Group and Count by Fives and Tens

Est. Class Sessions: 2–3

Developing the Lesson

Part 1: Count with Pennies, Nickels, and Dimes

Estimate Pennies. Briefly review skip counting by twos, fives, and tens using the class number line.

Show the class a plastic bag of 50 pennies. Ask students to estimate how many pennies are in the bag and to explain how they arrived at an estimate. Students may use what they learned about counting pennies when they completed a similar activity in Unit 5. Write students' estimates on the board.

Using a display of the Ten Frames, Pennies, Nickels, and Dimes page in the Student Activity Book, ask students to count the pennies as you place them in the ten frame. Point out the 5¢ symbol next to that row. Fill in the rest of the ten frame with five more pennies, as students count on by ones to ten. Write 10¢ next to the bottom row of the ten frame.

Show students the remaining pennies in the bag and ask:

I took out ten pennies. Look at what is left. Do you want to try to make a better estimate? Explain your thinking. (Possible response: I said 20 pennies before, but I can see now that you will be able to take many more groups of ten out of the bag.)

Fill in the remaining ten frames with pennies in the same manner as above, five at a time, and have students count by ones along with you until you have placed all 50 pennies in ten frames. Each time that you complete a row, record the total value of the pennies beside the row.

Once students have counted the 50 pennies, have them revisit their estimates.

Ask:

Which estimates were closest to 50?
How do you know?

Students may point to numbers on the class number line to visually show which estimates are closest.

Count by Fives and Tens with Coins. Next ask students for a faster way to count the pennies. Students may suggest counting by twos, fives, or tens. Ask them to demonstrate the methods they suggest.

Once the pennies are counted, show students a nickel. Remind students they used nickels in Unit 5. Review replacing five pennies at a time with nickels and counting the total by fives again to arrive at fifty cents.

Arrange the 50 pennies in the ten frames again. Show students a dime and tell them that it is worth ten cents. Ask students how many pennies can be replaced with one dime (10 pennies). Demonstrate replacing the ten pennies on each ten frame with one dime and count by tens to fifty cents. See Figure 1.

Discuss the relationships among pennies, nickels, and dimes further. Demonstrate even exchanges using pennies, nickels, and dimes on the ten frames.

Ask:

I am going to fill this ten frame with pennies so I have ten cents. How much is a nickel worth? (5¢) How many pennies can I exchange for a nickel and still have the same amount? (5 pennies)
If I want to replace ten pennies with nickels, how many nickels will I need? How do you know?
(2 nickels. Five cents and five cents make ten cents, so two nickels is the same as ten cents. You can replace the top row with a nickel and the bottom row with another nickel.)
I am going to fill the ten frame with pennies again. How much is a dime worth? (10¢) How many pennies can I exchange for a dime and still have the same amount? (10 pennies)
If I fill two ten frames with pennies, how many pennies will I have? How do you know? (20 pennies. I can count by tens: 10¢, 20¢)
If I want to replace 20 pennies with nickels, how many nickels will I need? How do you know?
(4 nickels; Possible responses: Each row is 5¢ or one nickel and there are four rows. I can count by fives for each nickel and check that I get to 20¢: 5, 10, 15, 20¢.)
I am going to fill two ten frames with pennies again. I want to replace the pennies with dimes. How many dimes do I need? How do you know? (2 dimes; Possible responses: Count tens for each dime: 10, 20¢. Each ten frame has enough pennies for one dime and there are two ten frames.)

Circle 10¢, 20¢, 30¢, 40¢, and 50¢ on the display as you replace ten pennies with each dime.

Explore Pennies, Nickels, and Dimes. Ask a volunteer to take a handful of pennies from your collection of fifty pennies. Display the pennies. Ask students to write down an estimate for the number of pennies in the handful.

Discuss efficient ways to count the pennies. Students will likely suggest organizing the pennies in ten frames and counting by fives or tens or trading pennies for nickels and dimes. Have students demonstrate the strategies. Compare students' estimates with the actual value. Note which estimates are closest using the class number line or using the ten frames themselves.

Provide each student pair with a bag of 35–50 pennies and a bag with nickles and dimes.

Give the following directions:

Estimate the number of pennies in your bag. Write down your estimate.
Count the number of pennies in your bag using an efficient method.
Trade as many pennies, nickels, and dimes as you can so you have the same amount of money.
Was your estimate close to your actual amount? How do you know?

If students are having difficulty, suggest that they use the ten frames on the Ten Frames, Pennies, Nickels, and Dimes page in the Student Activity Book. Provide time for students to complete the Packing and Counting pages in the Student Activity Book. Students may use pennies, nickels, and dimes as needed to determine answers. Observe students' strategies as they work.

Use the Packing and Counting pages with the Feedback Box to assess students' abilities to represent and identify quantities using coins and symbols [E1]; connect representations of quantities (e.g., ten frames, coins, symbols) [E2]; use skip counting by fives and tens to find the value of a set of coins [E3]; and group and count by fives and tens [E4].

For targeted practice, place copies of the Ten Frames, a container of pennies, and a container of nickels and dimes in a center. Students can practice exchanging handfuls of pennies for nickels and dimes, counting by fives and tens, and counting on by ones to find the value of the coins.