Getting Started 
Misconception/Error The student does not have an effective overall strategy for solving a multistep problem. 
Examples of Student Work at this Level The student:
 Does not provide any work or answer. Upon questioning, the student said, â€śI didnâ€™t know where to start.â€ť
 Confuses the final cost with the cost of the meal before the discount and tax have been applied.
 Writes a series of â€śequationsâ€ť that do not correctly model the problem.
 Adds 15% and %, and then attempts to determine 21.5% of the price.

Questions Eliciting Thinking What is the question asking? What information are you given? What do you need to solve the problem?
Can you explain your strategy for this problem? What do you need to calculate?
What does a 15% discount mean?
What does % tax mean? How is tax computed?
How can you determine the amount of discount? How can you determine the amount of tax? Is tax added to or subtracted from the bill?
Do you think the final price will be lower or higher than the original price? Why or why not? 
Instructional Implications Encourage the student to first develop an overall strategy when solving multistep percent problems by identifying major steps of the solution process, (e.g., first find the dollar amount of the discount and then use it to calculate the price of the meal. Next, find the dollar amount of the tax and add that to the price of the meal to get the final total cost). Review the meaning of discounts and tax and how they are applied in realworld contexts. Suggest the student use a flow chart or graphic organizer to model the steps of the problem and organize work. Give the student opportunities to solve similar types of problems but with â€śeasier/smallerâ€ť numbers, allowing the student to focus on developing a general strategy for solving the problem. Provide feedback as needed.
Assist the student in developing strategies for calculating percents of quantities. Review the meaning of percent and calculating the percent of a quantity using proportional reasoning. Emphasize the relationship between a percent and its ratio equivalent. Provide problems that include rational number percentages as well as whole number percentages. Use a tape diagram or double number line to help the student visualize the relationship among the part, the whole, the given percent, and 100%. Provide additional practice finding percent of a number in a variety of reallife contexts and multistep, reallife and mathematical problems posed with rational numbers in any form (whole numbers, fractions, and decimals). Consider implementing CPALMS Lesson Plan Letâ€™s Go Shopping: Calculating Percents (ID 2309).
Provide additional opportunities to solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, decimals, and percents). Initially focus on understanding the problem and developing an overall strategy to solve it. Ask the student to describe a strategy and provide feedback. Then assess the student on implementation of the strategy. Provide additional review, as needed, on operations with rational numbers. 
Moving Forward 
Misconception/Error The student does not have an effective strategy for calculating the percent of a quantity. 
Examples of Student Work at this Level The student has an effective overall strategy but makes errors in calculating percents. The student:
 Incorrectly sets up proportions to find the discount and the tax.Â
 Subtracts 15 from 53.52 and then adds 6.5 to the difference.Â

Questions Eliciting Thinking What does it mean to take 15% off? Is tax added or subtracted to the bill?
Is 15% of a going to be the same as 15% of b? Why or why not?
Are you calculating tax on the same price you are calculating the discount? Why or why not?
Does it matter which you calculate first, discount or tax?
You added 15% and 6.5%. What would 21.5% mean in the context of the problem? 
Instructional Implications Assist the student in developing strategies for calculating percents of quantities. Review the meaning of percent and calculating the percent of a quantity using proportional reasoning. Emphasize the relationship between a percent and its ratio equivalent. Provide problems that include rational number percentages as well as whole number percentages. Use a tape diagram or double number line to help the student visualize the relationship among the part, the whole, the given percent, and 100%. Provide additional practice finding percent of a number in a variety of reallife contexts.
Be sure the student understands the difference between the sequence of commands used to calculate percents on some calculators (e.g., 53.52  15%) and the actual calculation [53.52  (0.15)(53.52)]. Model 10% of $1 using dimes and nickels. Then model 10% of $2, $3, and $4 using dimes and nickels. Have the student subtract 10% of $4 from $4 and discuss how this is different from subtracting 10 or 0.10 from 4. Then ask the student Â to explain why subtracting 15 from the cost of the meal is not the same as subtracting 15% of the cost.
Consider implementing CPALMS Lesson Plan Invest in Your Education (Percents) (ID 11127). 
Almost There 
Misconception/Error The student makes a computational or rounding error. 
Examples of Student Work at this Level The student has an effective overall strategy for solving the problem and understands how to calculate discounts and percents. However, the student:
 Makes a minor multiplication, subtraction, or addition error.
 Rounds the answer incorrectly.

Questions Eliciting Thinking I think you may have made a calculation error. Can you check your work to see if you can find it?
What are the conventions for rounding? To what place value should you round numbers that represent money? 
Instructional Implications Guide the student to locate and correct his or her error. Have the student exchange papers with other Almost There students to analyze each otherâ€™s original work and to determine and correct any errors. Provide additional opportunities to solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, decimals, and percents).
If needed, review conventions for rounding decimal numbers that represent amounts of money.
Consider implementing MFAS task Gas Station Equations (7.EE.2.3). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student determines that Brittany did not figure out the bill correctly. The student determines the correct bill to be $48.45. The student calculates:
 1.065[$53.52(0.85)]=$48.45,
 $53.52 (0.85) = x, then 1.065x = $48.45, or
 $53.52 $53.52(0.15) = x, then x + 0.065x = $48.45.
The student calculates the discounted price of the meal ($45.49) and determines that Brittany should not get a price lower than that after adding tax and, therefore, concludes that Brittany is wrong.

Questions Eliciting Thinking Can you think of another way to solve the problem?
If the coupon was for 5% off and the tax was 5%, would you expect the final price to be lower, higher, or equal to the original price? Why? 
Instructional Implications Challenge the student to write his or her own multistep realworld problem, write an equation that models the relationship in the problem, and solve the equation. Then, challenge the student to provide another approach to solving the problem (e.g., writing an alternate equation or proportion).
Consider using MFAS task Reeling in Expressions (7.EE.2.3). 