The purpose of this activity is for students to subtract a fraction or a mixed number from a mixed number. There are multiple strategies available, and the differences are selected in order to highlight these strategies:

• Subtracting the whole-number parts and fraction parts of the numbers separately. 
• Rewriting the mixed number to facilitate subtraction.
• Adding on to find the difference.

In each case, students will need to choose a common denominator in their calculation. Students first identify expressions that are equivalent to the mixed number that appears in all of the differences they calculate. These expressions are deliberately chosen to support the listed techniques to find the values of the subtraction expressions. The goal of the Activity Synthesis is to compare and connect several different strategies and to consider the benefits and the challenges of each strategy.

When students adapt their subtraction strategy to the numbers, they look for and make use of structure (MP7).

This activity uses MLR7 Compare and Connect. Advances: conversing.

• “What is the same and what is different between the strategies?” (Some people added on or used a number line. Some people changed the mixed number to a whole number plus a fraction greater than 1. Some people changed the mixed number to a fraction. Some people got different, equivalent answers.)
• Display:
• “How do we know this is true?” (There are 8 eighths in 1, so I can break up the 3 as 2 and 1 and put the 1 with the to make .)
• Invite previously selected students to share how they found the value of .
• “How was rewriting as helpful in this calculation?” (I could take 1 from 2 and then rewrite  as  and take that away from from .)
• Invite previously selected students to share how they found the value of .
• “Why did you decide to use that strategy?” (I noticed that was really close to 1 so it was easy for me to count up.) 
• “How was rewriting as helpful in this calculation?” (I needed to add one-sixteenth to get to 2 and it’s easy to combine sixteenths and sixteenths.)
• “We are going to find the values of more differences of mixed numbers and fractions in the next activity.”
• Keep displays available for students to refer to during Activity 2.

The purpose of this activity is for students to find the values of differences of mixed numbers. The numbers are chosen to encourage a variety of strategies that were highlighted in the previous activity. Students should be encouraged to find the differences in a way that makes sense to them. This may mean choosing a different strategy, depending on the problem, but it also could mean writing each difference as a difference of fractions and then finding a common denominator. 

Action and Expression: Internalize Executive Functions. Invite students to verbalize their strategy for finding the difference of each expression before they begin. Students can speak quietly to themselves, or share with a partner.
Supports accessibility for: Organization, Conceptual Processing, Language

• Ask previously selected students to share in the given order.
• “Why did you decide to add on to ?” ( is really close to 1.)
• “Can you also subtract in two steps to find the value of ?” (Yes, I can subtract from to get 9 and then take away more to get . That’s the same idea as adding on.)
• “Why did you decide to use instead of ?” (It is easy to subtract  from .)