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Grade 4 SAMPLER
MCAS Mathematics
Student Set
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MCAS Finish Line
MCAS Performance Indicator
Contents
Introduction to MCAS Finish Line Mathematics 4. . . . . . . . . . . . . . . . . . . . . . 5
Understanding Mathematical Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Unit 1: Number Sense
Lesson 1 Whole Number Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Lesson 2 Comparing and Ordering Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Lesson 3 Rounding Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Lesson 4 Decimal Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Lesson 5 Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Lesson 6 Equivalent Forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Lesson 7 Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Number Sense Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Unit 2: Operations
Lesson 1 Operation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Lesson 2 Adding and Subtracting Whole Numbers . . . . . . . . . . . . . . . . . . . . . 49
Lesson 3 Multiplication and Division Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Lesson 4 Multiplying Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Lesson 5 Dividing Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Lesson 6 Adding and Subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Lesson 7 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Operations Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Unit 3: Geometry, Part 1
Lesson 1 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Lesson 2 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Lesson 3 Plane Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Lesson 4 Solid Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Lesson 5 Coordinate Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Lesson 6 Congruence and Similarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Lesson 7 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Geometry Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Unit 4: Patterns, Relations, and Algebra
Lesson 1 Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Lesson 2 Writing Open Sentences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Lesson 3 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Lesson 4 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Lesson 5 Proportional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Patterns, Relations, and Algebra Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Unit 5: Measurement
Lesson 1 Customary Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Lesson 2 Metric Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Lesson 3 Measurement Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Lesson 4 Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Lesson 5 Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Lesson 6 Estimating Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Lesson 7 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Measurement Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Unit 6: Data Analysis, Statistics, and Probability
Lesson 1 Tables and Tallies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Lesson 2 Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Lesson 3 Pictographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Lesson 4 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Lesson 5 Line Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Lesson 6 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Data Analysis, Statistics, and Probability Review. . . . . . . . . . . . . . . . . . . . . . 189
LESSON
4
Solid Figures
Indicators
,
,
4.G.1, 2, 9
A solid figure has three dimensions: length, width, and height.
Remember—
Some solids have curved surfaces.
A polygon is a closed
plane figure with line
segments for sides.
base
base
A cone has 1 base. The base
is a circle.
base
A cylinder has 2 bases. Both
are circles.
,
Other solids have flat surfaces that are based on polygons. Each
kind has a certain number of faces, edges, and vertices.
,
Prisms are solids with sides that are rectangles. They have two
faces that are bases. The base can be any polygon.
A sphere is a
round solid,
like a ball.
Vertex
Face
6 faces
8 vertices
12 edges
A rectangular prism has a
rectangle for the base.
,
A circle is a closed plane
figure, but it is not a
polygon.
5 faces
6 vertices
9 edges
A triangular pyramid has a
triangle for the base.
Unit 3
A cube is a special kind
of rectangular prism. All
the faces are squares.
A triangular prism has a
triangle for the base.
Pyramids are solids with sides that are triangles that meet at
one point. They have one face that is a base. The base can be
any polygon.
4 faces
4 vertices
6 edges
Edge
5 faces
5 vertices
8 edges
A rectangular pyramid has
a rectangle for the base.
A net shows what a solid
looks like unfolded.
This net of a cube shows
the 6 squares laid flat.
A pyramid always has
the same number of
vertices as it does faces.
89
Geometry
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Read each problem. Circle the letter of the best answer.
1 Nelson cut out this pattern.
P
R
S
4 How many vertices does this solid have?
V
T
When Nelson folds the pattern, which
point will meet point R?
A
point P
B
point S
C
point T
D
point V
A
3
C
5
B
4
D
6
5 Which solid figure has 5 faces and 9 edges?
The correct answer is B. The pattern has 6
sides, so it will fold to make a rectangular
prism. Point R will meet point S.
A
C
B
D
2 Which picture shows a cone?
A
C
6 Which shape has more than 1 square
face?
B
D
A
cube
C
cylinder
B
cone
D
square pyramid
7 Look at this figure.
3 How many edges does a rectangular prism
have?
A
4
B
6
Which of these patterns was used to
make the figure?
C
8
A
C
D
12
B
D
90
Unit 3
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Geometry
Read each problem. Write your answers.
8 Amanda wrote this clue to describe a geometric solid.
This solid has 4 faces and 4 vertices.
What is the name of the solid?
triangular pyramid
Answer: ____________________________________
Pyramids always have the same number of vertices as faces. If a pyramid has a total of 4
faces, then one must be the base and the other three, the sides. So the pyramid must be a
triangular pyramid.
9 Look at this pattern. Name the solid figure the pattern would form
when it is folded.
Answer: ____________________________________
10 A certain solid has a curved surface. It has no bases. It has no edges
or vertices. What is the name of the solid?
Answer: ________________________
11 This package has the shape of a solid. How many faces does
the solid have?
Han
d
Wit le
h
Car
e
Answer: ____________
12 In the space below, draw a cube.
Unit 3
91
Geometry
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Read the problem. Write your answer for each part.
13 Solana cut out these shapes and taped them together to make a
solid.
a. In the space below, draw the solid Solana made. Name the
solid. Explain how you know your answer is correct.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
b. How many faces, edges, and vertices does the solid have?
Show or explain how you got your answer.
Ask Yourself
How many edges will
there be after the
faces meet?
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
92
Unit 3
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Geometry
Question 17 is an open-response question.
• Be sure to answer and label all parts of the question below.
• Show all of your work (diagrams, tables, or computations) in the space provided.
• If you do the work in your head, explain in writing how you did the work.
17 The table shows how the number of passengers on a train
depends on the number of cars.
TRAIN PASSENGERS
Number of
Cars
Number of
Passengers
2
60
4
120
6
180
8
240
10
300
a. How many passengers are in each train car? Show or explain
how you got your answer.
Answer: ____________
b. How many passengers are on a train with 16 cars? Show or
explain how you got your answer.
Answer: ____________
c. If a train has n cars, explain how can you find the total number
of passengers.
___________________________________________________
___________________________________________________
Session One
10
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Stop
22 Each IN number is changed to an OUT
25 There are 20 students in Lily’s class. The
number by a rule.
IN
OUT
1
4
2
5
3
6
4
7
5
8
first letter of each student's name is
listed below.
A, B, C, C, E, G, H, H, J, J,
J, J, K, L, N, R, S, T, T, V
Which table shows how many names
start with A–F, G–L, M–R, and S–Z?
A
First Letter
Number
Which of these could be the rule?
A–F
5
A add 1
G–L
8
M–R
3
S–Z
4
First Letter
Number
A–F
5
G–L
8
M–R
2
S–Z
5
First Letter
Number
A–F
5
G–L
9
M–R
3
S–Z
3
First Letter
Number
A–F
5
G–L
9
M–R
2
S–Z
4
B add 3
C subtract 3
B
D multiply by 2
23 Which shape has a line of symmetry?
A
C
C
B
D
24 A pickup truck held
1
4
ton of gravel
and
ton of sand. What was the total
weight of the load?
3
8
1
2
ton
B
5
8
ton
C
3
4
ton
D
7
8
ton
A
D
26 A roll of quarters contains 40 quarters. If
Session Two
Aidan has n rolls of quarters, plus 15
extra quarters, which expression shows
the total number of quarters he has?
A 40 ⫹ n ⫹ 15
C 40 ⫻ n ⫹ 15
B 40 ⫹ n ⫻ 15
D 40 ⫻ n ⫻ 15
13
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