Factory patterns

Building Patterns Constantly 

Factory 1

Formative

1.  How many grey squares do we need for the first factory? The second? The third? 

2. How many grey tiles will we need for the tenth factory? The hundredth? The 3,298th? 

3. What is the number pattern for the grey squares? 

4. How many red squares do we need for the first factory? The second? The third? 

5. How many squares do we need altogether for the first factory? The second? The third? The fourth factory? Can someone come and show us how to make the fifth factory? 

6. What would be a good way of recording all of this data? 

7. Draw a graph of each of the 3 patterns (grey, red, total) for the first five factories

8. Write an equation in the language of algebra for each pattern

Summative

1. What is the number pattern that we are getting for the total number of squares? 

2. If we had 61 tiles, which numbered factory could we make?

Factory 2

Formative

1. How many grey squares do we need for the eighth factory? 

2. How many grey squares will we need for the hundredth factory? 

3. What is the number pattern for the grey squares? 

4. How many red squares do we need for the ninth factory? 

5. If there are 14 grey squares how many red squares are there? 

6. What is the number pattern for the red squares? 

7. How do we get the number of red squares for one factory from the number of red squares in the factory before that? 

8. What is the number pattern that we are getting for the total number of squares? 

9. Draw a graph of each of the 3 patterns (grey, red, total) for the first five factories

10. Write an equation in the language of algebra for each pattern

Summative

1. If we have to use exactly 36 red squares in making a factory, how many grey squares would we need? 

2. How many squares do we need altogether for the seventh factory? 

3. If we had 35 tiles, which numbered factory could we make? 

4. Which of these numbers are not a number of squares for one of these factories: 20, 21, 22, 23? 

Source: NZ Maths