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.
write fractions as decimals
use addition to solve money problems
Solve division problems by using multiplication facts.
Solve division problems by using multiplication facts.
use addition and a systematic approach to solve puzzles (Problem 1)
find outcomes using a diagram (Problem 2)
use algebraic thinking to solve problems (Problem 3)
use mental strategies to solve addition and subtraction problems
solve algebraic equations
solve multiplication and division problems using basic facts
- Select the appropriate number operation(s) to solve problems.
- Devise and use problem solving strategies (act it out, draw a picture, organised list).
use equipment to solve multiplication problems
solve subtraction problems using mental strategies
know division facts
find fractions of numbers
solve problems involving finding fractions of a number
arrange numbers and operations to make a target number
use mental strategies to calculate costs
calculate an exchange rate
use addition strategies to solve problems (Problems 1 and 4)
find outcomes using a table or diagram (Problem 2)
continue a pattern (Problem 3)
- Choose an appropriate strategy to solve addition and subtraction problems.
- Choose an appropriate strategy to solve multiplication problems.
A range of problems for which they have to decide whether or not a given strategy is appropriate.
Students will:
- use data and tables to make predictions in an authentic context.
Students should discover that:
- multiple factors need to be taken into account when estimating or predicting outcomes in the natural world
- an everyday benchmark can help make sense of large quantities (for example, 1 cumec =300
Solve addition and subtraction problems by using place value.
- Students will be able to express place value amounts in multiplicative terms (for example 10 thousand is 100 x 100)
- Students will be able to add and subtract whole number amounts to 1,000,000
use mental strategies to solve problems involing addition, subtraction, multiplication, and division
use basic facts to solve problems
use doubles and halves to solve problems