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GHSGT-Math-Obj. 33-Linear Expressions
INTERVENTION
LESSONS
FOR GHSGT
MATH
OBJECTIVE
33
Linear Expressions
1
GHSGT-Math-Obj. 33-Linear Expressions
2
Combining Like Terms
Lesson 1
GHSGT Objective #33:
Simplifies Expressions with and without grouping symbols
The student will correctly simplify algebraic expressions or demonstrate an understanding of the concept of
simplifying in algebra. Only number facts for integers from one to ten should be used. Expressions may include
one or two variables. Only integers should be used as coefficients.
Items should be of two types:
1.)
The student will recognize a correct or incorrect simplification of an expression.
2.)
The student will choose the correctly worked solution from the options.
Incorrect choices will represent errors such as a missing operation, a computational error, or an incorrect
operation.
Warm Up
Group the following terms into like and unlike terms and explain how you determined
which group to place each term.
5x, 3y, 2y, -4z, -3x, 5y, 3z, -4x, -3z, 5z, 3x, ½ y
Activator
To illustrate that only like terms can be combined through addition or subtraction:
Draw a simple two-piece puzzle with a picture of an apple on each one. Then draw
another two-piece puzzle with a picture of a banana or some other fruit on each one. When
you draw the puzzle edges, make certain the two different puzzles cannot fit together, i.e. the
apple piece only fits with the other apple piece. The banana piece only fits with the other
banana piece. Cut the pieces apart and give each student one piece of the puzzle. The
students should then try to find the piece that matches theirs. The idea of the exercise is that
apples only go with apples and bananas only go with bananas to illustrate the point of
combining like terms.
An extension of this activity would be to do a four-piece puzzle along the same
guidelines. All four apples pieces would fit together again, and so forth.
Work Session
PART 1
*Combining like terms
*Coefficients of 1
Things to Remember:

The understood coefficient is one (1).

The coefficient of 5n is 5, but the coefficient of d is 1.

Remember d = 1d.

Watch the operation!

Only like terms can be added or subtracted.

Exponents do not change in addition or subtraction.
GHSGT-Math-Obj. 33-Linear Expressions
3
Simplify the following expressions.
1.)
2.)
3.)
4.)
5.)
3x + 5x =
A.)
15x
C.)
8x
6.)
B.)
D.)
-2x
8x2
5y – 2y =
A.)
3
C.)
7y
B.)
D.)
3y
10y
2z + z =
A.)
3z
C.)
z
B.)
D.)
2z
2z2
f + 5f =
A.)
5f
C.)
6f2
B.)
D.)
6f
4f
3g + 2g + g =
A.)
5g
C.)
7g
7.)
8.)
9.)
10.)
B.)
D.)
6g
5g3
4x + 2z + 6x + 7z =
A.)
19xz
B.)
C.)
10x + 9z
D.)
6x + 13z
24x + 14z
5x + 3y – 2x + 4y =
A.)
3x + 7y
B.)
C.)
7x + 7y
D.)
3x – y
10xy
6x – 2y – 5x – 7y =
A.)
x + 5y
B.)
C.)
11x – 5y
D.)
x – 9y
x + 9y
4x – 3y + 2x + 3y =
A.)
6x – 6y
B.)
C.)
6x
D.)
2x
2x – 6y
5h – h + 4h =
A.)
10h
C.)
9h
0
8h
B.)
D.)
Closing
Have students show how they solved the problem and justify answers to the
class.
GHSGT-Math-Obj. 33-Linear Expressions
4
Simplify Expressions
Lesson 2
GHSGT Objective
Practice for Math Objective #33:
Simplifies Expressions with and without grouping symbols
The student will correctly simplify algebraic expressions or demonstrate an understanding of the concept of
simplifying in algebra. Only number facts for integers from one to ten should be used. Expressions may include
one or two variables. Only integers should be used as coefficients.
Items should be of two types:
1.)
The student will recognize a correct or incorrect simplification of an expression.
2.)
The student will choose the correctly worked solution from the options.
Incorrect choices will represent errors such as a missing operation, a computational error, or an incorrect
operation.
Warm up
Explain why you think the following expressions are equal or unequal.
3(2 + 5) = 6 + 15
Activator
To illustrate the idea of the distributive property:
You as the teacher are the “distributor” much like the number outside the parentheses.
All the students are numbers or terms “inside the parentheses”. Give or “distribute” a piece of
candy to each person on only one row of the class, and then ask whether it seems fair that
only part of the class participation in the distribution. The answer should be “no”, so you as the
“distributor” would now pique their interest by asking a question such as “Oh, so you think
everyone should get a piece of candy?” You then give everyone a piece of candy (You may
want to either take the piece from those from the first round and then give it back to them or let
them keep the first piece for participating and then make it clear that you are now showing
correct distribution.
The students should see from the second example that distribution is not correctly done
unless you give it to every term inside the parentheses.
Work Session
Work the Distributive Property Worksheet and compare answers with your partner.
Closing
Have students share their answers with the class by explaining how they arrived at their
answer.
GHSGT-Math-Obj. 33-Linear Expressions
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* Distributive Property Worksheet
Things to Remember:

