On track
This is a level 3 number activity from the Figure It Out series. It relates to stage 6 of the number framework. 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 equipment to explore multiplication facts and equations.
On track
Achievement objectives
NA3-2: Know basic multiplication and division facts.
Required materials
- Figure It Out, Levels 2–3, Basic Facts, "On track", page 16
See Materials that come with this resource to download:
- On track activity (.pdf)
Activity
This activity uses a length model for multiplication by getting students to make Cuisenaire rod tracks. Students who are not familiar with the length of the coloured rods can easily check these on the ruler.
Building tracks reinforces the links between the operations (see the relationships diagram for page 7).
Consider the 24-centimetre track below:
Equations that can be written about this track include:
6 + 6 + 6 + 6 = 24 4 x 6 = 24
24 – 6 – 6 – 6 – 6 = 0 24 ÷ 6 = 4
In this activity, students must systematically find all the possible tracks of a given length. This requires them to identify all the multiplication facts for that length. For example, with a track that is 20 centimetres long, the solutions are:
Results can be organised in a table:
length of rod |
1 |
2 |
4 |
5 |
10 |
|---|---|---|---|---|---|
number of rods |
20 |
10 |
5 |
4 |
2 |
This relationship produces an interesting pattern when graphed. The points lie along a hyperbola.
Activity 1
1.
Pat could also use white (1 cm), red (2 cm), light green (3 cm), and pink (4 cm) Cuisenaire rods.
2.
1 x 24 = 24, 2 x 12 = 24, 3 x 8 = 24, 4 x 6 = 24
Activity 2
1.
Rachel could make five different 20-centimetre tracks:
- white (20 x 1)
- red (10 x 2)
- pink (5 x 4)
- yellow (4 x 5)
- orange (2 x 10).
2.
She could make six different 36-centimetre tracks:
- white (36 x 1)
- red (18 x 2)
- light green (12 x 3)
- pink (9 x 4)
- dark green (6 x 6)
- blue (4 x 9).
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