Solving the Apple Tree and Conifer Tree Pattern Puzzle

In this mathematics unit, we explore a scenario where a farmer plants trees in a square pattern, with conifer trees surrounding the apple trees for protection against the wind. The task involves completing a table to understand the pattern for different numbers of rows of apple trees. Through this exercise, mathematical techniques like pattern recognition and table completion are applied to analyze the relationship between the apple and conifer trees' arrangement.

• Mathematics
• Trees
• Pattern Recognition
• Orchards

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Uploaded on Sep 24, 2024 | 2 Views

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Presentation Transcript

1. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? A farmer plants trees in a square pattern. In order to protect the apple trees against the wind he plants conifer trees all around the orchard. What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Here you see a diagram of this situation where you can see the pattern of apple trees and conifer trees for any number (n) of rows of apple trees: What have we learned? What have we learned? QUESTION 3.1 Complete the table:

2. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? A farmer plants trees in a square pattern. In order to protect the apple trees against the wind he plants conifer trees all around the orchard. What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Here you see a diagram of this situation where you can see the pattern of apple trees and conifer trees for any number (n) of rows of apple trees: What have we learned? What have we learned? QUESTION 3.1 Complete the table: Back to start Back to start

3. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? A farmer plants trees in a square pattern. In order to protect the apple trees against the wind he plants conifer trees all around the orchard. What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Here you see a diagram of this situation where you can see the pattern of apple trees and conifer trees for any number (n) of rows of apple trees: What have we learned? What have we learned? QUESTION 3.1 Complete the table: Back to start Back to start

4. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? A farmer plants trees in a square pattern. In order to protect the apple trees against the wind he plants conifer trees all around the orchard. What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Here you see a diagram of this situation where you can see the pattern of apple trees and conifer trees for any number (n) of rows of apple trees: What have we learned? What have we learned? QUESTION 3.1 Complete the table: Back to start Back to start

5. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? A farmer plants trees in a square pattern. In order to protect the apple trees against the wind he plants conifer trees all around the orchard. What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Here you see a diagram of this situation where you can see the pattern of apple trees and conifer trees for any number (n) of rows of apple trees: What have we learned? What have we learned? QUESTION 3.1 Complete the table: Back to start Back to start

6. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? QUESTION 3.2 There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 What have we learned? What have we learned? Number of conifer trees = 8? where ? is the number of rows of apple trees. There is a value of ? for which the number of apple trees equals the number of conifer trees. Find the value of ? and show you method of calculating this.

7. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? QUESTION 3.2 There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 What have we learned? What have we learned? Number of conifer trees = 8? where ? is the number of rows of apple trees. There is a value of ? for which the number of apple trees equals the number of conifer trees. Find the value of ? and show you method of calculating this. Back to start Back to start

8. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? QUESTION 3.2 There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 What have we learned? What have we learned? Number of conifer trees = 8? where ? is the number of rows of apple trees. There is a value of ? for which the number of apple trees equals the number of conifer trees. Find the value of ? and show you method of calculating this. Back to start Back to start

9. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? QUESTION 3.2 There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 What have we learned? What have we learned? Number of conifer trees = 8? where ? is the number of rows of apple trees. There is a value of ? for which the number of apple trees equals the number of conifer trees. Find the value of ? and show you method of calculating this. Back to start Back to start

10. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? QUESTION 3.2 There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 What have we learned? What have we learned? Number of conifer trees = 8? where ? is the number of rows of apple trees. There is a value of ? for which the number of apple trees equals the number of conifer trees. Find the value of ? and show you method of calculating this. Back to start Back to start

11. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 Number of conifer trees = 8? What have we learned? What have we learned? where ? is the number of rows of apple trees. QUESTION 3.3 Suppose the farmer wants to make a much larger orchard with many rows of trees. As the farmer makes the orchard bigger, which will increase more quickly: the number of apple trees or the number of conifer trees? Explain how you found your answer.

12. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 Number of conifer trees = 8? What have we learned? What have we learned? where ? is the number of rows of apple trees. QUESTION 3.3 Suppose the farmer wants to make a much larger orchard with many rows of trees. As the farmer makes the orchard bigger, which will increase more quickly: the number of apple trees or the number of conifer trees? Explain how you found your answer. Back to start Back to start

13. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 Number of conifer trees = 8? What have we learned? What have we learned? where ? is the number of rows of apple trees. QUESTION 3.3 Suppose the farmer wants to make a much larger orchard with many rows of trees. As the farmer makes the orchard bigger, which will increase more quickly: the number of apple trees or the number of conifer trees? Explain how you found your answer. Back to start Back to start

14. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 Number of conifer trees = 8? What have we learned? What have we learned? where ? is the number of rows of apple trees. QUESTION 3.3 Suppose the farmer wants to make a much larger orchard with many rows of trees. As the farmer makes the orchard bigger, which will increase more quickly: the number of apple trees or the number of conifer trees? Explain how you found your answer. Back to start Back to start

15. Mathematics Unit 3: Apples What do we want to find out? What do we want to find out? There are two formulae you can use to calculate the number of apple trees and the number of conifer trees for the pattern described: What useful information do we know? What useful information do we know? What other mathematical techniques do we need to apply? What other mathematical techniques do we need to apply? Number of apple trees = ?2 Number of conifer trees = 8? What have we learned? What have we learned? where ? is the number of rows of apple trees. QUESTION 3.3 Suppose the farmer wants to make a much larger orchard with many rows of trees. As the farmer makes the orchard bigger, which will increase more quickly: the number of apple trees or the number of conifer trees? Explain how you found your answer. Back to start Back to start