Lesson 13

This warm-up prompts students to consider data representations, which they worked with in a previous unit. When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first use less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses. 

• “What could the title of this diagram be?”

The purpose of this activity is for students to determine whether comparison statements about data are true or false and explain how they know. Students build on their work with asking and answering how many in all questions about data and their work with solving Compare story problems.

Students may use matching techniques to compare the physical data using objects and drawings. Students explain how they know whether the statements are true or false.

It is important to revoice student responses in which students use the word "less" instead of "fewer." For example, revoice "There are less students who chose crayons" as "There are fewer students who chose crayons."

• Groups of 2
• Give students access to connecting cubes or two-color counters.

• Read the task statement.
• “Priya and Han made some statements about their data. Your job is to decide whether you agree or disagree. Once you decide, circle it on your paper." 
• 3 minutes: independent work time
• “Now, explain to your partner how you know.”
• 3 minutes: partner discussion
• Monitor for two students who solve and represent problem 3 in different ways.

If students identify how many voted for each category, but label true statements as false, or false statements as true, consider asking:

• "How can you tell how many students voted for (crayons, paint, markers)?"
• "How could you use connecting cubes to compare the categories?"

• Invite previously identified students to share.
• “How are these representations the same? How are they different?”
• “What equation can I write to match their work?” (\(5 + 3 = 8\), \(8 - 5 = 3\))
• “How does each equation relate to the statement?” (Five is the number of votes for crayons, and then adding 3 shows the difference between crayons and markers; if you start with the number for markers and take away how many voted for crayons, you see that it is 3 fewer votes.)
• If needed, ask, “Which part of this equation represents the answer to the problem?”
• Draw a box around the 3.

The purpose of this activity is for students to solve Compare, Difference Unknown problems about data that include the language, “more” and “fewer”. Students write equations that match the story problems. They may use matching techniques to compare the data using objects and drawings, and during the synthesis, explore how to see the difference in a drawing and relate it to addition and subtraction equations (MP2). Students may want to tear out the page in their book with the data, so they can have it more readily available while working on each problem.  

• Groups of 2
• Give students access to connecting cubes or two-color counters.
• Display Favorite Art Supply data (do not include the problems).
• “What questions might you ask about this data?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

• Read the task statement.
• "Now you are going to answer some questions about the data."
• 5 minutes: independent work time
• “Share your thinking with a partner.”
• 5 minutes: partner discussion

• Display, 'How many more students voted for crayons than markers?'
• “We know that ten students voted for crayons and six students voted for markers. Let’s represent these votes using letters.”
• Record:

  

  

• “C stands for the number of votes for crayons and M stands for the number of votes for markers. How many more votes for crayons are there? How do you know?” (4. I can see that there are 4 extra Cs.)
• “What equations can we write?” (\(6 + \boxed{4} = 10\) or \(10- 6=\boxed{4}\))
• If needed, write \(10 - 6=\boxed{4}\).
• “What number in each equation represents the answer?” (4)
• “When you compare two numbers you find the difference. Each of these equations helped us find the difference. The difference between the number of students who voted for crayons and those who voted for markers is four."