Can you kayak?
This is a level 3 algebra activity from the Figure It Out theme series. It is focused on using diagrams or symbols to solve a problem. 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 diagrams or symbols to solve a problem.
Can you kayak?
Achievement objectives
NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
Required materials
- Figure It Out, Level 3, Theme: At Camp, "Can you kayak?", page 19
See Materials that come with this resource to download:
- Can you kayak activity (.pdf)
Activity
Question 1 is a possibilities and constraints problem. Similar problems can be found in Algebra, Figure It Out, Levels 2–3. A variety of strategies could be used:
- trial and improvement
Two dinghies and two kayaks can hold 10 people in total. So try a kayak holding one person and a dinghy holding four people ...
- using a table to organise the information
People in kayak |
People in dinghy |
People in three dinghies and one kayak |
|---|---|---|
1 |
4 |
13 too much |
2 |
3 (to make the first clue work) |
11 just right! |
- using patterns
Question 2 builds on this answer and provides a more complex possibilities and constraints problem. Similar strategies can be used, for example, trial and improvement using a table:
Number of dinghies |
Number of kayaks |
Total number of people |
|---|---|---|
15 |
0 |
45 too many! |
14 |
1 |
44 |
13 |
2 |
43 |
: |
: |
: |
: |
: |
: |
6 |
9 |
36 Yes! |
1.
a. 2
b. If 2 dinghies and 2 kayaks hold 10 people, then 1 dinghy and 1 kayak must hold 5 people.
If the kayak holds 1 person and the dinghy 4, then 3 dinghies and 1 kayak would hold 3 x 4 + 1 = 13 people. So this can’t be correct. Another possibility is that the kayak holds 2 people and the dinghy holds 3. This means 3 dinghies and 1 kayak hold 3 x 3 + 2 = 11 people, which agrees with the information given.
2.
6 dinghies and 9 kayaks
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