Use Properties of Operations to Generate Equivalent Expression
Common Core: Engage New York 7.EE.A.1 and 7.EE.A.2
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What does 7.EE.A.1 cover? Apply properties of operations as
strategies to add, subtract, factor, and expand linear expressions
with rational coefficients.
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What does 7.EE.A.2 cover? Understand that rewriting an
expression in different forms in a problem context can shed light
on the problem and how the quantities in it are related.
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Table of Contents DateTitlePage 12/9/13Post Investigation 1-
Check Up HW Assignment Due THURSDAY 12/12/13 HW Accuracy Grade (not
completion only) 12/10/137.EE.1- Engage NY Lesson 1: Generating
Equivalent Expressions *Attach worksheets* Fresh Left
12/13/137.EE.1- Engage NY Lesson 2: Generating Equivalent
Expressions *Attach worksheets* Fresh left 1/8/147.EE.2- Engage NY
Lesson 3: Writing Products as Sums and Sums as Products *Attach
worksheets* Fresh Left 1/14/147.EE.2- Engage NY Lesson 4: Writing
Products as Sums and Sums as Products *Attach worksheets* Fresh
Left
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Focus 6 Solving Equations Learning Goal Students understand
that rewriting an expression in different forms in a problem
context can shed light on the problem and how the quantities in it
are related.
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Today, my learning target is to Use an area model to write
products as sums and sums as products. Use the fact that the
opposite of a number is the same as multiplying by 1 to write the
opposite of a sum in standard form. Recognize that rewriting an
expression in a different form can shed light on the problem and
how the quantities in it are related.
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MY PROGRESS CHART Before we start the Learning Target Lesson,
think about the Learning Target for today. How much prior knowledge
do you have regarding that goal? Chart your prior knowledge using
your pre-target score icon.
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Teacher Directed Example 1 (4 minutes) Give students two
minutes to write equivalent expressions using the distributive
property for the first four problems. Then, ask students to try to
go backwards and write equivalent expressions for the last four
problems.
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What is happening when you go backwards to find equivalent
expressions for expressions e, f, g, and h? What are the terms
being divided by? Write the equivalent expression to 8+4. In the
same way dividing undoes multiplying, factoring undoes expanding.
They are being divided by a common factor. Would it be incorrect to
factor out a 2 instead of a 4? It would not be incorrect, but in
order to factor completely, we would need to factor out a 2 again.
Mathematicians have decided that "factoring" generally means
factoring with the greatest common factor of terms. 8+4 Commutative
Property 4(2)+4(1) Equivalent Expression 4(2+1) Distributive
Property
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Student Practice Exercise 1 (3 minutes)-
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Student Problem Set (part 1)
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Student Problem Set (part 1) Answers
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Teacher Directed Example 2 (5 minutes) In this example, let the
letters and stand for positive integers, and let 2, 12, and 8 stand
for the number of squares in a rectangular array. The goal is to
find three rectangular arrays for 2, 12, and 8 that have the same
number of rows. Let students explore different possibilities. For
example, a rectangular array for 2 that is 2 by or by 2. Make sure
you point out that there are many potential rectangular arrays for
12: 12 by, 3 by 4, 4 by 3, 2 by 6, etc. Once students see that
three rectangular arrays can be created with two rows each,
concatenate (link) them as in the picture below, and lead students
through the discussion below on GCF (i.e., the algebraic way to
recognize the factors).
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What does 2 represent in the rectangle above? That the
rectangle has an area of 2 or can be covered by 2 unit squares.
What does the large rectangle that contains the three smaller
rectangles represent? The large rectangle represents 2+12+8 smaller
boxes. It also represents a rectangular array of boxes given by a
product (the number of rows of boxes times the number of columns).
How many rows are there in this rectangular array? 2 What are the
missing values, and how do you know? X, 6y, and 4. If the products
are given in the area of the rectangular regions, divide the
regions by 2 to get the missing values. Write the expression as a
product of two factors and then as a sum. 2(+6+4)=2+12+8 How does
this exercise differ from the exercises we did during the previous
lesson? How is this exercise similar to the ones we did during the
previous lesson? We are doing the inverse of writing products as
sums. Before, we wrote a product as a sum using the distributive
property. Now, we are writing a sum as a product using the
distributive property.
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Student Practice Exercise 2 (3 minutes)- (++), ++ (++)(++)
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Teacher Directed Example 3 (4 minutes)
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Student Problem Set (part 2)
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Student Problem Set (part 2)Answers
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Student Problem Set (parts 3 & 4)
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Student Problem Set (parts 3 & 4) Answers
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Teacher Directed Example 4 (4 min) A new miniature golf and
arcade opened up in town. For convenient ordering, a play package
is available to purchase. It includes two rounds of golf and 20
arcade tokens, plus three dollars off. There is a group of six
friends purchasing this package. Let g represent the cost of a
round of gold and let t represent the cost of a token. Write two
different expressions that represent the total amount this group
spent. Explain how each expression describes the situation in a
different way. Two equivalent expressions are as follows: 6(2+203)
Each person will pay for 2 rounds of golf and 20 tokens and will be
discounted 3 dollars. This expression is 6 times the quantity of
each friends cost. 12+12018 The total cost is equal to 12 games of
golf plus 120 tokens, minus 18 dollars off the entire bill.
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Student Problem Set (part 5) 5. Xander goes to the movies with
his family. Each family member buys a ticket and two boxes of
popcorn. If there are five members of his family, let t represent
the cost of a ticket and p represent the cost of a box of popcorn.
Write two different expressions that represent the total amount his
family spent. Explain how each expression describes the situation
in a different way.
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Student Problem Set (part 5) ANSWERS
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Teacher Directed Example 5 (3 min)
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Student Practice Exercise 5 (3 min)
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Teacher Directed Example 6 (3 min)
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Student Practice Exercise 6 (7 min)
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Closing (3 min) In writing products as sums, what is happening
when you take the opposite of a term or factor? The term or factor
is multiplied by 1. In using the distributive property, every term
inside the parentheses is multiplied by 1. Describe the process you
used to write an expression in the form of the sum of terms as an
equivalent expression in the form of a product of factors. Writing
sums as products is the backwards process of writing products as
sums; so, instead of distributing and multiplying, the product is
being factored.
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Student Problem Set (parts 6 & 7)
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Student Problem Set (parts 6 & 7) ANSWERS
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Student Exit Ticket (4 min)- Lesson 4 Writing Products as Sums
and Sums as Products 1. Write the expression below in standard
form. 3 2(1+4 ) 2. Write the expression below as a product of two
factors. 6+8+4
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Exit Ticket - Lesson 4 Solution- Writing Products as Sums and
Sums as Products
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Today, I achieved my learning target by Using an area model to
write products as sums and sums as products. Using the fact that
the opposite of a number is the same as multiplying by 1 to write
the opposite of a sum in standard form. Recognizing that rewriting
an expression in a different form can shed light on the problem and
how the quantities in it are related.
Slide 37
MY PROGRESS CHART Before we start the Learning Target Lesson,
think about the Learning Target for today. How much prior knowledge
do you have regarding that goal? Chart your prior knowledge using
your pre-target score icon.
Slide 38
The End of Lesson 4 Writing Products as Sums and Sums as
Products