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.
use mental strategies to solve addition problems
use a combining strategy to solve problems
use compatible numbers to solve addition problems
use addition and multiplication to solve problems (Problems 1 and 4)
explore different two dimensional shapes (Problem 2)
explore reflections with paper folding (Problem 3)
This unit introduces the idea that fractions come from equi-partitioning of one whole. Therefore, the size of a given length can be determined with reference to one whole. When the size of the referent whole varies, then so does the name of a given length.
- Name the fraction for a given Cuisenaire rod with reference to one (whole).
- Find the one (whole) when given a Cuisenaire rod and its fraction name.
- Create a number line showing fractions related to a given one (whole).
- Identify equivalent fractions
use multiplication and division to solve problems
find unit fractions of regions using repeated division
- Describe multiplicative comparison between two quantities using appropriate language, such as, “three times more/greater/bigger”, “three times less/smaller.”
- Record multiplicative comparisons using equations, such as, 4 x 3 = 12 (for 12 is four times greater than three).
- Find the unknown scalar300
use addition facts to solve problems (Problem 1)
use subtraction facts and place value knowledge to solve problems (Problem 2)
find outcomes using a systematic approach (Problems 3 and 4)
- Apply the number operations to single digit numbers.
- Use a problem solving strategy to identify all the possible outcomes.
use addition and a systematic approach to solve problems (Problem 1)
use addition strategies in the context of calendar problems (Problem 2)
use transformations to make triominoes (Problem 3)
use addition facts to solve capacity problems (Problem 4)
solve problems using multiplication, division, addition, subtraction operations on a calculator
add and subtract fractions with the same denominator
convert fractions (tenths) to decimals
find fractions of a quantity
- Use addition with decimals.
- Know the idea of, and be able to construct, magic squares.
- Read and write decimals to two places.
- Represent decimals on linear scales, like thermometers.
- Add and subtract decimals to one decimal place using combining and partitioning strategies.
Solve addition and subtraction problems using decomposition, leading to a written algorithm.
add one digit number to two digit numbers
choose a mental strategy to solve an addition problem
choose a mental strategy to solve a subtraction problem
use addition and subtraction to solve money problems
use multiplication and divisibility rules to solve puzzles