Support (from Y7 teaching programme)
• Use simple tests of divisibility
• Understand negative numbers as positions on a number line; order, add and subtract positive and negative integers in context.
• Recognise the first few triangular numbers, squares of numbers to at least 12 ´ 12 and the corresponding roots

Extension (from Y9 teaching programme)
• Use the prime factor decomposition of a number (to find highest common factors and lowest common multiples)
• Use ICT to estimate square roots and cube roots
• Use index notation for integer powers and simple instances of the index laws

Starters

Main

ICT

Scaffolding

Key Questions

Notes

ATM 40 Problems
~ p15 Ages

KS3 Y8 Intervention
~ Lesson 8N1.1 Solving number problems 2

MAP

~ Summing Up – add/subtract integers

~ Developing Negatives – multiply/divide integers

~ The root of the problem
~ Consecutive products
~ Exploring primes activities : Numbers of factors; factors of square numbers; Mersenne primes; LCM sequence; Goldbach's theorem; n² and (n + 1)²; n² and n² + n; n² + 1; n! + 1; n! – 1;
~ Venn diagrams for HCF / LCM

Mymaths

Negative Numbers 1

Negative Numbers 2

Multiples (divisibility tests)

Squares and Triangles

MAP
~ Handling rules for primes, e.g. using the 4n-1 rule and comparing this to the list of square numbers; use a spreadsheet to find difference between consecutive cubes. This difference is always prime – true? What do you notice about the second difference?
~ Use a spreadsheet to show Eratosthenes' sieve in 6 columns - what do you notice when you highlight the primes?

~ Number line - extend to negative number line; consider negative movement along number line
~ Powers - HTU chart
~ Venn diagrams

MAP
~ Generic assessment criteria

What patterns arise when you multiply consecutive pairs / triples?

182 is the product of 2 consecutive integers, but the answer is not unique. Find both products

Are the prime factors of a number unique?

Is the prime factor decomposition of a number unique?

When finding prime factor decompositions using the ‘tree' method, does it matter how you break down the starting number?

What happens when you raise a number to a negative / fractional power?

Can every cube of a number be written as the difference of two squares?

Multiply the triangular numbers by 8 and add 1. What numbers do you get? Why?

Is there a pattern in the prime numbers?

MAP – Level Ladders
~ Powers, integers, roots

Extended tasks:
~ Consecutive products
~ Prime factors and numbers of factors

Able Y8
MAP
~ Exploring primes activities