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Chapter 6: Algebra and Statistics 57 trend Photo Line-Up Approach: Team Level: Year 8 Focus: Logic. Resources: Placement mat, 12 picture cards (numbered on back), 4 clue cards. Questions/instructions Sue is taller than Hone. Ben is standing somewhere between Tasi and Sim. There is only one person Arrange the cards numerically from 1-12 before giving them to the students. Here are the members of a sports team. There are 12 people in the team. Spread the picture cards out for the team to view. Bag of Beans between Sim and Tuku. The team is going to have its photograph taken, but they need to be arranged in a line from the tallest to the shortest. Here is a mat for placing them on. Allocate one clue card to each team member. You will need to use the clues on these cards to place the people in a row, from tallest to shortest. See how well you can work together to find out the order of the team. Discuss the best way to work together before you start. When the group agrees it has finished its arrangement write down the order of the names, then say: Now check your cards through one more time to make sure that the order you have them in matches the clues. Approach: One to one Level: Year 4 and year 8 Focus: Probability. Resources: Questions/instructions Zip is taller than Mary, but shorter then Hone. Jan is next to Sim. Jo is taller than the person wearing glasses. Bag of beans: 8 blue, 8 green, 8 orange, recording book. % responses y4 y8 Take beans out of bag, and place on the table. 1. I want you to choose 6 beans to put back into the bag. Choose them so that I would always pull out a green bean if I put my hand in to take one out. 6 green beans in bag 68 89 Cooperation level: Jo is shorter than Mary. Tuku is standing beside both Terri and Jan. There are seven people standing between Tuku and Jo. Hone is taller than Mary. Sim is shorter than Terri, but taller than Ben. The tallest person’s name starts with the letter “T.” % responses 2001 (’97) year 8 Final order fitted clues: all 15 81 (73) [15 clues] 14 6 (8) 13 6 (7) 10–12 4 (9)
58 NEMP Report 23: Mathematics 2001 Games Approach: Independent Level: Year 8 Focus: Combinations. Resources: none. Questions/instructions 6 teams play in a table tennis competition. Each team plays each of the other teams once. 1. What is the total number of games played in the competition? % responses y4 y8 15 15 ✗ 30 19 How Far? Approach: Independent Level: Year 8 Focus: Series. Resources: None. Questions/instructions Show how you worked that out: Complete the table to find out the kilometres the car will travel with different amounts of fuel. Litres 8 12 16 20 24 28 32 36 40 Kilometres computational method ( not listing games) 34 systematic listing of games 29 Seemingly random listing of games 7 % responses y8 all correct 49 1 or 2 errors 5 Commentary Only 15 percent of year 8 students determined the correct answer, with many of those who used a computational method counting each combination (game) twice.
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