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 involving mutliplication and division
explore patterns in mutliples of 7, 8, 9 multiplication facts (Problem 2)
identify parallelograms and trapeziums in geometric shapes (Problem 3)
explore the idea of equality in diagrams of scale balances (Problem 4)
Solve addition and subtraction problems using decomposition, leading to a written algorithm.
- Use seconds, minutes and hours.
- Discuss the size of a thousand.
- Read the time in digital and/or analogue form.
- Devise and use problem solving strategies.
explore patterns (Problem 1)
solve problems involving transformations (Problem 2)
use addition skills to solve problems relating to distances (Problem 3)
solve problems using addition (Problem 4)
find fractions of whole numbers
solve problems involving fractions
- Apply the concept of average to solve a problem.
- Devise and use problem solving strategies (draw a picture, use equipment, think).
use addition and subtraction to solve money problems
- Know common percentages as proportions of a whole amount.
- Express common percentages as fractions and vice versa.
- Express simple ratios as part-whole decimals.
- Calculate simple percentages of amounts.
round to the nearest dollar
find fractions and percentages of money
- Solve 3-digit addition problems.
- Know the idea of, and be able to construct, magic squares.
Find fractions of a set using multiplication and division.
Using multiplication facts to find a simple fraction of an amount
find fractions of whole numbers (Problem 1)
interpret three dimensional drawings (Problem 2)
solve puzzles related to three dimensional shapes
- Represent common fractions as decimals and vice versa.
- Relate decimals to decimat models that represent their size and composition.
- Combine and partition decimal place values to flexibly add and subtract decimals.
solve addition, subtraction, multiplication, division problems involving money
solve problems involving money
estimte then multiply to solve problems
use mental strategies to add money amounts
solve addition and subtraction problems involving money
calculate an average
use multiplication tosolve money problems