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.
Multiply by 10s, 100s, 1000s, and other multiples of 10.
- Use the properties of multiplication (factors) to solve problems.
- Devise and use problem solving strategies (be systematic, guess and improve).
find fractions of a whole
Solve addition and subtraction problems by compensating with tidy numbers (including equal additions).
use addition and subtraction to solve money problems
- Use a range of mental strategies to add to 90, 180, 270, 360.
- Find factors of 90, 180, and 360.
- Use additive strategies to balance equations.
- Use multiplicative strategies to balance equations.
- Fold paper to show an angle.
Students will learn
- To use relational thinking as a basis for a range of number strategies.
- To explain number strategies using materials and diagrams.
solve problems involving units of mass, volume, money and time
find fractions of whole numbers
- Understand and use the < and > relationship symbols.
- Recognise the relative size of unit fractions (numerator of one, e.g. 1/5).
- Recognise fractions as numbers that are positioned between, and with, whole numbers on a number line
- Recognise that whole numbers also have an infinite number of fraction300
use multiplication to solve money problems
use addition to solve money problems
solve addition problems using mental strategies
use basic facts and mental strategies to solve problems
use place value knowledge and addition to solve problems (Problem 2)
follow instructions to interpret a co-ordinate system (Problem 3)
use a systematic approach and addition and multiplication to solve problems (Problem 4)
use mental strategies to add costs
use multiplicative strategies to find yearly costs based on weekly costs
Solve problems using a combination of addition, subtraction, multiplication and division mental strategies.
use basic facts to solve a problem
- Recognise and demonstrate understanding of the relationship between fractions, decimals, and percentages.
- Use and explain percentage calculations (including with increase and decrease problems).
multiply with multiples of ten
simplify fractions
find fractions of a number
use basic facts tosolve problems (Problems 1 and 3)
solve addition problems using additive strategies (Problem 2)
find outcomes using diagrams (Problem 4)
- Add a series of two digit numbers.
- Double numbers.
- Systematically keep track of their calculations to compare numbers.