The concept of this math mini spark is straightforward. The probability of an event happening is the number of times you expect that event to happen out of many tries. Probabilities always fall between 0 and 1.

Spark your thinking!

1. Set up your math mini spark recording page: #104: Probability 

2. Make a chart like this on your recording page.

3.Watch this intro video.  Pause the video @ 3:40 and record the probability of each of the events on the chart on your recording page. You can use a calculator for the decimals.

4.  Copy this chart in your notebook.

5.  Number your recording page from 1-5. Read each example and record if it is experimental or theoretical. Scroll down to the bottom of this post to check your work. Add a star if it is correct or add in the correct answer.

Probability Puzzles: Theoretical or Experimental?

1. A fair six-sided die is rolled. What is the probability of rolling an even number? Is this theoretical or experimental probability?
2. Sarah flipped a coin 50 times and got 28 heads. What is the probability of getting heads based on Sarah’s experiment? Is this theoretical or experimental probability?
3. In a bag, there are 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of picking a blue marble without looking? Is this theoretical or experimental probability?
4. A weather station recorded that it rained on 12 out of the last 30 days. Based on this data, what is the probability that it will rain tomorrow? Is this theoretical or experimental probability?
5. A spinner has 4 equal sections colored red, blue, yellow, and green. Jack spun it 40 times and it landed on red 8 times. What is the probability of the spinner landing on red based on Jack’s results? Is this theoretical or experimental probability?

6. Share your math mini spark recording page with your teacher/EY coordinator.

1. A fair six-sided die is rolled. What is the probability of rolling an even number?theoretical
2. Sarah flipped a coin 50 times and got 28 heads. What is the probability of getting heads based on Sarah’s experiment? experimental
3. In a bag, there are 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of picking a blue marble without looking? theoretical
4. A weather station recorded that it rained on 12 out of the last 30 days. Based on this data, what is the probability that it will rain tomorrow? theoretical
5. A spinner has 4 equal sections colored red, blue, yellow, and green. Jack spun it 40 times and it landed on red 8 times. What is the probability of the spinner landing on red based on Jack’s results? experimental probability

Combinatorics is a branch of mathematics which is about counting – and we will discover many exciting examples of “things” you can count.  You can use combinatorics to calculate the “total number of possible outcomes”. 

Spark your thinking!

1. Set up your math mini spark recording page: #103: Combinatorics

To do this mini spark you need to know a little about factorials. Steps 2 and 3 will review them for you.

2. The factorial function (symbol: !) says to multiply all whole numbers from our chosen number down to 1. Example: 4! = 4 × 3 × 2 × 1 = 24.

Complete these two problems so that they look similar to the example:

Example: 6! = 6 x 5 x 4 × 3 × 2 × 1 = 720

5! =

9! =

Scroll to the bottom of this post to see if you are correct. If you got it correct, add a star. Add the correct answer if needed.

3. Watch this short video that show you how to divide factorials. Don’t worry. It isn’t hard. Do the problems with the teacher on your recording page.

4. Study the first two columns of this teaching page.  Write the type of the formulas and the formulas on your recording page.

5.  Watch this video. Do the first two math problems with the teacher on your recording page. Try the last problem by yourself on your recording page. The answer is at the end of this post.

Advanced: Check out this teaching page. Each of the sections has a mini lesson, a practice problem, and a solution.  Read each lesson and try the problem on your recording page. Check your work. If you complete this, talk with your EY teacher about using this as a badge option.

Factorials

Permutations

Combinations

Combinatorics and Pascal’s Triangle

Combinatorics and Probability

6. Share your math mini spark recording page with your teacher/EY coordinator

5! = 5 x 4 × 3 × 2 × 1 = 120

9! = 9 x 8 x 7 x 6 x 5 x 4 × 3 × 2 × 1 = 362,880

50 people are in a race. How many ways can gold, silver, and bronze be awarded?

Spark your math thinking!

1. Set up your math mini spark recording page: #102: Friendly Numbers

2. Review factors. Read this paragraph and when you are done write the factors of the number 40 on your recording sheet.

Factors are numbers you multiply together to get another number. A factor of a number divides the number evenly, with no remainder. What are all the factors of the number 8? 1 2 4 8 What are all the factors of the number 24? 1 2 3 4 6 8 12 24

3. Scroll down to the bottom of this page to see if you have the correct numbers for step 2. If you do put a star on your page. If you do not, add the correct numbers.

4. Look over these 6 questions before your start watching the video.

• Stop the video at 2:57. In two sentences, describe how 12 and 234 and are friendly numbers.
• How many perfect numbers are there. How has this number changed since 2011?
• What is is called if you don’t have a friend? Name a few of these types of numbers.
• Pause the video at 8:40 and write down all of the friendly numbers on his chart.
• What are the yellow numbers?
• What is 10’s index?

5. Share your math mini spark recording page with your teacher/EY coordinator

Answers for step 3

Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

There is a wealth of information when it comes to volleyball! Whether you’re examining individual player statistics, team standings, or breaking down a specific match… MATH IS EVERYWHERE IN VOLLEYBALL!

Spark your math thinking!

1. Set up your math mini spark recording page: #101: Volleyball Roster Math 
2. This Mini Spark has you looking at the 24-25 Westside High School Varsity and Junior Varsity Volleyball Roster.  Download and print a copy of the worksheet and roster.
3. Add a picture of your finished worksheet to your math mini spark page.
4. Share your math mini spark recording page and your worksheet with your teacher/EY coordinator.

Check out the Roster Math Badge at the EY website.

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.