NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
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
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.
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.
Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are designed for students to use independently to practise number properties.
Level Three
Number and Algebra
Units of Work
In this unit we use rectangular models or arrays to explore numbers from one to fifty. We practice expressing numbers as the product of two smaller numbers and in doing so identify all the factors of numbers systematically. We are also introduced to prime numbers.
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.
Level Three
Number and Algebra
Units of Work
The purpose of this unit is to develop the students’ deeper understanding of the way numbers behave, to enable them to use everyday language to make a general statement about these behaviours, and to understand the symbolic representation of these ‘properties’ of numbers and operations.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Level Three
Integrated
Units of Work
This unit introduces students to combinations as a type of situation that multiplicative thinking can be applied to.
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.
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.
Level Two
Level Three
Number and Algebra
This counting collections activity engages students in counting a collection of objects.
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.
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.
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.
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.
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.
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.