standard_description: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
problem_activity: Narrative
The purpose of this activity is for students to represent addition and subtraction equations on a number line. Students consider where to begin and in which direction to draw their arrows in order to accurately represent the operation in the given equation. Throughout the activity, encourage students to explain how they know their representation matches the equation. Listen for the way they explain how they know where to start and end their arrow, which direction they draw their arrow, and how they connect the length the jump represents to the equation (MP3).
MLR8 Discussion Supports.
Display sentence frames to support partner discussion: “Our number lines are the same because…”. “Our number lines are different because…”.
Advances:Speaking, Conversing
Launch
Groups of 2
“We have seen addition and subtraction equations represented on a number line. How can you tell whether a number line is representing addition or subtraction?” (Look at the direction of the arrow.)
30 seconds: quiet think time
Share responses.
Activity
“Now you are going to represent some equations on number lines. Be sure others will be able to tell from looking at your number line whether you are representing addition or subtraction.”
8 minutes: independent work time
Monitor for students who:
Mark the first number and last number in each equation with a point first. Then draw their arrow to match the operation.
Locate the first number in the equation, count a number of spaces forward or backward to match the operation, and draw an arrow to connect the two numbers.
“Compare your number lines with your partner. Explain how you know your representation matches the equation.”
3 minutes: partner discussion
Student Facing
Represent each equation on the number line.
\(15 + 7 = 22\)
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\(18 - 6 = 12\)
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\(46 + 7 = 53\)
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\(33 - 9 = 24\)
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Student Response
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Advancing Student Thinking
If a student's number line representation doesn't match the equation, consider asking:
“Will you please explain your representation?”
“How did you decide where to start or end on the number line?”
“How did you decide which direction to draw your arrow?”
Activity Synthesis
Display the equation and blank number line for
\(15 + 7 = 22\)
.
Invite previously selected students to share how they represented the equation on the number line.
Consider asking:
“How do you see each number in the equation in ____’s representation?”
“How do you know ___’s representation matches the operation (addition or subtraction)?”
As time permits, continue with the other equations.


aligns: no