers, provide an addition facts table to them, so they can quickly look up addition facts. After a while, they will most likely learn the facts through the use of the table and become less reliant on it. To make the tables more durable, print them on card stock and laminate them. They can be displayed on a screen or enlarged and printed on poster paper for whole class use.

• Addition Facts in One Square Table Addition Facts Table 1 to 10 (Filled In) Addition Facts Table 1 to 10 (Blank) Addition Facts Table 0 to 9 (Filled In) Addition Facts Table 0 to 9 (Blank) Left-Handed Addition Facts Table Left-Handed Blank Addition Facts Table All Addition Facts Tables Addition Facts Tables With One Fact at a time highlighted
• Addition Facts in Separate Tables Single Addition Facts Tables in Gray 1 to 12 Single Addition Facts Tables in Color 1 to 12 Single Addition Facts Tables in Montessori Colors 1 to 12

Five Minute Addition Frenzies

Five minute frenzy charts are 10 by 10 grids for addition fact practice. In each square, students write the sum of the column number and the row number.

Called mad minutes or timed drills by some, five minute frenzies are meant to be timed to add a little more excitement to practicing addition facts. They are ideally used to increase a student's ability to recall addition facts quickly which has all sorts of benefits later in their school life including preventing high school teachers from complaining about "how their students can't even add single-digit numbers without using a calculator."

A general goal to achieve would be to complete one chart in less than five minutes and score 98 percent or better, however, we recommend setting personal goals for students based on an initial test. If they are banging their head against the wall after a couple of minutes with only a few questions done, they really shouldn't be completing a timed addition facts drill at the moment. They still have some learning to do. We would recommend breaking out the manipulatives at this point. If they blast through the questions in 1.5 minutes and get almost all of them correct, they are probably ready for something a little more challenging.

One-per-page addition frenzies are not the most efficient use of paper resources, but they are a good starting point especially for younger students who have not quite mastered their penmanship enough to fit their numbers into a smaller chart. They are also great for displaying on screens or monitors for group activities. For example, you might use an interactive white board to fill out the chart.

• Five Minute Addition Frenzies Addition Frenzy ( 1 to 10 ) Addition Frenzy ( 11 to 20 ) Addition Frenzy ( 21 to 50 ) Addition Frenzy ( 51 to 100 )
• Left-handed Five Minute Addition Frenzies Left-handed Addition Frenzy ( 1 to 10 ) Left-handed Addition Frenzy ( 11 to 20 ) Left-handed Addition Frenzy ( 21 to 50 ) Left-handed Addition Frenzy ( 51 to 100 )

A wiser use of paper and photo-copy limits, having four charts on a page allows for multi-day practice, collaborative work or through the use of a paper-cutter, a quick stack of practice pages for students who finish early.

• Five Minute Addition Frenzies (Four Per Page) Four Addition Frenzies ( 1 to 10 ) Four Addition Frenzies ( 11 to 20 ) Four Addition Frenzies ( 21 to 50 ) Four Addition Frenzies ( 51 to 100 )
• Left-handed Five Minute Addition Frenzies (Four Per Page) Left-handed Four Addition Charts Per Page ( 1 to 10 ) Left-handed Four Addition Charts Per Page ( 11 to 20 ) Left-handed Four Addition Charts Per Page ( 21 to 50 ) Left-handed Four Addition Charts Per Page ( 51 to 100 )

Single-Digit Addition

Most people would agree that being able to add single-digit numbers quickly and in your head is an essential skill for success in math. The various addition worksheets in this section focus on skills that students will use their entire life. These worksheets will not magically make a student learn addition, but they are valuable for reinforcement and practice and can also be used as assessment tools.

• Single-Digit Addition with Some Regrouping 100 Single-Digit Addition Questions with Some Regrouping ✎ 81 Single-Digit Addition Questions with Some Regrouping ✎ 64 Single-Digit Addition Questions with Some Regrouping ✎ 50 Single-Digit Addition Questions with Some Regrouping ✎ 25 Single-Digit Addition Questions with Some Regrouping ✎ 12 Single-Digit Addition Questions with Some Regrouping ✎
• Single-Digit Addition with No Regrouping 100 Single-Digit Addition Questions with No Regrouping 64 Single-Digit Addition Questions with No Regrouping 25 Single-Digit Addition Questions with No Regrouping 12 Single-Digit Addition Questions with No Regrouping
• Single-Digit Addition with All Regrouping 100 Single-Digit Addition Questions with All Regrouping 64 Single-Digit Addition Questions with All Regrouping 25 Single-Digit Addition Questions with All Regrouping 12 Single-Digit Addition Questions with All Regrouping
• Horizontally Arranged Single-Digit Addition Horizontally Arranged Single-Digit Addition Facts (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts (50 Questions) ✎ Horizontal Numbers that Add to 10 Horizontally Arranged Single-Digit Addition Facts up to 5 + 5 (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts up to 6 + 6 (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts up to 7 + 7 (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts up to 8 + 8 (100 Questions) ✎
• Horizontally Arranged Single-Digit Addition of More than Two Addends Adding 3 Single-Digit Numbers Horizontally Adding 4 Single-Digit Numbers Horizontally Adding 5 Single-Digit Numbers Horizontally Adding 10 Single-Digit Numbers Horizontally
• Horizontally Arranged Single-Digit Addition with No Regrouping Horizontal Addition Facts with No Regrouping 100 per page Horizontal Addition Facts with No Regrouping and No Zeros 100 per page Horizontal Addition Facts with No Regrouping 50 per page
• Horizontally Arranged Single-Digit Addition with All Regrouping Horizontal Addition Facts with All Regrouping 100 per page Horizontal Addition Facts with All Regrouping 50 per page

The make ten addition strategy involves "spliting" the second addend into two parts. The first part combines with the first addend to make ten and the second part is the leftover amount. The strategy helps students quickly add amounts over ten in their head. For example, adding 8 + 7, students first recognize that they need to add 2 to 8 to get 10, so they split the 7 into 2 + 5. The 8 + 2 makes 10 and 5 more makes 15. The skill can be extended to many situations, for example adding 24 + 9, students recognize that they need 6 more to get to 30 and 9 can be split into 6 + 3, so 24 + 6 = 30 and 3 more makes 33. Continuing on, students can work on recognizing "complements" of other important numbers (see section further down) to develop this strategy further.

