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NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.

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Elaboration on this Achievement Objective

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.

 

Teaching resources for this Achievement Objective
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31 or None

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 number and algebra strand activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.A PDF of the student activity is included.

use basic facts to solve equations

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A Cat from the Animal Shelter

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 number and algebra activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.A PDF of the student activity is included.

use mental strategies to calculate costs

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Adding in Parts

Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are designed for students to use independently to practise number properties.
  • Solve addition problems with whole numbers by adding in parts.
  • Solve addition problems with decimnal numbers by adding in parts.
  • Use equal addition strategies to insert numbers to balance addition equations.
  • Use equal addition strategies to insert numbers and letter symbols to balance algebraic300
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Arrow Antics

Level Three
Integrated
Figure It Out activities
These are level 3 number, algebra, and geometry problems from the Figure It Out series.A PDF of the student activity is included.

explore patterns in mutliples of 7, 8, 9 multiplication facts (Problem 2)

identify parallelograms and trapeziums in geometric shapes (Problem 3)

explore the idea of equality in diagrams of scale balances (Problem 4)

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A study of number properties

Level Three
Number and Algebra
Units of Work
The purpose of this unit is to develop understanding of the way numbers behave, to enable the use of everyday language when making general statements about these behaviours, and to develop understanding of the symbolic representation of these ‘properties’ of numbers and operations.
  • Recognise that there are number of useful properties that describe the behaviour of number operations.
  • Understand that a generalisation of an important idea can be expressed using letters (variables).
  • Describe and apply the commutative properties of addition and multiplication.
  • Describe and apply the300
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Bagged Cubes

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 algebra strand link activity from the Figure It Out series. A PDF of the student activity is included.

use algebraic symbols in linear equations

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Bill's Dollars

Level Three
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using their number knowledge and skills to solve a problem requiring partitioning.
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Buy or Make?

Level Two
Level Three
Integrated
Figure It Out activities
This is a level 3 number and algebra activity and a level 2 statistics activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.A PDF of the student activity is included.

use mental strategies to add money amounts

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Caitlyn's Busking Business

Level Three
Integrated
Figure It Out activities
This is a level 3 number and algebra activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.A PDF of the student activity is included.

solve addition and subtraction problems involving money

calculate an average

use multiplication tosolve money problems

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Camping groups

Level Three
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using knowledge of basic facts, to solve a problem in context.
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Can you Kayak?

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 algebra activity from the Figure It Out theme series.A PDF of the student activity is included.

use diagrams or symbols to solve a problem

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Choice Calculations

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.A PDF of the student activity is included.

use basic facts knowledge to solve operation-sign problems

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Christmas Bonus

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 number and algebra activity and a level 2 statistics activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.A PDF of the student activity is included.

use times tables to calculate income

use mental strategies to calculate income totals

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Colourful Calculations

Level Three
Integrated
Figure It Out activities
These are level 3 measurement, algebra, and number problems from the Figure It Out series.A PDF of the student activity is included.

find volume of a cuboid (Problem 1)

continue a sequential pattern (Problem 2)

solve division problems (Problem 3)

use algebraic thinking to solve problems (Problem 4)

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Combos

Level Three
Integrated
Units of Work
This unit introduces students to combinations as a type of situation that multiplicative thinking can be applied to.
  • Use tree diagrams and two-way tables to find all the combinations for a simple pairing situation.
  • Use multiplication to count all the possible combinations (and permutations).
  • Use models of all the possible outcomes, and experimental results, to compare the chances of different outcomes.
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Comparing Costs

Level Two
Level Three
Integrated
Figure It Out activities
This is a level 2 number and statistics, level 3 algebra activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.A PDF of the student activity is included.

use additive strategies to add numbers

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Counting squares

Level Three
Level Four
Level Five
Number and Algebra
This counting collections activity engages students in finding the number of squares of any size on a chessboard.
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Count it (years 4-6)

Level Two
Level Three
Number and Algebra
This counting collections activity engages students in counting a collection of objects.
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Covering our bases

Level Two
Level Three
Level Four
Number and Algebra
This counting collections activity engages students in finding the number of studs on a Lego (or similar) baseplate.
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Cricket with no ticket

Level Three
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in applying their number knowledge and strategies to solve a problem.
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Cube Signs

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 algebra strand link activity from the Figure It Out series. A PDF of the student activity is included.

use a table to find a rule for a geometric pattern

write rule to describe a relationship

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Cup Capers

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 algebra strand activity from the Figure It Out series.A PDF of the student activity is included.

write equations using letter symbols

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Dazzler Digs On

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 algebra activity from the Figure It Out series.A PDF of the student activity is included.

write number stories for multiplication and division problems

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Doggone Expensive!

Level Two
Level Three
Integrated
Figure It Out activities
This is a level 2 number and statistics activity and a level 3 algebra activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.A PDF of the student activity is included.

use additive strategies to calculate costs

calculate costs by month and year/s

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Domino donuts

Level Three
Number and Algebra
Rich learning activities
The purpose of this activity is for students to apply additive and multiplicative thinking to find three addends with the same sum.