Table 1.
Tasks with solution templates.
| Task-set | Description | Formula | Example | Question |
|---|---|---|---|---|
| 1 | Squares are constructed with matches. | If x is the number of squares then the number of matches y can be calculated by y = 3x + 1. | Example: 4 squares can be made by y = 3x + 1 = 3·4 + 1 = 13 matches. | How many matches are needed for 6 squares? |
| 2 | Double-squares are constructed with matches | If x is the number of double-squares then the number of matches y can be calculated by y = 5x + 2. | Example: 4 squares can be made by y = 5x + 2 = 5·4 + 2 = 22 matches. | How many matches are needed for 7 squares? |
| 3 | Stone tiles are placed around flowers. | If x is the number of flowers, the number of stone tiles y can be calculated by y = 5x + 3. | Example: Around 4 flowers in a row y = 5x + 3 = 5·4 + 3 = 23 tiles are needed. | How many tiles are needed around 7 flowers in a row? |
| 4 | Stone tiles are placed around flower-triplets. | If x is the number of flower-triplets, the number of stone tiles y can be calculated by y = 11x + 7. | Example: Around 4 flower-triplets in a row y = 11x + 7 = 11·4 + 7 = 51 stone tiles are needed. | How many stone tiles are needed around 6 flower-triplets in a row? |
| 5 | Grey and yellow square tiles with a side length of 1 dm are mounted on a wall. | If the wall is a dm long and b dm high, the number of tiles K along the edges of the wall can be calculated by K = 2a + 2b −4. | Example: If the wall is 8 dm long and 6 dm high, K = 2·8 + 2·6–4 = 24 grey tiles are needed. | How many grey tiles are needed for the edge on a wall that is 9 dm · 7 dm? |
| 6 | Grey and white square tiles with a side length of 1 dm are mounted on a wall. | If the wall is a dm long and b dm high, the number of white tiles A can be calculated by A = ab -2a - 2b + 4. | Example: If the wall is 8 dm long and 6 dm high, A = 8·6–2·8 - 2·6 + 4 = 24 white tiles are needed. | How many white tiles are needed if the wall is 3 dm · 4 dm? |
| 7 | White square tiles with a side length of 3 dm is placed on a floor. Around the edge square grey tiles with side length 1 dm are placed. | If the rectangle with white tiles is a tiles long and b tiles wide, the number of grey tiles R can be calculated by R = 6a + 6b + 4. | Example: If the rectangle with white tiles is 3 tiles long and 2 tiles wide, R = 6·3 + 6·2 + 4 = 34 grey tiles are needed. | How many grey tiles are needed if the white rectangle is 3 tiles long and 4 tiles wide? |
| 8 | Matchstick houses are put together as a row house. | If x is the number of houses in a row house, the number of matches y can be calculated by y = 5x + 1. | Example: If the row house consists of 4 houses, y = 5·4 + 1 = 21 matches are needed. | How many matches are needed for a row house with 6 houses? |
| 9 | Matchstick houses are put together as a row house. | If x is the number of houses in a row house, the number of matches along the edge y can be calculated by y = 3x + 1. | Example: If the row house consists of 4 houses, y = 3·4 + 1 = 13 matches are needed for the edge. | How many matches are needed for the edge of a row house with 7 houses? |
| 10 | A quilt blanket is sewn out of light grey octagons, black squares, white, and dark grey triangles. The blanket has the shape of a square. | If the blanket contains n·n octagons, the number of dark grey triangles can be calculated by T = 4n – 4. | Example: If the blanket contains 3·3 octagons, T = 4·3–4 = 8 dark grey triangles are needed. | How many dark grey triangles are needed if the quilt blanket contains 5·5 octagons? |