• Make 10 Addition Strategy Make 10 Addition Strategy Make 10 Addition Strategy Blanks Make 20 Addition Strategy Make 30 Addition Strategy Make 40 Addition Strategy Make 50 Addition Strategy Make 60 Addition Strategy Make 70 Addition Strategy Make 80 Addition Strategy Make 90 Addition Strategy Make Multiples of 10 Addition Strategy

Focusing on one number at a time is necessary for some students. Maybe they get overwhelmed with too much information and need to experience success in small steps.

• Adding Focus or Target Facts (50 Questions) Adding 0 to Single-Digit Numbers (50 Questions) ✎ Adding 1 to Single-Digit Numbers (50 Questions) ✎ Adding 2 to Single-Digit Numbers (50 Questions) ✎ Adding 1 or 2 to Single-Digit Numbers (50 Questions) ✎ Adding 3 to Single-Digit Numbers (50 Questions) ✎ Adding 4 to Single-Digit Numbers (50 Questions) ✎ Adding 5 to Single-Digit Numbers (50 Questions) ✎ Adding 6 to Single-Digit Numbers (50 Questions) ✎ Adding 7 to Single-Digit Numbers (50 Questions) ✎ Adding 8 to Single-Digit Numbers (50 Questions) ✎ Adding 9 to Single-Digit Numbers (50 Questions) ✎
• Adding Focus or Target Facts (25 Large Print Questions) Adding 0 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 1 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 2 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 3 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 4 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 5 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 6 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 7 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 8 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 9 to Single-Digit Numbers (25 Large Print Questions) ✎
• Adding Focus or Target Facts (25 Questions) with Sums Limited to 12 Adding 1 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 2 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 3 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 4 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 5 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 6 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 7 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 8 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 9 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎
• Horizontally-Arranged Adding Focus or Target Facts 100 Horizontal Adding 1s to Single-Digit Numbers Questions 100 Horizontal Adding 2s to Single-Digit Numbers Questions 50 Adding 1s and 2s to Single-Digit Numbers Questions 100 Horizontal Adding 3s to Single-Digit Numbers Questions 100 Horizontal Adding 4s to Single-Digit Numbers Questions 100 Horizontal Adding 5s to Single-Digit Numbers Questions 100 Horizontal Adding 6s to Single-Digit Numbers Questions 100 Horizontal Adding 7s to Single-Digit Numbers Questions 100 Horizontal Adding 8s to Single-Digit Numbers Questions 100 Horizontal Adding 9s to Single-Digit Numbers Questions

Multi-Digit Addition

A variety of strategies can be used to learn multi-digit addition; it isn't necessary to rely only on paper and pencil methods. Base ten blocks can help students conceptualize addition. Teaching students a mental left-to-right addition skill will help them in future math studies and life in general. E.g. 34 + 78 would be 30 + 70 = 100, 100 + 4 = 104, 104 + 8 = 112. Don't forget about using estimation with these worksheets.

• Multi-Digit Addition with Some Regrouping 2-Digit plus 1-Digit Addition (25 Questions) ✎ 2-Digit Plus 1-Digit Addition (36 Questions) ✎ 2-Digit plus 1-Digit Addition (64 Questions) ✎ 2-Digit plus 1-Digit Addition (100 Questions) ✎ 2-Digit plus 1-Digit Addition ( Sums Less Than 100 ) (25 Questions) 2-Digit Addition (25 Questions) ✎ 2-Digit Addition (36 Questions) ✎ 2-Digit Addition (64 Questions) ✎ 2-Digit Addition (100 Questions) ✎ 3-Digit Plus 1-Digit Addition (25 Questions) ✎ 3-Digit Plus 1-Digit Addition (36 Questions) ✎ 3-Digit Plus 2-Digit Addition (25 Questions) ✎ 3-Digit Plus 2-Digit Addition (36 Questions) ✎ 3-Digit Plus 2-Digit Addition (49 Questions) ✎ 3-Digit Plus 2-Digit Addition (100 Questions) ✎ 3-Digit Addition (25 Questions) ✎ 3-Digit Addition (36 Questions) ✎ 3-Digit Addition (49 Questions) ✎ 3-Digit Addition (100 Questions) ✎ 4-Digit Plus 1-Digit Addition (25 Questions) ✎ 4-Digit Plus 1-Digit Addition (36 Questions) ✎ 4-Digit Plus 2-Digit Addition (25 Questions) ✎ 4-Digit Plus 2-Digit Addition (36 Questions) ✎ 4-Digit Plus 3-Digit Addition (25 Questions) ✎ 4-Digit Plus 3-Digit Addition (36 Questions) ✎ 4-Digit Plus 3-Digit Addition (49 Questions) ✎ 4-Digit Plus 3-Digit Addition (100 Questions) ✎ 4-Digit Addition (25 Questions) ✎ 4-Digit Addition (36 Questions) ✎ 4-Digit Addition (49 Questions) ✎ 4-Digit Addition (100 Questions) ✎ 5-Digit Addition (25 Questions) ✎ Various 2-digit to 4-digit Addition (25 Questions) ✎ Various 2-Digit to 4-Digit Addition (36 Questions) ✎ Various 2-digit to 5-digit Addition (20 Questions) ✎ Various 2-Digit to 5-Digit Addition (36 Questions) ✎ Various 3-digit to 5-digit Addition (20 Questions) ✎ Various 3-Digit to 5-Digit Addition (36 Questions) ✎ 6-Digit Addition (20 Questions) ✎ 7-Digit Addition (15 Questions) ✎ 8-Digit Addition (15 Questions) ✎ 9-Digit Addition (15 Questions) ✎ 3-Digit Expanded Form Addition

Regrouping is what long addition is all about; these worksheets give students a lot of practice since every step requires regrouping.

