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.
use addition and a systematic approach to solve problems (Problems 1 and 2)
explore features of two dimensional shapes (Problem 3)
explore symmetry (Problem 4)
explore the effects of place value
use mental strategies to sovle addition puzzles
- Apply the understanding that fractions can be quotients (i.e. the result of division), e.g. 3 ÷ 5 = 3/5.
- Model and represent division problems with fractions that involve a measurement or sharing interpretation of division.
- Write and solve division problems that involve fractions.
finding time before and after a given time
writing times in different ways
working with 12 and 24 hour clocks
find fractions and decimals of an hour
solve problems involving time zones
find fractions of mass and volume
Solve subtraction problems by using addition.
use addition to find the answer to subtraction problems
use place value understandings and multplication to solve problems involving large numbers
use doubling and halving strategies
find fractions of money amounts
solve nine times tables problems
Students will:
- gather and enter personal lifestyle data
- interpret data displays in order to identify patterns and trends
- change input variables and observe the effect on outputs
- estimate sources of variation in eco-footprints.
Students should discover that:
- outputs are a function of inputs.
- Derive from basic multiplication facts to solve multiplication problems with equal sets.
- Apply the commutative and distributive properties of multiplication to solve problems mentally and on paper.
- Recognise how both measurement and sharing division problems can be solved by ‘building up’ with300
solve addition and subtraction problems using a number line
use multiplication facts to solve problems
know equivalent fractions fro tenths and fifths
find half of a number
Solve subtraction problems using equal additions
Solve addition and subtraction problems by compensating with tidy numbers (including equal additions).
- Use relational thinking as a basis for a range of number strategies.
- Explain number strategies using materials and diagrams.