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Australian Curriculum: Mathematics

Students are entering a new section of math that consists of algebra, geometry, decimals, and more complicated division problems. When there is not a parent or teacher around, students have access to on-demand videos for their sixth-grade mathematical lessons. Our video tutorials are taught by math teachers who go through the problem solving process.

• The key to learning math is repetition, and our math teachers go through multiple examples. 
• Math teachers show students step-by-step directions on how to solve these more complex problems.
• Students learn money, ratios, decimals, graphing, and other concepts from the 6th grade curriculum.

Year 6 maths

IXL offers hundreds of Year 6 maths skills and games to explore and learn! Not sure where to start? Go to your personalised Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, national curriculum, or standardised test.

A. Place values and number sense

• 1 Convert between standard and expanded form
• 2 Place values
• 3 Convert between place values
• 4 Place value word problems
• 5 Writing numbers up to one million in words: convert words to digits
• 6 Writing numbers up to one million in words: convert digits to words
• 7 Writing numbers up to ten million in words: convert words to digits
• 8 Writing numbers up to ten million in words: convert digits to words
• 9 Compare numbers up to one million
• 10 Compare numbers up to ten million
• 11 Put numbers in order: up to one million
• 12 Put numbers in order: up to ten million
• 13 Roman numerals
• 14 Rounding: up to thousands place
• 15 Rounding: up to millions place
• 16 Even or odd: arithmetic rules

B. Addition and subtraction

• 1 Add and subtract whole numbers up to millions
• 2 Add and subtract whole numbers: word problems
• 3 Complete addition and subtraction sentences
• 4 Fill in the missing digits
• 5 Choose numbers with a particular sum or difference
• 6 Properties of addition
• 7 Add using properties
• 8 Inequalities with addition and subtraction
• 9 Estimate sums and differences of whole numbers up to four digits
• 10 Estimate sums and differences of whole numbers up to six digits
• 11 Estimate sums and differences: word problems up to six digits

C. Multiplication fluency

• 1 Multiplication facts to 10
• 2 Multiplication facts up to 10: find the missing factor
• 3 Choose the multiples of a given number up to 10
• 4 Multiplication facts to 12
• 5 Multiplication facts up to 12: find the missing factor
• 6 Choose the multiples of a given number up to 12

D. Multiplication

• 1 Multiply by 1-digit numbers
• 2 Multiply by 1-digit numbers: word problems
• 3 Multiplication patterns over increasing place values
• 4 Properties of multiplication
• 5 Multiply by a multiple of ten
• 6 Estimate products
• 7 Estimate products: word problems
• 8 Use one multiplication fact to complete another
• 9 Multiply 2-digit numbers by 2-digit numbers using area models I
• 10 Multiply 2-digit numbers by 2-digit numbers using area models II
• 11 Multiply 2-digit numbers by 2-digit numbers using partial products
• 12 Multiply 2-digit numbers by 2-digit numbers: complete the missing steps
• 13 Multiply 2-digit numbers by 2-digit numbers
• 14 Multiply 2-digit numbers by 2-digit numbers: word problems
• 15 Box multiplication
• 16 Lattice multiplication
• 17 Multiply 2-digit numbers by 3-digit or 4-digit numbers: complete the missing steps
• 18 Multiply 2-digit numbers by 3-digit or 4-digit numbers
• 19 Multiply 2-digit numbers by 3-digit or 4-digit numbers: word problems
• 20 Multiply three or more numbers up to 2 digits each
• 21 Multiply three or more numbers: word problems
• 22 Choose numbers with a particular product
• 23 Multiply numbers ending in zeroes
• 24 Multiply numbers ending in zeroes: word problems
• 25 Inequalities with multiplication

E. Division fluency

• 1 Division facts to 10
• 2 Division facts to 10: word problems
• 3 Division facts to 12
• 4 Division facts to 12: word problems

