NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
This means students will use words, symbols and diagrams to explain their number strategies to others. Recording also allows students to think through solutions to problems and allows them to reduce their working memory load by storing information in written form. This is particularly important for the solving of complex, multi-step problems. Students should be able to write the numerals for whole numbers to 1 000 000 at least, simple fractions, percentages and decimals. They should also be able to write addition, subtraction, multiplication and division equations with understanding of the meaning of these operations and of the equals sign as meaning “equal to”. Similarly, they should know which operation to perform on a calculator if the numbers are beyond their mental range. Students should also be familiar with using empty number lines to record addition and subtraction strategies, arrays to record multiplication and division strategies, and strip diagrams or double number lines to solve problems with fractions and percentages. Formal written algorithms for multi-digit addition and subtraction should be taught at Level Three after students have the nested place value knowledge required to understand them.
find a number rule
use a symbols to express the rule
- Use relational thinking as a basis for a range of number strategies.
- Explain number strategies using materials and diagrams.
explore tessellations with shapes (Problem 2)
use operation signs to make equations (Problem 3)
use additive strategies to add numbers
compare food prices
use additive strategies to calculate costs
use division to calculate costs per month and per year
use multiplication to calculate money earnt
use addition and a systematic approach to solve puzzles (Problem 1)
find outcomes using a diagram (Problem 2)
use algebraic thinking to solve problems (Problem 3)
use mental strategies to solve addition and subtraction problems
solve algebraic equations
explore equations puzzles
write an equation puzzle
- Choose an appropriate strategy to solve addition and subtraction problems.
- Choose an appropriate strategy to solve multiplication problems.
use mental strategies to add money amounts
use mental strategies to calculate multiplication problems
- Solve problems that involve multiplication and division
- Use equations to express a problem
write an equation to describe a relationship
- Perform addition with decimals.
- Order decimals.
- Devise and use problem solving strategies to explore situations mathematically.
write equations using basic facts
write equations using combinations of operations
find outcomes using a diagram (Problem 1)
interpret three dimensional drawings (Problem 2)
use algebraic thinking to solve problesm (Problem 3)
explore averages (Problem 4)
interpret three dimensional drawings (Problem 2)
use algebraic thinking to solve problems (Problem 3)
predict the results of paper folding reflections (Problem 4)
calculate a bank balance using addition and subtraction
- Perform calculations with algebraic quantities.
- Read, write and understand the multiplication and division symbols and the equals sign, and the language associated with these symbols.
- Write story contexts for given multiplication and division equations.
- Recognise that the operation of multiplication is commutative.
- Identify related multiplication300
use logic to solve equations (Problem 1)
explore tessellations with rectangles (Problem 2)
solve problems using algebraic thinking (Problems 3 and 4)
- Use a range of mental strategies to add to 90, 180, 270, 360.
- Find factors of 90, 180, and 360.
- Use additive strategies to balance equations.
- Use multiplicative strategies to balance equations.
- Fold paper to show an angle.
- Express numbers in a variety of ways.