Look at Flats

Estimated Class Sessions: 1–2

Developing the Lesson

Introduce Flats. Distribute 3–5 flats, about 20 skinnies, and 21 bits to each student pair. Holding up a flat, tell students this is another base-ten piece to be used with skinnies and bits. It stands for 100.

Ask:

How many skinnies will cover (fit side-by-side on) a flat? (10)

Ask student pairs to completely cover the flat with skinnies (one layer only) to confirm their conjectures.

Ask:

If you want to trade in skinnies, how many would you need to trade for a flat? (10)
How many bits do you need to trade in for a skinny? How do you know? (10; I see there are 10 bits in a skinny.)
How many bits do you need to trade for a flat? How do you know? (100; I can skip count by tens because there are 10 bits in a skinny.)

Play Capture the Flat. To explore how many bits in a flat, students play a game called Capture the Flat. Ask students to remove the Capture the Flat pages from their Student Activity Book. Students will take turns spinning, and after each spin, take the number of bits on the spinner and place them on the Capture a Flat Game Board. If a trade for a skinny is possible, students must trade in ten bits for a skinny. The student who is able to trade in ten skinnies for a flat first is the winner. Each student will record the number spun on their turn and their running total on the game board. Two game boards are included in each student's Student Activity Book.

When students have played the game at least once, have a discussion about what they have learned. Ask them what they think about trading the bits for skinnies and then trading the skinnies for a flat.

Ask:

What were some of the things you noticed about the base-ten pieces? (Possible responses: There are 10 bits in 1 skinny; 10 skinnies in 1 flat; 100 bits in 1 flat; the skinnies are easier to keep track of than all the little bits.)

Represent a Number with Base-Ten Pieces. Display one of each of the base-ten pieces. Tell students to display the same pieces at their desks.

Ask:

What number do these pieces represent? (111)
How do you know? (The flat is 100, the skinny is 10, and the bit is 1. Add them together and it is 111.)
What is a number sentence that matches the pieces? (100 + 10 + 1 = 111)

Write the number sentence on the board. Ask a student to point to each number and name the corresponding piece.

Write several numbers in the hundreds (for example, 132, 155, 140, etc.) on a display of the Show a Number with Base-Ten Pieces Master. Ask student pairs to model these numbers using their base-ten pieces. Accept models that do not use the fewest pieces and use them as a springboard for a discussion of trading and finding the representation that uses the Fewest Pieces Rule. See the chart in Figure 2.

Demonstrate how to fill in the chart for the first number. Student pairs then work to model the rest of the numbers. Ask volunteers to fill in the chart showing the representation they modeled. Have the other students tell whether the information entered accurately models the number given.

Ask questions similar to the following:

Is this a correct representation of the number?

Can any trades be made?

Does this representation use the Fewest Pieces Rule?

If it is the fewest pieces, what is a number sentence that describes it?

When students are comfortable representing numbers in the hundreds, ask them to use their base-ten pieces to represent numbers in the two hundreds (e.g., 242, 216, etc.). Use another display of the Show a Number with Base-Ten Pieces Master.

Reverse the activity by showing students a representation and asking them to identify the number. Use another display of the Show a Number with Base-Ten Pieces Master. Fill in either the number of flats, skinnies, and bits or the shorthand representation. See Figure 3.

Ask students to name the number and fill in the rest of the chart. Ask them to first model the number with base-ten pieces and then identify which representations are in the fewest pieces.

Adventure Book: