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Lesson 1: Generating Equivalent Expressions
Find the sum of (8a + 2b—4) and (3b—5)
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Lesson 2a: Generating Equivalent Expressions
Write the expression in standard form:
(4f—3 + 2g) - (-4g + 2)
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Lesson 2b: Generating Equivalent Expressions
Rewrite the expression in standard form:
27h ÷ 3h
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Lesson 3: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers
Bradley and Louie are roommates at college. At the beginning of the semester, they
each paid a security deposit of A dollars. When they move out, their landlord will deduct from this deposit any expenses B for excessive wear and tear and refund the remaining amount. Bradley and Louie will share the expenses equally.
• Write an expression that describes the amount each roommate will receive from
the landlord when his lease expires.
•
Evaluate the expression using the following information: Each roommate paid a
$125 deposit, and the landlord deducted $50 total for damages.
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Lesson 4: Writing Products as Sums and Sums as Products
A square fountain area with side length s is bordered by two rows of square tiles along
its perimeter as shown. Express the total number of light grey tiles needed (only the
outside border) in terms of s in three different ways.
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Lesson 5: Writing Products as Sums and Sums as Products
Write the expression below in standard form.
3h—2(1 + 4h)
Write the expression below as a product of two factors.
6m + 8n + 4
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Lesson 6: Using the Identity and Inverse to Write Equivalent
Expressions
Find the sum of 5x + 20 and the opposite of 20. Write an equivalent expression using
the fewest number of terms. Justify each step.
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Lesson 7a: Combining Rational Number Like Terms
For the problem
, Tyson created an equivalent expression to the
problem using the following steps:
Is his final expression equivalent to the initial expression? Show how you know. If the
two expressions are not equivalent, find Tyson’s mistake and correct it.
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Lesson 7b: Combining Rational Number Like Terms
Combine like terms in order to simplify the following expression.
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Lesson 8: Understanding Equations
Check whether the given value of x is a solution to each equation. Justify your answer.
1
/3 (x + 4) = 20; x = 48
3x—1 = 5x + 10; x = -51/2
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Lesson 9: Using If-Then Moves in Solving Equations
Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. If
Brand A scooter traveled 25 miles in 3 hours at top speed, at what rate would Brand B
scooter be traveling at top speed? Write an equation to determine the solution.
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Lesson 10: Comparing Tape Diagram Solutions to Algebraic
Solutions
Eric’s father works two part-time jobs; one in the morning and one in the afternoon. He
works a total of 40 hours each 5-day work week. If his schedule is the same each day,
and he works 3 hours each morning, how many hours does Eric’s father work in the
afternoon?
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Lesson 11: Solving Equations Using Algebra
Susan and Bonnie are shopping for school clothes. Susan has $50 and a coupon for a
$10 discount at a clothing store where each shirt costs $12.
Susan thinks she can buy 3 shirts, but Bonnie says that Susan can buy 5 shirts. The
equations they used to model the problems are listed below. Solve each equation algebraically, and determine who is correct and why.
Susan’s Equation
12n + 10 = 50
Bonnie’s Equation
12n—10 = 50
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Lesson 12: Solving Equations Using Algebra
Andrew’s math teacher entered the 7th grade students in a math competition. There
was an enrollment fee of $30 and also an $11 charge for each packet of 10 tests. The
total cost was $151. How many tests were purchased? Set up an equation to model
this situation, and then solve it.
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Lesson13:
Properties of Inequalities
Given the initial inequality 2 > -4, identify which of the following operations preserves
the inequality symbol and which operations reverse the inequality symbol. Write the
new inequality after the operations are performed.
Multiply both sides by –2
Add –2 to both sides
Divide both sides by 2
Multiply both sides by –1/2
Subtract –3 from both sides
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Lesson 14: Inequalities
Shaggy earned $7.55 per hour plus an additional $100 in tips waiting tables on Saturday. He earned at least $160 in all. Write an inequality and find the minimum number
of hours (to the nearest hour) that Shaggy worked on Saturday.
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Lesson 15: Solving Inequalities
Games at the carnival cost $3 each. The prizes awarded to winners cost the owner
$145.65. How many games must be played for the owner of the game to make at
least $50?
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Lesson 16a: Graphing Solutions to Inequalities
You get twice the allowance of your little sister. Together you get at least $15 each
week. Write and solve an inequality to show how much allowance your little sister
could get. Graph the results.
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Lesson 16b: Graphing Solutions to Inequalities
The middle school art club sells candles for a fundraiser. The first week of the fundraiser the club sells 7 cases of candles. Each case contains 40 candles. The goal is to
sell at least 13 cases. During the second week of the fundraiser, the club meets its
goal. Write, solve, and graph an inequality that can be used to find the possible number of candles sold the second week.
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Lesson 17: Angle Problems and Solving Equations
Write an equation for the angle relationship shown in the figure and solve for x. Find
the measures of angles RQS and TQU.
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Lesson 18: The Most Famous Ratio of All
Brianna’s parents built a swimming pool in the back yard. Brianna says the distance
around the pool is 120 feet. Is she correct? Explain why or why not.
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Lesson 19: The Area of a Circle
Complete each statement using the words or algebraic expressions listed in the word
bank below.
The length of the
the length of the
the circle.
of the rectangular region approximates
of
The
of
the rectangle approximates the length
as one-half of the circumference of the circle.
The circumference of the circle is
The
of the
2r.
The ratio of the circumference to the diameter is
Area (circle) = Area of (
Word Bank:
.
.
) = 1/2*circumference*r = 1/2(2πr) = π*r*r =
radius; height; base; 2πr; diameter; circle; rectangle; πr2; π
.
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Lesson 20: Unknown Area Problems on the Coordinate Plane
The figure ABCD is a rectangle. AB = 2 units, AD = 4 units, and AE = FC = 1 unit.
Find the area of rectangle ABCD.
Find the area of triangle ABE.
Find the area of triangle DCF.
Find the area of parallelogram BEDF.
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Lesson 21: Composite Area Problems
The unshaded regions are quarter circles. Find the area of the shaded region.
Use π = 3.14.
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Lesson 22: Surface Area
Six cubes are glued together to form the solid shown in the diagram. If the edge of
each cube measures 11/2 inches in length, what is the surface area of the solid?
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Lesson 23: The Volume of a Right Prism
The base of the right prism is a hexagon composed of a rectangle and two triangles.
Find the volume of the fight hexagonal prism using the formula V = Bh.
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Lesson 24: The Volume of a Right Prism
Lawrence poured 27.3328 liters of water into a right rectangular prism shaped tank.
The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank
was 2/3 full. 1 liter = 1000 cm3.
How deep is the water?
How deep is the tank?
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Lesson 25: Volume and Surface Area
Melody is planning a raised bed for her vegetable garden from the diagram. How
many square feet of wood does she need to create the bed?