Unlocking Equations: Writing One-Step Equations from Word Problems

Mathematics Grades 7th Grade 4:20 Video
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Lesson Description

Learn how to translate real-world scenarios into one-step algebraic equations, a crucial skill for problem-solving in mathematics.

Video Resource

How to write one-step equations for word problems | 6th grade | Khan Academy

Khan Academy

Duration: 4:20
Watch on YouTube

Key Concepts

  • Variable representation of unknown quantities
  • Translating verbal statements into mathematical expressions
  • Identifying the operation needed to represent the relationship in the word problem
  • Understanding the concept of 'total' and how it relates to the equation.

Learning Objectives

  • Students will be able to identify the unknown quantity in a word problem and represent it with a variable.
  • Students will be able to translate a one-step word problem into a corresponding algebraic equation.
  • Students will be able to determine the appropriate mathematical operation to represent the relationship described in the word problem.
  • Students will be able to write one-step equations involving multiplication and division.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a variable and its purpose in mathematics. Briefly discuss how variables are used to represent unknown quantities. Pose a simple real-world scenario (e.g., 'I have some apples, and I want to find out how many I have.') and ask students how they would represent the unknown number of apples.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'How to write one-step equations for word problems' (https://www.youtube.com/watch?v=2REbsY4-S70). Encourage students to take notes on the examples provided in the video.
  • Guided Practice (15 mins)
    Work through example word problems together as a class. Deconstruct each problem step-by-step, focusing on identifying the unknown quantity, assigning a variable, and translating the information into an equation. Use visuals or diagrams to aid understanding. Start with simpler problems and gradually increase the complexity.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of one-step word problems. Have them work individually to write the corresponding equations. Circulate the classroom to provide assistance and answer questions. Encourage students to check their work with a partner.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts covered in the lesson. Ask students to summarize the steps involved in translating word problems into equations. Administer a short quiz to assess their understanding.

Interactive Exercises

  • Equation Scramble
    Provide students with word problems and corresponding equation components (numbers, variables, operation symbols) on separate cards. Students must match the components to create the correct equation for each word problem.
  • Word Problem Generator
    Have students create their own one-step word problems and exchange them with a partner to write the corresponding equations.

Discussion Questions

  • What are some keywords in word problems that indicate specific mathematical operations (e.g., 'total' for addition, 'per' for multiplication)?
  • Why is it important to define your variables clearly before writing an equation?
  • Can you think of real-life situations where you might need to write and solve an equation?

Skills Developed

  • Problem-solving
  • Abstract reasoning
  • Mathematical communication
  • Analytical skills

Multiple Choice Questions

Question 1:

Sarah has 'x' number of books. John has 5 more books than Sarah. John has 12 books. Which equation represents this situation?

Correct Answer: x + 5 = 12

Question 2:

A pizza is cut into 8 slices. You eat 's' slices. You have 3 slices left. Which equation represents this?

Correct Answer: 8 - s = 3

Question 3:

A movie ticket costs $8. A group spent a total of $40 on tickets. Let 't' be the number of tickets. Which equation represents this?

Correct Answer: 8t = 40

Question 4:

A bag of candy is divided equally among 4 friends. Each friend receives 7 pieces. Let 'c' be the total number of candies. Which equation represents this?

Correct Answer: c/4 = 7

Question 5:

Lisa ran 'm' miles. Karen ran twice as far as Lisa. Karen ran 10 miles. Which equation is correct?

Correct Answer: 2m = 10

Question 6:

Mark earned $5 for each lawn he mows. If he earned $35 total, what equation represents the situation if 'l' is the number of lawns?

Correct Answer: 5l = 35

Question 7:

A school bought 'n' notebooks for $2 each and spent $50. Which equation shows the number of notebooks bought?

Correct Answer: 2n = 50

Question 8:

If a store is selling apples at $0.75 each, and someone spends $6.00 on apples, what is the equation where 'a' is the amount of apples purchased?

Correct Answer: 0.75a = 6.00

Question 9:

A rectangle has an area of 24 square inches. If the width is 4 inches, what is the equation representing the length 'l'?

Correct Answer: 4l = 24

Question 10:

If you divide a number 'y' by 3 and get 9, what equation correctly shows this?

Correct Answer: y/3 = 9

Fill in the Blank Questions

Question 1:

The goal is to raise $100 and for each car washed $10 is made. If 'c' represents the amount of cars washed, the equation to solve is 10___ = 100.

Correct Answer: c

Question 2:

If you divide a total of 20 cookies evenly between friends, and each friend got 5 cookies, what is the amount of friends. 'f' represents the amount of friends and the equation to use is 20/__ = 5

Correct Answer: f

Question 3:

Each CD costs $12 and a group of friends spend $36. What equation shows this if 'c' represents the number of CDs is 12___ = 36.

Correct Answer: c

Question 4:

If the temperature rose 'x' degrees and is now 75 degrees. The original temperature was 60. The equation that shows this is 60 + ___ = 75.

Correct Answer: x

Question 5:

The price of each donut is $2. If someone spent a total of $10, what equation models this where 'd' is donuts purchased? ___d = 10

Correct Answer: 2

Question 6:

If a number 'y' is multiplied by 6 to get 42, the equation representing this is 6___ = 42.

Correct Answer: y

Question 7:

If 45 is divided by 'x' to get 5, the equation representing this is 45/___ = 5.

Correct Answer: x

Question 8:

If $3 is deducted from 'p' amount of dollars to get a new amount of $12, the equation representing this is p - ___ = 12.

Correct Answer: 3

Question 9:

The cost of each movie ticket is $15. If someone paid $60, then the equation showing the number of movies 'm' is ___m = 60.

Correct Answer: 15

Question 10:

When 20 is split amongst 'f' friends, each friend has 4. The equation for this is 20/___ = 4.

Correct Answer: f

Educational Standards

7.A.3.1:Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. 7.A.3:Represent mathematical situations using equations and inequalities involving variables and rational numbers. 7.N.2.5:Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

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