Building Blocks of Math

Some lessons work out so well that I can’t help but share them with others. This is one of those.

So far my third grade Polite Pirates (what I call my students) have learned how to round to the nearest ten and hundred, plus three-digit addition and subtraction. As we move on to multiplication and division, I came up with a way to make reviewing and practicing our foundational arithmetic skills unbelievably fun: a game.

Usually, I’ll create a game around a story. This time, I kept it super simple: “Closest to a 1000 wins!” 

Old-school building blocks are magical. You could dump them out in front of a 4 year old or a 40 year old, and you’d see the same reaction; Building. Everyone wants to stack blocks. 

The first thing I did was write three-digit numbers on the sides of some blocks; I actually wrote the numbers on pieces of paper that I taped to the sides. Then I threw them in a box. The “Box O’ Blocks” is plain-old fun to say;) I told the Polite Pirates that it was a game… Instant positive vibes. 

Here’s how you play: 

1. Each team takes 3 blocks out of the box at random. 
2. Add the numbers up.
3. Closest to 1000 wins. “How do you tell who is closest?” Let students figure this out. There will be some teaching. (This is one of my favorite parts.) They’ll have to find the “difference” (subtract).
4. As a team, decide on one block to exchange in order to get closer to 1000. Move it to the side, but not back in the box.
5. Randomly take one more block out. 
6. Combine this number with the others. Make a prediction. Will your new total be closer or farther from 1000?
7. Add the numbers. Was your prediction correct? 
8. Repeat steps 5-8. 
9. Which combination of 3 blocks is closest to 1000?
10. Compare your sum with that of other teams. Who is closest to 1000? 
11. Start over; Play another round.

When I first introduced the game, I was astounded to witness the number sense that this little activity generated. Kids could instantly tell that their 3 blocks would exceed 1000 by quickly adding up the hundreds. But, they had to include the tens and ones to see which team was closer. 

Closest to a Thousand

Figuring out which team was closer to 1000 was a lot of fun, too. I had two teams competing during a math center, and everyone thought that the team with 1349 was closer than the one with 749. I drew a simple number line with 1000 in the middle. It was easy to see how far 1349 was from 1000. It’s just 349 past the 1000, but what about 749? The Polite Pirates were tricked into thinking that it was 749 units away from the mark (1000). When we subtracted 749 from 1000, the Polite Pirates saw that this team was only 251 units away from the 1000, making it the winner of that round. 

When kids have a purpose for playing, they will do any amount of math. I had the students who met with me at this center bring their Spiral Notebooks to work out their arithmetic. Some were trying to do the math in their heads. Others worked it out quickly on their papers and shouted out the answers. We figured out together how to play the game politely: Wait for everyone to solve the problem, and then compare numbers. Discuss how you got your answer. 

Multiple Strategies

We use Ready Math in my school district. One of the things I love most about Ready Math is the multiple ways to solve the same problem. I had kids drawing base-ten blocks to show their hundreds, tens, and ones. Some kids used expanded form to add up the three-digit numbers. There were kids who were able to add 3 three-digit numbers one on top of another, using the algorithm I grew up learning. 

One girl had added two numbers together, and then the third to that sum. She was thrilled to find that she could simply substitute that last step with a new number when her group chose a different block! It saved her a step. 

I was able to review regrouping on the board for those students still struggling with borrowing to subtract. Everyone was at a different level, using different tools and strategies, but we were all engaged in learning, reviewing, practicing, and having fun. 

If a kid finished before others, they simply messed with the 3 blocks, stacking them different ways, and that was perfectly okay! With only 3 they didn’t make much noise if they fell. The other mathematicians only hurried more to complete their work, too. They wanted to get their fingers on the blocks, also. “No dice till you finish figuring out how close to 1000 your group came.”

Commutative Property

Lastly, a surprising teaching moment arose when I was able to reintroduce the commutative property and mental math within adding 3 three-digit numbers. I was showing the algorithm style of adding 3 numbers on top of one another. “When you have a bunch of single-digit numbers, it can be difficult to add them all up in your head. Look for tens or combinations that are easier to work with,” I explained to my Polite Pirates. 

I showed this by pulling a column of 4 numbers out of the algorithm and writing it in a line. “You can add these ones in any order you like,” I told my learners. “Choose combinations that work best for you. Don’t forget any numbers.”

We didn’t want our center to end! Polite Pirates were reluctant to drop their blocks back in the box. But, what kid doesn’t like making noise? 

Enrichment

Finally, I will say that when I first dreamed up this simple game, I was thinking that I’d have my students buy blocks or measure how high they could build. I thought that I’d explain the three-digit numbers to represent how much mass each block was (some were more dense than others), and they could only build a 1000 kg structure… I could come up with a million scenarios for my block-building game, but it was unnecessary. Perhaps, it would be helpful if reintroducing the game to the same students down the road. 

When first explaining how to play, though, numbers on blocks in a box are all you need. If you like this lesson, give it a try. If you have thoughts on its implementation or ideas on improvement, let me know. Good luck and great teaching!