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 doubles and halves to solve multiplication problems
Solve multiplication and division problems by using proportional adjustment.
apply logic and number sense to solve problems
explore a multiplication strategy
- Multiply large numbers by 8.
- Find and describe patterns in numbers.
solve problems involving the 11 times table
Students will:
- investigate the meaning of derived quantities, such as energy density
- calculate energy and mass totals using energy density, percentage of water content, and mass
- predict and calculate the reduction of mass through dehydration.
Students should discover that:
- energy is the300
Students will:
- estimate the energy change of a system
- calculate the amount of energy converted by different activities
- use rates to determine inputs and/or outputs.
Students should discover that:
- energy transfer is proportional to work (the more force x distance, the more energy)
- different forms of energy300
order large numbers
add and subtract large numbers using rounding to estimate
use their knowledge of basic facts to identify common factors of numbers to 100.
explore factorials
find factors of numbers
generalise patterns for factors
use multiplication facts to solve puzzles
use simple proportions to solve problems
solve division problems using proportional adjustment
- Use a recursive rule to generate the sequence of Fibonacci numbers.
- Create a Fibonacci spiral using squares with Fibonacci side lengths.
- Find a pattern of odd and even numbers in the sequence.
- Identify and represent patterns we find for consecutive numbers in the sequence.
use proportional adjustment to sovle multplication problems
use addition, multiplication and systematic approach to solve problems (Problem 1)
interpret distance and direction information on a road map (Problem 2)
find fractions of whole number to solve problems (Problem 3)
use simple ratios to solve problems (Problem 4)
Solve division problems that involve remainders.
add and subtract decimals
use rounding to estimate a multiplication problem
finda percentage of a decimal number
use multiplicative strategie to solve problems (tidy numbers, partitioning, doubles and halves)
Students will:
- measure and record data on temperature change
- convert between temperature change and food energy units
- calculate the total energy needs and intake for sample menus, using food energy unit values
- investigate the relative proportions of energy provided by different foods in their diet.
Stude300
solve multiplication and division story problems
use mental strategies tosolve multiplication and division problems
find the mean