0

1

2

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9

Using the digits 0 to 9 to form five 2 digit numbers which are all multiples of three.

Hot Numbers Interactive

If you have access to computers, iPads or slates, this is the interactive version of this activity.
www.transum.org/go/?to=hot

Hot Number Challenges

www.transum.org/go/?to=hotchallenges

Topics: Starter | Number

• 9 Yellow, St Peters High School
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• "very good for a warm up activity" "kept mind active" from students.
The whole class could access this and 6 students were totally engrossed for virtually the whole lesson, wanting to move to the higher levels
• Y5, St Nicholas
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• We found another solution: 12, 36, 90, 87, 54.
We enjoyed it! It was fun!
• Mr Shepherd, St Lawrence Academy, Scunthorpe
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• Interesting extension for smart groups: How many different answers are there? This can be worked systematically by groups who know the "digit sum" rule for multiples of 3.
WORKING IT OUT (try it yourself first if you like):
The 1, 4 and 7 can only go with a 2 or 5 or 8
There are 6 possible pairings of these numbers.
Each of these two digit numbers can be reversed, so there are 2 cubed combinations once the 2-digit numbers are chosen.
The remaining digits 0,3,6,9 can be paired 3 ways.
In each case, a pairing contains a zero, and we assums that the zero cannot go first in a 2-digit number, so there are only two possibilities once pairings are chosen.
Overall then, the number of combinations (answers), ignoring their position on the answer grid (which would multiply the answer by 5 factorial), is:
6 x 23 x 3 x 2 = 288.
• Matthew, 3D, Craigslea State School
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• I found these:
15, 24, 30, 69 and 78.
• Transum,
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• Thanks to everyone for their comments. Yes this certainly is a worthwhile activity providing access to pupils of all abilities. It also lends itself to extension questions such as that suggested by Mr Shepherd (all 288 possible solutions are provided in the answer section below). If your pupils have access to computers, ipads etc it's a good idea to use the self-checking, multi-level version of this activity available here: Hot Numbers Interactive. Enjoy.
• Mrs K, Maths Musketeers
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• This was a great starter. We needed to know our 3 times table.
• Maths Brainy Badgers, United Kingdom
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• Our Year 6 class found it rather easy. Maybe we should try and find 10 different versions.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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