Download Tree Growth Problem

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 Problem
Several 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 3 + 2x represent?
Reasoning Abstractly and Quantitatively
2. 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.
1
3+ 3x = (3+ 2x ) + (3+ 2x )
5
Reasoning Abstractly and Quantitatively
3. 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
3 feet
(3 + x) ft. (3 + 2x) ft. (3 + nx) ft.
3+ nx =18
End of nth Year
Height