Review 1-6 A
Name_____________________________________
Date_________________ Class_______________
Directions: The goal of this assignment is to learn from and review with each other. Each concept
should be reviewed in groups of 2 to 4 people. On the line provided after each written concept, write
the names of the people in the group. Circle the name of the person (or people) leading the instruction.
If it is you, circle “me” written at the end of the line. You must have a different leader for each concept.
After reviewing with each other, complete the problems associated with each concept.
1. Converting between FDP and pictorial representations
Group: ____________________________________________________________________, me
A) Fill in the chart below with the equivalent simplified fractions, decimals, and percents.
Fraction
1
Decimal
Percent
7
9
0.035
3.02%
B) At far right is a Representations of a Portion Web (not a proportion web). Create a web to fit each
situation represented by the diagrams below.
a)
!
b)
2. Converting between FDP using repeating decimals
Group: ____________________________________________________________________, me
A) Fill in the chart below with the equivalent simplified fractions, decimals, and percents.
Fraction
2
Decimal
Percent
5
6
7.04
32.21%
3. Writing Equivalent fractions
Group: ____________________________________________________________________, me
A) Marcus throws all the fractions below into a bag. He will reach in and pull out a fraction at random.
What is the probability that the fraction he pulls out is equivalent to 20%? All of the fractions have
an equal likelihood of being picked. Circle the fractions equivalent to 20% and give the probability.
4. Operations with fractions, decimals, integers
Group: ____________________________________________________________________, me
A) Simplify the following expressions.
a)
−2.46 + 3.2(7.1x − 4) − 24.123x
c)
3
3
−4 − (−7.85) − 5
5
4
b)
3 ⎛ −2x
7⎞ ⎛ x
⎞
− ⎜
+ 1 ⎟ − ⎜ − 4⎟
⎝
⎠
⎝
⎠
4 5
9
5
B) Calculate the area and perimeter of the shape. All sides are either vertical or horizontal and the
shape has centered vertical and horizontal lines of symmetry (even if it doesn’t appear that way).
cm
cm
cm
cm
cm
Area=________________________
Perimeter =______________________
C) Draw a picture for each of the following situation (hint: splitting a rectangle, vertically for the first
fraction and then horizontally for the second, is easiest) and determine the fractional product.
a.
of
b.
of
D) Mr. Jones feeds his big cat
of a can of cat food and he feeds his small cat half that amount.
a. How much of a can does he feed his small cat?
b. How much of a can does he feed both cats?
5. Writing and solving proportions
Group: ____________________________________________________________________, me
A) Help! This year’s Pizza Day is tomorrow, and the teacher that orders all the pizza was just rushed
to the hospital with an appendicitis before she could order the pizzas! She left this note for your
team:
“I know I can count on you to order all the pizza! Last year when we had 360 students at the
school, we ordered a total of 120 pizzas. This year there are 390 students at the school. I
surveyed Mr. Brocamonti’s class and here is what I found out: 18 want pepperoni pizza, 5 like
cheese pizza, and 9 like veggie pizza. Use this information to order pizzas for tomorrow’s Pizza
Day. Don’t let me down. Thanks!”
Decide how many pizzas, as well as how many of each type, you will order. Justify your numbers
completely, because if you can’t, the principal will make YOU pay for all the pizzas instead of the
school paying for it!
6. Knowing equivalent proportions
Group: ____________________________________________________________________, me
A) Write three other proportions, using the same values, that are equivalent to this proportion:
5 shakes
x shakes
=
7 people 133 people
7. Probability
Group: ____________________________________________________________________, me
A) Maria has two new spinners to use for picking out her work uniform. One spinner is divided into
equal sections for kilt, pants, shorts and dress. The other spinner has three equal parts for the
colors teal, navy and maroon.
a. Draw and label two spinners that show these divisions.
b. Draw and label a probability rectangle below to help you decide the probability of
spinning each of the uniform items.
c. What is the probability of spinning a navy kilt?
d. What is the probability of spinning teal shorts or maroon pants?
e. What is the probability of spinning a black dress?
B) A game is played by spinning two spinners. If the colors match, the player wins. What is the
probability that a player wins? CLEARLY demonstrate how you are solving the problem.
(R = Red, G = Green, B = Blue)
B
R
R
G
G
B
8. Area and Perimeter
Group: ____________________________________________________________________, me
A) What is the area of the shape shown? Clearly show how the
area of each triangle and rectangle was calculated. All units
are in feet.
11
8
7
6
9
B) The perimeter of this rectangle is 22 inches. How long is m?
m
8.5 inches
9.
Constructing viable arguments and justifying reasoning
Group: ____________________________________________________________________, me
A) Each step of simplifying an expression is shown. On the line provided, write the name of the
property used in the simplification process or what the expression would be.
Step 1: 7x + (3x + 8) + (2x + 4)
Original expression
Step 2: (7x+ 3x) + 8 + (2x + 4)
____________________________________
Step 3: ___________________________
Combining like terms
Step 4: 10x + 8 + (4 + 2x)
____________________________________
Step 5: 10x + (8 + 4) + 2x
____________________________________
Step 6: ___________________________
Combining constant units (like terms)
Step 7: ___________________________
Commutative property
Step 8: ___________________________
Combining like term
B) A mother agreed to race her daughter in a 100-meter race on the condition that she get a 20 meter
head start. The daughter agreed and they took their marks. After five seconds the mother had run
42.5 meters while the daughter had run only 33.35 meters.
