options: 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.

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

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.

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.

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

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

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

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.

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.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Narrative
The purpose of this activity is for students to use a bar graph to compare two quantities and describe the methods they use to find the unknown difference. Monitor for students who draw on the graph and describe ways of finding the difference by counting on or counting back. If students draw on their graph or do not discuss both counting methods during the activity, create and display work so that each method can be discussed during the synthesis. The discrete segments of the bar graph are used to elicit these counting methods (MP5), however, some students may use addition or subtraction, including known sums, to find the difference. Encourage these students to connect their methods to the counting methods shared in the synthesis.
MLR8 Discussion Supports.
Provide all students with an opportunity to speak and to practice using comparison statements. Invite students to chorally repeat statements that use “more” and “fewer” in unison 1–2 times.
Advances: Speaking, Listening
Launch
Groups of 2
Display the image (graph with no scale).
“A group of third grade students were asked, ‘What pets do you have?’ Their responses are shown in the bar graph."
"What do you notice about the data in the graph? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Monitor for students to say: “More students have cats than have rabbits,” or wonder, “How many more students have cats than have rabbits?”
Share and record student responses.
If students do not make statements using “more” or “fewer,” display:
“There are more _____ than _____.”
“There are fewer _____ than _____.”
“How could you complete the sentences to make them true statements about the graph?”
1 minute: quiet think time
1 minute: partner discussion
Share responses.
Activity
“You noticed that more students have cats than have rabbits. Your job now is to figure out how many more students have cats than have rabbits. Think about two different ways you can find the answer and record them.”
3–4 minutes: independent work time
2–3 minutes: partner discussion
Monitor for a student who uses a counting on method and a student who uses a counting back method.
Student Facing
A group of third grade students were asked, "What pets do you have?" Their responses are shown in the bar graph.
What do you notice? What do you wonder?
[IMG]
Their responses are also shown in this bar graph.
[IMG]
How many more students have cats than have rabbits? Show two ways to find the difference.
Student Response
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Activity Synthesis
Invite previously identified students to share how they found the difference. If methods are only explained verbally, consider asking, “Can you show us on the bar graph how you could count on (or count back) to find how many more?”
Record student methods with an equation. For example, for students who describe counting on, write “8 + 9 = 17.”
"How are their methods similar? How are their methods different?" (One method starts with the smaller number of pets and counts on to the larger number, like adding 9 more. The other starts with the larger number of pets and counts back to the smaller number, like subtracting 9.)


correct_option_index: 9