NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
This means students will use a range of mental strategies based on partitioning and combining to solve addition and subtraction problems with multi-digit whole numbers and simple decimals (tenths). These strategies include standard place value, for example 603 – 384 = as 60 – 38 tens less one (219), rounding and compensating, for example 923 – 587 = as 923 – 600 + 13 = , and reversing (applying inverse), for example 923 – 587 = as 587 + = 923. Students should also connect known multiplication facts to solve multiplication and division problems, for example 13 x 6 = as 10 x 6 + 3 x 6 = (distributive property), 14 x 9 = as 2 x (7 x 9) = (associative property) and 36 ÷ 9 = using 4 x 9 = 36 (inverse). This multiplicative understanding allows students at Level Three to find fractions of quantities, for example two-thirds of 24 as 24 ÷ 3 x 2 = 16, find simple equivalent fractions related to doubling and halving, for example 3/4 = 6/8 , to add and subtract fractions with the same denominators, for example 3/4 + 3/4 = 6/4 = 1 2/4, and to convert improper fractions to mixed numbers, for example 17/3 = 5 2/3. Students should know the decimals and percentage conversions of simple fractions (halves, quarters, fifths, tenths) and use these to solve simple percentage of amount problems, for example 50% is fifty out of one hundred. 50% is one half so 50% of 18 is 9 or five is half of ten. Level Three corresponds to the Advanced Additive stage of the number framework.
continue a sequential pattern (Problem 1)
share regions into fractions (Problem 2)
explore divisibility rules for 3 (Problem 3)
use mental strategies to solve addition and subtraction problems
Solve subtraction problems by using addition.
Solve subtraction problems by using addition.
Solve addition and subtraction problems by compensating with tidy numbers (including equal additions).
solve addition and subtraction problems by compensating with tidy numbers
- Derive from basic multiplication facts to solve multiplication problems with equal sets and rates.
- Identify the factors and products in equations and explain the meaning of x and =.
- Apply multiplication to find the answers to division problems.
- Learn the basic multiplication facts.
use rounding to make sensible estimations for addition problems
find fractions of 1000
investigate palindrome numbers using place value and addition
Solve subtraction problems by using addition.
find fractions of a region (Problem 2)
use prime factors or square roots to solve problems (Problem 3)
find outcomes using a diagram (Problem 4)
use multiplication to solve perimeter and area problems.
solve subtraction problems
use addition and subtraction to solve money problems
find the chance of an event occurring
find fractions of money
Students will:
- gather and record data and use tables to identify patterns and relationships
- identify the relationship between the relative positions of the effort and load when balanced.
Students should discover that:
- turning force is a function of weight x distance from the fulcrum – in other words300
use addition and simple multiplicative strategies to solve problems involving money
Multiply by 10s, 100s, 1000s, and other multiples of 10.
use place value strategies to solve addition and subtraction problems
look for number patterns in puzzles (Problem 1)
use multiplication facts to solve problems (Problem 2)
solve problems involving multiplication and division facts