Lesson 6: Distinguishing between Two Types of Situations

Distinguishing between Two Types of Situations

After-School Tutoring

5 min

Problem

Write an equation for each story. Then find the number of problems originally assigned by each teacher. If you get stuck, try drawing a diagram to represent the story.

Five students came for after-school tutoring. Lin’s teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems. In all, 30 problems were assigned.
Five students came for after-school tutoring. Priya’s teacher assigned each of them the same number of problems to complete. Then she assigned 2 more problems to one of the students. In all, 27 problems were assigned.

Answer

$5(x+2)=30$ (or equivalent), solution: $x=4$ ; The teacher originally assigned 4 problems to each student.
$5x+2=27$ (or equivalent), solution: $x=5$ ; The teacher originally assigned 5 problems to each student.

Sample Response

$5(x+2)=30$ (or equivalent), solution: $x=4$ ; The teacher originally assigned 4 problems to each student.
$5x+2=27$ (or equivalent), solution: $x=5$ ; The teacher originally assigned 5 problems to each student.

Responding to Student Thinking

Points to Emphasizepoints_to_emphasize

Response: If most students struggle with interpreting a situation and writing an equation to match, plan to focus on strategies when opportunities arise over the next several lessons. For example, make sure to invite multiple students to share how they represented situations with equations in the following lesson:

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.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.

Building Toward

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.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?