IReady Lesson 19 Session 1 (Equivalent Expressions)

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Learning Targets

•Apply the properties of operations to
generate equivalent expressions.

•Identify when two expressions
are equivalent.​

•Use the distributive property to express a
sum of two whole numbers 1–100 with a
common factor as a multiple of a sum of
two whole numbers with no common factor.

SESSION 1

Equivalent Expressions

LESSON 19 • Write and Identify Equivalent Expressions​

SESSION 1

Equivalent Expressions

​Learning Targets

• Apply the properties of operations to generate equivalent expressions.

• Identify when two expressions are equivalent.

• Use the distributive property to express a sum of two whole numbers 1–100 with a

common factor as a multiple of a sum of two whole numbers with no common factor.

Categorize

Options (4)

6(8)

6(5+1)

4(3+6)

4(14-2)

Put the expressions under the correct column.

Same

Different

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• What is the problem about?
• What questions can you ask

that mathematics can answer?

Make sense of the problem

In the design for a new school, a classroom
needs to have the same width as a laboratory.
The architect wants the width to be as great as
possible. The length and width of each room
should be a whole number of meters.

In the design for a new school, a classroom needs to have the same width as a laboratory. The architect wants the width to be as great as possible. The length and width of each room should be a whole number of meters. 

What's the gist?

​

Try It!

In the design for a new school, a classroom needs to have the same width as a laboratory. The architect wants the width to be as great as possible. The length and width of each room should be a whole number of meters. 

What length and width should the architect use for each room?

​

Try It!

How can you determine the greatest
possible width of the rooms?

​

Discuss!

Open Ended

How will you find the greatest possible width for the rooms. Explain.

Draw

In the design for a new school, a classroom needs to have the same width as a laboratory. The architect wants the width to be as great as possible. The length and width of each room should be a whole number of meters. 

Open Ended

What length and width should the architect use for the classroom and the laboratory? Explain how you know.

Open Ended

Look at this picture. What can you tell me as much as you know about it. You may discuss as a group to help.

Fill in the Blanks

When two rectangles share a common side, the areas of the rectangles have a common factor. What is it? You can discuss.

The expressions 36+ 20and 4(9+ 5) both represent the area, in square feet, of the outer rectangle. They are equivalent expressions because they name the same value. Discuss what this means and how it makes sense, with your group.

​

Let's connect it!

Fill in the Blanks

Show that these expressions are equivalent by finding the value of each expression.

36 + 20 = _____. and

4(9 + 5) = 4 x _____=_____

Fill in the Blanks

You can also use the distributive property to show that the sum 36 + 20 is equivalent to the product 4(9 + 5).

To rewrite 36 + 20 as a product, you can use the greatest common factor (GCF) of 36 and 20 as one of the factors.

Rewrite the sum 42 + 35 as a product. Use the GCF of 42 and 35 as one of the factors. Use a sum as the other factor.

The GCF of 36 and 20 is _____.

Rewrite each term using GCF as a factor. _____ x 9 + _____ x 5

Use the distributive property. _____ (_____ + _____) Keep the number in order as shown.

Fill in the Blanks

Rewrite the sum 42 + 35 as a product.

Use the GCF of 42 and 35 as one of the factors. Use a sum as the other factor.

Open Ended

Reflect How can you use the distributive property to rewrite a sum of two terms as a product of two factors?

Draw

Fill in this graphic organizer of your knowledge of these terms. Let's put it in your notes.

Fill in the Blanks

Exit Ticket:

Rewrite the sum 15 + 45 as a product using the distributive property.