# NA4-1: Use a range of multiplicative strategies when operating on whole numbers.

This means students will apply the properties of multiplication and division (commutative, distributive, associative and inverse) to number problems, particularly those requiring multiplication and division. Students should exercise critical choice in their method of calculation - mental, machine or paper - and recognise situations in which estimation should be used, including the checking of calculated answers. Strategies expected at Level Four include: using common factors and multiples, for example 37 + 41 + 40 + 38 = as 4 x 40 – 4, using the distributive property, for example 24 x 36 = 20 x 36 + 4 x 36, 9 x 78 = 9 x 80 – 9 x 2, or 276 ÷ 12 = 240 ÷ 12 + 36 ÷ 12, using the associative property, for example 12 x 33 = 4 x 99, or 216 ÷ 12 = 216 ÷ 2 ÷ 2 ÷ 3, and inverse operations (reversing), for example 354 ÷ 6 = as 6 x = 354. This objective also involves calculating powers, for example 43 = 4 x 4 x 4 = 64, and factorials, for example 4! = 1 x 2 x 3 x 4 = 24. Students should have strong mental strategies for operations on whole numbers but also accurately carry out standard written algorithms, particularly for multi-digit multiplication and division. Level Four corresponds to the Advanced Multiplicative stage of the number framework.

Use multiplication to solve addition and subtraction problems.

choose from a variety of mental strategies to solve problems

use place value strategies to solve addition problems

find factors of numbers

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- Investigate quality and comparative costs of possible construction materials.
- Cost ‘fit for purpose’ construction materials and prepare a budget.
- Draw300

- Understand and describe proportion using the language of mathematics.
- Make accurate metric length measurements.
- Understand the principles of scale.
- Understand that the value of the scale factor of a reduction is less than 1 and for an enlargement is greater than 1.
- Understand that the300

use a variety of strategies to solve problems

- Students will construct model to illustrate their understanding of factorials.
- Students will be able to explain the power of the operation of multiplication and contrast it with addition.

Solve division problems that involve remainders.

- Model the numbers from 1 to 100 as rectangular arrays.
- Connect the possible arrays for a given number to the factors of that number.
- Identify the factors of the numbers 1 to 100 using divisibility.
- Identify whether natural numbers from 1 to 100 are prime, composite, or a special case (i.e300

Use multiplication to solve addition and subtraction problems.

use tidy numbers to solve multiplication problems

use addition to sovle money problems

use multiplication and division to solve problems

find percentage of a number

solve problems involving ratios

find fraction of a number

sovle problems involving addition, subtraction, multiplication and division of money

solve money problems involving multiplication and division

multiply decimals with multiples of ten

operate on fractions and decimals

use place value knowledge to check calculations

add and subtract using place value knowledge whole numbers and decimals

find a percentage of a decimal number

solve addition and subtraction problems

compare prices by using proportions