Getting better
This is a level 2 algebra activity from the Figure It Out theme series. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Continue a sequential pattern.
- Write a rule to describe a sequential pattern.
Getting better
Achievement objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Required materials
- Figure It Out, Levels 2–3, Theme: Gala, "Getting better", page 15
- a calculator (optional)
- square grid paper
See Materials that come with this resource to download:
- Getting better activity (.pdf)
Activity
This activity requires students to continue a pattern, first by observation and then by plotting a relationship onto a linear graph to make a prediction. Some students will spot the patterns quite quickly. Nevertheless, they will still need to organise the information to accurately plot the ordered pairs onto a number plane for question 3.
Organising data in a table is a useful way to find and describe patterns.
Encourage the students to explain the patterns in their own words, for example, "going up by four each game," "going up by one more each time," and so on.
The students can use the tables for questions 1 and 2 to list ordered pairs for question 3:
- (1, 23), (2, 27), (3, 31), (4, 35), (5, 39), (6, 43)
- (1, 6), (2, 11), (3, 17), (4, 24), (5, 32), (6, 41)
This will enable the students to plot the relationship between the two variables, games and scores, onto a linear graph. You will need to emphasise the importance of accuracy in plotting the points; otherwise, the students won’t be able to draw an accurate line. The students should draw graphs that are bigger than the ones shown in the students’ book. Larger squares make it easier to plot accurately. Make sure you also emphasise that the students put the game (the independent variable) on the horizontal axis and the score (the dependent variable) on the vertical axis.
In question 3b, future predictions can be made by extending the line a stage further and reading the corresponding dependent variable for game seven. Providing the line was drawn accurately, the prediction will also be accurate. Highlight and discuss with the students the comparison between the tables and their numeric predictions and the predictions on the graph.
As an extension, you could ask the students to compare their graph with a reducing pattern or an unpredictable score. For example:
- Ask them a question with scores that decrease at a constant rate (for example, four less each time). How does this change on the linear graph?
- Ask them a question with random scores showing no pattern. How will this appear on the graph?
- Ask them to discuss how Te Rata School could be sure to make a profit on this game. They will need to decide or find out:
- What do the players need to do to win a prize? (Do they need to reach a certain score, or will they be the players with the highest scores at the end of the day?)
- How much do the prizes cost?
- How much should they charge people to play?
1.
a. The scores improve by 4 each time (+ 4)
b. 39, 43
2.
a. The number added increases by 1 each time (+ 5, + 6, + 7)
b. 32, 41
3.
a. Students’ ball-throwing scores
b. Students’ ball-throwing scores
Kenny, with a predicted score of 51
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