Fiordland Holiday

Game

This board game uses multiplication strategies to calculate a score. The context is a Fiordland holiday, and the game features native birds, plants, and animals. (The information on the game cards may stimulate students to use resources such as the Internet to do some research, for example, on the endangered or rare species or places of interest in Fiordland.)

Note that a colour version of the game board is provided in the centre of these notes. You could use this as it is or photocopy it on a colour photocopier and laminate it. A black and white version for photocopying is also provided (see copymaster), along with the game cards, which could be photocopied onto coloured paper for added appeal.

The game instructions explain the basics of the game, and the facing page provides students with strategy suggestions. The multiplications in the game have been chosen to fall within the range of what students at stage 6 should be able to do mentally. The score is important, so the responsibility for checking whether or not the multiplications are correct will fall to other players. (The added incentive for players to check each other’s scores is that the player whose turn it is forfeits points for an incorrect answer!) This gives all the players plenty of practice in using multiplicative strategies. To ensure that the extra practice is in fact taking place, you might want to emphasise that the checking has to be done without the aid of a calculator.

You could change the checking and forfeiting instruction to suit the groups using the game. For example, in a mixed-ability group, those better at using multiplicative strategies could help the weaker players to work out their score, without any penalty. A group of lower stage students could all be helping each other, again without penalty. However, for a higher stage group, catching out another player and seeing them lose points may well be a good incentive to do the extra working out!

The game could be introduced to the whole class initially. It could be played by the class divided into two teams, using an enlarged version of the game board as a shared resource. This would allow you to demonstrate the rules and to show how to keep a running total.

To help students keep a running total while they are playing, you could provide them with a thousands book or a hundreds square to help them calculate their total. Alternatively, you could allow the students to keep the running total on a calculator, emphasising mental calculation of the multiplications on the game squares and cards. (They may need to jot down their scores on paper as well after their turn, in case they lose track or press a wrong button on the calculator.)

If you are playing with an instructional group, you could ask the students to refer back to the list of strategies on page 17 when they have a problem to solve and to say which they think would be best for the problem they have before them. This encourages students to make meta-level choices about appropriate strategies and to think about the numbers they have been given and how those numbers dictate what will be a useful method. Sometimes a strategy is suggested; discuss why the numbers make this strategy particularly useful. We don’t want students to memorise particular strategies because this can become like learning an algorithm. The aim is for them to develop a range of strategies so that they can select the best one for a particular situation. Some strategies (such as doubling and halving) are only effective with some combinations of numbers. This game prompts the use of some strategies that students are less likely to use spontaneously, although they suit the numbers given. This is an attempt to broaden the students’ strategies rather than to tell them to master a particular method. As always, discussion about strategy selection is vital.

You could simplify the game by making a set of cards with easier multiplications on them. Groups of students could add to the game cards with facts and ideas of their own. Adaptations of the game could be made to match topics of study,  such as the Rocky Shore or Space.

Answers to Game

A game using multiplicative strategies
“Adventures and mishaps” game card answers and some possible methods:
3 x 27 = 9 x 9 = 81
12 x 5 = 60. 12 x 5 is 2 x 5 = 10 more than 10 x 5. 10 x 5 = 50 and 50 + 10 = 60, so 12 x 5 = 60.
20 x 7 = 140. 2 x 7 = 14. 14 x 10 = 140, so 20 x 7 = 140.
5 x 36 = 180. 5 x 30 = 150 and 5 x 6 = 30. 150 + 30 = 180, so 5 x 36 = 180.
565 x 0 = 0
6 x 11 = 66. 6 x 11 is 6 more than 6 x 10. 6 x 10 = 60 and 60 + 6 = 66, so 6 x 11 = 66.
53 x 3 = 159. 50 x 3 = 150; 3 x 3 = 9. 150 + 9 = 159, so 53 x 3 = 159.
3 x 99 = 297. 3 x 100 = 300. 300 – 3 = 297. (Or: 3 x 99 is 3 less than 3 x 100. 300 – 3 = 297)
5 x 18 = 90. 5 x 18 is 5 x 2 = 10 less than 5 x 20. 5 x 20 = 100 and 100 – 10 = 90, so 5 x 18 = 90.
5 x 44 = 220. 5 x 44 = 10 x 22 = 220
3 x 300 = 900. 3 x 3 = 9; 9 x 100 = 900, so 3 x 300 = 900.
39 x 0 = 0
5 x 19 = 95. 5 x 19 is 5 less than 5 x 20. 5 x 20 = 100. 100 – 5 = 95
6 x 9 = 54. 6 x 10 = 60. 60 – 6 = 54
45 ÷ 5 = 9. 5 x ? = 45; 5 x 9 = 45
102 x 4 = 408. 102 x 4 = 4 x 102. 4 x 100 = 400 and 4 x 2 = 8; 400 + 8 = 408
36 ÷ 4 = 9. 4 x ? = 36; 4 x 9 = 36
7 x 198 = 1 386. 7 x 198 is 7 x 2 = 14 less than 7 x 200. 7 x 200 = 1 400. 1 400 – 10 = 1 390; 1 390 – 4 = 1 386
56 ÷ 7 = 8. 7 x ? = 56; 7 x 8 = 56, so 56 ÷ 7 = 8.
4 x 18 = 72. 4 x 18 is 4 x 2 = 8 less than 4 x 20. 4 x 20 = 80. 80 – 8 = 72. (Or use doubling and halving: 8 x 9 = 72.)
5 x 80 = 400. 5 x 8 = 40 and 40 x 10 = 400
120 ÷ 5 = 24. 120 ÷ 5 = 240 ÷ 10 = 24
9 x 6 = 54. 10 x 6 = 60; 60 – 6 = 54
“Rare species” game card answers and some possible methods:
12 x 8 = 96. 10 x 8 = 80 and 2 x 8 = 16. 80 + 16 = 96
21 x 3 = 63. 21 x 3 = 3 x 21; 3 x 20 = 60 and 3 x 1 = 3; 60 + 3 = 63
7 x 8 = 56. 5 x 8 = 40 and 2 x 8 = 16. 40 + 16 = 56
15 x 10 = 150. 15 x 10 = 10 x 15; 10 x 10 = 100 and 10 x 5 = 50; 100 + 50 = 150
2 x 231 = 462. (2 x 200) + (2 x 30) + (2 x 1) = 400 + 60 + 2 = 462
4 x 20 = 80. 4 x 20 = 8 x 10 = 80
7 x 4 = 28. 7 x 4 = 4 x 7 = 28 Or: 4 x 4 = 16. 3 x 4 = 12. 16 + 12 = 28
17 ÷ 1 = 17. 1 x ? = 17; 1 x 17 = 17
42 ÷ 6 = 7. 6 x ? = 42; 6 x 7 = 42
26 x 5 = 130. 26 x 5 = 13 x 10 = 130
24 x 2 = 48. 24 x 2 = 12 x 4 = 6 x 8 = 48