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 addition and problem solving strategies to solve problems (Problems 1-4)
find number of painted faces on 3 dimensional shapes (Problem 2)
use addition and multiplication to solve problems (Problems 3 and 4)
find a fraction of a number
use Roman numerals
- Use their mathematical knowledge to invent problems.
- Solve other students’ problems.
Students will:
- calculate the cost of walking to school
- calculate the cost of a daily breakfast.
Students should discover that:
- the decisions we make often ignore important costs and benefits
- estimates need to be evaluated in context for reasonableness.
choose a mental strategy to solve problems
multiply by multiples of 100 and by 1000
find fractions of dollar amounts
find outcomes using a tree diagram (Problems 1 and 3)
use addition and subtraction facts to solve problems (Problem 4)
use multiplication facts to solve problems
use diagrams or tables to solve problems
use mental strategies to solve addition problems
find fractions of a number
use basic facts and mental strategies to solve multiplication problems
solve problems involving sequential patterns (Problems 1 and 4)
use simple multiplicative strategies to solve problems (Problem 2)
solve problems involving enlargements (Problem 3)
- Find fractions of whole numbers.
- Devise and use problem-solving strategies (draw a picture, guess and check).
round to the nearest ten
use mental strategies to solve addition problems
find a fraction of a whole
use mental strategies to add money amounts
use mental strategies to calculate multiplication problems
Students will:
- use a protractor to measure angles
- interpret data displays and draw conclusions from graphs and tables
- investigate the relationship between season, latitude, and the angle of the Sun.
Students should discover that:
- daylight hours are a function of latitude – the lower the latitude, the300
- Solve problems that involve multiplication and division
- Use equations to express a problem
Solve division problems by using multiplication facts.
use addition to solve problem (Problem 3)
find the pattern for the number of diagonals in polygons (Problem 4)