• Multi-Digit Addition with All Regrouping 2-Digit Plus 1-Digit Addition with ALL Regrouping in the Ones Place (25 Questions) ✎ 2-Digit Addition with ALL Regrouping (25 Questions) ✎ 2-Digit Addition with ALL Regrouping (36 Questions) ✎ 3-Digit Addition with ALL Regrouping (25 Questions) ✎ 4-Digit Addition with ALL Regrouping (25 Questions) ✎ 5-Digit Addition with ALL Regrouping (20 Questions) ✎ 6-Digit Addition with ALL Regrouping (20 Questions) ✎ 7-Digit Addition with ALL Regrouping (15 Questions) ✎ 8-Digit Addition with ALL Regrouping (15 Questions) ✎ 9-Digit Addition with ALL Regrouping (15 Questions) ✎

If you haven't quite mastered all the addition facts or the long addition algorithm, these might be the worksheets for you. These worksheets don't require any regrouping, so they provide an extra in-between skill for students who require a little more guidance.

• Multi-Digit Addition with No Regrouping 2-Digit Plus 1-Digit Addition with NO Regrouping (25 Questions) ✎ 2-Digit Addition with NO Regrouping (25 Questions) ✎ 2-Digit Addition with NO Regrouping (36 Questions) ✎ 2-Digit Addition with NO Regrouping (64 Questions) ✎ 2-Digit Addition with NO Regrouping (100 Questions) ✎ 3-Digit Plus 1-Digit Addition with NO Regrouping (25 Questions) ✎ 3-Digit Plus 2-Digit Addition with NO Regrouping (25 Questions) ✎ 3-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Plus 1-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Plus 2-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Plus 3-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Addition with NO Regrouping (25 Questions) ✎ 5-Digit Addition with NO Regrouping (20 Questions) ✎ 6-Digit Addition with NO Regrouping (20 Questions) ✎ 7-Digit Addition with NO Regrouping (20 Questions) ✎ 8-Digit Addition with NO Regrouping (15 Questions) ✎ 9-Digit Addition with NO Regrouping (15 Questions) ✎

Horizontal addition can encourage students to use mental math or other strategies to add numbers. One of the most common mental math strategies for addition is a left-to-right (also called front end) addition strategy. This involves adding the greater place values first. Other strategies for adding multi-digit numbers include using base ten blocks or other manipulatives, number lines, decomposing numbers and adding the parts, and using a calculator.

• Horizontally Arranged Multi-Digit Addition Adding to 20 with the Second Addend Greater 2-Digit Plus 2-Digit Horizontal Addition with no Regrouping Horizontally Arranged 2-Digit Plus 2-Digit Addition ✎ Horizontally Arranged 3-Digit Plus 2-Digit Addition ✎ Horizontally Arranged 3-Digit Plus 3-Digit Addition ✎ Horizontally Arranged Various 2- and 3-Digit Addition ✎ Horizontally Arranged 4-Digit Plus 3-Digit Addition ✎ Horizontally Arranged 4-Digit Plus 4-Digit Addition ✎ Horizontally Arranged Various 2- to 4-Digit Addition ✎
• Horizontally Arranged Multi-Digit Addition of More Than Two Addends Adding 3 Two-Digit Numbers Horizontally Adding 4 Two-Digit Numbers Horizontally Adding 5 Two-Digit Numbers Horizontally Adding 10 Two-Digit Numbers Horizontally
• Adding Focus or Target Facts Greater Than 9 25 Adding 10s Questions ✎ 50 Adding 10s Questions ✎ 50 Adding 11s Questions ✎ 50 Adding 12s Questions ✎ 50 Adding 13s Questions ✎ 50 Adding 14s Questions ✎ 50 Adding 15s Questions ✎ 50 Adding 16s Questions ✎ 50 Adding 17s Questions ✎ 50 Adding 18s Questions ✎ 50 Adding 19s Questions ✎ 50 Adding 20s Questions ✎

Using a comma to separate thousands is the most common way to format large numbers in the English world.

• Multi-Digit Addition with Some Regrouping (Comma-Separated Thousands) Adding 4-Digit Numbers (Comma Separated) (25 Questions) ✎ Adding 5-Digit Numbers (Comma Separated) (20 Questions) ✎ Adding 6-Digit Numbers (Comma Separated) (20 Questions) ✎ Adding 7-Digit Numbers (Comma Separated) (15 Questions) ✎ Adding 8-Digit Numbers (Comma Separated) (15 Questions) ✎ Adding 9-Digit Numbers (Comma Separated) (15 Questions) ✎
• Multi-Digit Addition with All Regrouping (Comma-Separated Thousands) Adding 4-Digit Numbers with ALL Regrouping (Comma Separated) (25 Questions) ✎ Adding 5-Digit Numbers with ALL Regrouping (Comma Separated) (20 Questions) ✎ Adding 6-Digit Numbers with ALL Regrouping (Comma Separated) (20 Questions) ✎ Adding 7-Digit Numbers with ALL Regrouping (Comma Separated) (15 Questions) ✎ Adding 8-Digit Numbers with ALL Regrouping (Comma Separated) (15 Questions) ✎ Adding 9-Digit Numbers with ALL Regrouping (Comma Separated) (15 Questions) ✎
• Multi-Digit Addition with No Regrouping (Comma-Separated Thousands) Adding 4-Digit Numbers with NO Regrouping (Comma Separated) (25 Questions) ✎ Adding 5-Digit Numbers with NO Regrouping (Comma Separated) (20 Questions) ✎ Adding 6-Digit Numbers with NO Regrouping (Comma Separated) (20 Questions) ✎ Adding 7-Digit Numbers with NO Regrouping (Comma Separated) (15 Questions) ✎ Adding 8-Digit Numbers with NO Regrouping (Comma Separated) (15 Questions) ✎ Adding 9-Digit Numbers with NO Regrouping (Comma Separated) (15 Questions) ✎

Using a space to separate thousands in large numbers is common in some languages. In the English world, you will most likely find Canadians formatting their numbers in this way.

