Aim Straight

Activity One

In this activity, the students will need to think about number combinations to solve puzzles involving addition and subtraction. They should be able to find the correct answers by using mental estimates and trial and improvement.
As a starter, you could ask the students to brainstorm how many different ways they can see that one of the friends could score 50 points in one round. For example,
20 + 15 + 15, double 5 + 20 + 20, double 20 + 5 + 5, double 15 + double 5 + double 5.
The students should be able to find answers to questions 2 and 3 if they use a guess-and-improve strategy and work from a systematic list of numbers possible to hit. Encourage the students to mentally estimate the answer before they confirm it with a calculator. They will need to find the sum of combinations of up to three of the numbers listed below. Encourage them to look for more than one answer. You may like to point out that if a ball misses the board altogether, the player scores no points for that ball. The students could work in groups and then compare results with
other groups.
Possible green totals each throw (that is, the numbers shown on the game board):
3, 4, 5, 8, 11, 12, 15, 20.
Possible yellow totals each throw (that is, twice the numbers shown on the game board): 6, 8, 10, 16, 22, 24, 30, 40.
Possible orange totals each throw (that is, three times the numbers shown on the game board): 9, 12, 15, 24, 33, 36, 45, 60.
Some students may wish to investigate the scores more systematically by listing all the possible combinations, that is, if all three shots are trebles, doubles, or single scores; if two shots hit one target area and one of the others; and so on. Finding all the possible combinations will take a considerable amount of time.
 

Activity Two

This activity gives the students practice adding and multiplying one- and two-digit whole numbers. Encourage the students to do the calculations mentally or on paper. Calculators may be used to check calculations. The students could use string, coloured chalk, and cricket wickets to describe circles. You will need to discuss with the students issues such as the relative size of concentric circles for targets and how far back and how to stand for the throw. The students will need to decide what to do for a stone or bag that lands half in one section and half in another.
As an extension, you could develop the game by changing the rules, for example:
• The person scoring closest to a specified number, for example, 200, wins. This will encourage mental estimation.
• Increase the number of throws in a round.

Answers to Activity

Activity One
1. Bella, with 111 points
2. Liam would score 174 – 39 = 135 points in the second round. He could hit the numbers 5, 15, or 20:
• three balls in orange 15
• two balls in orange 20 and one in green 15
• two balls in orange 20 and one in orange 5
• one ball in orange 20, one in yellow 15, and one in orange 15
3. Feana scored 66 points in her second round. She could hit any of the numbers, for example:
• one in orange 20 and two in green 3
• three in yellow 11
• one in orange 12 and two in green 15
• one in yellow 15, one in green 20, and one in yellow 8
• two in orange 11 and one ball missing the board
Activity Two
Practical activity