F. Division

• 1 Divide by 1-digit numbers
• 2 Divide by 1-digit numbers: word problems
• 3 Division patterns over increasing place values
• 4 Estimate quotients
• 5 Estimate quotients: word problems
• 6 Estimate quotients using compatible numbers
• 7 Divide by 2-digit numbers using models
• 8 Divide by 2-digit numbers using partial quotients
• 9 Divide 2-digit and 3-digit numbers by 2-digit numbers
• 10 Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems
• 11 Divide 4-digit numbers by 2-digit numbers
• 12 Divide 4-digit numbers by 2-digit numbers: word problems
• 13 Adjust quotients
• 14 Multi-step word problems: multiplicative comparison
• 15 Relate multiplication and division
• 16 Complete the division sentence: 2-digit divisors
• 17 Choose numbers with a particular quotient
• 18 Divide numbers ending in zeroes
• 19 Divide numbers ending in zeroes: word problems

G. Number theory

• 1 Divisibility rules
• 2 Divisibility rules: word problems
• 3 Identify factors
• 4 Find all the factor pairs of a number
• 5 Prime and composite numbers: up to 20
• 6 Prime and composite numbers: up to 100
• 7 Prime factorisation
• 8 Highest common factor
• 9 Lowest common multiple

H. Decimals

• 1 What decimal number is illustrated?
• 2 Model decimals and fractions
• 3 Understanding decimals expressed in words
• 4 Place values in decimal numbers
• 5 Relationship between decimal place values
• 6 Convert decimals between standard and expanded form
• 7 Equivalent decimals
• 8 Round decimals
• 9 Decimal number lines
• 10 Compare decimals on number lines
• 11 Compare decimal numbers
• 12 Put decimal numbers in order
• 13 Convert fractions to decimals
• 14 Convert mixed numbers to decimals
• 15 Convert decimals to fractions
• 16 Convert decimals to mixed numbers
• 17 Convert decimals between standard and expanded form using fractions
• 18 Compare decimals and fractions on number lines
• 19 Compare decimals and fractions
• 20 Put assorted decimals, fractions and mixed numbers in order
• 21 Number sequences involving decimals

I. Add and subtract decimals

• 1 Add decimal numbers using blocks
• 2 Add decimal numbers
• • New! Use properties to add three decimals
• 3 Subtract decimal numbers
• 4 Add and subtract decimal numbers
• • New! Use compensation to add and subtract decimals
• 5 Add and subtract decimals: word problems
• 6 Choose decimals with a particular sum or difference
• 7 Complete the decimal addition or subtraction sentence
• 8 Inequalities with decimal addition and subtraction
• 9 Estimate sums and differences of decimals

J. Multiply decimals

• 1 Estimate products of two-digit whole numbers and decimals
• 2 Estimate products of decimals
• 3 Multiply a decimal by 10, 100 or 1,000
• 4 Multiply by 0.1 or 0.01
• 5 Multiply by a power of ten with decimals: find the missing number
• 6 Multiply a decimal by a one-digit whole number using blocks
• 7 Multiply a decimal by a one-digit whole number using the distributive property
• 8 Multiply a decimal by a one-digit whole number
• 9 Multiply a decimal by a one-digit whole number: word problems
• 10 Inequalities with decimal multiplication
• 11 Multiply a decimal by a two-digit whole number using area models
• 12 Multiply a decimal by a two-digit whole number
• 13 Multiply a decimal by a one- or two-digit whole number: word problems
• 14 Multiply three or more numbers, one of which is a decimal

K. Divide decimals

• 1 Estimate decimal quotients
• 2 Divide a whole number by 10, 100 or 1,000: decimal quotients
• 3 Divide a decimal by 10, 100 or 1,000
• 4 Decimal division patterns over increasing place values
• 5 Divide two whole numbers: decimal quotients
• 6 Divide a decimal by a power of ten with decimals: find the missing number
• 7 Divide decimals using blocks: complete the equation
• 8 Divide decimals using area models: complete the equation
• 9 Divide decimals by one-digit whole numbers
• 10 Division with decimal quotients and rounding
• 11 Division with decimal quotients: word problems

L. Fractions and mixed numbers

• 1 Fractions review
• 2 Fractions of a whole: word problems
• 3 Fractions of a group: word problems
• 4 Equivalent fractions
• 5 Patterns of equivalent fractions
• 6 Write fractions in lowest terms
• 7 Lowest common denominator
• 8 Mixed numbers
• 9 Convert between improper fractions and mixed numbers
• 10 Graph and compare fractions on number lines
• 11 Compare fractions and mixed numbers
• 12 Put fractions in order
• 13 Arithmetic sequences with fractions
• 14 Geometric sequences with fractions
• 15 Round mixed numbers
• 16 Reciprocals
• 17 Relate division and fractions
• 18 Understand fractions as division: word problems
• 19 Fractions as division: decimal quotients

