Answer to Question #126177 in Algebra for Sphesihle Zuma

Question

Follow the instructions Below to create your own pattern:

A, draw the first three terms of a simple ascending geometrical pattern with a constant difference.
B, describe the pattern in words.
C, write down the rule of the pattern.
D,using the rule, extend the pattern to the fourth and the tenth term.
E, describe the pattern in a flow diagram (spider diagram)
F, describe the pattern in a table.
G, describe your pattern in a graph.
H, reflect on the ease of the activity.

Answer 1

A) draw the first three terms of a simple ascending geometrical pattern with a constant difference.

here the first three terms with shapes 1, 4, and 7 that has constant difference of +3 between them.

B) Describe the pattern in words.

This is a simple ascending geometrical pattern in which one or more elements of the sequence or arrangement increases following a specific pattern rule. In this pattern, the number of squares are increasing with increase in pattern type. Type 1 has one square, type 2 has four squares and type 3 has seven squares.

C) Write down the rule of the pattern.

1. To get from 1 square to 4 squares, you have to add 3 squares. To get from 4 squares to 7 squares, you have to add 3 squares. To get from 7 squares to 10 squares, you have to add 3 squares. So continue to add 3 squares for each pattern
2. Alternatively, multiply the pattern type (number) by 3, and subtract 2. So pattern 20 will have 20*3−2 squares.

D) Using the rule, extend the pattern to the fourth and the tenth term.

To get the fourth term, $4*3-2=10$ $squares$ or $7squares+3=10 squares$

To get the tenth term, $10*3-2=28$ $squares$ or $25$ $squares$ $+3=28$ $squares$

E) Describe the pattern in a flow diagram (spider diagram)

F) Describe the pattern in a table.

Pattern Type : 1 2 3 4 5 6 7 8 9 10

Number of squares :  1 4 7 10    13    16    19 22    25 28

G) Describe your pattern in a graph.

H) Reflect on the ease of the activity.

I found the above activities very helpful in terms of modelling mathematical language and thinking. It makes is easy to understand the number pattern and predict the pattern of a geometrical pattern.