Subtracting Fractions Justifications

Explicit Instruction/Teacher modeling

• Model the importance of changing denominators so they are alike, using bar models or a number line. Use the fraction from the board that does not belong with the other problems to model finding the least common denominator and then subtracting the fraction.
• Show students what the answer would be if you not found the common denominator, using bar models or number lines to represent the fractions.
• Use sequencing terms while you model explaining the process you used to subtract the fractions (i.e., explain your answer) and write the process on the board. Some phrases may include:
  • "First, I ____."
  • "After I ____, I ____."
  • "Then, I ____."
  • "My next step was ____."
• Have an advanced EL with a good understanding of the academic content restate the process you used to solve the subtraction problem to help explain their answer.

Guided Practice

• Assign students a new subtraction problem they can complete in pairs (e.g., ⁵⁄₇ − ³⁄₈) on the back of the Refine Your Justifications! worksheet. After they've finished the problem, have the same partners explain their answers to each other using whichever vocabulary and phrases they choose and write their explanations down in their the 1st Explanation section of the front page.
• Listen for student conversations and write their explanations on the Formative Assessment: Peer Persuasion Checklist.
• Share two student explanations: one that needs improvement and another one that has good sequence words and key vocabulary (e.g., "common denominator," etc.).
• Ask students to share aloud which explanation is more convincing. Based on the students ideas about the two example explanations, write some of the improvements students will make to their explanations to guide their next conversation.
• Lead them to understand that they may need more examples and that they may need to explain their thinking more than in their first explanation.

Group work time

• Use the example from the explicit teaching section to model explaining what you know and how you know it. For example, "I know that the two denominators need to be the same because we need to have the same size piece to take away the right portion during a subtraction problem. I know this because of the bar models I drew to show the correct sizes of the fractional pieces."
• Tell students they will now refine their explanations with more evidence to support their answers in the Refine Your Justifications! worksheet in the 2nd Explanation section. Explain they will answer the following question: "What do you know about the problem and how do you know it?" Possible sentence frames can include, "I know that ____," and "I know this because ____."
• Have advanced ELs with a good understanding of the academic content restate what they know and how they know it about their subtraction problem. Model asking questions about a student's answer. For example, "Why wouldn't you do ____?" or "How can you know ____?" or "What else do you know that makes you sure you know the answer?"
• Assign students the 3rd Explanation section where they rewrite their explanation of their answer for the last time. Remind them to consider the necessary evidence (e.g., bar models, number lines, non-examples, etc.) to support questioning from their peers.