M. Add and subtract fractions

• 1 Decompose fractions multiple ways
• 2 Add and subtract fractions with the same denominator using number lines
• 3 Add and subtract fractions with the same denominator
• 4 Add and subtract fractions with the same denominator: word problems
• 5 Add three or more fractions with the same denominator
• 6 Add three or more fractions with the same denominator: word problems
• 7 Add and subtract mixed numbers with the same denominator
• 8 Add and subtract mixed numbers with the same denominator: word problems
• 9 Add up to 4 fractions with denominators of 10 and 100
• 10 Add fractions with different denominators using models
• 11 Add fractions with different denominators
• 12 Subtract fractions with different denominators using models
• 13 Subtract fractions with different denominators
• 14 Add and subtract fractions with different denominators
• 15 Add and subtract fractions with different denominators: word problems
• 16 Add three or more fractions with different denominators
• 17 Add three or more fractions with different denominators: word problems
• 18 Complete addition and subtraction sentences with fractions
• 19 Inequalities with addition and subtraction of fractions
• 20 Estimate sums and differences of mixed numbers
• 21 Add mixed numbers with different denominators
• 22 Subtract mixed numbers with different denominators
• 23 Add and subtract mixed numbers with different denominators
• 24 Add and subtract mixed numbers with different denominators: word problems
• 25 Complete addition and subtraction sentences with mixed numbers
• 26 Inequalities with addition and subtraction of mixed numbers

N. Multiply and divide fractions

• 1 Multiply unit fractions by whole numbers using number lines
• 2 Multiply unit fractions by whole numbers using models
• 3 Multiples of fractions
• 4 Multiply unit fractions and whole numbers: sorting
• 5 Multiply fractions by whole numbers using number lines
• 6 Multiplying fractions by whole numbers: choose the model
• 7 Multiply fractions and whole numbers: sorting
• 8 Multiply fractions by whole numbers
• 9 Multiply fractions by whole numbers: input/output tables
• 10 Fractions of a number
• 11 Fractions of a number: word problems
• 12 Scaling whole numbers by fractions: justify your answer
• 13 Scaling whole numbers by fractions
• 14 Multiply two unit fractions using models
• 15 Multiply two fractions using models
• 16 Multiply two fractions
• 17 Multiply fractions: word problems
• 18 Complete the fraction multiplication sentence I
• 19 Complete the fraction multiplication sentence II
• 20 Divide unit fractions by whole numbers using models
• 21 Divide unit fractions by whole numbers using area models
• 22 Divide unit fractions by whole numbers
• 23 Divide fractions by whole numbers

O. Integers

• 1 Understanding integers
• 2 Integers on number lines
• 3 Graph integers on horizontal and vertical number lines
• 4 Understanding opposite integers
• 5 Compare integers
• 6 Put integers in order

P. Add and subtract integers

• 1 Add integers using number lines
• 2 Subtract integers using number lines
• 3 Add and subtract integers using number lines

Q. Mixed operations

• 1 Add, subtract, multiply and divide whole numbers
• 2 Add, subtract, multiply and divide whole numbers: word problems
• 3 Write numerical expressions
• 4 Evaluate numerical expressions
• 5 Evaluate numerical expressions with brackets
• 6 Evaluate numerical expressions with brackets and square brackets
• 7 Evaluate numerical expressions with brackets in different places
• 8 Missing operators
• 9 Add, subtract, multiply and divide decimals
• 10 Add, subtract, multiply and divide decimals: word problems
• 11 Equations with mixed operations: true or false
• 12 Add, subtract, multiply and divide fractions and mixed numbers
• 13 Add, subtract and multiply fractions and mixed numbers: word problems

