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nit1. For Design 1:
(a) Describe in words how the design works.
(b) Complete this table. Do not count the beads in Size 1 and Size 2 one by one, but try to see bigger units and use calculation plans.
Size 1 2 3 4 5 30
No. of white beads No. of black beads No. of yellow beads No. of green beads Total no. of beads
(c) Describe and discuss the methods you used to complete the table. Also describe and discuss patterns you see in the table.
(d) Write down a calculation plan for the number of beads of each colour, and for the total number of beads.
(e) Use your calculation plans to calculate the number of beads of each colour for Size 10, Size 20 and Size 100.
2. For Design 2, answer the same questions as for Design 1.
3. For Design 3, answer the same questions as for Design 1.
CHALLENGE Did you see this pattern in the bracelets?
No. of green beads = 1 + 3 + 5 + 7 + 9 + 11
If this numeric pattern is continued, complete the table and discuss how patterns can make calculation easier.
No. of rows No. of green beads
1 1
2 1 + 3 = 4
3 1 + 3 + 5 = 9
4 1 + 3 + 5 + 7 = 16
5 ?
20 ?
4.2 Writing calculation plans
1. Thabo uses beads to make a pattern of Xs like this:
X1 X2 X3 X4 If Thabo continues the pattern, how many beads will there be in X5, how many in X6, how many in X50 and how many in X60?
2. Mary uses clever counting to answer question 1! Try to follow her reasoning. Explain her plan to a classmate.
X2
X1 X3 X4
➔ ➔
X1 = 4 × 1 + 1
➔ ➔
Then here:
X2 = 4 × 2 + 1
➔ ➔
Then here:
Four threes plus 1
X3 = 4 × 3 + 1
Mary starts here:
I see four, four, four, four greens plus one yellow X4 = 4 × 4 + 1 Xnumber = 4 × number + 1
It means “multiply the number by 4, then add 1”.
So X5 = 4 × 5 + 1 So X6 = 4 × 6 + 1 So X50 = 4 × 50 + 1 So X60 = 4 × 60 + 1
Mary writes a calculation plan (rule):
Xnumber = 4 × number + 1 Now she can calculate Xnumber for any number.
3. Suzi uses beads to make this growing V-pattern:
V1 V2 V3 V4 V5
(a) Describe V6, V60 and V87 in words.
(b) Write your plan as a flow diagram and then calculate the number of beads in V6, V60 and V87.
(c) Write down your calculation plan, and then use it to calculate the total number of beads in V6, V60 and V87.
(d) What is the biggest V-number that can be made with 100 green beads and one yellow bead? How many beads are left over?
4. Sam uses beads to make these alphabet patterns.
Answer the same questions as in question 3 for these T, C and L patterns.
T1 T2 T3 T4 T5
C1 C2 C3 C4 C5
L1 L2 L3 L4 L5
4.3 Describing patterns
Purple tiles and white tiles are arranged to make this growing pattern:
Size 1 Size 2 Size 3 Size 4
1. Complete the table. Describe your methods.
Size 1 2 3 4 5 6 30
No. of purple tiles 2 4 6 No. of white tiles 0 1 2 Total no. of tiles 2 5 8
2. Describe horizontal numeric patterns (number patterns) for the purple titles, for the white tiles and for the total number of tiles in the table.
How can you use these horizontal patterns to calculate the number of purple tiles, the number of white tiles and the total number of tiles?
3. Describe vertical numeric patterns for the purple tiles, for the white tiles and for the total number of tiles in the table.
How can you use these patterns to calculate the number of purple tiles, the number of white tiles and the total number of tiles?
4. How many purple tiles are there in a Size 50 pattern?
5. How many white tiles are there in a Size 50 pattern?
6. How many tiles are there in total in a Size 50 pattern?
“horizontal” means from left to right;
“vertical” means from top to bottom.
7. Here are three other growing geometric patterns made with purple and white tiles.
Answer the same questions as in questions 1 to 6 for each tile pattern.
Pattern X
Size 1 Size 2 Size 3 Size 4
Pattern Y
Size 1 Size 2 Size 3 Size 4
Pattern Z
Size 1 Size 2 Size 3 Size 4
4.4 From pictures to tables
In this tile pattern, Size 1 is made of 4 green tiles and 5 smaller purple tiles. The pattern is then continued as shown.
Size 1 Size 2 Size 3
1. Complete this table and describe your methods.
Size 1 2 3 4 5 30
No. of green tiles 4 No. of purple tiles 5
2. Describe horizontal numeric patterns for the green and for the purple tiles in the table.
How can you use these patterns to calculate the number of green tiles and the number of purple tiles?
3. Describe vertical numeric patterns for the green and for the purple tiles in the table.
How can you use these patterns to calculate the number of green tiles and the number of purple tiles?
4. Write down a calculation plan (rule) to calculate the number of green tiles instead of counting them.
How many green tiles are there in a Size 50 pattern?
5. Write down a calculation plan (rule) to calculate the number of purple tiles.
How many purple tiles are there in a Size 50 pattern?
4.5 More pictures and tables
In this tile pattern, Size 1 is made of 8 green tiles and 9 smaller purple tiles. The pattern is then continued as shown.
Size 1 Size 2 Size 3
1. Complete this table and describe your methods.
Size 1 2 3 4 5 30
No. of green tiles 8 No. of purple tiles 9
2. Describe horizontal numeric patterns for the green tiles and for the purple tiles in the table.
How can you use these patterns to calculate the number of green tiles and the number of purple tiles?
3. Describe vertical numeric patterns for the green tiles and for the purple tiles in the table.
How can you use these patterns to calculate the number of green tiles and the number of purple tiles?
4. Write down a calculation plan (rule) to calculate the number of green tiles instead of counting them.
How many green tiles are there in a Size 50 pattern?
5. Write down a calculation plan (rule) to calculate the number of purple tiles.
How many purple tiles are there in a Size 50 pattern?
6. This growing pattern of light blue, dark blue and white tiles is used for a large supermarket floor.
Size 1 Size 2 Size 3 Size 4
Complete the table.
Describe your method, and describe the patterns that you see in the table.
Size 1 2 3 4 5 6 10 30
No. of light blue tiles 1 2 No. of dark blue tiles 12
7. Make your own growing geometric pattern with squares, ask your own questions, and then answer your questions.