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How Many Ways?

Number and OperationsAlgebra
Grace M. Burton
Location: unknown

Children extend their investigation of the previous day to include nickels. They estimate the value of collections of pennies, nickels and dimes then determine the exact amount by exchanging sets of pennies or nickels for dimes.

Distribute plastic bags containing 24 pennies, 3 nickels and 3 dimes to each child. Next hold up a nickel and ask the children to find a nickel in their bag. As they describe the nickel record their descriptions on chart paper.

558 money bag558 nickle

Now ask the children to place a piece of paper over a nickel and to rub the paper with a crayon to make impressions of both sides of the coin. Ask them to record the coin’s value in both words (5 cents) and using cent sign notation. Then ask the children what similarities and differences they notice about the three coins they have studied. Add the word “nickel” to the word wall. To set the stage for this lesson, read 26 Letters and 99 Cents, asking children to take turns modeling various amounts to 60 cents using the coins. Then ask them suggest other amounts to model.

pdficonTen Frame Activity Sheet

Next give each child a copy of the Ten Frame Activity Sheet and model trading pennies for nickels and nickels for dimes. Model trading pennies for nickels by placing 1 penny in each cell of the top row of the ten frame, and when the row is full, exchanging the 5 pennies for 1 nickel. Then repeat with the bottom row. Then ask them to find out how many nickels would equal a dime, and guide them through making that exchange.

Now put the children in pairs and have the children return their coins to their plastic bags. Invite the children to take turns showing to their partner a handful of coins and having him or her guess the total value of the coins. Then ask them to work together to find the actual value, exchanging for nickels and dimes whenever possible.

When the children have had several turns, call them together and ask them to use their coins to display a given amount such as 34 cents. Call on a volunteer to show the coins they chose, then ask if anyone showed the amount a different way. Display their choices on a chart such as that shown at the end of the unit. For example, students might make 34 cents in the following ways:

3 dimes, 0 nickels, 4 pennies
0 dimes, 6 nickels, 4 pennies
2 dimes, 2 nickels, 4 pennies
...and so on
[You may wish to use paper copies of over-sized coins on a large chart to demonstrate the combinations.]

At the end of the lesson, ask children to choose two of the rows from the above chart and draw a picture illustrating two different ways to make an amount. They may wish to display these on the classroom bulletin board and to add them to their portfolio.

  • Book: 26 Letters and 99 Cents 
  • Plastic bags, each containing pennies, nickels, and dimes  
  • Chart paper  
  • Crayons  
  • Ten-Frame Activity Sheet  


  1. Provide paper coins, coin stamps, or actual coins in a center and encourage the children to make coin patterns with three repeats. Encourage the children to trace the coins if they use actual coins. The children can then determine the total amount shown in the pattern.
  2. Move on to the next lesson, Trading for Quarters.

Questions for Students 

1. How many pennies have the same value as a nickel? As a dime?

[5 pennies have the same value as a nickel; 10 pennies have the same value as a dime.]

2. How many nickels should you trade for a dime?

[2 nickels.]

3. What coins could you use to show 26 cents? How would you do it another way? Is there still another way? Repeat with other amounts.

[Student responses may include: 1 quarter and 1 penny; or, 2 dimes, 1 nickel, and 1 penny; or 26 pennies; etc.]

4. Suppose you had 5 nickels. What could you trade them for?

[A quarter; or, 2 dimes with one nickel leftover; or, 25 pennies.]

5. Suppose you want to buy some juice from a machine, and the juice costs 35 cents. What coins can you put in the machine if it doesn’t take pennies?

[A quarter and a dime; or, two dimes and a nickel; or seven nickels; etc.]

Teacher Reflection 

  • Which students met all the objectives of this lesson? What extension activities are appropriate for these students?
  • Which students did not meet the objectives of this lesson? What caused them particular difficulty?
  • Can most of the students estimate the value of a small set of coins?
  • Can most of the students find the value of a small set of coins?
  • Which pairs worked well together?
  • What parts of the lesson went smoothly? Which parts would you change the next time you teach this lesson?

Exploring Pennies and Dimes

In this lesson children examine pennies and dimes and model subtraction as they listen to a children’s book. They model amounts to 60 cents with coins. They use coin rubbings of pennies and dimes and make a chart comparing the two coins. At the conclusion of the lesson, they begin a word wall and make an entry in their portfolios. 

Trading For Quarters

In this lesson, children listen to a poem about money, and then examine a quarter. They find sets of coins equivalent to a quarter using pennies, nickels and dimes. They also estimate and count coin collections and count by fives and tens using actual and online calculators and pose and answer coin puzzles.

Modeling Prizes

Children use pennies, nickels, dimes, and quarters to model amounts to 70 cents. Next they answer money puzzles and estimate the number of pennies in a jar. They also add to the word wall.

Making Change


To begin this lesson, children model prices mentioned in a children’s book. Then they make change from a given amount by counting on from the price.

Note: Counting on to make change is a very challenging activity. In initial instruction, it is best to restrict the coins used in making change to pennies and dimes.


Looking Back and Moving Forward

This final lesson of the unit reviews the work of the previous lessons. Children discuss and model prices and the words on the word wall and play games to facilitate continuing practice. They add to their portfolio and listen to another children’s book. Questions for summative evaluation are suggested.

Learning Objectives

Students will:

  • Identify and state the value of a nickel.
  • Estimate the value of a collection of penny, nickels and dimes.
  • Find the value of a collection of pennies, nickels and dimes.
  • Construct sets of coins which have a given value.

NCTM Standards and Expectations

  • Count with understanding and recognize "how many" in sets of objects.
  • Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  • Use multiple models to develop initial understandings of place value and the base-ten number system
  • Sort, classify, and order objects by size, number, and other properties.