Getting Started 
Misconception/Error The student is unable to interpret one or both parts of the expression. 
Examples of Student Work at this Level The student:
 Interprets the parts of the coefficient as amounts of money.
 Correctly interprets 0.075 but misinterprets 1.

Questions Eliciting Thinking If you went into a store to purchase a clothing item priced at $20, would you be able to pay with just a $20 dollar bill? Why or why not?
How is the sales tax you pay on your purchases calculated?
If you spend $10 on an item and the rate of tax is 5%, how would the total cost of your purchase be calculated? 
Instructional Implications Introduce the student to the concept of sales tax and how it is typically described (i.e., as a rate or percent of a purchase). Review how to calculate the percent of a quantity by converting the percent to a decimal and multiplying [e.g., 5% of 10 is equal to 0.05(10)]. Model for the student the calculation of sales tax given a 5% rate and the total purchase price of an item that costs $10. Guide the student to observe that the equation T = x + 0.05x where x is the pretax cost of the purchase (or subtotal) can be used to calculate the total cost of a purchase. Be sure the student understands what each part of the expression x + 0.05x contributes to the total cost. Then, make the coefficient of x explicit and transform the expression 1x + 0.05x to (1 + 0.05)x and finally to 1.05x. Relate the â€ś1â€ť and the â€ś0.05â€ť to the coefficients of x in the original expression x + 0.05x and describe these values as decimal versions of percents. Explain that 1.05 represents 105% and 1.05x represents 105% of x, the pretax cost of the purchase. Ask the student to apply these ideas to the interpretation of the â€ś1â€ť and â€ś0.075â€ť in the equation T = 1.075x.
Provide additional opportunities for the student to interpret parts of expressions used to calculate quantities in context. 
Making Progress 
Misconception/Error The student is unable to clearly and completely interpret the parts of the formula in the context of the problem. 
Examples of Student Work at this Level The student understands that the â€ś1â€ť relates to the cost of the clothing and the â€ś.075â€ť relates to the sales tax. However, the student does not make explicit that each is a rate that multiplies the purchase price to get the total cost of the clothing and the dollar amount of the tax.

Questions Eliciting Thinking You said the â€ś1â€ť represents the clothing cost. Does that mean the clothing cost is $1?
You said the â€ś0.075â€ť represents the sales tax. Does that mean the sales tax is $0.075? 
Instructional Implications Guide the student to observe that the equation T = x + 0.075x where x is the pretax cost of the purchase (or subtotal) can be used to calculate the total cost of a purchase. Be sure the student understands what each part of the expression x + 0.075x contributes to the total cost. Then, make the coefficient of x explicit and transform the expression 1x + 0.075x to (1 + 0.075)x and finally to 1.075x. Relate the â€ś1â€ť and the â€ś0.075â€ť to the coefficients of x in the original expression x + 0.075x and describe these values as decimal versions of percents. Explain that 1.075 represents 107.5% and 1.075x represents 107.5% of x, the pretax cost of the purchase.
Provide additional opportunities for the student to interpret parts of expressions used to calculate quantities in context. 
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 explains that the â€ś1â€ť represents 100%, so when it multiplies x, the pretax cost of Cindy's purchase, the result is the pretax cost of Cindy's purchase. The â€ś0.075â€ť represents the rate of tax, 7.5%, so when it multiplies x, the result is the dollar amount of tax. The student may also explain that multiplying x by 1.075 results in the total cost of Cindy's purchase. 
Questions Eliciting Thinking Why did the 1 and the 0.075 get combined into 1.075 in the formula? What does 1.075x represent in this problem? 
Instructional Implications Ask the student to consider the equation T = x + 0.075x as an alternative to T = 1.075x and to explain each term in this expression. Then ask the student to show how the two expressions are equivalent.
Consider implementing MFAS tasks Dot Expressions (ASSE.1.1) and What Happens? (ASSE.1.1). 