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.
Students will learn
- To use relational thinking as a basis for a range of number strategies.
- To explain number strategies using materials and diagrams.
explore equation puzzles (level 3)
use symbols to generalise the pattern (level 4)
solve equations involving symbols (Problem 2)
find outcomes using diagrams (Problem 4)
solve sets of equations
use mental strategies to add costs
use multiplicative strategies to find yearly costs based on weekly costs
- Consolidate understanding of simple properties of addition, subtraction, multiplication and division.
- Discover and use some more complex properties of addition, subtraction, multiplication and division.
use symbols in equations
use symbols to represent unknowns in linear equations
use a diagram to find a number pattern
use additive strategies to add and subtract numbers to find costs and profits
use simple multiplicative strategies to solve problems
solve sets of equations
use addition and subtraction to solve money problems
find the chance of an event occurring
use <, >, = symbols in equations
use letter symbols in an equation
multiply single digits by 10 and 100
write family of facts based on a given equation
choose a strategy to solve addition and subtraction problems
find patterns for adding odd and even numbers
find patterns for multiplying odd and even numbers
calculate interest amounts
use mental strategies to calculate costs
use a calculator/spreadsheet to calculate addition and subtractions problems
- Recognise that the order of operations matters in practical real life situations.
- Understand and explain the relationship between addition and subtraction, and between multiplication and division.
- Recognise the ambiguity in expressions and equations that include more than one operation.
- Recognise the300
use algebraic symbols in equations
find a relationship in a set of equations
use words to describe a rule