Ups and downs
This is a level 3 algebra strand activity from the Figure It Out 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:
- Use a graph to show a relationship in sequential patterns.
Ups and downs
Achievement objectives
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Required materials
- Figure It Out, Level 3, Algebra, "Ups and downs", page 9
- number line (optional)
See Materials that come with this resource to download:
- Ups and downs activity (.pdf)
Activity
This activity requires students to construct two graphs of the movements of two different snails. The graph at the bottom right-hand side of the page models the correct procedures for labelling and setting out graphs.
Students could calculate the number of hours, but generally they will draw the pattern on the graph. Make sure that they start plotting their graph on the left-hand side of their page, as the snails may take more hours than they would expect.
As a discussion point, if students calculate the number of hours, they may see that over a period of 2 hours, Slimey climbs a total of 3 metres. Dividing 26 metres by 3 metres and multiplying it by 2 hours gives a total of 17.3 hours. The catch is that Slimey reaches the top during one of his 5 metre ascents rather than after a 2 metre slide down. Students’ graphs should show that Slimey reaches the top in 15 hours (presuming that he remains resting at the top of the well rather than sliding down again!).
Sluggish the Snail’s climb is along similar lines, but the rate is different. As an extension exercise, students could compare the slope of each graph. If the slopes are different, the snails must have been moving at a different speed.
Ask students,
- “Would a steeper slope mean that that snail is faster or slower?
- Is Slimey faster or slower than Sluggish?”
1.
Slimey’s Climb
It takes Slimey 15 hours to get to the top of the well.
2.
Sluggish’s Climb
It takes Sluggish 11 hours to get to the top of the well.
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