• Multi-Digit Addition with Some Regrouping (Space-Separated Thousands) Adding 4-Digit Numbers (Space Separated) (25 Questions) ✎ Adding 5-Digit Numbers (Space Separated) (20 Questions) ✎ Adding 6-Digit Numbers (Space Separated) (20 Questions) ✎ Adding 7-Digit Numbers (Space Separated) (15 Questions) ✎ Adding 8-Digit Numbers (Space Separated) (15 Questions) ✎ Adding 9-Digit Numbers (Space Separated) (15 Questions) ✎
• Multi-Digit Addition with All Regrouping (Space-Separated Thousands) Adding 4-Digit Numbers with ALL Regrouping (Space Separated) (25 Questions) ✎ Adding 5-Digit Numbers with ALL Regrouping (Space Separated) (20 Questions) ✎ Adding 6-Digit Numbers with ALL Regrouping (Space Separated) (20 Questions) ✎ Adding 7-Digit Numbers with ALL Regrouping (Space Separated) (15 Questions) ✎ Adding 8-Digit Numbers with ALL Regrouping (Space Separated) (15 Questions) ✎ Adding 9-Digit Numbers with ALL Regrouping (Space Separated) (15 Questions) ✎
• Multi-Digit Addition with No Regrouping (Space-Separated Thousands) Adding 4-Digit Numbers with NO Regrouping (Space Separated) (25 Questions) ✎ Adding 5-Digit Numbers with NO Regrouping (Space Separated) (20 Questions) ✎ Adding 6-Digit Numbers with NO Regrouping (Space Separated) (20 Questions) ✎ Adding 7-Digit Numbers with NO Regrouping (Space Separated) (15 Questions) ✎ Adding 8-Digit Numbers with NO Regrouping (Space Separated) (15 Questions) ✎ Adding 9-Digit Numbers with NO Regrouping (Space Separated) (15 Questions) ✎

Using a period as a thousands separator is not generally seen in English-speaking countries, but since there are people from around the world who use these addition worksheets, they are included.

• Multi-Digit Addition with Some Regrouping (Period-Separated Thousands) Adding 4-Digit Numbers (Period Separated) (25 Questions) ✎ Adding 5-Digit Numbers (Period Separated) (20 Questions) ✎ Adding 6-Digit Numbers (Period Separated) (20 Questions) ✎ Adding 7-Digit Numbers (Period Separated) (15 Questions) ✎ Adding 8-Digit Numbers (Period Separated) (15 Questions) ✎ Adding 9-Digit Numbers (Period Separated) (15 Questions) ✎
• Multi-Digit Addition with All Regrouping (Period-Separated Thousands) Adding 4-Digit Numbers with ALL Regrouping (Period Separated) (25 Questions) ✎ Adding 5-Digit Numbers with ALL Regrouping (Period Separated) (20 Questions) ✎ Adding 6-Digit Numbers with ALL Regrouping (Period Separated) (20 Questions) ✎ Adding 7-Digit Numbers with ALL Regrouping (Period Separated) (15 Questions) ✎ Adding 8-Digit Numbers with ALL Regrouping (Period Separated) (15 Questions) ✎ Adding 9-Digit Numbers with ALL Regrouping (Period Separated) (15 Questions) ✎
• Multi-Digit Addition with No Regrouping (Period-Separated Thousands) Adding 4-Digit Numbers with NO Regrouping (Period Separated) (25 Questions) ✎ Adding 5-Digit Numbers with NO Regrouping (Period Separated) (20 Questions) ✎ Adding 6-Digit Numbers with NO Regrouping (Period Separated) (20 Questions) ✎ Adding 7-Digit Numbers with NO Regrouping (Period Separated) (15 Questions) ✎ Adding 8-Digit Numbers with NO Regrouping (Period Separated) (15 Questions) ✎ Adding 9-Digit Numbers with NO Regrouping (Period Separated) (15 Questions) ✎

For various reasons, sometimes you need addition questions in a larger font. These should fit the bill.

• Large Print Multi-Digit Addition with Some Regrouping 2-digit Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 3-digit Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ Various Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 2-digit Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 3-digit Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ Various Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 3-digit Plus 3-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 3-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 4-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 5-digit Plus 5-digit Addition with SOME Regrouping (Large Print) (12 Questions) ✎ 6-digit Plus 6-digit Addition with SOME Regrouping (Large Print) (12 Questions) ✎
• Very Large Print Multi-Digit Addition with Some Regrouping 2-Digit Plus 1-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 2-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 3-Digit Plus 1-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 3-Digit Plus 2-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 3-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Plus 1-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Plus 2-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Plus 3-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ Various 2- to 4-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎
• Large Print Multi-Digit Addition with All Regrouping 2-Digit Addition with ALL Regrouping (Large Print) (16 Questions) ✎ 3-Digit Addition with ALL Regrouping (Large Print) (16 Questions) ✎ 4-Digit Addition with ALL Regrouping (Large Print) (16 Questions) ✎ 5-Digit Addition with ALL Regrouping (Large Print) (12 Questions) ✎ 6-Digit Addition with ALL Regrouping (Large Print) (12 Questions) ✎
• Large Print Multi-Digit Addition with No Regrouping 2-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 3-Digit Plus 2-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 3-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 4-Digit Plus 3-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 4-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 5-Digit Addition with NO Regrouping (Large Print) (12 Questions) ✎ 6-Digit Addition with NO Regrouping (Large Print) (12 Questions) ✎ LP 2-Digit Addition with Sums up to 99 ( 25 Questions ) LP 2-Digit Addition with Sums up to 99 ( 12 Questions )

Multi-Digit Addition with Grid Support

Adding with grid support helps students who have trouble lining up place values themselves. Perhaps with a little practice, they might get a better understanding of not only lining up the place values, but why this is done. Pointing out that the 5 in 659 means 50, for example, is useful in helping students understand place value as it relates to addition.