R. Problem solving

• 1 Make the largest possible quotient
• 2 Write numerical expressions for word problems
• 3 Multi-step addition and subtraction word problems
• 4 Multi-step word problems
• 5 Multi-step word problems involving remainders
• 6 Multi-step word problems: identify reasonable answers
• 7 Word problems with extra or missing information
• 8 Guess-and-check problems
• 9 Find the order
• 10 Use Venn diagrams to solve problems

S. Ratios and rates

• 1 Write a ratio
• 2 Write a ratio using a fraction
• 3 Write a ratio: word problems
• 4 Identify equivalent ratios
• 5 Write an equivalent ratio
• 6 Ratio tables
• 7 Unit rates
• 8 Equivalent rates
• 9 Ratios and rates: word problems
• 10 Do the ratios form a proportion?
• 11 Solve the proportion
• 12 Scale drawings: word problems

T. Percents

• 1 What percentage is illustrated?
• 2 Understanding percents: bar models
• 3 Convert fractions to percents using grid models
• 4 Convert between percents, fractions and decimals
• 5 Convert between percents, fractions and decimals: word problems
• 6 Compare percents to each other and to fractions
• 7 Compare percents and fractions: word problems
• 8 Percent of a number
• 9 Percent of a number: word problems
• 10 Compare percents of numbers
• 1 Add and subtract money amounts
• 2 Add and subtract money amounts: word problems
• 3 Multiply money amounts
• 4 Multiply money amounts: word problems
• 5 Multiply money amounts with decimals
• 6 Multiply money amounts with decimals: word problems
• 7 Divide money amounts
• 8 Divide money amounts: word problems
• 9 Divide money amounts with decimals
• 10 Divide money amounts with decimals: word problems
• 11 Price lists
• 12 Unit prices

V. Number sequences

• 1 Use a rule to complete an addition or subtraction pattern
• 2 Use a rule to complete a number pattern
• 3 Use a two-step rule to complete a number pattern
• 4 What is true about the addition pattern?
• 5 What is true about the multiplication pattern?
• 6 Complete a linear number sequence
• 7 Complete an increasing number sequence
• 8 Complete a geometric number sequence
• 9 Linear sequences: word problems
• 10 Number sequences: word problems
• 11 Number sequences: mixed review
• 12 Shape patterns

W. Coordinate plane

• 1 Describe the coordinate plane
• 2 Objects on a coordinate plane
• 3 Graph points on a coordinate plane
• 4 Coordinate planes as maps
• 5 Objects on a coordinate plane - all four quadrants
• 6 Graph points on a coordinate plane - all four quadrants
• 7 Quadrants

X. Equations and variables

• 1 Write variable expressions
• 2 Write variable expressions: word problems
• 3 Evaluate variable expressions
• 4 Properties of addition with variables
• 5 Properties of multiplication with variables
• 6 Identify equivalent expressions using bar models
• 7 Write a one-step equation from words
• 8 Model and solve one-step equations using algebra tiles
• 9 Write and solve one-step equations that represent diagrams
• 10 Solve one-step addition and subtraction equations with whole numbers
• 11 Solve one-step multiplication and division equations with whole numbers
• 12 Solve one-step equations with whole numbers
• 13 Write one-step equations: word problems
• 14 Solve one-step equations: word problems
• 15 Does (x, y) satisfy an equation?
• 16 Find a value using two-variable equations
• 17 Complete a table for a two-variable relationship
• 18 Complete a table from a graph
• 19 Graph a two-variable relationship
• 20 Write a two-variable equation

Y. Data and graphs

• 1 Read a table
• 2 Interpret pictograms
• 3 Create pictograms
• 4 Interpret line graphs
• 5 Create line graphs
• 6 Interpret bar graphs for categorical data
• 7 Create bar graphs for categorical data
• 8 Interpret double bar graphs for categorical data
• 9 Create double bar graphs for categorical data
• 10 Interpret bar graphs for grouped data
• 11 Create bar graphs for grouped data
• 12 Interpret line plots
• 13 Create line plots
• 14 Interpret frequency charts: one-step problems
• 15 Interpret frequency charts: multi-step problems
• 16 Create frequency charts
• 17 Interpret stem-and-leaf plots
• 18 Create stem-and-leaf plots
• 19 Pie charts
• 20 Pie charts and central angles
• 21 Choose the best type of graph

