The Percentage Game
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This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
finder percentages of whole numbers
Number Framework Links
Use this activity to:
• help students consolidate and apply their knowledge of percentages (stage 8)
• develop confidence in students who are beginning to use advanced proportional strategies (stage 8)
This game is different in two ways. Firstly, the percentage questions are not all framed in the traditional way. Secondly, the winning strategy is not related to the speed that players travel round the board. As the Number Framework links above suggest, the game is for students needing skills
reinforcement; it is not intended as an introduction to percentages.
Students will be used to statements where the unknown (the missing element) comes last, for example: 30% of 90 = , but the questions on the game board have the unknown at the beginning or in the middle. In addition to this, while each question could be written as an equation, it isn’t. For these reasons, before introducing the game take some time to give students practice at rewriting questions as equations in their different formats and solving them.
Ask your students to consider and compare each of these equations or statements:
i. 30% of 90 =
ii. 30% of = 90
iii. 27 is % of 90
iv. is 30% of 90
i and iv are effectively the same: both are asking for the same part (30%) of the same whole (90). But i is expressed as an equation (a statement with an equals sign) while iv is not. Ask your students to identify the part of iv that is the equivalent of the equals sign. (It’s the word “is”.) iii asks what percentage one number (27) is of another (90). In ii, 90 is 30% of a number. The number must be greater than 90. The problem is to find what it is.
The player answering a question must do so without a calculator. But a competitor can use a calculator to check and challenge another player’s answer. For this reason, it would be a good idea to have your students practise using the correct sequence of keystrokes. Encourage them to enter 30% as 0.3, 25% as 0.25 and so on, instead of 300/100 or 25/100 or by means of the percentage key. This will reinforce the fact that the percentage and its decimal equivalent are exactly the same mathematically, will ensure that students can work with percentages on a calculator that doesn’t have a percentage key, and will often save completely unnecessary keystrokes.
Introduce the game by getting two or three students to play while the others watch. Make sure that everyone understands the rules and how the Choose option works. Model the answering and checking process. By checking with a calculator, the other players are also reinforcing useful skills. Make sure that everyone knows what they are meant to do with the 4 x 4 grid.
Students should dispose of any pencil and paper calculations they do so that they have to work them out afresh each time they play the game.
Once the players understand the way the game works, they can think about game strategy. Those who are able to work out the answers in their head will have an advantage because they can work out which squares they need to land on to complete their 3-in-a-rows.
The variation suggested has the potential to prolong the useful life of the game at the same time as it offers an excellent opportunity for students to come up with their own percentage questions, modelled on the patterns they have been given. New questions should be peer-reviewed before they get into circulation to ensure that the calculations don’t involve tricky fractions or decimals.
Note that the variation uses the 5 x 5 grid. A winning line of 4 counters can be created using only numbered circles, or only blank circles, or a combination of numbered and blank circles.
Answers to Activity
Answers (clockwise from Start):
28 is 40% of 70
16 is 25% of 64
40% of 26 is 10.4
19 is 20% of 95
40% of 28 is 11.2
26 is 50% of 52
18 is 40% of 45
30% of 95 is 28.5
48 is 80% of 60
9 is 45% of 20
16 is 50% of 32
24 is 30% of 80
36 is 60% of 60
20% of 90 is 18
72 is 75% of 96
18 is 10% of 180