• Adding 2 Addends With Grid Support Adding 2-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding 3-Digit + 3-Digit Numbers on a Grid (2 Addends) Adding 3-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding 4-Digit + 4-Digit Numbers on a Grid (2 Addends) Adding 4-Digit + 3-Digit Numbers on a Grid (2 Addends) Adding 4-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 5-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 4-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 3-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding Various Digit Numbers on a Grid (2 Addends)
• Blank Addition Grids Blank Addition Grids for 2-Digit Numbers (2 Addends) ✎ Blank Addition Grids for 3-Digit Numbers (2 Addends) ✎ Blank Addition Grids for 4-Digit Numbers (2 Addends) ✎ Blank Addition Grids for 5-Digit Numbers (2 Addends) ✎
• Adding 3 Addends With Grid Support Adding 2-Digit Numbers on a Grid (3 Addends) Adding 3-Digit Numbers on a Grid (3 Addends) Adding 4-Digit Numbers on a Grid (3 Addends) Adding 5-Digit Numbers on a Grid (3 Addends) Adding Various-Digit Numbers on a Grid (3 Addends)
• Adding 4 Addends With Grid Support Adding 2-Digit Numbers on a Grid (4 Addends) Adding 3-Digit Numbers on a Grid (4 Addends) Adding 4-Digit Numbers on a Grid (4 Addends) Adding 5-Digit Numbers on a Grid (4 Addends) Adding Various-Digit Numbers on a Grid (4 Addends)
• Adding 5 Addends With Grid Support Adding 2-Digit Numbers on a Grid (5 Addends) Adding 3-Digit Numbers on a Grid (5 Addends) Adding 4-Digit Numbers on a Grid (5 Addends) Adding 5-Digit Numbers on a Grid (5 Addends) Adding Various-Digit Numbers on a Grid (5 Addends)

Various Other Addition Worksheets

Column addition is not just an exercise in accounting, it also develops mental addition skills that are useful in everyday life. Various strategies are available for adding columns of numbers. The traditional method is to use a pencil and paper approach, also known as right-to-left addition, where students add and regroup starting with the smallest place (ones in this case) and proceed up to the greatest place. A mental approach might involve students going from left-to-right where the greater place is added first. This is easier to keep track of in your head, but does require the occasional adjustment in previous answers. An example is to add 345 + 678 + 901. First add the 300, 600 and 900 to get 1800, then add 40, 70 and 0 in turn to get 1910, then deal with the 5, 8 and 1 to get 1924. Along the way you had to adjust your total, but keeping a running total in your head is a lot easier than transfering a pencil and paper method into your head.

• Column Addition with Single-Digit Numbers Adding Three Single-Digit Numbers Adding Four Single-Digit Numbers Adding Five Single-Digit Numbers Adding Six Single-Digit Numbers
• Column Addition with Two-Digit Numbers Adding Three Two-Digit Numbers Adding Four Two-Digit Numbers Adding Five Two-Digit Numbers Adding Six Two-Digit Numbers
• Column Addition with Three-Digit Numbers Adding Three Three-Digit Numbers Adding Four Three-Digit Numbers Adding Five Three-Digit Numbers Adding Six Three-Digit Numbers
• Column Addition with Four-Digit Numbers Adding Three Four-Digit Numbers Adding Four Four-Digit Numbers Adding Five Four-Digit Numbers Adding Six Four-Digit Numbers
• Column Addition with Various-Digit Numbers Adding Three Various-Digit Numbers Adding Four Various-Digit Numbers Adding Five Various-Digit Numbers Adding Six Various-Digit Numbers

Games help students develop mental addition skills but in a fun context. For the adding with playing cards worksheets, a Jack is counted as 11, a Queen as 12, a King as 13 and an Ace as 1. Playing math games while enjoying some social time with their friends is a great way to develop strategic thinking and math fluency in children.

• Adding With Games Adding 2 Playing Cards Adding 3 Playing Cards Adding 4 Playing Cards Adding 5 Playing Cards Adding 6 Playing Cards Adding 7 Playing Cards Adding 8 Playing Cards Counting Cribbage Hands Identify and Count Yahtzee! Combinations

Finding complements of numbers can help students a great deal in developing mental arithmetic skills and to further their understanding of number.

• Adding Complements of 9, 99 and 999 Adding Complements of 9 (Blanks in First or Second Position Mixed) Adding Complements of 9 (Blanks in First then Second Position) Adding Complements of 9 (Blanks in First Position Only) Adding Complements of 9 (Blanks in Second Position Only) Adding Complements of 9 (Blanks in Any Position, Including Sums) Adding Complements of 99 Adding Complements of 999
• Adding Complements of 10, 100 and 1000 Adding Complements of 10 Adding Complements of 100 Adding Complements of 1000
• Adding Complements of 11 Adding Complements of 11 (Blanks in First or Second Position Mixed) Adding Complements of 11 (Blanks in First then Second Position) Adding Complements of 11 (Blanks in First Position Only) Adding Complements of 11 (Blanks in Second Position Only) Adding Complements of 11 (Blanks in Any Position, Including Sums)

Using an adding doubles strategy can help students to process addition questions more quickly using mental math. To use this strategy, students must recognize that the two numbers are close to the same value (usually by one or two). They also must recognize by how much and whether it is greater or less than the first addend. A typical dialogue with the question, 15 + 16, might be, "I see that the second number is greater than the first number by 1. If I double the first number and add 1, I will get my answer. 15 doubled is 30 plus one is 31. 15 + 16, therefore, is 31."

