Overcoming barriers in mathematics

Example review questions

Work out 575 ÷ 25, explaining your method.
Peter says that, if you want to divide a number by 12, you can divide it by 4 then by 3. Is he right? Explain how you know. Work out 768 ÷ 12 using Peter's method and using another method. Do you get the same answer?
How many 35p packets of stickers can I buy with £5? Explain how you know.

Coaches have 56 seats for passengers. How many coaches are needed to take 275 people on a trip?
Complete this calculation: 943 ÷ 41 = 2
Work out whether or not 29 is a factor of 811.

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 an appropriate non-calculator method for dividing a three-digit integer by a two-digit integer? | 32KB new window

Consolidation and practice

These resources are to support children in guided or independent work.

PDF file National curriculum in action: example of children's work | 694KB new window

DOC file Division using factors activity | 36KB 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. Pencils come in packs of 12. How many packs does a school need to buy to get 310 pencils?
Problems involving money and measures, e.g. My mobile phone costs 18p per minute for national calls. If I put £5 on my card, how many minutes can I talk for?
The area of a rectangular games hall is 384 square metres. If the length is 24 metres, how wide is it?

Conversions, e.g. Convert 35,000 seconds into hours, minutes and seconds.
Finding fractions of amounts, e.g. Find ⁵/₁₂ of 600.
Missing number calculations, e.g. Write in the missing digits 23 × = 78

Confirming learning

Ask probing questions such as:

When 37 ÷ 17, it has a remainder of 5. Work out what the missing digit is.
I bought some pencils that cost 15p each. I paid £5.85. How many pencils did I buy?
12 inches are the same as 1 foot. How many feet and inches are the same as 320 inches? Explain how you worked this out. How did you use your knowledge of number facts and place value to help you?

Write in the missing digits: 323 × 7 = 1518.
Explain the steps you would take to work out 675 ÷ 45
What is the remainder when 693 is divided by 20?

Overcoming barriers in mathematics –

helping children move from level 4 to level 5

Example review questions

Teaching guidance

Consolidation and practice

Opportunities to use and apply

Confirming learning