Lesson 11: Using Equations to Solve Problems

Using Equations to Solve Problems

The Basketball Game

5 min

Problem

Diego scored 9 points less than Andre in the basketball game. Noah scored twice as many points as Diego. If Noah scored 10 points, how many points did Andre score? Explain or show your reasoning.

Answer

14 points. Sample reasoning:

Equation: $2(x-9)=10$ , where $x$ is the number of points scored by Andre. $x-9=5$ , $x=14$ .
Reasoning: Diego scored half as many points as Noah, so he scored 5 points. Andre scored 9 points more than Diego, or 14 points.
Diagram: One possibility is two boxes each with $x-9$ showing a total of 10. Each box represents 5 points, so $x$ is 14.

Sample Response

14 points. Sample reasoning:

Equation: $2(x-9)=10$ , where $x$ is the number of points scored by Andre. $x-9=5$ , $x=14$ .
Reasoning: Diego scored half as many points as Noah, so he scored 5 points. Andre scored 9 points more than Diego, or 14 points.
Diagram: One possibility is two boxes each with $x-9$ showing a total of 10. Each box represents 5 points, so $x$ is 14.

Responding to Student Thinking

More Chancesmore_chances

Response: Students will have more opportunities to understand the mathematical ideas addressed here. There is no need to slow down or add additional work to the next lessons.

Standards

Addressing

7.EE.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.EE.4.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?
7.EE.B.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
7.EE.B.4.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?