• Adding Doubles Up to 9 Adding Doubles (Up to 9) Adding Doubles Plus One (Up to 9) Adding Doubles Plus Two (Up to 9) Adding Doubles Minus One (Up to 9) Adding Doubles Minus Two (Up to 9) Adding Doubles Mixed Variations (Up to 9)
• Adding Doubles Up to 15 Adding Doubles (Up to 15) Adding Doubles Plus One (Up to 15) Adding Doubles Plus Two (Up to 15) Adding Doubles Minus One (Up to 15) Adding Doubles Minus Two (Up to 15) Adding Doubles Mixed Variations (Up to 15)
• Adding Doubles Up to 30 Adding Doubles (Up to 30) Adding Doubles Plus One (Up to 30) Adding Doubles Plus Two (Up to 30) Adding Doubles Minus One (Up to 30) Adding Doubles Minus Two (Up to 30) Adding Doubles Mixed Variations (Up to 30)

Not commonly taught in modern schools, adding in other base number systems can stretch students' minds and have quite a few important applications, especially in technology. For example, you will find binary, octal and hexadecimal systems are quite often used in computer technology. Quaternary numbers can be used in genetics to store DNA sequences. The duodecimal system is sometimes suggested as a superior system to the decimal system

• Adding in Other Base Number Systems Adding Binary Numbers (Base 2) Adding Ternary Numbers (Base 3) Adding Quaternary Numbers (Base 4) Adding Quinary Numbers (Base 5) Adding Senary Numbers (Base 6) Adding Octal Numbers (Base 8) Adding Duodecimal Numbers (Base 12) Adding Hexadecimal Numbers (Base 16) Adding Vigesimal Numbers (Base 20) Adding Hexatrigesimal Numbers (Base 36) Adding Various Numbers (Various Bases)

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Mental Maths Worksheets UK Hub Page

Welcome to the Math Salamanders Mental Maths worksheets for developing quick and accurate mental arithmetic and problem solving skills.

Here you will find a wide range of free printable maths questions which will help your child improve their mental calculation skills, develop their problem solving and learn their Maths facts.

We also have links to our Maths fact resources and online practice zones to help develop mental arithmetic.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Mental Maths Worksheets

Our selection of mental maths worksheets is a great way of practising your number and maths skills.

The sheets can be used in a variety of ways, as a test or revision practise, or as part of a weekly quiz to help reinforce skills.

They can also be used as an oral and mental starter to a lesson to get brains working!

One of the best ways to use these sheets is to get children to work in pairs, discussing the questions as they work through them.

The questions have been designed to practise a range of maths skills from number to geometry and measurement facts, including using time and money.

The quizzes are in order of difficulty with the questions getting slightly harder in each quiz.

The best way to improve your mental arithmetic and develop mental maths skills is to practise regularly. Even 5 minutes daily practise can make a huge difference in a matter of weeks.

Below are links to our selection of mental maths worksheets for each year group from years 2 to 6.

The sheets have been set up for children in the UK, with mainly metric (and some imperial) units, and UK £ and p.

There are also some other links to worksheets and activities designed to develop mental skills for students in the UK.

Mental Maths sheets UK

Here you will find a range of printable mental math quizzes for your child to enjoy.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Year 2 Printable Mental Maths
• Year 3 Mental Maths Tests Series A
• Year 3 Mental Maths Tests Series B
• Year 4 Mental Maths Test sheets
• Year 5 Mental Maths Worksheet
• Year 6 Mental Maths Tests

Here you will find a selection of number bond sheets designed to help your child improve their recall of their number bond facts.

Online Number Bonds Practice

In our Number Bonds Practice area, you can practice your number bonds to a variety of numbers. Test your numbers bonds to 10, 20 , 100 or even 1000. Want to try decimals - you can do that too!

Select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

• Number Bonds Practice Zone

Number Bond Sheets

• Number Bonds to 10 and 12
• Number Bonds to 20
• Number Bonds to 50 and 100

Addition Mental Math Sheets

Here you will find a selection of free mental maths worksheets designed to help your child improve their recall of Addition Facts.

• Addition Practice Zone

Here is our online learning math addition zone, where you can practice a range of integer addition calculations.

Test yourself on the following addition facts:

• up to 5+5, 10+10, 20+20, 50+50, 100+100, or 1000+1000;
• 2 digit numbers adding ones;
• 2 digit numbers adding tens;
• 3 digit numbers adding hundreds;

Addition Worksheet Generator

Here is our free generator for addition worksheets.

This easy-to-use generator will create randomly generated addition worksheets for you to use.

Each free math worksheet comes complete with answers if required.

The areas the generator covers includes:

• addition with numbers up to 10, 15, 20, 50, 100 and 1000;
• addition by 10s with 2 digit numbers;
• addiiton by 100s with 3 digit numbers;
• addition with numbers to 10 with one decimal place;
• addition with numbers to 1 with 2 decimal places.

These generated sheets can be used in a number of ways to help your child with their addition fact learning.

• Free Addition Worksheets (randomly generated)

Subtraction Fact Sheets

Here you will find a selection of Mental Subtraction sheets designed to help your child improve their recall of Subtraction Facts.

Online Subtraction Practice Zone

Here is our online learning math subtraction practice area where you can test yourself on your subtracting skills.

Test yourself on the following integer subtraction facts:

• up to 10, 15, 20, 50, 100, 200, 500 or 1000;
• 2 digit subtract ones;
• 2 digit subtract tens;
• 3 digit subtract hundreds.
• Subtraction Practice Zone

Subtraction Worksheet Generator

Here is our free generator for subtraction worksheets.

This easy-to-use generator will create randomly generated subtraction worksheets for you to use.

