Can You Translate That?

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Objective

SWBAT solve word problems involving multiplicative and additive comparison, e.g., by using drawings.

Big Idea

Student always ask me to translate something for them so they can understand better, In this lesson students will explore how to distinguish the correct comparison form needed in order to solve the given equation.

Warm Up!

20 minutes

Materials:illustration.doc

In this lesson I want my students to explore how drawings can help them to translate comparative situations into equations. To start I invite students to the carpet to demonstrate how to effectively reason when solving equations. I want you guys to focus on what amount would be added to one quantity in order to result in the other.  I write a problem on the board.

Problem:

A red boat costs $3. A blue truck costs 6 times as much. How much does the blue truck cost?

What do we need to know?

How much does the blue truck cost.

What information does the problem give us?

The problem tells us that the red boat cost $3. So, let 3 equal the amount of the red boat.  The blue truck costs 6 times as much  the red boat. So, let 6 equal the amount of the red boat. So, then to find the total ( 3 X 6 = product)

The cost of the red boat is $18.00

To make sure that all students fully understand what they will be doing in this lesson I repeat these steps using a different problem.

Problem:

A phone costs $18. That is 3 times more than an I- Pod. How much does a Pod cost?

(18 ÷ p = 3 or 3 x p = 18).

 As students actively discuss how to solve this equation, I use their responses to determine if additional practice is needed.

In this lesson we will focus on the following Mathematical Practices:

MP2: Reason abstractly and quantitatively.

MP4: Model with mathematics.

MP5: Use appropriate tools strategically.

MP7: Look for and make use of structure.

Turning and Talking!

20 minutes

 Materials:drawing paper.pdf

In this portion of the lesson I want students to focus on how to reason when distinguishing multiplicative comparison from additive comparison. To do this I write two problems on the board.  

 Problem:

Carol has 3 chocolate bars and Tony has 5 candy bars. How many more chocolate bars does Tony have?

What do we need to know?

How many more chocolate bars does Tony have.

What information does the problem tells us?

That Carol has 3 bars and Tony has 5.

Are there any key words?

Yes! How many more are key-words. It tells us that we should subtract to find the answer.

How can you set this up?

5 - 3 =

I point out that additive comparisons focus on the difference between two quantities.  Now let’s take a look at another problem!

Problem:

Pam flew 5 times as many miles as Deb.  Deb flew 25 miles. How many miles did Pam fly?

 What do we need to know?

How many miles did Deb fly?

What information does the problem tells us?

That Pam flew 5 times as many miles as Deb. Deb flew 25 miles.

Are there any key-words?

Yes! 5 times as more tells us that we should multiply to get our answer.

So, 5 X 25 = product

I point out that multiplicative comparisons focus on comparing two quantities by showing that one quantity is a specified number of times larger or smaller than the other. 

I ask students to explain how to determine the difference between multiplicative comparisons and additive comparisons.  Several students pointed out the key words used in the word problem. I ask students to turn and talk to their neighbor. I want them to discuss how they can represent each problem using an illustration. I tell them that after their talking time is up each of them will have to choose a problem to illustrate on their own.  As students, are discussing I circle the room to check the level of understanding.  I use students’ responses to determine if additional time should be given on this objective.

Student Work Sample

Try it Out!

20 minutes

Materials: Try it out Work.doc

You guys have done a fantastic job in distinguishing multiplicative comparison from additive comparison. I think you guys are ready to explore a bit on your own. Are you? Students yell out, “We are ready!”

I quickly review some questions to help the students stay focus on the purpose of this lesson.

 Essential Questions:

Is the problem a additive, or a multiplicative comparison?

What do we need to know?

What information does the problem give us?

Are there any key words?

How can you set the problem up?

 I give students about 15 minutes or so to solve and explain their equations. As students are working, I circle the room to reinforce the purpose of this lesson by asking some of the essential questions above. I use students’ responses to determine if a high-level of mastery has been met.