options: Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
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
[IMG]
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.
[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.


correct_option_index: 1