Lesson 19

This warm-up prompts students to compare four different base-ten representations. It gives students a reason to use language precisely. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, especially as it relates to tens, ones, and the value of digits.

• 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.

• “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to create a collection of 65 using only 5 towers of 10 and single cubes. Students are told that they cannot physically create any new towers or take apart any towers. As students work, they recognize that there are only 5 tens and consider how many ones are needed to get to 65. Some students may count on from 50 to 65 and other students may apply what they have learned in previous lessons to determine they need 1 more ten and 5 more ones, or 15 (MP2). As students represent their collection, they may show the number of towers of 10 they used and how many ones, including 5 tens and 15 ones, or that they grouped 10 of the ones in some way. This includes clearly marking a group of 10 ones.

Students may label their drawings using numbers, a combination of numbers and words, or expressions (MP6).

• Each group of 3-4 needs a bag of connecting cubes in 5 towers of 10 and 4 or 5 handfuls of singles.

• Groups of 3–4
• Give each group one bag of connecting cubes.

• Read the task statement.
• 10 minutes: partner work time
• As students work, consider asking:
  • “How did you organize your count?”
  • “How will you show how you organized and counted?”
• Monitor for students who represent the count as 5 tens and 15 ones in different ways.

If students start counting the ones and are not sure what to do when they do not have enough, consider asking:

• “Tell me more about how you are planning to make 65.”
• “How can we use the towers of 10 to help us make 65?”

• Invite previously identified students to share.
• “How do each of these representations show 65? How are these representations the same? How are they different?” (They all show some tens and some ones. One shows 15 ones and the other shows 10 ones in a group and then 5 more ones. One shows an expression and the others don't.)

The purpose of this activity is for students to represent 37 with tens and ones in different ways. It is not necessary that students find all the ways to represent 37, rather that they see that the number can be represented with different amounts of tens and ones. Students are given connecting cubes in towers of 10 and singles, and they represent their thinking on paper using drawings, numbers, or words. Some students may initially represent 37 using 3 tens and 7 ones and then notice that they can decompose a tower of 10 into 10 singles and have 2 tens and 17 ones and use this structure to find other ways. Students may represent 37 as \(36 + 1\), \(35 + 2\), etc., which are all valid ways to represent the number. The lesson synthesis focuses on representing 37 with different groups of tens and ones.

• Groups of 2
• Give each group connecting cubes in towers of 10 and singles.
• “We just saw that we can make 65 without using six tens. Now you are going to find different ways to make the number 37. Find as many different ways as you can with the connecting cubes. Then show each different way with drawings, numbers, or words.”

• 2 minutes: quiet think time
• 5–6 minutes: partner work time
• Monitor for students who strategically find different ways to compose 37 using towers of 10 and singles including:
  • Start with 3 tens and 7 ones, and decompose each tower of 10 into singles.
  • Start with 37 ones and then compose towers of 10.

• Invite previously identified students to share.
• Record each way students made 37.
• “What do you notice about the ways they made 37?” (They both made 37 in the same ways. One student started with all ones and made one ten at a time. The other student started with 3 tens and broke one ten apart at a time. Each time a ten was made, there were 10 fewer ones. Each time a 10 was broken apart, there were 10 more ones.)

The purpose of this activity is for students to choose from activities that offer practice working with two-digit numbers. 

• Greatest of Them All
• Get Your Numbers in Order
• Grab and Count

• Gather materials from previous centers:
  • Greatest of Them All, Stage 1
  • Get Your Numbers in Order, Stage 1
  • Grab and Count, Stage 2

• Groups of 2
• “Now you are going to choose from centers we have already learned.”
• Display the center choices in the student book.
• “Think about what you would like to do.”
• 30 seconds: quiet think time

• Invite students to work at the center of their choice.
• 10 minutes: center work time

• “How did you work with two-digit numbers during center time?”