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.
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use equipment to explore multiplication facts and equations
Activity One
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
Activity Two
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:
This relationship produces an interesting pattern when graphed. The points lie along a hyperbola.
Answers to Activity
Activity One
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 Two
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)