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.
make estimations and calculations using addition, multiplication, subtraction and divisioin
solve addition and subtraction puzzles on a calendar
explore factors and arrays
use additive strategies to calculate costs
solve problems involving time (Problem 1)
explore fractions of regions (Problem 2)
solve problems using addition and logic strategies (Problem 3)
Solve addition and subtraction problems by using place value.
use times tables to calculate income
use mental strategies to calculate income totals
use basic facts to solve division problems
identify a fraction of a region
identify equivalent fractions
use multiplication facts and mental strategies to solve multiplication problems
Students will:
- decide on appropriate ways to measure the amount of water lost in Activity Two
- calculate percentages of large numbers and percentages of percentages.
Students should discover that:
- a small percentage of a large number can itself be a large number
- a familiar context can help give meaning to300
solve problems using multiplication facts
find volume of a cuboid (Problem 1)
continue a sequential pattern (Problem 2)
solve division problems (Problem 3)
use algebraic thinking to solve problems (Problem 4)
- Use tree diagrams and two-way tables to find all the combinations for a simple pairing situation.
- Use multiplication to count all the possible combinations (and permutations).
- Use models of all the possible outcomes, and experimental results, to compare the chances of different outcomes.
Students will:
- use a variety of multiplicative and additive strategies when playing the game
- use mathematical knowledge to strategise and predict how to win the game.
Students should discover that:
- social games in which one player’s actions affect everyone require multiple-move strategies and300
Addition and subtraction of fractions with like denominators
find fraction (half, quarter) of money amounts
multiply money amounts by 2 and 10
use mental strategies to solve addition and subtraction problems