Videos to help Grade 6 students learn how to solve two-step problems by using their knowledge of order of operations and the properties of equality.

New York State Common Core Math Module 4, Grade 6, Lesson 28

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Common Core For Grade 6

Student Outcomes

Students calculate the solution of two-step problems by using their knowledge of order of operations and the properties of equality for addition, subtraction, multiplication, and division. Students employ tape diagrams to determine their answer.

Students check to determine if their solution makes the equation true.

Mathematical Modeling Exercise

Juan has gained 20 lb. since last year. He now weighs 120 lb. Rashod is 15 lb. heavier than Diego. If Rashod and Juan weighed the same amount last year, how much does Diego weigh? Allow j to be Juan’s weight last year (in lb.) and d to be Diego’s weight (in lb.).

Draw a tape diagram to represent Juan’s weight.

Draw a tape diagram to represent Rashod’s weight.

Draw a tape diagram to represent Diego’s weight.

What would combining all three tape diagrams look like?

Write an equation to represent Juan’s tape diagram.

Write an equation to represent Rashod’s tape diagram.

How can we use the final tape diagram or the equations above to answer the question presented?

Calculate Diego’s weight.

We can use identities to defend our thought that .d + 35 - 35 = d

Does your answer make sense?

Example 1

Marissa has twice as much money as Frank. Christina has $20 more than Marissa. If Christina has $100, how much money does Frank have? Letf represent the amount of money Frank has in dollars and m represent the amount of money Marissa has in dollars.

Draw a tape diagram to represent the amount of money Frank has.

Draw a tape diagram to represent the amount of money Marissa has.

Draw a tape diagram to represent the amount of money Christina has.

Which tape diagram provides enough information to determine the value of the variable m? Write and solve the equation.

The identities we have discussed throughout the module solidify that m + 20 - 20 =m What does the 80 represent?

Now that we know Marissa has$80 , how can we use this information to find out how much money Frank has?

Write an equation.

Solve the equation.

What does the 40 represent?

Does 40 make sense in the problem?

Exercises

Use tape diagrams to solve the problem.

Raeana is twice as old as Madeline and Laura is 10 years older than Raeana. If Laura is 50 years old, how old is Madeline? Let m represent Madeline's age in years and let r represent Raeana's age in years.

Carli has 90 apps on her phone. Braylen has half the amount of apps as Theiss. If Carli has three times the amount of apps as Theiss, how many apps does Braylen have? Let b represent the number of Braylen's apps and represent the number of Theiss' apps.

Reggie ran for 180 yards during the last football game, which is 40 more yards than his previous personal best. Monte ran more 50 yards than Adrian during the same game. If Monte ran the same amount of yards Reggie ran for his previous personal best, how many yards did Adrian run? Let r represent the number yards Reggie ran during his previous personal best and a represent the number of yards Adrian ran.

Lance rides his bike at a pace of 60 miles per hour down hills. When Lance is riding uphill, he rides 8 miles per hour slower than on flat roads. If Lance's downhill speed is 4 times faster than his flat road speed, how fast does he travel uphill? Let f represent Lance's pace on flat roads in miles per hour and u represent Lance's pace uphill in miles per hour.

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