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Tree Growth Problem

This educational resource focuses on solving a real-life tree growth problem through numerical and algebraic expressions and equations. It guides learners in representing quantities with variables, constructing equations, and solving word problems that lead to specific rational number equations. By examining the growth of a tree planted years ago, it methodically teaches how to formulate and solve equations such as px + q = r and p(x + q) = r. It emphasizes understanding the relationship between algebraic and arithmetic solutions, enhancing reasoning about quantities in practical scenarios.

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Tree Growth Problem

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  1. Tree Growth Problem 7.EE - Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

  2. 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?

  3. 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?

  4. Reasoning Abstractly and Quantitatively 1. Explain how the chartbelow models the following statement: ‘ Several years ago, I planted a 3-foot tree that has grown the same amount each year.’ What does nxrepresent? What does x represent? What does 3 + 2xrepresent?

  5. Reasoning Abstractly and Quantitatively 2. Explain how the equationbelow 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.’ What does 3+3x represent? What does 1/5 (3+2x) represent? What is the value of x?

  6. 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?’ What does nrepresent? What does 3+nx represent? What is the value of n?

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