• subtraction with numbers up to 10, 15, 20, 50, 100 and 1000;
• subtraction by 10s from 2 digit numbers;
• subtraction by 100s from 3 digit numbers;
• subtraction with numbers to 10 with one decimal place;
• subtraction with numbers to 1 with 2 decimal places;
• subtraction involving negative numbers.
• Free Subtraction Worksheets (randomly generated)

Multiplication Times Tables Sheets

Here you will find a selection of Mental Maths Worksheets designed to help your child improve their mental recall of Multiplication Facts and learn their times tables.

Online Multiplication Test

Here is our online learning math practice zone for multiplication facts.

Using this zone is a great way to test yourself on your facts and see how many you can do in a minute.

Then re-test yourself and see if you can improve your score.

Using this zone, you can:

• choose tables up to 5x5, 10x10 or 12x12 to test yourself on;
• select one or more tables to test yourself on;
• practice multiplying whole numbers by 10 or 100.
• Online Multiplication Zone

Multiplication Worksheet Generator

Here is our free generator for multiplication worksheets.

This easy-to-use generator will create randomly generated multiplication worksheets for you to use.

Each sheet comes complete with answers if required.

• Multiplying with numbers to 5x5;
• Multiplying with numbers to 10x10;
• Multiplying with numbers to 12x12;
• Practicing a single times table;
• Practicing selected times tables;

These generated sheets can be used in a number of ways to help your child with their times table learning.

• Times Tables Worksheets (randomly generated)

Division Fact Sheets

Here you will find a selection of Mental Division sheets designed to help your child improve their recall of Division Facts and to apply their facts to answer related questions.

Online Division Practice Area

Here is our free division practice area.

If you want to practice your division facts, or take a timed division test, then this is the place for you.

In this area, we cover the following division facts:

• division facts up to 5x5, up to 10x10 or up to 12x12;
• division facts linked to individual tables facts;
• dividing by 10 and 100.
• Division Practice Zone

Division Worksheet Generator

Here is our free generator for division worksheets.

This easy-to-use generator will create randomly generated division worksheets for you to use.

• Dividing with numbers to 5x5;
• Dividing with numbers to 10x10;
• Dividing with numbers to 12x12;
• Dividing with a single times table;
• Practicing division with selected times tables;

These generated sheets can be used in a number of ways to help your child with their division table learning.

• Division Facts Worksheets (randomly generated)
• Money Worksheets UK

The following worksheets have been designed to help children learn to count and add up money amounts.

UK coinage is used throughout, with pictures of each coins correctly sized.

There are a range of counting money sheets, starting with counting pennies, going up to money amounts to £5.

Math Fact Games

Here you will find a range of Free Printable Math Fact Games.

The following games develop a range of mental Math skills in a fun and motivating way.

Using these sheets will help your child to:

• learn their Math facts;
• develop their strategic thinking skills.
• Maths Addition Games
• Subtraction Games
• Maths Multiplication Games
• Maths Division Games

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

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Mental Maths Questions

We all know mental maths is an essential skill while performing mathematical calculations. Mental maths questions with solutions and tricks are provided here for students to improve their mental calculation skill. Train your brain with these mental maths questions and perform any arithmetic calculations within seconds.

Also refer:

• Mental Maths for Class 2
• Mental Maths for Class 5
• Maths Quiz Questions

Let us have a look at some shortcuts to do addition and subtraction mentally.

• Addition without carrying : Suppose we have to add two numbers 35 + 89

Step I: 30 + 80 = 110

Step II: 110 + 5 = 115

Step III: 100 + (15 + 9) = 124

• Addition by grouping: Suppose we have to add numbers 90 + 19 + 51

Step I: 19 = 10 + 9

Step II: 90 + 10 = 100

Step III: 51 + 9 = 60

Step IV: 100 + 60 = 160

• Left-to-right Addition: Generally, we are taught to add numbers from right to left. But while adding mentally, it sometimes becomes hard to recall the numbers backwards after calculating them right to left. Use this method to calculate quickly.

For example, 59 + 23

Step I: 59 + 20 = 79

Step II: 79 + 3 = 82

• Subtracting by Rounding : While subtracting numbers, if one number can be rounded to the nearest tens, hundreds or thousands makes our calculation easier.

For example: 346 – 96

Step I: Add 4 to 96, 96 + 4 = 100

Step II: 346 – 100 = 246

Step III: 246 + 4 = 250

• Subtract by Adding: This technique work when we have to subtract a single-digit number from a teen number.

Example: 11 – 7

Step I: 10 – 7 = 3

Step II: Add the ones-digit of 11 to 3, 1 + 3 = 4

• Left-to-right subtraction: Just the same process as left-to-right addition.

For example: 385 – 178

Step I: 385 – 100 = 285

Step II: 285 – 70 = 215

Step III: 215 – 8 = 207 (here we can use the trick to subtract a single-digit number from a teen number)

• Subtraction without Borrowing: Suppose we have to subtract 2176 from 3456:

3456 – 2176

In the tens place, we see that there is 5 – 7 which is not possible hence we take 45 – 17 which is possible, and 45 – 17 (we can find this by subtraction by rounding).

Thus, 45 – 17 = 28

∴ 3456 – 2176 = 1280.

Mental Maths Questions with Solution

Let us practice some mental maths questions to train our brain.

Question 1: Calculate mentally:

(i) 120 + 80 + 756 + 40

(ii) 74 + 23

(iii) 57 + 89

(iv) 340 + 30 + 40

(v) 208 + 92

(i) 120 + 80 + 756 + 40 = 996

We shall use the addition by grouping

120 + 80 = 200

50 + 40 + 6 = 96

700 + 200 + 96 = 996

(ii) 74 + 23 = 97

We shall use left-to-right addition

74 + 20 = 94

94 + 3 = 97

(iii) 57 + 89 = 146

We can use addition without carrying but it is easier to use addition with grouping

(56 + 1) + 89 = 56 + 90 = 146

We can use addition by grouping

40 × 2 + 30

= 80 + 30 = 110

110 + 300 = 410

Question 2: Calculate mentally:

(ii) 17 – 9

(iii) 294 – 189

(iv) 34 – 27

(v) 2378 – 1876

(i) 12 – 8 = 4

We use the trick to subtract a single-digit number from a teen number.

