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?
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?
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