UbD (Understanding by Design) Lesson Plan

Math (8th Grade Data Analysis and Probability)

# Stage 1 – Desired Results

Established Goals:

(M8D2). Students will determine the number of outcomes related to a given event.

(M8P1). Using appropriate technology the student will solve problems that arise in

mathematics and in other context.

(M8P5). Students will create and use pictures, manipulatives, models and symbols to

organize, record, and communicate mathematical ideas.

Understandings:

## Students will understand that…

·         the use tree diagrams can be used to determine the number of outcomes of a given event.

·         the outcomes of an event can be determined by using the addition and/or multiplication counting principles.

Essential Questions:

·         How can a tree diagram be used to determine the number of outcomes of a given event?

·         How can outcomes of given events be determined using the addition counting principal?

·         How can outcomes of given events be determined using the multiplication counting principal?

## ·         that tree diagrams will display the number of outcomes of a given event.

·         the significance of using the addition and multiplication counting principles to determine outcomes of given events.

## Students will be able to…   (verbs)

·         create and read a tree diagram displaying the outcomes of given events.

·         explain the relationship between the addition and multiplication counting principles and tree diagrams in determining the outcomes of given events.

·         use the counting principles to determine outcomes of given events.

### Stage 2 – Assessment Evidence

G:  Assist the students at your middle school with lunch

decisions.

R:  You are one of five friends who sit together at lunch.

A:  The target audience is your other four friends.

S:  You will determine the outcomes of several different lunch tasks.

Solve a logic problem from given clues.  There are five friends who sit together at lunch, Jeremy, Daman, Conway, Dara and Nelli.  All of them pack their own sack lunch which consists of a sandwich and some fruit.  Use the following clues to find out what each person had to eat today.

·         Jeremy is allergic to peanut butter.

·         The person with the banana had bologna.

·         Daman had brought a ham sandwich & a green piece of fruit but switched with Dara and got a banana and her sandwich.

·         The boy who ate peanut butter sandwich also ate the strawberries.

·         Jeremy didn’t have salami or an orange.

·         The person with the apple didn’t have turkey.

The friends want to make a different sandwich for tomorrow.  The sandwich is made up of three main ingredients and they can pick and choose what they want from each one.  Here are the choices.

1)      White, wheat or sour dough bread.

2)      Ham, bologna, salami, or turkey.

3)      Cheese or no cheese.

How many different possible combinations of ingredients are there for sandwiches?  Show the results in a tree diagram.  Use the Intermath Dictionary to compute the number of possible outcomes using The Counting Principle.

For fun at lunch the group tosses coins.  If each person tosses a quarter (5 quarters total).

What is the probability that there will be at least 2 heads in the group?

What is the probability that there will be at most 4 heads in the group?

What is the probability that there will be exactly 1 head in the group?

Show the results in the form of P(A or B) or P(A and B).  Explain which is appropriate to use and why.

After they were finished eating, Jeremy got up to throw away the bags.  The four people left sitting at the table decided to switch seats.  How many moves would it take to move each individual so that they all switch seats?  (They can only move forward and can jump another person but they cannot jump over the person that started sitting on the same side as they did.  What if there were 10 people at the table?  How many moves would it take then?

Show your results in chart form such as the example below:

Original Seating

End Result

It is now time for PE.  The five friends happen to be captains of the speedball teams.  The PE class consists of 5 teams.  Over the course of the semester, each team will play three games against each of the other teams.  How many games will be played in all?

Display your answer on a chart using a tree diagram and The Counting Principle.

P:  Your product performance and purpose should identify the mathematics that is needed to effectively use the tree diagrams and The Counting Principle.  You should be prepared to discuss your use of these strategies as well as prepare a visual.  You may use Powerpoint to present your work as well as Excel or any other software you prefer.

S:  Standards and Criteria for Success should include your presentation, either written or in powerpoint, any graphs or diagrams you create, copies of work done on software programs, etc.

Other Evidence:

§         Display of student work in write-up

§         Journal entries

§         Written explanations to justify work

§         Class discussions

§         Teacher observation of students working on tasks

§         Chart showing results in the form of a tree diagram

§         Comparison of the tree diagram and The Counting Principal.

# Stage 3 – Learning Plan

Learning Activities: (From Intermath)

Zack is going on a job interview and has to decide what to wear.  He needs to decide between a black suit and a blue suit, black shoes and brown shoes, a red tie and a blue tie, and a plain shirt and a striped shirt.  How many different outfits are possible?

***

A fair coin is tossed ten times and lands on the heads all ten times! What is the probability that this outcome can occur? What do you think will happen on the next toss? Heads or Tails? What is the probability that the next toss will land heads?

***

In writing, explain the difference between P(A or B) and P(A and B).

***

Use the InterMath Dictionary to help compute the number of possible outcomes using The Counting Principle.

***

Four people line up single file to board a roller coaster. One person refused to be first in line. In how many different ways is it possible for the people to line up?

***

There are 8 men and women at a business meeting. Everyone in the room needs to shake hands with everyone else. How many handshakes take place?