nz maths problem solving level 3

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Level 3 - Maths

nzmaths.co.nz

Click on the link for level 3 rich learning activities.

Click on the link for level 4 problem solving questions.

Figure It Out

The link will take you to the carousel interface. Click on the coloured squares at the bottom. The green squares and some of the purple squares are around level 3.

mathgametime.com

Click on the link for a range of games, tutorial videos, and worksheets across the number strand at curriculum level 3.

mathsgames.com

The link will take you to a homepage with year level options. Click on 'Year 5' or 'Year 6' to practise skills across the different mathematical strands.

kidsmathsgamesonline.com

This site has some cool logic and problem solving puzzles as well as maths games suitable for a variety of levels. Either click on the coloured tabs along the top or the small links in blue text just underneath.

Level 3 Maths

Below you will find access to all standards that My Study Series offers at Level 3 Mathematics and Statistics for NCEA. By clicking on an achievement standard, you will be presented a list of video lessons for you to observe. Each lesson is concluded with an automated, self graded quiz allowing you to check your understanding of the lesson content.

MATH AS91573 (3.1)

Apply the geometry of conic sections in solving problems.

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MATH AS91574 (3.2)

Apply linear programming methods in solving problems.

MATH AS91575 (3.3)

Apply trigonometric methods in solving problems.

MATH AS91576 (3.4)

Use critical path analysis in solving problems.

MATH AS91577 (3.5)

Apply the algebra of complex numbers in solving problems.

MATH AS91578 (3.6)

Apply differentiation methods in solving problems.

MATH AS91579 (3.7)

Apply integration methods in solving problems.

MATH AS91587 (3.15)

Apply systems of simultaneous equations in solving problems.

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Elaborations on Level Three: Number and Algebra

The Ministry is migrating nzmaths content to Tāhurangi.             Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).  When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.  e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Number strategies

Number knowledge.

NA3- 2: Know basic multiplication and division facts. This means students will know basic multiplication facts are those that range from 0 x 0 = 0 to 9 x 9 = 81. The division basic facts are the inverse of the multiplication facts. So 6 x 4 = 24, 4 x 6 = 24, 24 ÷ 6 = 4 and 24 ÷ 4 = 6 are all basic facts. Students should commit their basic facts to memory as soon as they understand the meaning of the equations and can use number properties to work them out, 8 x 7 = 56 means "eight sets of seven" and can be worked out by doubling 4 x 7 = 28. Note that 56 ÷ 7 can mean "fifty-six shared among seven" or "how many sevens are in fifty-six". Supporting teaching resources .

NA3- 3: Know counting sequences for whole numbers. This means students will know the forward number word sequence for whole numbers is the counting pattern of words and symbols, 0, 1, 2, 3, 4..., ∞ (infinity) while the backward sequence is the pattern 1000 000, 999 999, 999 998, 999 997... beginning with any whole number. At Level Three students should know these sequences in multiples of one, ten, for example 358, 348, 338..., one hundred, for example 247, 347, 447..., one thousand, etc. An important part of knowing these sequences is being able to name the number before and after a given number since this relates to taking an item off or putting an item onto an existing set, for example If a set contains 43 560 items, 43 559 items are left if one is removed and 43 561 items are in the set if one is added. This also applies to the sequence in tens, hundreds, thousands, etc. for example ten thousand removed from a set of 701 000 results in 691 000 objects left. At Level Three students should also have experience with counting sequences in tenths, for example 4.6, 4.7, 4.8, 4.9, 5... Supporting teaching resources .

NA3- 5: Know fractions and percentages in everyday use. This means students will understand the meaning of the digits in a fraction, how the fraction can be written in numerals and words, or said, and the relative order and size of fractions with common denominators (bottom numbers) or common numerators (top numbers). Fundamental concepts are that fractions are iterations (repeats) of a unit fraction, for example 3/5 = 1/5 + 1/5 + 1/5 and 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3. This means the numerator (top number) is a count and the denominator tells the size of the parts, for example in 5/3 there are five parts. The parts are thirds created by splitting one into three equal parts. This means that fractions can be greater than one, for example 4/3 = 1 1/3, and that fractions have a counting order if the denominators are the same, for example 1/3, 2/3, 3/3, 4/3,... The size of the denominator also affects the size of the parts being counted in a fraction. For example, thirds of the same whole are smaller than halves of the same whole. So fractions with common numerators have an order of size based on the size of the parts, for example 2/7 < 2/5 < 2/3 (< means “less than”). Students at Level Three should know simple common fraction-percentage relationships, including 1/2 = 50%, 1/4 = 25%, 1/10 = 10%, 1/5 = 20%, and use this knowledge to work out non-unit fractions as percentages, for example 3/4 = 75%. Supporting teaching resources .

Equations and expressions

NA3- 6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality. This means students will use words, symbols and diagrams to explain their number strategies to others. Recording also allows students to think through solutions to problems and allows them to reduce their working memory load by storing information in written form. This is particularly important for the solving of complex, multi-step problems. Students should be able to write the numerals for whole numbers to 1 000 000 at least, simple fractions, percentages and decimals. They should also be able to write addition, subtraction, multiplication and division equations with understanding of the meaning of these operations and of the equals sign as meaning “equal to”. Similarly, they should know which operation to perform on a calculator if the numbers are beyond their mental range. Students should also be familiar with using empty number lines to record addition and subtraction strategies, arrays to record multiplication and division strategies, and strip diagrams or double number lines to solve problems with fractions and percentages. Formal written algorithms for multi-digit addition and subtraction should be taught at Level Three after students have the nested place value knowledge required to understand them. Supporting teaching resources .

Patterns and relationships

“There is always one more peg than the number of towels. The first towel took two pegs.” Supporting teaching resources .

Click to download a PDF of second-tier material relating to Level 3 Patterns and Relationships (319KB)

NCEA Level 3 Calculus

How a student will experience Level 3 Calculus will largely depend on how well they've understood the concepts from the last 2 years. The curriculum this year expects students to fully grasp their algebraic, differentiation, and geometric basics. It is not recommended for students to take on Level 3 Calculus unless they have merits or excellences from the previous year, this is not an easy curriculum.

Here are some of the things students should look out for this year:

• Complex numbers will be a new and strange concept, it is highly recommended for students to pay attention to this early in the year and regularly revisit the topic.
• Differentiation this year will introduce Rate of Change and Optimisation type questions. Students will need to develop clear thinking and problem solving skills.
• The internals this year are each challenging topics on their own, thorough understanding and long workings will be required for these assessments.

I strongly recommend hiring a tutor early this year, the more deeply a student understands the concepts this year the easier time they will have when exam time comes. Tutoring this year will focus on deep level understanding of maths and problem solving involving calculus. Please get in touch to discuss how I can best support you this year.

91573 Apply the geometry of conic sections in solving problems (3 credits)

91575 apply trigonometric methods in solving problems (4 credits), 91587 apply systems of simultaneous equations in solving problems (3 credits), 91577 apply the algebra of complex numbers in solving problems (5 credits), 91578 apply differentiation methods in solving problems (6 credits), 91579 apply integration methods in solving problems (6 credits).

My 15 year old daughter ... got her results back last week - she passed with Excellence! Unbelievable.

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