Table time
This is a level 2 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:
- Using tables to show patterns.
Table time
Achievement objectives
NA2-8: Find rules for the next member in a sequential pattern.
Required materials
Figure It Out, Levels 2–3, Algebra, "Table time", page 7
See Materials that come with this resource for download:
- Table time activity (.pdf)
Activity
This activity is designed to highlight the usefulness of tables as a means of organising number sequences and looking for patterns. All these patterns involve multiples, so the addition constant on a calculator could be used. Some students will need to use counters as a physical representation of the problems.
Extending the table of values is an excellent way of predicting future terms, which some questions ask for. For example, in pattern 1, the table can be extended as shown to find how many people buy 24 gumboots:
People |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Gumboots |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
22 |
24 |
Encourage students to look for patterns “down the table”, that is, the rule directly connecting each variable in the top row of the table with the corresponding variable in the bottom row, as well as patterns across. For example, in pattern 3, the table would be:
In pattern 4, the pattern down the table is difficult and involves subtracting three times the number of customers from 30 to get the number of books left. For example:
Note: This question assumes that customers each buy only one book.
1.
People |
1 |
2 |
3 |
4 |
5 |
6 |
|---|---|---|---|---|---|---|
Gumboots |
2 |
4 |
6 |
8 |
10 |
12 |
2.
Cars |
1 |
2 |
3 |
4 |
5 |
6 |
|---|---|---|---|---|---|---|
Tyres |
4 |
8 |
12 |
16 |
20 |
24 |
3.
Cars |
1 |
2 |
3 |
4 |
5 |
6 |
|---|---|---|---|---|---|---|
Tyres |
5 |
10 |
15 |
20 |
25 |
30 |
4.
Customers |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|---|---|---|---|---|---|---|---|
Books left |
27 |
24 |
21 |
18 |
15 |
12 |
9 |
5.
Groups |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|---|---|---|---|---|---|---|---|---|
Seats left |
35 |
30 |
25 |
20 |
15 |
10 |
5 |
0 |
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