# Highest Number Years (K), 1 - 10

A game for two players

### Preparation

Years 2 - 10

• Two pages like the photo - one for each player - or print and cut this Playing Board
• Two set of playing cards (one red and one black) showing Ace, 2, 3, 4, 5, 6 - one for each player - Ace is worth 1
• 1 dice

### Getting Started

Rules
• Take turns to roll the dice.
• The number shows which card to place in any empty column.
...ONES column or TENS column or HUNDREDS column.
• Once the card is placed it cannot be moved.
• Continue playing until all three columns are filled.
• If you roll a number that you have already used, roll again.
• The winner is the player with the higher number.
Look at the photo above.
The player has scored four hundred and twelve (412).
• Discuss which card you think they placed first, then second, then third.
The photo also shows that in their previous game they scored six hundred and forty-one (641).
• Discuss which card you think they placed first, then second, then third.
Play five (5) games for fun, but record your score whether you win or lose.

### Investigating Highest Number

• Open this Highest Number Starter.
You can read it on screen or print it.
• You have already done the first part of the Starter.
Begin at Question 2.
Remember to record the strategies you discuss.
Continue until you finish the Starter.
Have fun exploring Highest Number.

Reports from two Year 4 boys who had spent
about 30 minutes playing Highest Number.
Click the photo to enlarge it.

Unfortunately they worked a bit quickly and
forgot to use one of the rules of the game.
Which rule?
How do you know?

They weren't wrong. They were just playing a different game. However, the thing they were doing differently changes strategies in the game.

• In your journal, explain the rule they left out.
• Give one example of how you would change your thinking if the boys' rule was allowed.
Years K - 1

• About 100 popsticks, pick-up-sticks, twigs or similar. Popsticks can be found in \$2 Shops or craft shops.
• Rubber bands
• 1 dice
• Two pages similar to the photo but showing only the Tens and Ones columns - one page for each player
The activity can be adapted to equipment such as patty cake papers with pasta twists.

### Getting Started

• Children this age will need to play with an adult or older child.

First you work together to make bundles of 10 sticks (or patty papers of pasta).

We're going to play a game with this dice in a little while, but first we have to make stuff to play with.
• You need at least 6 bundles each as well as at least 6 'left overs'.
This is an opportunity to talk mathematics and count in different ways to make 10. Make it feel like a game as you use any and all of these ways (and more) to make the tens:
• Spread one hand with the palm down and match one stick to each 'finger' to make 5. Then do it again to make another 5. Count and talk about two fives making ten. If you do the second five leaving the hand and the first five where they were, you can also talk about five twos making ten.
• Count by ones.
• Start with a calculator showing zero. Count one stick and write 1 on the calculator. Count the second stick. Clear the calculator and write 2. Continue. When the learner is ready you can convert to doing 1 + 1 + 1 + ... on the calculator in conjunction with the counting.
• Count by twos. How do you teach the calculator to do this?
• Count by fives. How do you teach the calculator to do this?
• Count by threes and add 1. How do you teach the calculator to do this?
• ...
Rules

The aim of the game is to collect the most sticks each round.

• Player A rolls the dice.
• Suppose it's a 4. The player chooses whether they will put 4 sticks on the board, or 4 bundles of ten sticks.
• Sticks stay where they are put.
• Player A rolls again to put something in the other column.
• If they roll the same number it doesn't count and they roll again.
Before they roll, ask questions like:
• What number would you like to roll?
• What number do you think you will get?
• Are you sure you will get it?
• Do you think you have no chance, a little bit of a chance or a really good chance?
• Sticks stay on the board and Player B rolls to make their collection on their own board.
• Record the result in the learner's journal.
Who has the most sticks?
How do we know?
Can we check it another way?
As appropriate shift the language to asking who has the higher (or lower) number and how much higher or lower. You can also encourage number sense by sketching a vertical number line with arrowheads on both ends and marking zero somewhere. Then
• My number goes here. Put a mark and write it.
• Where do you think yours should go?
This is about number sense, not accurate measurement. It's also about reasons and discussion, not right and wrong.

Keep in mind that this is a game, so it has to feel like fun. But it's also a game that presents opportunity for learning and that's where the older person becomes artful at asking questions.

Have fun exploring Highest Number.

We suggest that if you use it 10 to 15 minutes a day, two or three times a week over several weeks, you will see learning develop. You might use the same number line for a week and watch the record of scores build up.

### Extension

• Play the game twice before asking who has had the higher number of sticks counting both games.
Record after the first time, as above, then start again. Each player will then have a written record in the journal and the sticks on the board from which their two-game totals will have to be worked out. Feel free to use a calculator to help.

### Bonus

If you are using pasta then sometimes you can eat it afterwards. Cook it, then stir fry with a few veggies for lunch. Or boil it up in milk and add dissolved custard powder and a bit of honey to thicken into a delicious dessert before bed. Slices of fruit on top goes well.

Years 5 - 10

The Starter does just that.
It starts you thinking more deeply about strategy.
A strategy is a plan that makes it more likely that you will win.

• Open Highest Number Investigation Guide A.
You can read it on screen or print it.
• It helps you ask questions and do tests that lead to a strategy.
• Work with a partner on this guide if you can. Almost all mathematics discovered since the 1950s has been by mathematician teams.
• Part 4 of the guide is about using software to help create a strategy.
If your school is a member of Maths300 your teacher can provide that software.

### Using Probability and Statistics

Years 6 - 10

In this game there is no strategy that makes it certain you will win.
But some strategies give you a better chance of winning than other strategies.

• Open Highest Number Investigation Guide B.
You can read it on screen or print it.
• It asks you to calculate probabilities in the game.
• Then it asks you to imagine you are going to make money by using this game at a carnival.
• Keep on working with a partner if you can.

### Just Before You Finish

Read your Working Like A Mathematician page again and put a mark beside everything on the list that you did during this problem.
• In your journal copy and complete this list.

In Highest Number I was working like a mathematician when:
...
...
... (list everything that proves you were working like a mathematician)

• Does this activity make you think of something you want to learn better, or perhaps something new you want to know?