Tree Growth Problem

7.EE - Solve real-life and mathematical problems

using numerical and algebraic expressions and

equations.

4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Tree Growth ProblemSeveral years ago, I planted a 3-foot tree that has grown the same amount each year.

At the end of the third year, the tree was 1/5 taller than it was at the end of the second year.

The tree is now 18 feet tall.

How many years ago did I plant the tree?

Reasoning Abstractly and Quantitatively

1. Explain how the chart below models the following statement:

‘ Several years ago, I planted a 3-foot tree that has grown the same amount each year.’

Original Height

End of 1st Year Height

End of 2nd Year Height

End of nth Year Height

3 feet (3 + x) ft. (3 + 2x) ft. (3 + nx) ft.

What does x represent?

What does 3 + 2x represent?

What does nx represent?

Reasoning Abstractly and Quantitatively2. Explain how the equation below models the following statement:

‘At the end of the third year, the tree was 1/5 taller than it was at the end of the second year.’

Original Height

End of 1st Year Height

End of 2nd Year Height

End of nth Year Height

3 feet (3 + x) ft. (3 + 2x) ft. (3 + nx) ft.

What does 3+3x represent?

What does 1/5 (3+2x) represent?

What is the value of x?

Reasoning Abstractly and Quantitatively3. Explain how the equation below models the following statement:

‘ The tree is now 18 feet tall. How many years ago did I plant the tree?’

Original Height

End of 1st Year Height

End of 2nd Year Height

End of nth Year Height

3 feet (3 + x) ft. (3 + 2x) ft. (3 + nx) ft.

What does n represent?

What does 3+nx represent?

What is the value of n?