Z. Probability and statistics

• 1 Understanding probability
• 2 Find the probability
• 3 Find the probability as a fraction
• 4 Experimental probability
• 5 Use collected data to find probabilities and make predictions
• 6 Make predictions
• 7 Identify statistical questions
• 8 Find the mode
• 9 Find the mean
• 10 Find the median
• 11 Find the range
• 12 Mode: find the missing number
• 13 Mean: find the missing number
• 14 Median: find the missing number
• 15 Range: find the missing number
• 16 Interpret charts to find mode
• 17 Interpret charts to find mean
• 18 Interpret charts to find median
• 19 Interpret charts to find range
• 20 Identify representative, random and biased samples
• 1 Convert time units
• 2 Add and subtract mixed time units
• 3 Elapsed time
• 4 Find start and end times: word problems
• 5 Convert between 12-hour and 24-hour time
• 6 Time zones - 12-hour time
• 7 Time zones - 24-hour time
• 8 Schedules and timelines - 12-hour time
• 9 Schedules - 24-hour time
• 10 Time patterns

BB. Units of measurement

• 1 Choose the more reasonable temperature
• 2 Calculate temperature differences
• 3 Choose the appropriate metric unit of measure
• 4 Compare and convert metric units of length
• 5 Compare and convert metric units of mass
• 6 Compare and convert metric units of volume
• 7 Convert metric mixed units
• 8 Add and subtract metric mixed units
• 9 Multi-step problems with metric unit conversions
• 10 Choose the appropriate imperial unit of measure
• 11 Compare and convert imperial units of length
• 12 Compare and convert imperial units of weight
• 13 Compare and convert imperial units of volume
• 14 Imperial mixed units
• 15 Convert between miles and kilometres
• 16 Convert between metric and imperial units
• 17 Precision

CC. Two-dimensional figures

• 1 Is it a polygon?
• 2 Regular and irregular polygons
• 3 Number of sides in polygons
• 4 Interior angles of polygons
• 5 Sort polygons into Venn diagrams
• 6 Properties of polygons
• 7 Lines, line segments and rays
• 8 Parallel, perpendicular and intersecting lines
• 9 Parts of a circle
• 1 Types of angles
• 2 Measure angles with a protractor
• 3 Draw angles with a protractor
• 4 Find a missing angle - vertical angles
• 5 Find a missing angle - adjacent angles
• 6 Find a missing angle - supplementary angles
• 7 Find a missing angle - vertical, adjacent and supplementary angles
• 8 Find a missing angle - complementary angles
• 9 Find measures of complementary and supplementary angles

EE. Triangles and quadrilaterals

• 1 Classify triangles
• 2 Find missing angles in triangles
• 3 Parallel sides in quadrilaterals
• 4 Sides and angles of quadrilaterals
• 5 Identify parallelograms
• 6 Identify trapeziums
• 7 Identify rectangles
• 8 Identify rhombuses
• 9 Classify quadrilaterals
• 10 Pick all the names for a quadrilateral
• 11 Draw quadrilaterals
• 12 Graph triangles and quadrilaterals
• 13 Identify the relationships between quadrilaterals
• 14 Describe relationships among quadrilaterals
• 15 Find missing angles in quadrilaterals

FF. Symmetry and transformations

• 1 Lines of symmetry
• 2 Draw lines of symmetry
• 3 Count lines of symmetry
• 4 Rotational symmetry
• 5 Rotational symmetry: amount of rotation
• 6 Identify reflections, rotations and translations
• 7 Translations: graph the image
• 8 Reflections: graph the image
• 9 Combinations of reflections, rotations and translations
• 10 Identify congruent and similar figures
• 11 Identify similar triangles and quadrilaterals

GG. Three-dimensional figures

• 1 Identify three-dimensional figures
• 2 Count vertices, edges and faces
• 3 Which figure is being described?
• 4 Nets of three-dimensional figures
• 5 Three-dimensional figures viewed from different perspectives

