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.
explore number puzzles using addition (Problem 1)
find outcomes by using diagrams (Problem 2)
Solve multiplication and division problems by splitting factors.
use ratios to solve problems (Problem 1)
use addition facts and logic to solve puzzles (Problem 2 and 4)
use "doubles and halves" strategy to solve multiplication problems
find 10% and 20% of money amounts
use addition and subtraction to solve money problems
find factors of numbers
- Identify and describe patterns in numbers.
- Use expressions and words to describe number patterns.
- Work systematically to find the possible outcomes.
use mental strategies to solve multiplication problems
find factors and multiples of numbers
Use multiplication to solve addition and subtraction problems.
use common factors to help solve addition and subtraction problems
- Mentally solve whole number multiplication and division problems using:
- proportional adjustment
- place value partitioning
- rounding and compensation
- factorisation.
- Use appropriate recording techniques.
- Predict the usefulness of strategies for given problems.
- Evaluate the effectiveness of selected strategies300
use mental strategies to solve multiplication problems
Solve multiplication and division problems by using proportional adjustment.
find a pattern using mutliplication
explore the commutative property
explore the Napier's Bones multiplication pattern
use rates to calculate exhange rates
find a percentage of a number
use multiplicative strategies to solve money problems
use estimation and number strategies to solve problems
Use divisibility rules for 2, 3, 4, 5, 6, 8, 9.
- Use a range of mental strategies to add to 90, 180, 270, 360.
- Find factors of 90, 180, and 360.
- Use additive strategies to balance equations.
- Use multiplicative strategies to balance equations.
- Fold paper to show an angle.
investigate strategies to solve multiplication problems
explore different multiplication strategies
analyse survey questions
interpret information from graphs
find percentages of numbers
use addition and subtraction to solve money problems