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6.2 Add all the numbers from 1 to 20 inclusive. Look for a pattern and a short way. Write down what you did and your answer on the dotted line below. Then check your answer the long way. You may use a calculator to do so.
7. Another interesting pattern can be seen in the answers if you add:
8. More patterns with shapes. The following pattern may be made with toothpicks, one for each straight line.
Number of triangles  1  2  3  4  5  6  17  25 
Number of toothpicks 
Hint: Maybe you could look at the toothpicks needed for six triangles and use them to calculate how many toothpicks are needed for 17 triangles, or you could think that you know the general pattern and just apply it to find out how many toothpicks are needed for 17 triangles. Your discussion is important, so the answers are not being given to you.The same applies to the 25 triangles.
8.4 Write down how you calculated the answers for
9. Complete the table:
In  1  2  3  4  5  6  10  20  50 
Out  8  15  22  29  36 
TEST YOUR PROGRESS
1. Do the following show tessellation? Write “yes” or “no” for each one.



2. Write down one way in which the sides of a trapezium differ from the sides of a
parallelogram .
3. Why is the triangle used in the building of the framework of the roofs of houses?
4. On a floor there are 10 tiles in a row and there are 17 rows of tiles. How many tiles are there altogether?
5. Dad uses 135 tiles to tile a stoep. He places 9 tiles across the width of the stoep. How many tiles are there in the length of the stoep?
6. Make a diagram to show what a square tiled area would look like if 16 square tiles were used to cover it. Use your ruler to draw in the tiles.
7. Complete the table:
1  2  3  4  5  6  10  12  20 
4  7  10  13  16 
8. Complete this table:
1  2  3  4  7  8  
1  4  9  16  100 
9. Thirty squares are made with toothpicks as shown in the diagram (one toothpick for each straight line). How many toothpicks are needed?
Learning outcomes(LOs) 
LO 2 
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. 
Assessment standards(ASs) 
We know this when the learner: 
2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns: 

2.1.2 not limited to sequences involving constant difference or ratio. 
2.2 describes observed relationships or rules in own words. 
LO 4 
measurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts. 
We know this when the learner: 
4.8 investigates and approximates (alone and /or as a member of a group or team): 
4.8.2 area of polygons (using square grids and tiling) in order to develop an understanding of square units;

ACTIVITY 1area of polygons
1.1 to 1.3 Practical own work and recording of it.
2. 4 whole blocks and 5 and a bit blocks = about 9 blocks
3.1 6
3.2 12
8.1 Yes
8.2 Drawing
9. 23 x ? =736
32 tiles
10. 75 x 54 = 4 050 tiles!
ACTIVITY 2 Patterns
1.4
4 shapes
2. Multiples of 9 – the digits forming each multiple of 9 add up to 9, so 54 is a multiple of 9; 72 is a multiple of 9. This is useful for checking answers.
Output numbers: 7; 14; 21; 28; 35; 42; 49; 56; 63; 70
4.1
1  2  3  4  7  8  9  10  20  50 
7  12  17  22  37  42  47  52  102  252 
4.2 Flow diagram:
Input numbers: 1; 2; 3; 4; 7; 8; 9; 10; 20; 50
Operators: x 5 + 2
Output numbers: 7; 12; 17; 22; 37; 42; 47; 52; 102; 252
4.3 multiplied by 5 and 2 was added to the answer.
5.1
1  2  3  4  5  6  9  11  12  20 
3  5  7  9  11  13  19  23  25  41 
5.2 multiplied by 2 and 1 was added to the answer
5.3
In  1  2  3  4  5  6  7  10  14 
Out  3  7  11  15  19  23  27  39  55 
5.3 multiplied by 4 and 1 was subtracted from the answer.
6.2 1 + 20; 2 + 19; 3 + 18; 4 + 17; 5 + 16; 6 + 15; 7 + 14; 8 + 13; 9 + 12; 10 + 11
10 x 21 = 210
7. 55; 155; 255; 355; 455 etc.
Own
8.1 2
8.2
Triangles  1  2  3  4  5  6  17  25 
Toothpicks  3  5  7  9  11  13  35  51 
8.4 (a) 17 x 2 + 1
(b) 25 x 2 + 1
9.
In  1  2  3  4  5  6  10  20  50 
Out  8  15  22  29  36  43  71  141  351 
1.1 Yes
1.2 Yes
1.3 No
2. Only 1 pair of opposite sides are parallel; they are not equal in length.
3. It is a rigid shape.
4. 170 tiles
5. 15 tiles
6. Diagram 4 by 4
7.
1  2  3  4  5  6  10  12  20 
4  7  10  13  16  19  31  37  61 
8.
1  2  3  4  7  8  10 
1  4  9  16  49  64  100 
10. 5; 13; 21; 29; 37; 45
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