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.
Students will:
- extract appropriate data from tables
- perform calculations with percentage and rate data
- convert between percentages and absolute quantities.
Students should discover that:
- significant amounts of time and money are wasted in traffic jams.
Students will:
- read elevation values off a contour map and a line graph
- calculate potential energy
- sketch a graph of potential energy.
Students should discover that:
- there is a relationship between potential energy, mass, and height gained
- a graph of potential energy looks the same as a graph of elevation300
- Think logically about the sums of single digit numbers.
- Devise and use problem solving strategies (guess, and check work systematically).
Change the order of the factors to make a multiplication problem easier.
use mental strategies (eg estimating) to add thousands numbers
find fractions of regions (Problem 1)
solve addition problems involving money (Problem 2)
explore rotational symmetry (Problem 3)
investigate bar and pie graphs (Problem 4)
use addition and subtraction facts to solve problems (Problem 1)
find patterns in multiplication equations (Problem 2)
find outcomes using diagrams (Problem 3)
use addition and mutliplication to solve problems (Problem 4)
- Solve addition and subtraction using mental strategies.
- Explain how a mental strategy works using an example.
estimate fractions of a region
solve problems involving operation-signs and basic facts
use common multiples to solve problems (Problem 1)
use addition and problem solving strategies to solve problems (Problem 2)
continue a sequential pattern to find a rule and predict a future member (Problem 3)
use multiplication facts to solve problems
explore multiples and factors of numbers
solve story problems
write own story problems
Solve addition and subtraction problems by compensating with tidy numbers (including equal additions).
Students will:
- accurately measure, record, and average data with 2 variables (water temperature is the dependent variable; wind is the independent variable)
- use a table to identify patterns and/or relationships and calculate the heat energy effect of wind.
Students should discover that:
- the rate of300
interpret 3 dimensional drawings (Problem 2)
use addition strategies to solve problems (Problem 3)
solve problems involving money
find the conversion factor
solve conversion problems by multiplying and dividing