Number patterns

Mathematics

Grade 9

Number patterns, graphs, equasions,

Statistics and probability

Module 12

Number patterns

ACTIVITY 1

To use a table to arrange information

[LO 2.1, 2.2]

1. Alice is making necklaces by using triangular motifs that she places on a wire necklet (as shown in Diagram 1 below). Each motif is made from three black beads, six white beads and six coloured beads. It is important that she has the right number of beads of each colour. She wants to make 50 necklaces with black, white and red beads, 40 with black, white and yellow beads, 40 with black, white and blue beads and 30 with black, white and green beads.

Question: Calculate how many beads of each colour she has to buy.

2. She also combines three of these motifs in a bigger necklace (as shown in Diagram 2 above). The two top motifs in each necklace have the same design as before, but the bottom motif is made of 15 coloured beads only. She makes only half as many of these necklaces in each colour as she makes of the smaller necklaces referred to in Question 1.

Question: How many beads of each colour will she need for these necklaces?

3. She finds that the bigger necklaces are very popular, so she decides to use bigger motifs, and to combine more motifs in one necklace. The ne x t two diagrams show her new plans.

Alice wants to use four colours in these motifs. Use the diagram above to make your own four-colour design.

Question: Repeat the calculation exercises above for these necklaces.

4. These triangular motifs can be made larger and larger, of course. Not all of them are suitable for necklaces though!

Exercise: Below you see equilateral triangular Motifs 1 to 4. Draw Motifs 6 and 7 in the same sequence.

The Motif 3 above has 1 black bead, 3 white beads and si x red beads. You will need to refer to it in problem 6 below.

5. Data gathering: The beads in the motifs have a diameter of 1 cm each. Thus, the surrounding triangle in Motif 1 in the sequence has a side length of 2 cm. Complete the table below by referring to the triangles above as well as the ones you have drawn.

6. Investigation: Alice makes her necklaces by combining triangular motifs as in diagrams 2 and 4. She uses the 10-bead motifs (Motif 3). The smallest necklace has one motif (size 1) and the next necklace has three motifs (size 2) with a triangular gap in the middle. Visualise the next sizes (3, 4, etc) of the necklaces (or draw them) and complete the table below. Try to complete the last column as well.

7. Investigation: Do the same for the next table, if Alice now uses the 15-bead motif that we saw in the very first diagram.