Hundreds, Tens, and Ones

Est. Class Sessions: 2

Developing the Lesson

Part 1. Group Chocos by 100s, 10s, and 1s

You may be tempted to refer to the bits as ones, skinnies as tens, flats as hundreds, and packs as thousands. However, when studying decimals in later grades, the same blocks will be used to represent parts of a whole. For example, the flat can be the unit. Then the skinny is .1 (one-tenth) and the bit is .01 (one-hundredth).

Trade Bits for Skinnies. Remind students of the TIMS Candy Company. This imaginary company is producing many more Chocos and has decided to use a more efficient set of blocks to keep track of them.

Distribute 50 bits (1 cm × 1 cm × 1 cm blocks), and 30 skinnies (1 cm × 1 cm × 10 cm blocks) per student pair. Tell students the bits will represent the individual Chocos, just as the connecting cubes did. The new set has a block to represent ten cubes already snapped together. This block is called a skinny.

Working with base-ten pieces differs from working with connecting cubes in that students must trade pieces instead of snapping cubes together. Explain that whenever students have ten bits, they can exchange them for one skinny.

If students keep the base-ten pieces that are not being used in a box or separate area, it will help them better organize their trading. When they have 10 bits, they can place them in the box and remove 1 skinny. Similarly, 1 skinny can be exchanged for 10 bits.

Ask:

Line up the bits beside the skinnies. Count the bits marked on the skinnies. How many bits are in one skinny? (10)

Display 24 bits and remind students that when they trade 10 bits for 1 skinny, they must be sure to take away the bits.

Ask them to model problems with bits and skinnies as you call them out.

For example:

Eric made 24 Chocos. Show this amount by counting out 24 bits.

Distribute copies of the Base-Ten Recording Sheets 1 Master. Record 24 bits on a display of the Base-Ten Recording Sheet Master. See Figure 1. Students should also record it on their recording sheets.

Ask:

Are there other ways to show twenty-four? Work in pairs to find different ways to package 24 Chocos. (Twenty-four bits can be shown as 1 skinny and 14 bits or as 2 skinnies and 4 bits.)

Ask a student to model these amounts for the class and demonstrate trading 10 bits for 1 skinny. Have students record each model and write number sentences to show the partitions on their recording sheets. See Figure 1.

Ask volunteers to name other two-digit numbers and have students show them with their base-ten pieces.

For example, display 5 skinnies and 6 bits and ask:

Show this amount in as many ways as you can. Record the partitions on a base-ten recording sheet.

Observe students as they make trades and model different partitions of each number. Figure 2 shows six possible partitions of 56. Students can record them in any order, and it is not essential for every student to find all the partitions. They should write number sentences to show their partitions.

Play Make a Flat. Distribute 1 flat (1 cm × 10 cm × 10 cm blocks) to each student.

Ask:

How many skinnies fit side-by-side on a flat? (10)
How many bits make a flat? (100) How do you know? (Each skinny has 10 bits. Counting bits by tens, 10, 20, 30 … gives 100 bits.)

Students will play Make a Flat to reinforce the concept that they can trade 10 bits for one skinny and that there are 10 skinnies in a flat. Ask students to follow the game directions on the Make a Flat pages in the Student Activity Book as you demonstrate several rounds with a Make a Flat Game Board display. In this game, students spin to determine a number of bits and skinnies (ones and tens) to place on their Make a Flat Game Board. The first player to fill a flat is the winner.

Organize pairs to play Make a Flat. Each student should have 20 bits, 20 skinnies, and 1 flat to ensure that students make frequent trades.

After students have played several rounds of the game, ask:

How did you know what your “Running Total” was? Did you have to count by ones? (I just counted the number of skinnies on my game board and the number of bits. Four skinnies and 3 bits left over means 43.)

Distribute the remaining flats so that student pairs have 14. Pose several questions that ask students to find equivalent representations of numbers with base-ten pieces.

For example, ask:

How many flats can be made from 21 skinnies? (2 flats with 1 skinny left over)
How many bits are in 21 skinnies? (210) How do you know? (I counted by tens. Or, there are two flats, each flat has 100 and ten bits left over. I know that 100 + 100 + 10 = 210 bits.)
Work with your partner and use your base-ten pieces. What number is represented by:
22 skinnies and 6 bits? (226)
7 skinnies and 28 bits? (98)
17 skinnies and 4 bits? (174)
7 flats, 18 skinnies, and 19 bits? (899)
How many skinnies are in 4 flats? (40)