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
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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 algebraic...
Secondary activities
Number and Algebra
Level Three
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.
Model the numbers from 1 to 50 as rectangular arrays. Identify the factors of the numbers 1 to 50. Identify whether whole numbers from 1 to 50 are prime or composite (or a special case, i.e. 1).
Units of Work
Number and Algebra
Level Three
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)
Figure It Out activities
Number and Algebra
Level Three
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.
Recognise that there are number properties and that these describe the behavior of number operations. Understand that a generalisation of an important idea can be expressed using letters (variables). Describe the commutative property of addition and the commutative property of multiplication, name...
Units of Work
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
The purpose of this activity is to engage students in using knowledge of basic facts, to solve a problem in context.
Rich learning activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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)
Figure It Out activities
Geometry and Measurement
Level Three
This unit introduces students to combinations as a situation type that multiplicative thinking can be applied to.
Use models such as 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...
Units of Work
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Two
This counting collections activity engages students in finding the number of squares of any size on a chessboard.
Number and Algebra
Level Three
This counting collections activity engages students in counting a collection of objects.
Number and Algebra
Level Two
This counting collections activity engages students in finding the number of studs on a Lego (or similar) baseplate.
Number and Algebra
Level Two
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Two
The purpose of this activity is for students to apply additive and multiplicative thinking to find three addends with the same sum.
Rich learning activities
Number and Algebra
Level Three
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
Figure It Out activities
Number and Algebra
Level Three