Overcoming barriers in mathematics – Knowing and using number facts

Example review questions

I am thinking of a number that is a factor of 24 and a factor of 40. What is the largest possible number I could be thinking of?
How many factors does a prime number have? Work out whether 51 is a prime number.
What is the lowest common multiple of 4 and 6?

Write down the first five numbers that are multiples of 6 and multiples of 8. Describe what you notice about the sequence and predict the next two common multiples.
Write a different prime number into each box to make the calculation true: × × = 231
I need to pay 51p postage using only 12p and 5p stamps. How many of each should I put onto my parcel?

Teaching guidance

This teaching guidance document suggests some of the key vocabulary, models, images and practical equipment that children should experience and be able to use. It also includes some teaching tips to provide a few starting points for ways of supporting children with this area of mathematics.

PDF file Teaching guidance: Can I use knowledge of factors and multiples? | 73KB new window

Consolidation and practice

These resources are to support children in guided or independent work. Roll over the highlighted resource for a description.

PDF file How to use number grid ITP | 358KB new window

SWF file Number grid ITP | 63KB new window

XLS file Find the multiples spreadsheet | 29KB new window

PDF file Sum, product, difference, quotient guidance | 95KB new window

XLS file Sum, product, difference, quotient spreadsheet | 328KB new window

XLS file Which number where spreadsheet | 321KB new window

DOC file Using multiples activity | 93KB new window

DOC file Carroll diagram multiple and factor activity | 40KB new window

Visit the nrich website new window for further activities to support practice and application.

Opportunities to use and apply

Possible contexts include:

Word problems, e.g. In a shape sequence, every third shape is a triangle and every fifth shape is red. Where in the sequence will the fourth red triangle lie?
Number properties, e.g. Find the prime numbers to 100 using the Sieve of Eratosthenes.
Fractions, e.g. write ²⁴/₃₂ in its simplest form. How did you use highest common factors to do this?

Data handling sorting diagrams, e.g. Where in this Carroll diagram should the number 8 go? Write an appropriate number into the bottom left cell.

PDF file 'Mathematics Challenges' Year 5 and 6: | 1.2MB new window Make 5 numbers; Zids and Zods

Confirming learning

Ask probing questions such as:

Find a number between 230 and 240 that is a multiple of 9.
List all the factors of 36. How many does it have? Most numbers have an even number of factors. Why is 36 a special case?
Which is larger, ⁷/₈ or ⁵/₆? Explain how you worked this out. Could you have used a smaller denominator?

Jake and Darren did a sponsored run. Jake earned £5 for every complete mile he ran. Darren earned £6 for every complete mile. They each raised the same amount of money, which was over £40 but under £80. How much money did each boy raise? How many miles did each boy run?
It is possible to make the number 42 by multiplying together three prime numbers. Find them.
Consider the numbers 20 and 12. What is their lowest common multiple? What is their highest common factor?

Overcoming barriers in mathematics –

helping children move from level 4 to level 5

Example review questions

Teaching guidance

Consolidation and practice

Number grid

Opportunities to use and apply

Confirming learning