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.
solve multiplication problems
find fractions of a number
use simple proportions to solve problems
use basic facts and mental strategies to solve problems
use multiplication to solve problems involving money
find Cartesian products using multiplication
use place value strategies to solve multiplication
use number strategies to solve puzzles (Problems 1, 2 and 4)
explore areas of geometric shapes on geoboards (Problem 3)
solve money problems using multiplication and division
use knowledge of multiplication and division facts to solve problems with remainders
Students will:
- perform calculations with percentages
- gather and interpret statistical data.
Students should discover that:
- they can create a statistical map that shows the air pollution of different parts of the school environment.
Solve multiplication and division problems by using proportional adjustment.
- Choose strategies for investigating number problems.
- Find a common multiple of a group of numbers.
solve problems using repeated factors and divisors
solve multiplication problems
find factors of numbers
- Students will explore several key concepts from the world of mathematics through narrative and through the construction of models.
- Students will be able to express their observations about patterns and groups of numbers with an accurate vocabulary.
Solve multiplication and division problems by using proportional adjustment.
use mental strategies to solve multiplication and division story problems
find factors of a number
Students will:
- collect and accurately measure amounts of water
- calculate percentages for retention of water.
Students should discover that:
- rates of dry and saturated (wet) water retention are independent of each other.
Solve division problems that have fraction answers.
Students will:
- extract appropriate data from tables
- perform calculations with percentage and rate data
- convert between percentages and absolute quantities.
Students should discover that:
- significant amounts of time and money are wasted in traffic jams.
solve division problems involving remainders
use mental strategies towork out 15 times table
Use divisibility rules for 2, 3, 4, 5, 6, 8, 9.