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 basic facts and order of operations to solve problems
use multiplication facts and arrays to solve problems
use order of operations to solve problems
Use a range of strategies to solve problems that involve a combination of addition, subtraction, multiplication, and division.
Solve multiplication and division problems by using tidy numbers.
Students will:
- work with very large numbers
- express large number fractions as percentages
- use ratios in different contexts
- identify the appropriate numerical information and operations needed to solve a problem or answer a question.
Students should discover that:
- it is possible to have a percentage of a300
use mental strategies to solve multiplication problems involving money
find a percentage of a money amount
find 1/3 of a money amount
use addition and subtraction to solve money problems
use multiplication to solve money problems
convert fractions to percentages
find mean of a set of numbers
use a proportional strategies to solve multiplication problems
Solve division problems that involve remainders.
investigate number properties in division problems
solve division problems where the remainders are fractions
use mental strategies to solve multiplication problems
solve multiplication problems using multiples of ten
Students will:
- solve problems using rates and unit conversions.
use a spreadsheet to calculate costs
find a percentage of a number
Solve multiplication and division problems by using proportional adjustment.
investigate the relationship between area and perimeter (Problem 1)
solve problems involving proportions (Problem 2)
investigate a sequential pattern (Problem 3)
use multiplication and addition to solve money problems (Problem 4)
solve problems involving division remainders
Solve division problems that involve remainders.
write a remainder as a fraction and as a decimal
- Identify a need and an opportunity.
- Research and develop a small business plan.
- Understand costs, including start up costs.
- Understand profit, credit and cashflow.
- Apply number skills to audit a business plan and cashflow.
- Compare profit with returns and explain variance.
- Understand how300
Students will:
- practise inductive reasoning
- calculate percentages and rates for savings and loans.
Students should discover that:
- small changes over time can lead to big savings.
use place value knowledge and addition and subtraction to solve problems (Problems 1 and 2)
use simple proportions to solve problems (Problems 3 and 4)