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 word problems involving addition, subtraction and multiplication
know multiplication facts
adiing simple decimal numbers.
- Perform addition with decimals.
- Order decimals.
- Devise and use problem solving strategies to explore situations mathematically.
use additive strategies to solve problems (Problems 1 and 4)
arrange 3 dimensional pieces to make a cube (Problem 2)
solve problems involving addition and capacities (Problem 3)
use estimation to solve addition and subtraction
Students will be able to create a contextualized problem and provide alternative strategies for solving it.
compare addition and subtraction strategies
Students will:
- carry out a statistical investigation into the relationship between weight, height, and potential energy
- measure and record weight, height, and energy data
- identify relationships in their data, judge their accuracy, and use the relationships to make predictions.
Students should discover300
choose an operation (addition, subtraction, multiplication, division)to solve a word problem
use basic facts
find outcomes using a diagram (Problem 1)
interpret three dimensional drawings (Problem 2)
use algebraic thinking to solve problesm (Problem 3)
explore averages (Problem 4)
Solve problems using a combination of addition, subtraction, multiplication and division mental strategies.
use mental strategies to solve addition and subtraction problems
use addition and subtraction to solve money problems
use arrays to solve multiplication facts
- Solve problems involving finding a fraction of a fraction, using a regional model.
- Understand that the language ‘of ‘ and ‘times’ is interchangeable.
- Notice, explain and generalise what is happening to the numbers in a multiplication algorithm.
- Record, respond to, pose and solve a range of fraction300