Using Manipulatives to Solve Probability Problems

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you'll learn about and solve probability problems with the help of everyday objects such as a coin. Figure out your chances of rolling a 6 when playing with dice.


Your probability problems are those problems that deal with chance and statistics. Probability tells you how likely something is to happen. For example, a weatherman predicting the weather for the day may say that the chances of rain happening is 70 percent. This means that it is more likely for it to rain today but there is still a 30 percent chance of it not raining today. So, be prepared and have your umbrella ready. Now, if the weatherman says there is a 100 percent chance of it raining, then that means rain will happen today. There is no chance of it not raining.

While probability seems to be a field for those who live and breathe math and statistics, it really isn't. If you've ever played with flipping coins or any game that uses dice, then you are already playing with probability. And guess what? It wasn't boring and dry. You had fun, no doubt. And if you didn't, then perhaps, after reading this lesson, you'll have more fun since you'll understand the underlying concepts better.

So, let's tackle several probability problems with the help of some manipulatives, or objects to help you understand a concept, and in this case, that's probability.


VE NOTE: In this section, I think using the tables on screen is ideal but it makes narration a little tricky. Narrator, for the first table, read it like this: In your first toss, you get heads, with your second toss, you land on heads again, in your third toss, you get tails, and in the fourth toss, you land on heads again. VE can you display the table then highlight the row in time with narration? So maybe just put a colored highlighted field over each row in time with the words. For the next table, though, can we put the table onscreen and just read the text, so no need to read the table this time, and instead, can we highlight all the heads in time with the narration and all the tails in time with narration? So the narrator says '… your results now show that you have an equal amount of heads and an equal amount of tails. Heads showed up 5 times and tails showed up 5 times. ' Can we highlight heads when we say equal amount of heads and then highlight tails when we say equal amount of tails and then highlight both in different colors with the last statement that says heads showed up 5 times and tails showed up 5 times?

First, let's use some coins, any coin with a head on one side and something else on the other. Quarters work well for this activity as they're larger and easier to handle. What you do is you simply start tossing the coin up in the air and seeing which side is up when the coin lands on the floor or table. Record your results.

This activity shows you how probability works. If you have two choices that both have an equal chance of happening, then you'll find that after playing for a while, you'll have roughly equal amounts for both.

For example, tossing your quarter 4 times might give you these results.

Toss Result
1 H
2 H
3 T
4 H

You've only tossed the coin 4 times, and so far, heads is winning. Does this mean that heads has more of a chance of winning? No. If you keep tossing the coin, you'll find that tails has an equal chance of winning too.

Toss Result
1 H
2 H
3 T
4 H
5 T
6 T
7 H
8 H
9 T
10 T

In this example, after tossing the coin a total of 10 times, your results now show that you have an equal amount of heads and an equal amount of tails. Heads showed up 5 times and tails showed up 5 times.

In math terms, both your heads and your tails have a 1 in 2 chance of winning. The probability of heads winning is 1/2 or 50 percent. The same is true for tails. When looking at a physical quarter, you can simply count the number of heads on a quarter and then count the number of total choices and then you'll have your probability which is 1/2 or 1 head over 2 choices. the top is your winning choice and the bottom is your total number of possibilities.


Next, let's work with spinners. Spinners have a wheel divided into separate sections. You spin the wheel and whatever section the wheel stops at is your result. Sometimes the sections are all equal in size and sometimes some sections are larger or smaller than the rest. If all the sections of your wheel are the same, then all the sections have an equal chance of winning. But if one section is larger, then that section will have a greater chance of winning than the other sections. And vice versa, if the section is smaller, then it will have less chance of winning. The classic game Wheel of Fortune uses a spinner.

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