# Red & Black Card Game

### Task 47 ... Years 4 - 8

#### Summary

Players shuffle and share a pack of cards. The game they play, each using their half deck, is about adding and subtracting the value on the cards, beginning at zero. Players take turns to add their top card to the pile. Red cards subtract, black cards add, so negative numbers are possible. Player A wins if the total reaches +15 or more. Player B wins if the total reaches -15 or less.

The initial challenge is from the viewpoint of a game manufacturer who wants a game which takes, on average, 10 cards to finish. That is, 5 turns each for a round. What should the target number be to achieve this?

#### Materials

• Pack of playing cards

#### Content

• basic integer arithmetic
• probability concepts
• probability distribution
• statistics: natural variation, expected values

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

• A mathematician would collect data about how many cards it takes to get a win for a certain target. Show me the data you have collected? Do you think you have enough data to make a decision?
• In what ways could you organise and display your data?
• Mathematicians use numbers called statistics to describe the picture of a set of data. As appropriate introduce your students to measurements such as range, mode, median or mean (average).
• Some of your games were over very quickly (sometimes just 2 cards played). Can you explain why? (Consider the proportion of cards in the pack with a value of 10.)
• What happens if ...we change the target total? ...we change the values given to the Royal cards? ...we change the number of cards in the original deck, perhaps by including the Joker and giving it a special value?
• Pretend you are the game manufacturer. Choose your own deck, number values and target to make what you think is a good game. Research to show the average length of your game. Prepare an advertising campaign to market your game.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

You will need a pack of cards for each group (perhaps pairs). The advantages of a whole class investigation based around the iceberg questions above are the speed with which lots of data can be collected and the valuable contributions to discussion made by a broad cross-section of students. Also, if you go as far as the design project suggested, you will produce some great display work and potentially achieve many learning outcomes in literacy, IT and art.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 89, Red & Black Card Game.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Red & Black Card Game task is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Number & Computation Years 7 & 8

The Red & Black Card Game lesson is an integral part of:

• MWA Chance & Measurement Years 5 & 6