Lesson 1

This warm-up prompts students to carefully analyze and compare features of different representations of two-digit numbers. When they share their comparisons, listen for the vocabulary they use to talk about the characteristics of tape diagrams, bar graphs, and base-ten diagrams and provide them opportunities to clarify their meaning (MP6).

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “How does each representation show the difference between cloudy and sunny days?” (C maybe shows the difference with blocks. If the top train of blocks is sunny days, you can see there are more sunny days. B shows it with a tape diagram, the part with the question mark shows the difference. D uses a bar graph. You can see sunny days has more than cloudy days and you could count the number of spaces they are apart. A shows with blocks too, but they are in towers of ten and single cubes. You can see sunny days has ten more.)

The purpose of this activity is for students to compare different methods for solving problems within 100 using data presented in a bar graph. Students may use whatever method makes the most sense to them. The synthesis focuses on sharing multiple methods that students use to find the difference. Monitor for students who use methods that rely on using the bar graph to count on or count back and those that use more abstract methods, such as adding or subtracting by place value.

For example, when combining categories, some students may choose to use the graph to count on. Other students may choose to combine tens and ones with or without drawing a base-ten diagram or other representation.

• Create towers of 10 with the connecting cubes.
• Have single connecting cubes available.

• Groups of 2
• Display the bar graph.
• “What does this graph tell us?” (students’ favorite movie snacks, students picked their favorite movie snacks)
• 1 minute: quiet think time
• 1 minuter: partner discussion
• Share responses.
• Give students access to connecting cubes in towers of ten and singles.

• “Use the bar graph to answer the questions. Show your thinking using drawings, numbers, or words.”
• “You can use the connecting cubes or any of the other representations we saw in the warm-up to help you.” 
• 8 minutes: independent work time
• “Now compare your methods with your partner. How are they similar or different?”
• 4 minutes: partner discussion
• As students work, monitor for students who:
  • use the bar graph to count on or count back
  • use the connecting cubes or base-ten drawings to show adding or subtracting tens with tens and ones with ones

• Invite previously identified students to share the method they used to find how many more students chose nachos than chose popcorn.
• As needed, record student methods using equations.
• Consider asking:
  • “How are these methods the same? How are they different?”
  • “How does the method work? Why does each method find the same value?”

The purpose of this activity is for students to solve Compare problems within 100 using methods based on place value and the relationship between addition and subtraction. Connecting cubes are used as a representation in this activity to support students in their transition from subtraction methods based on counting on or counting back by one to methods based on subtracting tens from tens and ones from ones. Students build trains out of towers of 10 and single connecting cubes. Invite students to use the methods that make the most sense to them when they work to find the difference. Monitor for students who use blocks or other representations to show adding or subtracting tens and tens and ones and ones to share in the synthesis.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• Create towers of 10 with the connecting cubes.
• Have single connecting cubes available.

• Groups of 2 
• Assign Partner A and Partner B.
• Give students access to towers of ten and loose connecting cubes.
• Display the image of the cubes.
• “What do you notice? What do you wonder?” (Lin has more cubes. They have 40 cubes all together. Lin has ten more cubes.)
• Monitor for students who notice the groups of ten cubes and use this structure to find the total number of cubes or the difference.
• 30 seconds: quiet think time
• Share responses.

• “You and your partner will each build a train with connecting cubes. Then, answer the questions about your trains.”
• “Show your thinking using drawings, numbers, or words.”
• 8 minutes: partner work time
• Monitor for students who:
  • count on or combine tens and ones to find the difference
  • count back or separate tens and ones to find the difference

• “How did you choose which blocks to use when you built your number?”
• “How could you use the towers of 10 to build your number?”

MLR7 Compare and Connect

• “Create a visual display that shows your thinking about the difference between the number of cubes you and your partner used. You may want to include details such as diagrams, drawings, and labels to help others understand your thinking.”
• 5–7 minutes: gallery walk 
• Invite previously identified students to share their methods for finding the difference using cubes. 
• “What is the same and what is different between the way these two groups found the difference?” (Both groups found the same value. One group shows adding on tens and ones. The other group shows taking away tens and ones.)
• 30 seconds quiet think time
• 1 minute: partner discussion
• If time, consider asking:
  • “What other methods did you see groups use? How are they the same and how are they different from these two methods?” (Other groups added on and subtracted to, but they showed it with different diagrams and drawings. Some used only equations. Some showed counting by ones.)