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.
find outcomes (Problem 1)
solve problems using multiplication (Problem 2)
solve problems using addition (Problem 3)
find diagonal lines in 2 dimensional shapes (Problem 4)
divide numbers by 10 and 100
use mental strategies to solve multiplication problems
Students will:
- perform calculations with percentages
- gather and interpret statistical data.
Students should discover that:
- they can create a statistical map that shows the air pollution of different parts of the school environment.
calculate interest amounts
use mental strategies to calculate costs
use a calculator/spreadsheet to calculate addition and subtractions problems
- Subtract using decimals.
- Find ½ of a decimal number.
- Devise and use problem solving strategies (act it out, draw a picture, guess and improve, make a table).
- Find strategies for investigating number problems.
- Draw conclusions from data collected in a survey.
- Use addition and multiplication strategies to make estimates and solve problems.
- Make scale drawings.
- Design a net.
- Use linear scales to measure lengths.
- Calculate volumes of cuboids.
- Students will be able to construct a model of time using metric units of length to represent years.
- Students will be able to work accurately with different scales when constructing accurate timelines.
solve addition and subtraction problems using mental strategies
use addition, subtraction, multiplication and division to solve problems involving rates of pay
find all possible outcomes
explore the experimental probabilities by playing a simple probability game
decide if a game is fair
add and multiply with fractions
- solve simple number problems
- solve simple fraction problems involving halves and quarters using addition and subtraction
- solve fraction problems using addition and subtraction where the fractions have a range of denominators
use tidy numbers to solve addition and subtraction problems
estimate and calculate multiplication using multiples of 10
- Plan and carry out a statistical investigation to assess the reasonableness of a statement.
- Check the reasonableness of answers obtained using a calculator by calculating mentally and using approximations.
sovle addition and subtraction problems involving money
- Calculate accurately using units of time and speed.
- Explain their methods and reasoning using correct mathematical terms.
- Devise and use problem solving strategies to explore situations mathematically (guess and check, draw a diagram).
Students will:
- collect and accurately measure amounts of water
- calculate percentages for retention of water.
Students should discover that:
- rates of dry and saturated (wet) water retention are independent of each other.
use addition and problem solving strategies to solve problems (Problems1 and 2)
identify triangles in a puzzle shape (Problem 3)
solve addition problems on a number line