The thousands game
Problem
The Thousands Game printable sheet
Class 3 were playing a game. There were ten cards with the digits $0$ to $9$ on them.
These cards were put into a bag and players took out four cards and made a number out of them. At first they made the highest number they could. Sinita took out
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and made | Image
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Then they made the lowest number they could. Jamie took out
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and made | Image
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"You can't put zero at the beginning of a number," objected Paul. The class discussed this and decided that Jamie had made four hundred and fifty-seven.
Next they played to make the highest even number. Jill took out
and Vincent took out
Who won? Why?
Then they played to make the highest odd number. Belinda took out
and Ali took out
Who won? Why?
Next they played to make the lowest even number. Rohan took out
and Ben took out
Who won? Why?
The last game they played was to make the closest number to $5000$. Alice took out
and Chloe took out
Who won? Why?
Play some of the different versions of this game with a friend. Which digits are the most helpful? Why?
Once you've played this game a few times, have a go at playing Nice or Nasty. This game is very similar except you draw and place the digits one at a time, so you'll need to think carefully about where to put each one!
Getting Started
What kind of number will the units digit need to be to make an even number? What about an odd number?
To make the highest possible number, where would it be best to put the highest digit card?
If you want to make the lowest number, where would it be best to put the lowest digit card?
Don't forget to tell us your reasons for each child being the winner.
Student Solutions
You had to think very carefully to answer this question. Amy from St Albans Primary School, Kevin from CIS, Hong Kong, Kirsty who goes to Steeple Morden and Ruth all reasoned it through very clearly. Here is Amy's argument:
When Jill did it, she picked out $7, 8, 6$ and $3$. To make the biggest even number she got $8736$. Vincent picked out $4, 2, 9$ and $1$. The biggest even number is $9412$. Vincent won because he had the highest even number. I worked this out because $9000$ is bigger than $8000$.Next it was the highest odd number. Belinda picked out $4, 0, 6$ and $9$. The highest odd number from these is $6409$. Ali picked out $5, 2, 1$ and $7$. His highest odd number is $7521$. Ali's number is higher than Belinda's because $7000$ is higher than $6000$.
Next is the lowest even number. Ben picked out $7, 0, 3$ and $9$ and the lowest even number is $3790$. Rohan picked $8, 1, 5$ and $4$ and his number is $1458$. Rohan won because $1000$ is lower than $3000$.
Alice got $7, 8, 4$ and $9$ and Chloe got $1, 0, 3$ and $5$. The numbers they got which are nearest to $5000$ are $4987$ and $5013$. I used an abacus to show that the difference is $13$ for both and so it is a draw.
Thank you for a very clear solution, Amy.
Teachers' Resources
The Thousands Game
The Thousands Game printable sheet
Class 3 were playing a game. There were ten cards with the digits $0$ to $9$ on them.
These cards were put into a bag and players took out four cards and made a number out of them. At first they made the highest number they could. Sinita took out
Image
|
and made | Image
|
Then they made the lowest number they could. Jamie took out
Image
|
and made | Image
|
"You can't put zero at the beginning of a number," objected Paul. The class discussed this and decided that Jamie had made four hundred and fifty-seven.
Next they played to make the highest even number. Jill took out
and Vincent took out
Who won? Why?
Then they played to make the highest odd number. Belinda took out
and Ali took out
Who won? Why?
Next they played to make the lowest even number. Rohan took out
and Ben took out
Who won? Why?
The last game they played was to make the closest number to $5000$. Alice took out
and Chloe took out
Who won? Why?
Once you've played this game a few times, have a go at playing Nice or Nasty. This game is very similar except you draw and place the digits one at a time, so you'll need to think carefully about where to put each one!
Why do this problem?
Possible approach
At the end of the lesson the group can gather together to discuss, not only place value and comparing and ordering numbers, but also odd and even numbers. There should be plenty of opportunities to emphasise the appropriate vocabulary for the work they have been doing.
Key questions
Which digit is most important if you are making the largest/smallest number possible?
Possible extension
Learners could play an alternative version of the game in which two players take turns in taking a digit card (unseen) and placing it on their board before taking the next card. This requires considerable thought and understanding. Children will enjoy playing Nice and Nasty after having a go at this activity.
Possible support
Some children find place value difficult and even alarming. They could start with a similar activity using only three-digit numbers or even just two. Reading the numbers out loud may help turn what seems to them just a jumble of digits into something meaningful.