Objectives
The student will be able to:

Evaluation Questions for each Objective

1.  Perform 2-digit multiplication.

2. Use problem-solving skills and knowledge of place value to maximize a product of a 2x2 multiplication problem when given four numbers.

3. Use problem-solving skills and knowledge of place value to minimize a product of a 2x2 multiplication problem when given four numbers.

Engagement

What the Teacher Will Do

Eliciting Questions/ Student Responses

What the Students Will Do

The teacher will display the “Carnival Candy” transparency.

The teacher will select several students to share their suggestions or questions about the “Carnival Candy” problem.

The teacher will conclude the discussion about the “Carnival Candy” problem before any final answer is given or any resolution to the problem is found.  The teacher and students will revisit the problem at the end of the lesson.

Without doing any multiplication, which store do you think has more lollipops for Mrs. Jenkins to buy? Why?
-The Sweet Shop because they have so many more bags of lollipops than the other store
-The Candy Shack because even though there are less bags, there are more lollipops in every bag

Is there any way for Mrs. Jenkins to be sure before she chooses a store?
-Yes
-No

A student volunteer will read the “Carnival Candy” problem out loud.

In pairs, students will spend 2-4 minutes discussing the problem and if it can be done without doing any multiplication.

Student will share their thoughts about the “Carnival Candy” problem so far.

TRANSITION

You will have a chance to continue thinking about the “Carnival Candy” problem at the end of the lesson.  For our next activity, we will play a game called “Maximize Your Product.”  While you play the game, think about how the game might help you find the answer to the “Carnival Candy” problem.

Exploration

What the Teacher Will Do

Eliciting Questions/ Student Responses

What the Students Will Do

The teacher will display the “Maximize Your Product” transparency. 

The teacher will roll a die 4 times and announce the resulting number to the class.

The teacher will determine who has the largest product by asking students what product they got and having students with larger products stand up.  The teacher continues to ask students their products until only students with the largest products remain standing.

The teacher will repeat the game several times.  Note: The explanation section of the lesson will occur between each game.

What is a product?
A product is what you get when you multiply two numbers together

What does maximize mean?
Create the largest possible number of something

 How did you decide where to put each number?
I tried to wait for bigger numbers to put in the 10s column instead of in the 1s column.

How does the placement of your numbers compare with that of your neighbor’s?  How does their product compare to yours?
Answers will depend on the numbers rolled and students’ placement of the numbers.
Sample answer: My partner put a higher number in the 10s place than I did and she got a larger product.

If you could change the placement of your numbers now that you know what all 4 numbers are, how would you change them.
Answers will depend on what numbers were rolled.  Sample answer: I was waiting for a 5 or a 6 to put in the 10s place, but I never got one, so now I would put the 4 in the 10s place since it is the biggest number.

Are you noticing any patterns that help you create the largest product?
When the 2 numbers are closer together, they tend to make a larger product; when the 2 numbers are farther apart, they tend to make a smaller product.

 Each student will copy the multiplication template from the “Maximize Your Product” transparency on a piece of paper or into their notebook.

After each die roll, each student will write the number rolled in any space on their multiplication template.  Once they choose a space for a number, they may not change its location.  After all 4 numbers have been placed, students will multiply their 2 digit numbers together.  The goal of the game is for students to try to get the largest possible product.

Students will compare the placement of their 4 numbers with those of their partners or group members. 

Students will draw another multiplication template and play the game again using what they learn each time to try and obtain the highest product. 

TRANSITION

Now that you have placed your 4 numbers, you will get to compare what you did with your classmates.

Explanation 
Repeat this section between each game during the exploration

What the Teacher Will Do

Eliciting Questions/ Student Responses

What the Students Will Do

After each game, the teacher will select 2 students to share their answers.  Select 1 student with the largest product and 1 student without the largest product.  The teacher will use this time to identify and illuminate any common mistakes that are being made on the 2 digit multiplication.

Why did you place the numbers in those locations? 
I applied the patterns I saw in the previous examples and tried to place the higher numbers in the 10s column.  I also tried to create 2 numbers that were closer together because I noticed their products were larger than 2 numbers that were farther apart numerically

Are you sure this is the largest product?  What makes you sure?
-I tried some other arrangements and they all had lower products
-Yes, based on the patterns I have seen so far

Why do you think this placement creates the largest product?
Answers will depend on the numbers rolled.

If you could change your number placement, how would you change it?
Answers will depend on the numbers rolled and the student’s original placement of the numbers

What patterns do you see? 
Two numbers that are closer together in value seem to have higher products than two numbers that are farther apart in value, assuming both numbers use the highest numbers in the 10s column

The selected students will explain the reasoning behind their number placements and will show the steps of their 2 digit multiplication on the board or overhead.  The remaining students will evaluate the process of 2 digit multiplication to make sure the product is correct.

TRANSITION

You have seen many patterns in our game to try and maximize your product.  Now we will play the game again, but this time your goal is to minimize the product.

Elaboration

What the Teacher Will Do

Eliciting Questions/ Student Responses

What the Students Will Do

The teacher will roll the die 4 times and announce the result to the class each time.

How will your strategy be different this time?
This time I will try to put lower numbers in the 10s column

What patterns do you see in this game?
I see the same patterns only opposite.  For example, now I am trying to make two numbers that are further apart in order to get the smallest product

After each die roll, each student will write the number rolled in any space on their multiplication template.  Once they choose a space for a number, they may not change its location.  After all 4 numbers have been placed, students will multiply their 2 digit numbers together.  The goal of the game is for students to try to get the smallest possible product.

The teacher will remind students of the “Carnival Candy” problem.

What advice would you give Mrs. Jenkins so she can buy the most candy for the carnival?  Why?
Mrs. Jenkins should go to The Candy Shack because those numbers are closer together so when you multiply them you would get a larger product

How can we check our answer?
Perform the actual multiplication

Students will apply what they have learned during the Maximize Your Product game to answer the “Carnival Candy” problem.

Students will calculate how many lollipops are at each store to confirm their answer to the “Carnival Candy” problem.

Congratulations, you have solved the “Carnival Candy” problem.  Now you will have the opportunity to show what you have learned.

Evaluation