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.
- Describe what it means for a sequence to carry on infinitely.
- Look for patterns using linear combinations of 4 and 7.
- Describe what it means for a sequence to carry on infinitely.
- Look for patterns in linear combinations of numbers.
- Devise and use problem solving strategies (guess and check, make a table, look for patterns).
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
- Identify a utility need or opportunity within the school and plan a response .
- Create a design incorporating key attributes identified.
- Investigate quality and comparative costs of possible construction materials.
- Cost ‘fit for purpose’ construction materials and prepare a budget.
- Draw plans300
- Understand and describe proportion using the language of mathematics.
- Understand the principles of scale.
- Create scale drawings.
- Calculate scale dimensions.
- Make accurate metric length measurements.
- Understand that the value of the scale factor of a reduction is less than 1 and for an enlargement is300
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.e. 1).
- Calculate300
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