# 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.**

use basic facts to solve equations

use mental strategies to calculate costs

- 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).

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)

- 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 multiplication300

use algebraic symbols in linear equations

use mental strategies to add money amounts

solve addition and subtraction problems involving money

calculate an average

use multiplication tosolve money problems

use diagrams or symbols to solve a problem

use basic facts knowledge to solve operation-sign problems

use times tables to calculate income

use mental strategies to calculate income totals

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)

- 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.

use additive strategies to add numbers

use a table to find a rule for a geometric pattern

write rule to describe a relationship

write equations using letter symbols

write number stories for multiplication and division problems

use additive strategies to calculate costs

calculate costs by month and year/s