**Reasoning with Number **

## OVERVIEW

Students will review and extend their mental strategies focussing on using a known number fact to find other facts. Working with equivalence between fractions, decimals and percentages will be developed within the context of probability. Factors and multiples will be revisited and connected to students understanding of prime numbers.

## BUILDING ON

Arithmetic with decimals and fractions

FDP equivalence

Factors & Multiples

Forming and Solving equations

## POWERFUL KNOWLEDGE

- Understand that probabilities of all possible outcomes sum to 1
- Enumerate sets and unions/intersections of sets systematically using Venn diagrams
- Prime factorisation including using product notation and the unique factorisation property
- Identify the HCF and LCM of sets of numbers
- Make and test conjectures about patterns and relationships; look for proofs and counterexamples

## LESSON RESOURCES

**Sets and Probability**

Lesson 1 – Creating a Venn Diagrams

Lesson 2 – Working with a Venn Diagram

Lesson 3 – Probability of a single event

Lesson 5 – Sum of probabilities

EXIT TICKET

**Prime Numbers and Proof**

Lesson 6 – Prime Factor Decomposition

Lesson 7 – Working with Prime Factors

Lesson 10 – HCF & LCM with Venn Diagrams

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**Fractions and Percentages of amounts**

This block of lessons was unable to fit in Spring 1, please complete during Summer 2 if time.

Fraction of an amount (no calculator)

Percentage of an amount (no calculator)

Percentage of an amount – using a calculator

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Updated July 2022