The number outside is distributed onto each number inside.
o Example:
3(6a + 4b) = 3¢6a + 3¢4b = 18a + 12b

Distribution can also be done from the back end of the problem.
o Example:
(5c – 2d)6 = 6¢5c – 6¢2d = 30c – 12d
Simplify the following expressions.
1.)
5(3x – 2) =
A.)
15x – 10
C.)
8x – 2
B.)
D.)
A.)
C.)
15x – 2
8x – 7
7.)
2.)
6(4x + 1) =
A.)
24x + 1
C.)
24x + 6
B.)
D.)
10x + 1
10x + 7
8.)
3.)
(5x + 2)3 =
A.)
5x + 6
C.)
8x + 5
B.)
D.)
15x + 6
21x
9.)
4.)
(x + 4)2 =
A.)
2x + 8
C.)
x+8
B.)
D.)
2x + 6
2x + 4
10.)
5.)
6.)
4(c – 1) =
A.)
4c
C.)
4c – 4
2(3x + 4y) =
B.)
D.)
4c – 1
c–4
6x + 8y
5x + 6y
B.)
D.)
6x + 4y
5x + 4y
3(x – 2y) =
A.)
3x – 2y
C.)
3x – 5y
B.)
D.)
3x – 6y
6xy
(3a + 2b)4 =
A.)
7a + 2b
C.)
12a + 8b
B.)
D.)
7a + 6b
12a + 2b
(7x – y)2 =
A.)
7x – 2y
C.)
9x – 2y
B.)
D.)
14x – 2y
14x – y
2(x + y) =
A.)
2x + y
C.)
x + 2y
B.)
D.)
2xy
2x + 2y
GHSGT-Math-Obj. 33-Linear Expressions
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Simplify Expressions
Lesson 3
GHSGT Objective
Practice for Math Objective #33:
Simplifies Expressions with and without grouping symbols
The student will correctly simplify algebraic expressions or demonstrate an understanding of the
concept of simplifying in algebra. Only number facts for integers from one to ten should be used.
Expressions may include one or two variables. Only integers should be used as coefficients.
Items should be of two types:
1.)
The student will recognize a correct or incorrect simplification of an expression.
2.)
The student will choose the correctly worked solution from the options.
Incorrect choices will represent errors such as a missing operation, a computational error, or an
incorrect operation.
Warm Up
Judy, Charlotte, and Suzanne had all saved money for their mother’s
birthday present. Judy had saved three times as much as Charlotte. Their
dad said if Charlotte and Suzanne would put their money together, he would
double it. Write and expression for how much money the three girls have
together. Be sure and define what each variable represents in the expression.
Activator
To illustrate the idea of distributive property and combining like terms later:
Draw a large set of parentheses and two plus signs on the board (or cut
out a set from a piece of poster board). Select two students to be “inside the
parentheses” and one to be “outside”. As the distributor, remind the students you
only distribute to those inside the parentheses. The student outside must be told
“you are outside my boundaries. I cannot distribute to you.”
The students could act out a problem like 3(x + 2) + 1 by cutting out
numbers and variables:
Distributor: “x, I multiply you by three and rename you 3x.”
[distributor takes the x and
gives 3 x’s in return]
Distributor: “2, I multiply you by three and rename you 6.”
[distributor takes the 2 and
gives a 6 in its place]
Student “1”: “What about me?”
Distributor: “1, you are outside my boundaries, but now that I am
finished, 6 may join you.
[Student “6” joins with Student “1”]
GHSGT-Math-Obj. 33-Linear Expressions
Distributor:
7
“6 and 1, I now join you, and you shall be called 7.”
[distributor takes the 6 and
1 cards and gives a 7 for
the students now joined.]
(The skit is hokey, but if it gets the point across … )
Work Session
Students work with a partner to solve the Distributive Property and
Combining Like Terms Worksheet.
Closing
Partners come up and explain to the class how they arrived at the answer for
each problem. They should use correct math terminology.
GHSGT-Math-Obj. 33-Linear Expressions
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Distributive Property and Combining Like Terms Worksheet
Things to Remember:

Do distributive property first. Then combine like terms.
o Example:
3(2x + 4) – 5 = 6x + 12 – 5 =
6x + 7
o Example:
2(4x + y) + 3x = 8x + 2y + 3x = 11x + 2y

