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.
Solve problems using a combination of addition, subtraction, multiplication and division mental strategies.
use mental strategies to calculate costs
Add and subtract fractions with like denominators
Identify fractions that equal one
Identify fractions bigger than one
- Mentally solve whole number addition and subtraction problems using:
- compensation from tidy numbers including equal additions
- place value
- use appropriate recording techniques.
- Predict the usefulness of strategies for given problems.
- Evaluate the effectiveness of their300
- Choose appropriately among strategies such as using standard place value, using tidy numbers with compensation, and equal adjustments to solve addition and subtraction problems with whole numbers.
- Choose correct operations to solve joining, separating, and difference problems with whole numbers. 300
- Add and subtract fractions with like denominators.
- Explore and record equivalent fractions for simple fractions in everyday use.
- Recognise that equivalent fractions occupy the same place on the number line.
- Recognise and apply the multiplicative relationship between simple equivalent fractions300
- multiply and divide to find quantities of bricks for given lengths, heights, and areas.
Students should discover that:
- area is the product of length by width; volume is the product of length by width by height.
use mental strategies to solve addition and subtraction problems
use addition and subtraction to solve money problems
compare probability chances
solve addition problems involving singe and multi digit numbers
make estimations for addition problems
solve multiplication problems by rounding up to a tidy number and then compensating
solve multiplication problems by rounding down to a tidy number and then compensating
Derive multiplication facts from 2, 5 and 10 times tables.
find the area of a rectangle (Problem 1)
solve puzzles involving 3 dimensional drawings (Problem 2)
use addition to solve puzzles (Problem 3)
find outcomes using a diagram (Problem 4)
know multiplication facts
- make a scale drawing of an eco-kennel to suit a given volume
- scale up the drawing by specifi ed percentages.
Students should discover that:
- volume is length by width by height
- increasing dimensions by 50% or less can double the volume of a cuboid.
use strategies to solve addition patterns
investigate adding odd and even numbers
- Model the numbers from 1 to 50 as rectangular arrays.
- Identify the factors of the numbers 1 to 50.
- Identify whether whole numbers from 1 to 50 are prime or composite (or a special case, i.e. 1).
solve problems involving mutliplication and division