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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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Double Rules

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.

find a number rule

use a  symbols to express the rule

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Equality with multiplication and division

Level Three
Number and Algebra
This unit of work investigates how relational thinking is applied to multiplication and division.
  • Use relational thinking as a basis for a range of number strategies.
  • Explain number strategies using materials and diagrams.
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Eye Antics

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

explore tessellations with shapes (Problem 2)

use operation signs to make equations (Problem 3)

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Fishy Friends

Level Two
Level Three
Number and Algebra
Figure It Out activities
This is a level 2 number and 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

compare food prices

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Fresh Eggs for Sale!

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 additive strategies to calculate costs

use division to calculate costs per month and per year

use multiplication to calculate money earnt

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Going Around

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

use addition and a systematic approach to solve puzzles (Problem 1)

find outcomes using  a diagram (Problem 2)

use algebraic thinking to solve problems (Problem 3)

 

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Good as Gold

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 mental strategies to solve addition and subtraction problems

solve algebraic equations

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Guess my Number

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.

explore equations puzzles

write an equation puzzle

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Homework sheet: stage 6 – 7, Revision of add-sub and mult-div 2

Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use as a week’s homework to practice number properties
  • Choose an appropriate strategy to solve addition and subtraction problems.
  • Choose an appropriate strategy to solve multiplication problems.
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How many pieces? (years 4-6)

Level Two
Level Three
Level Four
Integrated
This counting collections activity engages students in finding the number of sheets in a roll of toilet paper.
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Living Expenses

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.

use mental strategies to add money amounts

use mental strategies to calculate multiplication problems

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Loads of Sugar

Level Three
Integrated
Rich learning activities
The purpose of this activity is to engage students in using mathematical strategies to solve a measurement problem in context.
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Lollies, lollies, lollies

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Solve problems that involve multiplication and division
  • Use equations to express a problem
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Losing Your Marbles

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 an equation to describe a relationship

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Make 4.253

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
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Making Equations

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 equations using basic facts

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Making Numbers

Level Three
Number and Algebra
Figure It Out activities
This is a level 3 number activity from the Figure It Out series.

write equations using combinations of operations

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Mixing Fruit

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

find outcomes using a diagram (Problem 1)

interpret three dimensional drawings (Problem 2)

use algebraic thinking to solve problesm (Problem 3)

explore averages (Problem 4)

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Money and More

Level Three
Integrated
Figure It Out activities
These are level 3 geometry, and algebra problems from the Figure It Out series.

interpret three dimensional drawings (Problem 2)

use algebraic thinking to solve problems (Problem 3)

predict the results of paper folding reflections (Problem 4)

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Money-making Mice

Level Two
Level Three
Integrated
Figure It Out activities
This is a level 2 number and statistics and 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.

calculate a bank balance using addition and subtraction

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Multiples of a

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Perform calculations with algebraic quantities.
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Multiplication and division symbols, expressions and relationships

Level Three
Number and Algebra
Units of Work
This unit develops an understanding of multiplication and division, including the inverse relationship between the two operations, and when and how to use them in problem solving situations. Students learn the conventions of how multiplication and division operations are represented as equations.
  • Read, write and understand the multiplication and division symbols and the equals sign, and the language associated with these symbols.
  • Write story contexts for given multiplication and division equations.
  • Recognise that the operation of multiplication is commutative.
  • Identify related multiplication300
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Mystery Amounts

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

use logic to solve equations (Problem 1)

explore tessellations with rectangles (Problem 2)

solve problems using algebraic thinking (Problems 3 and 4)

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Number in Geometry

Level Three
Level Four
Integrated
Secondary activities
These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10...
  • Use a range of mental strategies to add to 90, 180, 270, 360.
  • Find factors of 90, 180, and 360.
  • Use additive strategies to balance equations.
  • Use multiplicative strategies to balance equations.
  • Fold paper to show an angle.

 

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Number plates

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Express numbers in a variety of ways.