Tens and Ones

Est. Class Sessions: 1

Developing the Lesson

The word partition is used in different, but related, ways in mathematics. A partition of a number is a way to write the number as the sum of whole numbers. For example, 12 = 10 + 2 is a partition of the number 12. A partition of a set is a way to divide it into separate parts. For example, 10 bits (one skinny) and 2 bits is a partition of the set of 12 bits. We will use the word in both situations as we work with base-ten pieces.

Partition 36. Begin the lesson with DPP Task B, which explores different ways to partition the number 36. Students write partitions that come up naturally with coins such as 36 = 25 + 10 + 1; a partition involving dozens, 36 = 12 + 12 + 12; and partitions into tens and ones such as 36 = 10 + 10 + 10 + 1 + 1 + 1 + 1 + 1 + 1 and 36 = 30 + 6. Explain that in this unit they will focus on partitions of a number that involve ones, tens, hundreds, and thousands.

Introduce the TIMS Candy Company. Use the Tens and Ones page in the Student Guide to set the context for partitioning numbers into tens and ones. The class is going to help the TIMS Candy Company investigate ways to package their chocolate candies. The candies are called Chocos. One individually wrapped Choco is called a bit (an individual cube). A box of ten bits is called a skinny.

In this lesson, students use connecting cubes to represent bits. They snap 10 cubes together to make skinnies. In subsequent lessons, they will use skinnies from base-ten sets.

Have students work in pairs and use connecting cubes to answer Questions 1 and 2. For Question 1, students represent the two packages of 10 Chocos with two stacks of 10 cubes and 16 single cubes. For Question 2, they will find that there are two more ways to package 36 Chocos as shown below:
1 skinny and 26 bits 36 = 10 + 26
3 skinnies and 6 bits 36 = 30 + 6

Ask pairs to do the following:

Use connecting cubes to show different ways to package 12 Chocos for the TIMS Candy Company.
(12 bits or 1 skinny and 2 bits)

Draw and display a table on the board to record this two ways. First show 12 bits as in Figure 1.

Demonstrate snapping the ten cubes together to make a skinny. Two bits remain. Record 1 skinny and 2 bits in the table as shown in Figure 2. Write the number sentence 12 = 10 + 2 to show the partition of 12 represented by the pieces.

Partition Numbers into Tens and Ones. Draw and display a table on the board. Ask students to help you complete the table as they describe their ways to package the Chocos. See Figure 3.

Ask:

Find different ways to package 26 Chocos.

Direct students' attention to the Packaging Sheets page in the Student Activity Book. The first sheet on the page has been completed for 26 Chocos.

Ask:

What partitions of 26 are represented in the table?
(26 = 20 + 6 and 26 = 10 + 16)

Ask students to work with a partner to find different ways to package other amounts of Chocos such as 17, 23, and 35 and to record them on the Packaging Sheets page. Allow them to use connecting cubes. As students work, discuss their ways to package the numbers, and ask them to tell a number sentence that describes one of the partitions. Write the number sentence on the board.

For example, ask:

Show me how you packaged 35 Chocos. (Possible response: 1 skinny and 25 bits)
How did you record that on the packaging sheet?
(I wrote a 1 in the first column of the table to show that I have 1 skinny or 1 group of 10, and 25 in the second column to show that I have 25 bits or ones.)
Show me a different way to package 35 Chocos. (Possible response: 2 skinnies and 15 bits or 3 skinnies and 5 bits.)
Write a number sentence to show 35 as 3 skinnies and 5 bits. (10 + 10 + 10 + 5)
What does [number] mean on your packaging sheet?

Pack 'Em Up. After they have explored several numbers, ask students to complete the Pack 'Em Up! pages in the Student Activity Book. In Questions 1–3, students simulate snapping bits together to make skinnies. In Questions 4–9, they explore different ways they can partition numbers into tens and ones.

After students have completed the questions, ask them to look back at the tables they completed for Professor Peabody in Questions 4–6.

Ask:

What do you notice about the numbers on the tables? (I see a pattern. The numbers in the bits columns go down by 10 and the numbers in the skinnies columns go up by 1.)
Why do you think this pattern exists on the tables? (Every time we group 10 bits together to make a skinny, we take 10 bits from that column and add 1 skinny to the skinny column.)
In Question 7, Maruta packaged 43 Chocos as 1 skinny and 33 bits and as 2 skinnies and 23 bits. Does 10 + 33 = 20 + 23? Show me with your connecting cubes. (Yes.)
For Question 8, show how you packaged 27 Chocos. (1 skinny and 17 bits and 2 skinnies and 7 bits)
Write number sentences showing these partitions.
(10 + 17 = 27 and 20 + 7 = 27)

Use Check-In: Question 9 on the Pack 'Em Up pages in the Student Activity Book to assess students' abilities to compose numbers into tens and ones [E2], show different partitions of numbers using connecting cubes and number sentences [E3], and recognize that different partitions of numbers have the same total (e.g., 10 + 35 = 40 + 5) [E4].

The Lesson 6 Workshop: Place Value provides targeted practice.

Student Guide: 70

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