standard_description: Solve quadratic equations with real coefficients that have complex solutions.
problem_activity: Narrative
The purpose of this activity is for students to use what they know about counting within 1,000 to make sense of number lines that show counting on or counting back by 10 or 100. This work helps build fluency with counting within 1,000 and connects to an upcoming lesson where students add and subtract multiples of 10 or 100 using equations.
MLR8 Discussion Supports.
Invite students to begin partner interactions by repeating the question, “What pattern do you notice?” This gives both students an opportunity to produce language.
Advances: Conversing
Launch
Groups of 2
Display the number line with jumps of 100.
“On this number line there are 5 tick marks, but only 3 are labeled. What are the missing numbers and how do you know?” (534 and 634 because the jumps are the same length and they must be jumps of 100. The hundreds place is increasing by 1, but the other places are not changing.)
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
“You recognized that the length between each tick mark must represent 100. The tick marks and arrows show counting on by 100 on the number line.”
Activity
“For each of the problems, use what you know about counting, representing numbers on the number line, and place value to find the missing numbers.”
10 minutes: partner work time
Monitor for a student to share their reasoning for _____, _____, 332, 342, 352
Student Facing
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Fill in the missing numbers.
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Does this number line show counting on by 10 or counting on by 100?
Fill in the missing numbers.
[IMG]
Does this number line show counting on by 10 or counting on by 100?
Fill in the missing numbers.
[IMG]
Does this number line show counting on by 10 or counting on by 100?
Fill in the missing numbers to show counting on by 10.
739, 749, __________, 769, __________
Explain how you can tell your numbers show counting on by 10 and not counting on by 100.
Student Response
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Advancing Student Thinking
If students find the missing numbers by counting by 1 instead of using patterns increasing by 10 or 100, consider asking:
“What digit is changing? Is it going up or down?”
“How can that help you figure out the count?”
Activity Synthesis
Invite a student to share their reasoning for _____, _____, 332, 342, 352.
“How did you figure out the starting number?” (I saw that it was going up by 10, so I knew I had to count back by 10 to find the starting numbers.)
Record responses with an open number line and equations.


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