The purpose of this activity is to support students in using a table of values and the spatial structure of a growth pattern to predict further shapes.
Use the PowerPoint as the source of growth patterns. The focus of this lesson is on predicting a further shape in the pattern, not the next shape.
Show the pattern on slide 2 of the PowerPoint and create a table of values, as shown below.
Day | 1 | 2 | 3 | 4 | 5 | … | 9 |
Number of squares | 1 | 2 | 3 | 4 | 5 | … | ? |
Use slide 3 of the PowerPoint to develop a table of values in the same way. If using a shared screen, animate the slide as you fill in the table.
Day | 1 | 2 | 3 | 4 | 5 | … | 11 |
Number of squares | 1 | 3 | 5 | 7 | ? | … | ? |
Day | 1 | 2 | 3 | 4 | 5 | … | 20 |
Number of squares | 1 | 3 | 5 | 7 | 9 | … | 39 |
The structure of the 20th shape should be a central stem of 21 squares and branches left and right of 19 squares. The central stem square numbers are one more than the day numbers and the branches numbers of squares are always one less. 21 + 19 + 19 = 59. Alternatively, note that the number of squares increases by three for each extra day. The 20th day pattern will be made up of 2 + 19 x 3 = 59 squares, two representing the first shape (day 1) and 19 x 3 the addition of nineteen lots of three.
Day | 1 | 2 | 3 | 4 | 5 | … | 9 |
Number of squares | 2 | 5 | 8 | 11 | 14 | … | 59 |
Next steps
Explore rule finding from tables of values alone. You might use the context of the function machine in which numbers enter the machine, the same operation/s are performed, and numbers exit the machine. For example:
What rule is the function machine using?
In | Out |
1 | 5 |
5 | 25 |
8 | 40 |
… | … |
10 | ? |
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/predicting-ahead at 9:02pm on the 26th February 2024