Based on this, Rocha says “The mother was ahead at the start of the race, since she got a head start,
and she is ahead after five seconds. This means the mother will win the race.”
Stephan says “In five seconds, the mother has lost ground, and the distance between the two is only
about 9 meters. I think the daughter will catch up.”
Tricia says, “The mother is running at a rate of 4.5 meters per second, but the daughter is running at a
rate of 6.7 meters per second. Since the daughter is running at a faster rate, she will win.”
Usef says, “The daughter might be running at a faster rate, but it may not be fast enough to catch her
mom within the 100 meter distance of the race. I don’t think we can figure out who will win.”
Comment on each person’s remarks on the race, as to whether or not the statements are accurate or
reasonable to conclude. Then make your own conclusions, justifying your statements completely. Who
do you think will win and why?
10. Graphing and scaling
Group: ____________________________________________________________________, me
A) Complete the scales on the number lines.
a. b.
125
12
0
-2
B) The graph at right is used to compare the age of a painting with its value. On the axes, place a dot
and label it:
a.
V for a new and very valuable painting.
b.
W for a not-too-old but worthless painting.
c.
X for a very old and very valuable painting.
Value
Age
11. Divisibility
Group: ____________________________________________________________________, me
Directions: Place a check in the box if the number on the left is divisible by the number on the top of
the column.
2
3
4
5
6
9
10
5,862
70,065
7,056
12. Similar figures and scale drawings
Group: ____________________________________________________________________, me
A) A rectangular classroom measures 30 feet by 26 feet. Use the scale 8 feet = 1 cm to draw a scaled
version of this rectangle in the space below.
B) If the two shapes below are similar, calculate the value of x.
21
51
2x + 3
34
13. Unit rates
Group: ____________________________________________________________________, me
A) Find the rates for each of the following situations. Show your work on each.
a.
Jennifer babysat for 7 hours and earned $52.50. What is her hourly rate of pay?
b.
Zeke drove 346 miles in 8 hours. What is his average rate of speed (mph)?
c.
Will bought 14 feet of rope for $ 10.50. What does the rope cost, per foot?
B) Bamboo is a fast growing plant. One type, Black Bamboo, grows at a rate of 11 cm per month,
while another, Golden Bamboo, grows at a rate of 1.2 meters per year. Which bamboo grows
faster? Explain.
C) Which is a better deal: five tulips for $3.00 or seven tulips for $4.00? Explain.
D) Suppose two swimmers jump in from opposite sides of a swimming pool, and begin to swim
towards each other. If one swimmer swims at a rate of 70 meters per minute, and the other swims
at a rate of 80 meters per minute, and the pool is 480 meters long, how long before they bump
heads? Show all work.
E) A rocket travels 16,133.5 feet every half a second. How fast is the rocket traveling in “miles per
hour”? Show your work!
14. Properties
Group: ____________________________________________________________________, me
A) Steve thought of the following steps in a number trick:
Think of a number, double it, add four and then multiply the result by five.
Let x represent the number in the trick above. Write the result of these four steps both as an expression
with parentheses and another simplified expression without parentheses.
B) Factor (or undo the distributive property in) the following expressions. Factor out the GCF.
a)
36x − 9 _____________________________________
b)
−4x − 6 ______________________________________
c)
5x 2 + 30x − 15 _________________________________
C) Name the property.
a)
(7 + 5) + 3 = (5 + 7) + 3___________________________________________________
b)
x = 1x____________________________________________________________
c)
8 + 0 = 8____________________________________________________________
D) Apply the given property to the given expression.
a) Zero Property of Multiplication: ______ . 37 = ______
b) Inverse Property of Multiplication: ______ . 37 = ______
c) Inverse Property of Addition: _______ + 11x = ______
d) Distributive Property: _______( 6x + ______) = −24x − 28
15. Combining Like terms
Group: ____________________________________________________________________, me
xy
A) Complete each Diamond Problem below. The pattern is shown at right.
x
y
x+y
a.
b.
–x
4x
c.
2x
7x
7x
12x
B) Can you combine x3 and x2? Why or why not? Explain completely.
C) The figure at right is made up of algebra tiles.
a) What is the perimeter of the shape? Simplify your
answer as much as possible.
x
1
1
1
x x
b) What is the area of the shape? Simplify your answer as much as possible.
c) If the algebra tiles were rearranged, how would the area change? Why?
D) When Tanya was given this problem to simplify:
8x – 16 + 7x2 – 4 + 3x + 9x – 4x2
she rewrote it like this:
–4x2 + 3x – 4
7x2 + 8x – 16
+ 9x
What in the world do you think Tanya is doing? Explain completely.
x
x
x
x
x
1
16. The 5D process
Group: ____________________________________________________________________, me
A)
A free-lance Web designer makes $17 per hour for the first 40 hours of work each week, and
$25.50 per hour for work in excess of 40 hours. One week she earned $896.75. How much
overtime did she work that week? Complete the 5-D process to answer the question.
Declarative sentence:
17.Algebraic inequalities
Group: ____________________________________________________________________, me
A) Solve and graph the solution (on the line provided). Use a ruler to scale properly.
3
− x+4 ≥ x−8
5
18. Metric Conversions
Group: ____________________________________________________________________, me
A) Convert the following:
a) 78 kL = __________dL
c) 4650 cm = __________m
b) 0.9 hg = __________g
d) 90.5 mg = _________dag