The purpose of this activity is for students to describe how representations of subtraction on the number line show the difference between two numbers in different ways. The number choices in the activity encourage students to use methods based on taking away or counting back that may be represented as a jump to the left from the greater number. Other number choices encourage students to consider methods that show their understanding of subtraction as an unknown addend problem. Students may start at the lesser addend and find the length of the jump to the right to reach the total.

Students may also place both known numbers on the number line and find the length of the space between them by counting on from the lesser number to the greater number or by counting back from the greater number to the lesser number. Monitor for each strategy and the ways students represent them on the number line. All of these strategies show an important understanding of numbers and operations and how they can be represented on a number line (MP7).

The Synthesis focuses on describing and comparing how the difference is represented on the number line. If a student uses a method that would be difficult to represent on the number line, pair the student with another student who uses a conceptually similar method. For example, if a student finds the value of as , , , acknowledge the method would be hard to show on a single number line, and partner them with someone who shows jumps to the left on the number line based on place to compare methods.

• Invite previously identified students to share their response and reasoning for or draw the number lines and select the identified students to share their reasoning.

• “Both of these number lines show strategies for finding ”
• If it does not come up when students share, ask:
  • “Which representation shows subtraction as taking away?”
  • “Which representation shows subtraction as finding an unknown addend?”
• “How do both representations show the difference?” (In the first number line, the arrow is pointing to the difference. In the second one, the total length of the jumps shows the difference.)
• As needed, gesture and restate student responses to emphasize how the difference is represented as a length in each representation.
• “When we show subtraction as taking away on the number line, the difference is the number the last arrow points to. It’s represented as a length from 0 to where the arrow is pointing.”
• “When we show subtraction as an unknown addend problem on the number line, the difference is shown as the length of the space between the two numbers.”

The purpose of this activity is for students to compare methods for solving subtraction problems. Students compare representations of methods that show subtraction as taking away and those that show subtraction as an unknown addend problem. Students discuss how some representations may better show the actions in a problem and others may show a different way to find the unknown value (MP2). In the Synthesis, students consider how to select a strategy based on the numbers in the problem.

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

• Invite students to share responses and reasoning for Elena’s string.
• Invite previously identified students to share their thinking and number lines for Han’s string.
• If it doesn’t come up, show how you could locate the 85 and 87 on the number line and find the difference.
• “Which method would you prefer to use to solve Elena’s string problem? Why?” (I prefer taking away 33 because it matches the story. I prefer adding on from 33 because I know I could add tens and ones and not have to compose or decompose a ten.)
• “Which method would you prefer to use for Han’s string problem? Why?” (I prefer finding the unknown addend because the numbers are so close together. That means the difference is small.)