Illustrative Mathematics Unit 6.6, Lesson 4: Practice Solving Equations and Representing Situations with Equations

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Illustrative Math
Grade 6

Lesson 4: Practice Solving Equations and Representing Situations with Equations

Let’s solve equations by doing the same to each side.

Illustrative Math Unit 6.6, Lesson 4 (printable worksheets)

Lesson 4 Summary

The following diagram shows how to write and solve equations.

Lesson 4.1 Number Talk: Subtracting From Five

Find the value of each expression mentally.

• 5 - 2
• 5 - 2.1
• 5 - 2.17
• 5 - 2 7/8

• See Video for Whole Lesson

Scroll down the page for the solutions to the “Are you ready for more?” section.

Lesson 4.2 Row Game: Solving Equations Practice

Solve the equations in one column. Your partner will work on the other column.
Check in with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error and correct it.

Lesson 4.3 Choosing Equations to Match Situations

• Circle all of the equations that describe each situation. If you get stuck, draw a diagram.
• Find the solution for each situation.

1. Clare has 8 fewer books than Mai. If Mai has 26 books, how many books does Clare have?
2. A coach formed teams of 8 from all the players in a soccer league. There are 14 teams. How many players are in the league?
3. Kiran scored 223 more points in a computer game than Tyler. If Kiran scored 409 points, how many points did Tyler score?
4. Mai ran 27 miles last week, which was three times as far as Jada ran. How far did Jada run?

Are you ready for more?

Mai’s mother was 28 when Mai was born. Mai is now 12 years old. In how many years will Mai’s mother be twice Mai’s age? How old will they be then?

• Show Answer

  Let x = additional years
  28 + x = 2(12 + x)
  28 + x = 24 + 2x
  28 + x - x = 24 + 2x - x
  28 = 24 + x
  4 = x
  Mai’s mother be twice Mai’s age in 4 years
  Mai’s mother will be 32 years old and Mai will be 16 years old.

Lesson 4 Practice Problems

1. Select all the equations that describe each situation and then find the solution.
   a. Kiran’s backpack weighs 3 pounds less than Clare’s backpack. Clare’s backpack weighs 14 pounds. How much does Kiran’s backpack weigh?
   i. x + 3 = 14
   ii. 3x = 14
   iii. x = 14 - 3
   iv. x = 14 ÷ 3
   b. Each notebook contains 60 sheets of paper. Andre has 5 notebooks. How many sheets of paper do Andre’s notebooks contain?
   i. y = 60 ÷ 5
   ii. y = 5 · 60
   iii. y/5 = 60
   iv. 5y = 60
   
2. Solve each equation.
   a. 2x = 5
   b. y + 1.8 = 14.7
   c. 6 = 1/2 z
   d. 3 1/4 = 1/2 + w
   e. 2.5t = 10
   
3. For each equation, draw a tape diagram that represents the equation.
   a. 3x = 18
   b. 3 + x = 18
   c. 17 - 6 = x
   
4. Find each product.
   a. (21.2) · (0.02)
   b. (2.05) · (0.004)
   
5. For a science experiment, students need to find 25% of 60 grams. Jada says, “I can find this by calculating ¼ of 60.” Andre says, “25% of 60 means 25/100 · 60.” Lin says both of their methods work. Do you agree with Lin? Explain your reasoning.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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