### Count all of the squares on the checkerboard or a chessboard- This is a classic problem. You will look at how to solve it using drawings, using patterns, and solving a simpler problem. Also look at how how to solve a variation of this type of problem that may pop up on math contests.

### Spark your math thinking!

1. Set up your math mini spark recording page: #100: Checkerboard Math

2. Print a paper copy of a checkerboard.

3. The challenge for this mini spark is to count **ALL** of the squares on the checkerboard. Start watching this video, pause to copy the chart he creates and **STOP** at 2:40. Record the answers to these 3 questions.

How many squares on an 8 X 8 board?

How many squares on an 1 X 1 board?

How many squares on a 2 X 2 board?

4. Figure out the next answers using your chart and the copy of the board you printed. Without watching the rest of the video try to find the answers for each of the following questions.

How many squares on a 4 X 4 board?

How many squares on a 5 X 5 board?

How many squares on a 6 X 6 board?

How many squares on a 7 X 7 board?

5. When you have a solution click to watch the rest of the video to see if you have recorded the correct numbers.

6. Solve this second problem written by CEMC math. Print this board if you want a new copy to help you. Record all of your work and your answers on your mini spark recording sheet.

**Bart and Lisa counted all squares on a checkerboard. On the same checkerboard, they decided to count the number of small rectangles-1 unit by 2 units or 2 units by 1 unit. **

**They were careful to count all of the overlapping rectangles. If they counted correctly, what was their total? Look at this picture before you start. **

***Reminder for your teacher that the solution can be found in the math mini spark folder.

7. Share your math mini spark recording page and boards with your teacher/EY coordinator.

You can use step #6 as one of your problems for the Problem of the Week CEMC Math badge that can be found on the EY badge page.