Sort them out (2)
Problem
This challenge is best done in a group of at least four and preferably more.
Share all the cards out amongst the group.
Work out what the answer is to each question on your cards.
What do you notice?
How could you sort the cards?
Once you've completed this task, you may like to try it again using this sheet of slightly harder questions.
Getting Started
You could check your calculations with someone else or by using a calculator.
Student Solutions
Thank you to those who submitted solutions to this problem. There were plenty of opportunities to practise calculations, and also to share different strategies.
Courtenay and Max from Ickford Combined School looked at the set of fifteen cards, as did Ms Bean's Math Whizzes from Sylvan Park. They both noticed that the answers are numbers between $21$ and $35$, and could be arranged in ascending or descending order. Courtenay and Max explained how they sorted their cards:
First we sorted them into the five time tables and the two times table. Then we sorted them into ones that have a digit that is a two or three and ones which have both. All cards were used.Maya, Max, Josh, Amy, Dylan and Imi from Weeke Primary solved the set of twenty cards:
All of the answers when put in order from smallest to largest go from $110$ to $129$.$10\times$ $5$th prime number = $110$
$37\times3 = 111$
$16\times 7 = 112$
$191 - 78 = 113$
$57\times2 = 114$
$23\times5 = 115$
$29\times4 = 116$
$13\times9 = 117$
twice $59$ = $118$
$17\times7 = 119$
$8\times15 = 120$
square of the $5$th prime number = $121$
double $61$ = $122$
$41\times3 = 123$
$4\times31 = 124$
$5$ squared x $5$ = $125$
$7\times18 = 126$
$216 - 89 =127$
$2$ squared x $2$ squared x $2$ squared x $2$ = $128$
$3\times43 = 129$
Well done, and thank you very much to all who submitted solutions!
Teachers' Resources
Sort Them Out (2)
This challenge is best done in a group of at least four and preferably more.
You'll need to print out this sheet cut into fifteen separate cards.
Share the cards out amongst the group.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
You may like to try using this sheet of twenty cards in the same way, which contain slightly harder questions.
Why do this problem?
The intention of this problem is that learners will work together as a team. It should help in developing mathematical language as well as providing interesting practice in varied number work and possibly offer opportunities to share calculation strategies. It will probably not take a whole lesson to do.
Possible approach
One of these sheets needs to be printed out: the sheet of fifteen cards has easier questions than the second sheet of twenty cards. The sheets will need to be cut into separate cards. You must give out all the cards in the set you chose to do!
To begin with, give learners time to work individually on the questions on their own cards. After a suitable period of time, encourage them to ask each other about the questions and answers on other cards. At this stage, members of the group can help each other with the questions, but discourage them from simply giving someone else an answer.
A short plenary should provide an opportunity for the groups to explain the organisation they chose and for such remarks as "I knew my answer was wrong when it didn't fit in with anyone else's".
Key questions
Possible extension
Learners who find these questions easy may not have solved the problem! How can the cards be organised, arranged; or ordered? Such pupils could help other members of the team check all the answers. Some learners may want to devise their own set of cards to be used in a similar way.
Possible support
You can purposely give certain cards to certain children if you do not want to take them too far out of their comfort zone where the calculation is concerned. It may be appropriate for one group of children to work using the cards in the simpler version of the problem. The principles are exactly the same, but the calculations involve addition and subtraction up to $25$.