HH. Geometric measurement

• 1 Find the perimeter of rectangles using formulas
• 2 Perimeter with whole number side lengths
• 3 Perimeter with decimal side lengths
• 4 Area of squares and rectangles
• 5 Understanding area of a parallelogram
• 6 Area of parallelograms
• 7 Understanding area of a triangle
• 8 Area of right triangles
• 9 Area of triangles
• 10 Area of compound figures
• 11 Area between two rectangles
• 12 Area and perimeter of figures on grids
• 13 Area and perimeter: word problems
• 14 Use area and perimeter to determine cost
• 15 Relationship between area and perimeter
• 16 Volume of figures made of unit cubes
• 17 Volume of cubes and cuboids
• 18 Relationship between volume and the area of the base: word problems
• 19 Compare volumes and dimensions of cuboids: word problems

II. Financial literacy

• 1 Identify advantages and disadvantages of payment methods
• 2 Evaluate payment methods
• 3 Reading financial records
• 4 Keeping financial records
• 5 Balance a budget
• 6 Adjust a budget

Maths: Age 10–11 (Year 6)

In Year 6, your child will apply the maths they already know alongside developing new skills to help solve more complex problems. They will work with numbers up to 10 million and begin to learn about algebra and ratio. They will convert measurements, calculate volumes and learn about circles. They will draw and interpret pie charts and find averages.

They’ll be taught long division for dividing four-digit by two-digit numbers. They’ll be able to use brackets in calculations and explain remainders. They’ll learn to multiply and divide with fractions and decimals, and calculate percentages.

Don’t worry if some methods that your child learns are new to you! There are still simple things you can do at home to support their development.

How to help at home

You don’t need to be an expert to support your child with maths or help them develop a good sense of number! Here are three simple, but effective learning ideas that you can try with your child using everyday items at home.  

1. Look for large numbers

Talk about large numbers in the real world, such as house prices, electricity meter readings or football transfer values. When you see big numbers, ask your child to read them aloud. Can they write large numbers accurately if you say them?

2. Rewrite the recipe book

Cooking is a great way to explore ratio and proportion. Try adjusting recipes to make different quantities. For example, ask your child: ‘A recipe uses 240 g of oats to make 18 flapjacks. What quantity of oats is needed for 24 flapjacks?’.

3. Find an average

Explore the ‘mean’ average in real life. Find a football team’s mean number of goals per match by adding all the goals scored and dividing the total by the number of matches played. Or find the mean number of minutes the school run takes over a week.

You’ll find more activity ideas in our Kids’ activities section

What your child will learn at school

Number & place value in year 6 (age 10–11).

In Year 6, children will be expected to read, write, order, compare and round numbers up to 10,000,000 and begin to learn about algebra, ratio and proportion. This includes:

• using number lines to add and subtract negative numbers
• using simple formulae and following rules such as 2n + 3 to find numbers in a sequence
• solving problems involving place value, ratio, scale factors, and equations expressed

More information and activity ideas for Year 6

Addition & subtraction in Year 6 (age 10–11)

In Year 6, children will be expected to be able to solve problems, including multi-step word problems, involving adding, taking away, multiplying and dividing with large numbers. This includes:

• choosing efficient methods to solve problems and checking their answer using a different method
• exploring the order of operations using brackets
• rounding answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50, and so on.

Multiplication & division in Year 6 (age 10–11)

In Year 6, children will be expected to be able to multiply and divide with large numbers using formal written methods including long division. This includes:

• multiplying four-digit numbers by two-digit numbers using long multiplication
• dividing four-digit numbers by two-digit numbers using long division
• solving multi-step problems using addition, subtraction, multiplication and division choosing which methods to use and explaining why.

Fractions, decimals & percentages in Year 6 (age 10–11)

In Year 6, children will be expected to be able to calculate and solve problems using fractions, decimals and percentages. This includes:

• using common factors to simplify fractions
• multiplying pairs of fractions and dividing fractions by whole numbers
• multiplying one-digit numbers with up to two decimal places by whole numbers, for example 1.25 x 2.

Geometry in Year 6 (age 10–11)

In Year 6, children will be expected to be able to solve problems by calculating and converting measurements with up to 3 decimal places, including between miles and kilometres. This includes:

• working out areas of shapes including triangles and parallelograms
• working out volumes of cubes and cuboids
• knowing and using a formula to work out areas and volumes of some shapes.

