Lesson 13

The purpose of this warm-up is to activate students’ previous experiences in which they looked for ways to make a ten—specifically, when one addend is 9. The ability to make a ten will help students develop fluency within 20 and will be helpful later in this lesson and in upcoming lessons when students add and subtract within 20.

When students look for ways to make a ten and notice similarities in the addends and values in each of the expressions, they look for and make use of the structure of whole numbers and the properties of operations (MP7).

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

• Share and record answers and strategy.
• Repeat with each statement.

• "How can you justify your answer without adding?" (I see that 9 + 4 and 9 + 1 + 3 are the same because 1 + 3 = 4.)

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.

• 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.

• “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.

• 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.)

The purpose of this activity is for students to use graphs to make comparison statements and solve Compare problems. Students represent their comparisons with equations. In the synthesis, students connect the graph, their comparison statements, and their equations.

When students describe how they see their equations in the graph and how their equations relate to the context, they think abstractly and quantitatively (MP2).

• Groups of 2
• Display the Dogs in the Park graph.
• “What statement can you make that compares the number of huskies to the number of bulldogs?” (There are more bulldogs than huskies. There are fewer huskies than bulldogs. There are 6 more bulldogs than huskies.)
• 1 minute: partner discussion
• 1 minute: whole-class discussion
• Share statements that use “more” and “fewer.”

• “Now you are going to write some statements using ‘more’ and ‘fewer’ and write equations to show how to find the difference.”
• 5 minutes: independent work time
• “Now check with your partner. Are their statements true?”
• 3 minutes: partner discussion
• Monitor for different equations students use for each comparison.

If students write statements that are not true, consider asking:

• "How did you decide which group had fewer?"
• "Where do you see this on the graph?"

• Invite 1–2 previously identified students to share their statements using fewer and one equation. (Sample response: There are fewer pugs than bulldogs. There are 12 fewer. 8 + 12 = 20)
• Record equation.
• “What other equations could we write to show how many fewer for _____’s statement?” (Sample response: We could use subtraction. 20 – 12 = 8 shows you can count back 12 from 20 to get to 8.)  
• Record equations.
• For each equation, ask, “What does each number represent in the equation?” (20 represents the number of bulldogs. 8 represents the number of pugs. 12 represents how many fewer pugs.)