**5.NBT.7 5.MD.5**

**Act 1**

Watch the video:

How many pennies is that? How much money is that?

Estimate.

What would be an estimate that is too high? To low?

**Act 2**

**NOTE: From experience (mine and other teachers), students never ask for the coin specifications. They do, however, ask for pennies and a ruler along with the dimensions of the cube. **

**When they ask, I give groups/pairs of students a small dixie cup of pennies (about 20 or so) and a ruler. **

If students do ask for the dimensions of a penny, they can still be found below.

**Act 3**

Share your solution and strategies. Compare your strategies and results.

How reasonable was your estimate?

What might you do differently if you were to do this again?

**Sequels:**

**Penny Cube 1.5: The Weight of it All!**

How much does this Penny Cube Weigh?

**Penny Cube 2: Invasion of the Quarters!**

Quarters would fit nicely in this cube as well. Which would you rather have, a cube of pennies or a cube of quarters?

**Penny Cube 3: Return of the Pennies!**

If this cube was one cubic foot, how much money would it hold?

I am using this lesson tomorrow and was just checking how I would solve this and I got 100 pennies, not 104 in the height. How did you find 104 when 6 inches/0.06 in (the thickness of 1 penny) = 100 pennies? Thanks!

I HAD THE SAME THING HAPPEN WHEN I FIGURED THIS OUT BEFORE I MADE THE CUBE AND PUT THE PENNIES IN. I FOUND THAT ALL PENNIES ARE NOT CREATED EQUAL! I ACTUALLY CHANGED THE WAY I DO THIS NOW. I GIVE STUDENTS SOME PENNIES AND A RULER (WHEN THEY ASK IN ACT 2). I’VE FOUND STUDENTS ARE MORE ENGAGED AND ARE MORE CREATIVE IN THEIR SOLUTION PATHS WHICH IS ALWAYS GREAT. LET ME KNOW HOW IT GOES. I’D LOVE TO HEAR HOW YOUR STUDENTS SOLVE IT.

The discussion of why answers differ is the best part of act 3!

Thanks for that info! I teach for an online school, so we just had to go with the numbers. The kids did great! Some had some other ideas I never would have thought of (like finding the volume of the penny and dividing the cube by the volume of the penny). They usually have troubles working together in groups, but actually did really well and were really engaged! Thank you for the great lesson! I’m teaching it again tomorrow and for the kids who come to both of my classes, they will solve for another coin and also find the weight.

Katy,

Excellent! Keep me posted on how it all goes. Quarters work really well (because they fit nicely). Is it more profitable to have a cube with pennies or quarters? What’s the difference between the solution with the volume of the cube divided by volume of the penny? Why is one larger than the other solutions? I’m curious how they find the weight and how close they come. The reveal should be exciting on that!

I actually got 102 pennies per 6″ stack, with a total of $65.28 worth of pennies in the 6″ x 6″ cube. It’s close to the answer in the “reveal” and provides an opportunity for some discussion as to how close we are to the answer in Act 3. GREAT task!! Thanks for creating and sharing this!

Well done! We’ve gotten solutions from $64 to near $70. Glad you enjoyed the task. I’m actually redoing the task with some additions. Should be ready by August. Stay tuned and thank you for sharing your solution and thoughts!

I converted the cube into millimeters so that it would be more accurate. Each side was 152.4 mm. Then I got penny dimensions and divided 152.4 by 1.55 (height of penny). That gave me about 98 pennies per stack. Then I multiplied that by 8 because 8 pennies next to each other is 6 inches, or 152.4mm. that gave me 1 row which was 784 pennies. Then I multiplied the row by 8 because there are 8 rows, so that gave me a total of 6,272 pennies. Then I divided 6,272 by 100 to give me the price which was $62.72.

Julian, 5th grade

Hi Julian!

Thank you for sharing your math thinking. Using millimeters is a much more precise way to measure. I kind of wish I had thought to use millimeters now! When you watch the reveal in the third act (if you haven’t already) that shows how many pennies actually fit in the cube, how does your answer compare? If you were to notice a difference between your answer and the actual number of pennies in the cube, how might you account for that? I look forward to hearing about more of your math thinking. Thanks again for sharing!

Mike Wiernicki, Math Teacher

I guess, using Julian the 5th grader’s results, A cubic foot container would hold 8 times as much or 50,176 pennies (plus or minus 64 pennies). I looked this blog up because a friend told me he would give me $1M in pennies. I wanted to know how much space I would need to store them (and the weight).

I estimate the answer this way: 100,000.00 pennies / 50,176 pennies = 1992.98 Cu Feet of pennies which would fill a 20 X 20 foot room stacked 5 feet high and would weigh 281.25 tons

Hey John,

Thanks for stopping in and sharing your thinking. I wish I had a friend who would offer to give me $1M in pennies! But considering the weight, I might have to store them in my basement. I think my floors might buckle!

You have some solid reasoning. It makes me wonder what take up more space (and weigh more), though:

$1M in pennies or $1M in nickels?

Thanks again for the comment! Hope to hear from you again soon!

how did you multiply the penny cube when the pennies inside the penny cube where stacked?

uh but…

i don’t get it. not even at all. how are you soooooooo good at understanding all. of. this.

stuff.i,m super impressed with your knowlege.

like are you freaking kidding me man? this is awesome. i can’t believe it.

Ilyona,

Thank you for stopping by! No one has ever asked about how I multiplied the numbers while they were stacked! Thankfully, I planned ahead and counted each penny as I set it in the cube. Once I had all of the numbers, all I had to do was compute!

I’m glad you like the videos!

Mike