Items added or subtracted outside the parentheses cannot be
combined with items inside the parentheses until after you have
distributed.
Simplify the following expressions.
1.)
2.)
3.)
4.)
5.)
6.)
7.)
4(2x – y) + 3x
A.)
11x – 4y
B.)
5x – 4y
C.)
3(3x + 2y) + 2y
A.)
9x + 12y
B.)
9x + 8y
C.) 6x + 7y
4(3a + 3b) – 3b
A.)
7a + 9b
B.)
12a
6(c – 2d) + 2c
A.)
18c – 12d
B.)
8c – 12d
C.)
2(4x + 3) + 2
A.)
6x + 8
B.)
8x + 10
C.) 8x + 8
3(3x + 4) - 2
A.)
21x – 2
B.)
9x + 10
6(x + 4) - 1
A.)
6x + 23
B.)
6x + 18
C.)
11x – y
12a + 9b
D.) 20x – 4y
D.)
D.)
8c – 2d
15xy + 2y
12a + 4b
D.)
18c
D.)
14x + 2
C.)
9x + 6 D.)
21x – 6
C.)
24x – 1
D.)
6x + 9
GHSGT-Math-Obj. 33-Linear Expressions
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Simplify Expressions
Lesson 4
GHSGT Objective
Practice for Math Objective #33:
Simplifies Expressions with and without grouping symbols
The student will correctly simplify algebraic expressions or demonstrate an understanding of the
concept of simplifying in algebra. Only number facts for integers from one to ten should be used.
Expressions may include one or two variables. Only integers should be used as coefficients.
Items should be of two types:
1.)
The student will recognize a correct or incorrect simplification of an expression.
2.)
The student will choose the correctly worked solution from the options.
Incorrect choices will represent errors such as a missing operation, a computational error, or an
incorrect operation.
Warm Up
John had 6 pieces of Bubble Gum. His mother gave him 12 more pieces.
John decided to share his bubble gum with 2 of his friends. He worked out
the problem and said that he and each of his friends would get 14 pieces of
Bubble Gum. Explain why you think his work is correct or incorrect.
6 + 12 = 2 + 12 = 14
3
Activator
To illustrate that both terms must be divided by the bottom term:
The only idea we have found at this time is to maybe do a problem with
numbers only and no variables. Students would need to see that by not dividing
BOTH parts that the combined answer would be wrong.
Example:
12 + 18 =
12 + 18 = 2 + 3 = 5
(12 + 18 = 30
= 5)
6
6
6
6
6
If students had only canceled one part, they may get this:
12 + 18 = 2 + 18 = 20
6
Work Session
Work the Simplify by Division Worksheet with a partner.
Closing
A pair will come and explain to the whole class how they solved their
problem.
GHSGT-Math-Obj. 33-Linear Expressions
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Simplify with Division Worksheet
Things to Remember:

Separate the fraction into individual parts and simplify the
parts.
o Example:
6x + 9y = 6x + 9y = 2x + 3y
3
3
3

Never cancel individual pieces.
o Example:
6x + 8y = 3x + 8y is wrong because they only
2
canceled the 6x and 2 instead of breaking apart into
two fractions.
Simplify the following expressions.
1.)
4x – 10y =
2
A.)
2x – 5y
B.)
2x – 10y
C.)
-3xy D.)
4x – 5y
2.)
3.)
4.)
5.)
6.)
6a + 8b =
4
A.)
3a + 8b
2
16c + 12d =
8
A.)
4c + 3d
2
15e – 25f =
5
A.)
3e – 5f
10g – 4h =
6
A.) 4g – 2h
24j – k =
6
A.) 4j – 6k
B.)
B.)
3a + b
2 2
C.)
6a + 2b
4
D.)
B.)
2c + 6d
4
C.)
2c + 3d
2
D.) 2c + 4d
B.)
10e – 5f
C.)
3e – 25f
5g – 4h
3
B.) 4j – k
6
C.)
10g – 2h
3
3a + 2b
2
D.) 15e – 5f
D.)5g – 2h
3
3
C.) 18j – 6k D.) 4j – k
GHSGT-Math-Obj. 33-Linear Expressions
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Simplify Expressions Assessment
GHSGT Objective #33
Name___________________________________ Date_______________
1. 14x – 4y – 8x – 7y =
2. 4x – 2y + x + 3y =
3. 6h – h + 3h =
4. 8(x – 2y) =
5. (3a + 2b)5 =
6. 6(3x + 4) =
7. 5(c – 2d) + 3c =
GHSGT-Math-Obj. 33-Linear Expressions
8. 2(3x + 6x – 4y – 5x – 7y) =
9. 4(2a + 2b) – 3b =
10.
6a + 8b =
3
11. 16c + 12d =
4
12. 15e – 25f =
3
12