Skip to main content

How to Make Change for a Dollar? Ah, Let Me Count the Ways!

 

Hi All,


This is a very interesting exploration for grades 4 - 6. It features algebraic thinking, patterns, logical thinking, money, addition, and subtraction. I had a great time doing this one myself. (But then again, I'm a bit of a nerd for stuff like this.) This is a great problem for partners or small groups and I would highly recommend making that an option. Also having coins available as manipulatives is a good idea as well.

We begin with the question, “How many ways are there to make change for $1.00?” At first it seems simple and it is fun to begin by having students estimate how many ways they think are possible. There are actually 293. Most students estimate far less.

Talk about an opportunity for logical thinking! Where should we start? Are there patterns? Let's slow down. Here's a reasonable sequence you may want to follow with your students.

a. List All the Coins: Before they begin exploring, ask students to name all the coins and list these on board or screen; penny, nickel, dime, quarter, half dollar, dollar coin.

b.  Examples of Making Change: Ask for an example of one way to make change for a dollar. Someone might say, "Four quarters." Write this down. As for another that uses pennies. Write this down.

c. Explain the Challenge: Now tell students, "There is definitely more than one way to make change for a dollar, but how many do you think there are?" Record estimates. Explain, "Today and probably tomorrow too, I'd like you to find all the ways to make change for a dollar and to record them."

d. How to Record? : Ask if there is an easier way to record an answer other than writing it all out with words. Some students like to draw circles with a number value inside. Others like to just give the coin a letter symbol ie; N = nickel. Share these ideas together.

e. How to Approach the Problem? : There's going to be a lot to keep organized. Lined notebook paper works well. Some students like graphic paper. Neat work will help students not to miss any ways.

The challenge in this for students is in trying to develop a logical, systematic approach to the problem instead of just randomly listing combinations they know well.  There is no one right way to approach this, but being systematic is key. 

f. Share Strategies: After about ten minutes of work, have students share strategies for creating their combinations as well as how they are checking and staying organized to be sure they don’t miss a possible combination.

Before you teach this one, you might want to try it out yourself or with another teacher or spouse (see how much fun you can have at home?!) You'll find some interesting patterns and strategies if you do.

 All the best,

Bob


 

Comments

Post a Comment

Popular posts from this blog

What Does Not Belong?

 Hi All,   "What Does Not Belong" is such a great little concept and can be applied to so many different areas of math as well as other content areas. Great little game when you are waiting, like for buses to be called or for the day to begin. Also a great game for long car or bus rides where if there are no written numbers or pictures you really have to do the mental math. Present a group of numbers. Start with maybe six. Say, 10     56     17     122     4     98 Ask the players to identify which number does not belong and have them explain why. We want players to look at the characteristics of the numbers and compare them to try to find the selection criteria or "rule" so they can determine which does not belong. For example, we have a mix of 1, 2, and 3 digit numbers, so it's not the "rule" is not the number of digits. We have five even numbers and only one odd number. That's it! 17 does not belong,...
2 comments
Read more

EGG BOX SHAKE! IT'S WHATEVER YOU WANT IT TO BE.

Hi All, Shake it up! Egg Box Shake is noisy and fun! That's a big plus right there for most kids. Students like to create and keep their own math tools, and this is a great opportunity to do that as well. And, teachers can adapt the game to fit any level or mathematical operation. Win. Win. Win. Egg Box Shake originated as a coin identification and addition game for grades 1 – 3. I had students bring in an egg carton from home and then provided them with play money or coin stamps, ink pads, and card stock. They stamped out pictures of the coins onto card stock, front and back images, and then cut out the pictures. Students glued these pictures into the bottom of the twelve sections of the egg carton. Each player would get two beads, beans, chips, marbles, or any other small manipulative. They put these into the box and closed it. They then shook the box. When they stopped they opened it and saw where the beads had landed. Players added those two coins o...
1 comment
Read more

What's in a Name? A lot of Math!

Hi All, Welcome back! With school starting one way or another in various parts of the country, I figured it was time again to bring back the math blog. No matter what's going on or how it's going on, I'm hoping this content will still be useful to you.  So, let's talk about names! When classes start, one of the first things both teachers and students must learn about each other are their names. A child's name is a very powerful and important thing. It's also a great springboard to learning. Kids are always interested in their own names. "Names Add Up" is an easy activity for K-2 (though older kids like it as well) that combines counting, addition, and money, as well as vowel and consonant identification. You'll need a pile of pennies and nickels. Explain to children that for this activity vowels will be worth a nickel and consonants will be worth a penny. Have children take the coins that correspond to the letters in their first names and...
Post a Comment
Read more