Getting Started 
Misconception/Error The student uses incorrect strategies to multiply rational numbers. 
Examples of Student Work at this Level The student multiplies mixed numbers by multiplying all the whole numbers then multiplying all the fraction parts.
The student completes calculations by working from left to right rather than using the correct order of operations.
The student rewrites fractions with common denominators instead of multiplying them.

Questions Eliciting Thinking How do you multiply fractions?
How do you multiply mixed numbers?
What steps did you use to multiply the mixed numbers? Are there any other steps you should take when multiplying mixed numbers?
In what order did you do your operations for #2? How should you decide which order to do operations in when there are several in a problem? What is the correct order of operations? 
Instructional Implications Review multiplication of fractions and mixed numbers. Guide the student to interpret mixed numbers such as Â as sums, e.g., . Then review the Distributive Property and apply it to multiplying mixed numbers by whole numbers (e.g., ). Next use the Distributive Property to multiply mixed numbers by mixed numbers (e.g., rewrite Â as ). Then rewrite the expression by applying the Distributive Property (e.g., ). Continue using the Distributive Property to complete the calculation.
Review other properties such as the Commutative Properties, the Associative Properties, the Additive and Multiplicative Inverse Properties and guide the student to look for opportunities to use these properties as strategies for adding, subtracting, multiplying, and dividing rational numbers. Provide examples in which these properties have been employed and ask the student to identify the use of the properties. 
Moving Forward 
Misconception/Error The student evaluates the expressions using order of operations rather than properties. 
Examples of Student Work at this Level The student evaluates the expressions using order of operations rather than properties. The student may make a minor error.

Questions Eliciting Thinking You did a good job using order of operations, but can you think of any properties of operations that you could have used to make your work easier?
What properties do you remember? How does each one work?
Can you read through your problem to look for any math errors? 
Instructional Implications Show the student how properties of operations could have been used to complete the two problems on the worksheet. Review other properties of operations and guide the student to look for opportunities to use these properties as strategies for adding, subtracting, multiplying, and dividing rational numbers. Provide examples in which these properties have been employed and ask the student to identify the use of the properties. 
Almost There 
Misconception/Error The student uses properties of operations as the strategy to multiply rational numbers but is unable to identify the use of properties in his or her work. 
Examples of Student Work at this Level The student demonstrates the use of the properties but is unable to identify the properties used. The student:
 Rearranges the factors in #1Â to multiply Â before multiplying by the factor .
 Factors out a seven from each term in #2Â before adding the mixed numbers.

Questions Eliciting Thinking How did you rearrange the expression you wrote in your work? How do you know you can change it like that?
What is it called to rearrange/regroup the factors?
Why did you factor out the seven? What property ensures that the answer will be the same as that of the original expression when you use this strategy? 
Instructional Implications Identify the properties of operations used by the student in his or her work. Provide examples in which these properties have been employed and ask the student to identify the use of the properties. Pair the student with a Got It student to compare answers and reconcile differences. 
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 correctly rewrites Â as Â and finds the product of Â and 3 mentally. The student correctly finds the product of 4Â and Â and indicates a use of the Commutative and Associative Properties to reorder and regroup the factors to get an answer of 10.
The student rewrites Â as Â and correctly completes the calculation by mentally adding Â and Â and then multiplying the sum by 7 getting a final answer of 42. The student indicates having used the Distributive Property. 
Questions Eliciting Thinking Can these properties be used with all kinds of numbers (e.g., whole numbers, integers, rational numbers, and irrational numbers)?
Is there a Commutative Property of Subtraction? Why or why not?
Is there a Commutative Property of Division? Why or why not? 
Instructional Implications Ask the student to make a comprehensive list of properties of operations that includes explanations and examples. Provide an opportunity for the student to copy and share the list with classmates. Consider using other MFAS tasks related to multiplication and division of rational numbers from 7.NS.1.2 as well as tasks with rational number addition and subtraction in 7.NS.1.1. 