Name: Brandon Harvill

Title of lesson: Not What You Might Expect

Date of lesson:

More towards the middle of the semester

Length of lesson:

50 minutes

Description of the class: Project Based portion of 9^th or 10^th grade math

Name of course: Algebra I or II

Grade level: 9th or 10th

Honors or regular: This lesson could be used for honors 9^th grade and regular 10^th grade.

Source of the lesson:

http://www.mste.uiuc.edu/reese/cereal/intro.html

TEKS addressed:

(2)  Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students study algebraic concepts and the relationships among them to better understand the structure of algebra.

(A1)

(A)  describe independent and dependent quantities in functional relationships;

(B)  gather and record data and use data sets to determine functional relationships between quantities;

(A2)

(D)  collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

I. I. Overview

I want the students to understand the difference between what they expect to happen out in the field and what actually does happen, why that is, and the likelihood of what they saw actually happening.

II. Performance or learner outcomes

Students will be able to: assess the probability of a variety of outcomes and compare the results of what actually happens to what they would expect to happen.

III. Resources, materials and supplies needed

 Dice is the only thing not in most classrooms that students would need.

IV. Supplementary materials, handouts.

Tally Sheet handout
Five-E Organization

Teacher Does Probing Questions Student Does

Engage:  I want to start off talking about cereal box prizes and McDonald’s Happy Meal Toys

How many of you used to get Happy Meals when you were young? Think about some of your favorite toys that were there. Were there any series where you wanted to collect all of the toys in the collection?   Today we are going to try to find out how many times you would have to go eat to get all the toys in the collection.

Yummm Happy Meals! Yeah I liked when they had the mini beanie babies! My mom took me there all the time, I wanted all the Batman toys.

Explore:  Students will be placed in groups and given a dice and a tally sheet. They will then be told to roll the dice, mark down which number came up, and continue until all 6 numbers had a tally. Depending on the amount of time, I would have them do this about 10 times per group, so in groups of 5 each person could roll and tally twice.

First I would ask them to guess how many rolls they think it would take to roll all 6 numbers on the dice.  So how is rolling the dice similar to getting a Happy Meal or buying a box of cereal with toys inside?

Some students may think that it will only take 6 rolls, which would be the minimum. Others will realize it will take more. I will write their predictions up on the board for them to look at later. Hopefully they will realize that each number on the dice represents a different toy, and in fact I may have them select toys that will be represented for each number rolled.

Explain: After students have done the activity I will have them come up and write down the average and median (which they will have learned earlier) number of rolls needed to roll all 6 numbers on the dice.

From these averages, I will have them all calculate the class average number of rolls that it took. Next we will calculate the amount of rolls we would expect it to take to roll all 6 numbers on the dice. Then I will have them compare this number to their own numbers and the class average number. To simplify this for them it may be easier to start with a coin or two sided dice and build up from there. Also it would be good to explain that the more times that we did this, the closer our average would get to 14.7.

This is they key portion of the lesson, that they learn how to do this, so most of the lesson should be focused on teaching them how to find the expected value of rolls with a 6 sided dice, and doing it in such a way that they could do it for any dice.

Extend / Elaborate: Another critical aspect of expected value is the odds of it taking a certain amount of rolls. In this portion they would be looking more closely into what the chances are of it taking each amount of rolls.

By starting with a coin here, I would ask them how many times they would expect to flip it to get both sides of the coin. Then I would ask them what the probability is that it would take 2 coin flips, then 3 then 4 and so on until we could establish a pattern. On this part we may just scratch the surface of probability but it would be good for them to know.

I think this portion will be very difficult for them to master as college students still have trouble with it at times but I also think it would be good to introduce them to things like probability and get them thinking about the chances of their results happening and how likely something is.

Evaluate: The important things are for them to realize that their theoretical values and actual values won’t always match up. This is important for down the road

I would tell them they had to collect 8 toys and then ask them how many Happy Meals they would expect to have to eat to get all 8. Hopefully they will apply what they have learned to a new scenario. I would also ask them to explain why the theoretical and the actual values were different. This would help me see what they do and do not understand and give me a chance to go over it again if necessary.

I would imagine some students would still have trouble but for the most part I think students will be able to apply what they have learned.