Measurement in Year 6 (age 10–11)

Statistics in year 6 (age 10–11).

In Year 6, children will interpret and present discrete and continuous data in a range of ways. This includes:

• connecting work on angles, circles, fractions, and percentages to make and interpret pie charts
• solving problems by interpreting and making line graphs
• calculating and interpreting mean averages.

Ratio and proportion in Year 6 (age 10–11)

In Year 6, your child will begin to learn about ratio and proportion. This includes:

• solving ratio problems using their knowledge of multiplication and division
• using their knowledge of percentages and the fact that the number of degrees in a circle is 360° to calculate angles of pie charts
• solving problems involving unequal sharing and grouping using their knowledge of fractions and multiples.

Algebra in Year 6 (age 10–11)

In Year 6, your child will begin to learn about algebra. This includes:

• using simple formulae to solve problems
• generating and describing linear number sequences
• using letters to represent unknown numbers when solving number problems.
• Age 3–4 (Early Years)
• Age 4–5 (Reception)
• Age 5–6 (Year 1)
• Age 6–7 (Year 2)
• Age 7–8 (Year 3)
• Age 8–9 (Year 4)
• Age 9–10 (Year 5)
• Age 10–11 (Year 6)
• Year 1 (age 5–6)
• Year 2 (age 6–7)
• Year 3 (age 7–8)
• Year 4 (age 8–9)
• Year 5 (age 9–10)
• Year 6 (age 10–11)
• Help with times tables
• Ratio & proportion
• Learning to tell the time
• Numicon parent guide
• MyMaths parent guide
• Maths activity books

35 year 6 maths questions

Practise 35 year 6 maths questions that will help your child stay on track!

Author Amber Watkins

Published February 2024

• Key takeaways
• Year 6 maths word problems help students apply mathematical concepts to real-world scenarios.
• In year 6 maths, it’s important to master fractions, decimals, and order of operations.
• Hard problems  can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

• Word problems
• Numbers & place value

Multiplication

If this maths page has 5 sections of maths questions  with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 year 6 maths questions for us to practise. Without realising it, you just solved one of our first year 6 word problems . Excellent work! Together we will review year 6 maths problems with decimals, fractions, order of operations, and rounding. We will even consider hard maths problems, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

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Year 6 maths word problems

Let’s begin by covering maths word problems.

Mia’s water bottle can hold 300 millilitres of water. She drinks two and a half water bottles each day. How many total millilitres of water does Mia drink each day? 

The playground is made up of four rectangular lots that are each 10 metres by 7 metres. What is the total area of the playground?

 Josh lives 2.5 kilometres away from the park. Josh rides his bike to the park and back home four days a week. How many kilometres does Josh ride his bike each week?

Since we are solving word problems, a word should always be in our answer.

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Numbers & place value

In this section, we will cover maths questions that use place values, word form to standard form, standard form to word form, and expanded form.

Place value

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

In this section, we will cover year six maths questions that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review maths questionss for year six that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations.

Adding and subtracting whole numbers by transformation

A large portion of year 6 maths problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practise adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50 

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate! 

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320- 200 = 120 The answer is 120

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Remember that the steps Multiply or Divide can be done in any order. Also, the steps Add or Subtract can be done in any order, do the operation that comes first.

Some of the hardest maths questions involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practise a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

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Word problem answer sheet

Mia drinks 750 millilitres  of water each day.

Explanation: 300 x 2 = 600. 300 / 2 = 150. 600 + 150 = 750.

280 square metres.

Explanation: The area of one lot is 10 x 7 = 70 metres. Take that area and times it by four, so 70 x 4 = 280 metres.

Josh rides 20 kilometres on his bike each week.

Explanation: Each day Josh rides 5 total kilometres: 2.5 kilometres to the park and 2.5 kilometres back home. If we multiply that number by 4 days a week, it equals 20 kilometres in all.

Writing numbers answer sheet

2 is in the hundreds place.

0 is in the tens place.

2 is in the ones place.

Division using area models answer sheet

Multiplying using square models answer sheet

Multiplying fractions and whole numbers using expanded form answer sheet

Multiplying fractions using a number line answer sheet

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓. 

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring students in maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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