(ii) 17 – 9 = 8

(iii) 294 – 189 = 105

We shall use the technique of subtraction without borrowing

94 – 89 = 5 (Use subtraction by rounding)

∴ 234 – 189 = 105

(iv) 34 – 27 = 7

Use subtraction by rounding

34 – 30 = 4

∵ 27 + 3 = 30

∴ 4 + 3 = 7

Question 3: Calculate mentally:

(i) 248 – 25 + 87

(ii) 305 + 45 + 23

(iii) 820 + 23 – 20

(i) 248 – 25 + 87 = 310

Step I: 248 + 87 = 245 + 90

= 200 + (90 + 45)

= 200 + 135 = 335

Step II: 335 – 25 = 310

(ii) 305 + 45 + 23 = 373

300 + (45 + 5) = 350

350 + 20 = 370

370 + 3 = 373

(iii) 820 + 23 – 20 = 823

23 – 20 = 3

820 + 3 = 823

• Vedic Mathematics Tricks
• Maths Tricks
• Multiplication Tricks
• Divisibility Rules

Question 4: Calculate mentally:

(i) 14 × 11

(ii) 98 × 11

(iii) 47 × 11

(iv) 456 × 11

(i) 14 × 11 = 154

Caluclate like this, 14 × 11 = 1(1+4)4.

(ii) 98 × 11 = 1078

Since, 9(9+8)8 = 9(17)8 = 1078

1 of 17 is carried over to 9, 9 + 1 = 10.

(iii) 47 × 11 = 517

Since, 4(4+7)7 = 4(11)7 = 517

1 of 11 is carried over to 4, 4 + 1 = 5.

(iv) 456 × 11 = 5016

Just add 4560 + 456 = 5016.

Question 5: Calculate mentally:

(i) 26 × 25

(ii) 35 × 17

(iii) 46 × 15

(iii) 154 × 25

(i) 26 × 25 = 650

Half 26 and double 25, 13 × 50

Now, 13/2 = 6.5 and 6.5 × 100 = 650.

(ii) 35 × 17 = 595

Half 17 and double 35, so that we get 8.5 × 70

Simply calculate 85 × 7 = (80 + 5) × 7 = 560 + 35 = 595.

(iii) 46 × 15 = 690

Half 46 and double 15, so that we get 23 × 30 = 690.

(iv) 154 × 25 = 3850

Half 154 and double 50, so that we get 77 × 50

Then, 77/2 × 100 = 38.5 × 100 = 3850.

Question 6: Calculate mentally:

(i) 387 ÷ 2

(ii) 8761 ÷ 2

(iii) 47 ÷ 2

(iv) 91 ÷ 2

(i) 387 ÷ 2 = 193.5

386 ÷ 2 = 193

∴ 387 ÷ 2 = 193.5

(ii) 8761 ÷ 2 = 4380.5

(iii) 47 ÷ 2 = 23.5

(iv) 91 ÷ 2 = 45.5

Question 7: Calculate:

(i) 234 ÷ 25

(ii) 827 ÷ 5

(iii) 1356 ÷ 125

(iv) 187 ÷ 50

(i) 234 ÷ 25 = 9.36

Step I: 234 × 4 = 936

Step II: 936/100 = 9.36

(ii) 827 ÷ 5 = 165.4

Step I: 827 × 2 = 1654

Step II: 1654/10 = 165.4

(iii) 1356 ÷ 125 = 10.848

Step I: 1356 × 8 = 10848

Step II: 10848/1000 = 10.848

(iv) 187 ÷ 50 = 3.74

Step I: 187 × 2 = 374

Step II: 374/100 = 3.74

Question 8: Calculate the following:

(i) 282 ÷ 75

(ii) 45 ÷ 75

(iii) 351 ÷ 75

(i) 281 ÷ 75 = 3.76

Step I: 282 ÷ 3 = 94

Step II: 94 × 4 = 376

Step III: 376 ÷ 100 = 3.76

Step I: 45 ÷ 3 = 15

Step II: 15 × 4 = 60

Step III: 60 ÷ 100 = 0.6

Step I: 351 ÷ 3 = 117

Step II: 117 × 4 = 468

Step III: 468 ÷ 100 = 4.68

Question 9: Convert the following into percentages:

(i) 3.4/17 (ii) 18/50 (iii) 29/45

(i) 3.4/17 = 20%

Step I: 3.4 × 100 = 340

Step II: 340/17 = 20%

(ii) 18/50 = 360%

Step I: 18 × 100 = 1800

Step II: 1800/50 = 36%

(iii) 29/45 = 64.44% (approx)

Step I: 29 × 100 = 2900

Step II: 2900/45 = 64.44

Question 10: Evaluate the following:

(i) 7% of 250 (ii) 16% of 45

(i) 7% of 250 = 17.5

Step I: 7/10 = 0.7 and 250/10 = 25.0

Step II: 0.7 × 25 = 17.5

(ii) 16% of 45 = 7.2

Step I: 16/10 = 1.6 and 45/10 = 4.5

Step II: 1.6 × 4.5 = 7.2

Practice Questions on Mental Maths

1. Calculate mentally:

(i) 2896 + 386

(ii) 345 + 90

(iii) 347 – 94

(iv) 12 – 34 + 4

(v) 267 – 56 – 32

(vi) 11 × 234

(vii) 25 × 116

(viii) 567 ÷ 2

(ix) 1947 ÷ 2

(x) 239 ÷ 25

2. Convert the following into percentages:

(i) 38/7 (ii) 65/8 (iii) 45/3

3. Evaluate the following:

(i) 12% of 225 (ii) 11% of 200

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