Highest Number

Years 1 - 8

Summary

The concept of the game is simple. You and I both make a number - the higher number wins. Every teacher knows this game in some form, but this variation is based around the questions:
  • By how much?
  • How do you know?
  • Can you check it another way?
  • How many ways can you check it?
Now it's not just me/you/win until one of us wins best out of 5. Now the game is being used to challenge children's thinking and develop much more mathematics than A is greater than B. Then, ask What happens if we change the card pack? and you learn much more about place value too. Suitable for threading.

Materials

  • One calculator
  • One dice: 6-face or 10-face
  • One pack of playing cards
  • A classroom rich in mathematics resources
 Highest Number

Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.
  • Visit the Home Page for more Background.
  • For this specific activity click the Learners link and on that page use Ctrl F (Cmd F on Mac) to search the task name.

Procedure

At Dederang Primary, as a Discussion Lesson, I introduced Highest Number to a Year 3/4. It's a task from the Mathematics Task Centre - actually it's two tasks; one uses a six-face dice and one uses a ten-face dice. It is also included as a fabulous whole class lesson and a threaded activity in Year 1 of Working Mathematically with Infants. It's a well known game requiring the children to quickly sketch a hundreds/tens/ones board big enough to place a playing card in each column. Players take turns to roll a 6-sided dice, perhaps revealing a 5, and have to decide whether this is 5 hundreds, 5 tens or 5 ones. Each player only has one of each card from 1 to 6 and the higher 'score' after three rolls is the winner.

But, in this class, being the winner wasn't enough. The pair had to work out by how much the winner won. And, calling on the Working Mathematically process, had to check their answer another way. They used materials in the room such as MAB 10, Unifix and calculators and displayed insightful mental arithmetic with comments like:

  • It would have been 100 because of that column but the ones column is 6 for the winner and 8 for the loser, so the total is 2 less, so 98.
The children enjoyed the game much more because of the added challenges and the learning was much deeper than it would have been had I simply expected them to keep track of how many times each person won.

Doug. Williams, Consultant

 

Content

  • addition facts beyond 10
  • addition facts to 10
  • complementary addition
  • counting
  • decimal calculations
  • decimal interpretation
  • likely, less likely and unlikely events
  • mathematical conversation
  • place value
  • probability
  • recording - written
  • subtraction
The above version of the game - cube dice, black/red cards 1 to 6 and a board marked in 100s, 10s and 1s (or just 10s and 1s) - is the version used in Maths300 Lesson 26, in which the focus is on exploring probability and interpreting statistics to develop a winning strategy. This Calculating Changes version focuses on mental arithmetic, place value and addition and subtraction. The two intersect in the first two options of the Maths300 companion software in which children can play the game against the computer.

Regardless of the version, the focus for the students following each win is these investigation questions:

  • By how much?
  • Can we check it another way?
  • In our journals, record the difference and two ways (at least) of knowing in it.
Now consider variations on the game.
  1. Use a ten-sided dice (0-9) and playing cards 1 - 9. Another card placed face down can be a zero. (Or an empty place can be a zero which was a system used by several civilizations before the invention of a symbol for zero.)
  2. Forget the dice and just use cards 1 - 9. If you want zero included choose one of the royals (say a Jack) and, if it is drawn, place it face down. Begin with a shuffled set of the chosen cards in all four suites. Players take turns to draw from this pack.
  3. Include the four 10 cards in the pack. Will I use it as ten hundreds, ten tens or ten ones? Whichever is chosen, the card is placed in that column and a recalculation has to be made before the person's final score is decided, and especially before it is written.
  4. Include all the cards in the pack and use J = 11, Q = 12 K = 0. Or, sometimes card packs have a Joker in which case you can use J = 11, Q = 12, K = 13, Joker = 0.
  5. What happens if ... the winner is the person with the higher score after three rounds as in the photo above, or five rounds as in the photo here, and then we ask the investigation questions?
    Highest Number
  6. What happens if ... we play the game with three in a group instead of two and the objective after each win is to order the three numbers from highest to lowest and calculate the difference between 1st & 2nd, 2nd & 3rd and 1st & 3rd?
  7. What happens if we ... we play the game using a board with a zero and decimal point in the ones column (see Calculator Slido) and the tenths, hundredths and thousandths as the playing columns?
This is clearly an activity rich in mathematics with a familiar structure, but opportunity for new challenge any time it is played. So it can be threaded - used for 10 minutes a day three or four times a week over several weeks. What's more, it is an activity that can be used at several levels through the school. How will you plan for it to be used over the years?


Return to Calculating Changes Activities

Calculating Changes ... is a division of ... Mathematics Centre