# 7th Grade Estimation and Computation

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```					7th Grade Estimation and Computation

Estimation: The student solves problems (including real-world situations) using
estimation by:

[7] E&C-1 Identifying or using [a variety of L] strategies, including truncating,
rounding, front-end estimation, and compatible numbers, to check for
reasonableness of solutions (M3.3.1) and

[7] E&C-2 (L) Comparing results of different strategies (M3.3.1)

Solve problems 1-5 using a variety of estimation techniques to determine various
solutions when using the same data.

Mary and Jim bought the following items at a school supply store:

Item purchased           Number purchased           Cost of each item
Pencils                      2                            \$1.49
Pens                         4                              2.74
Puzzles                      6                              3.25
Posters                      2                              4.19
Packs of paper               4                               .79
Notebooks                    2                            12.95

1. Use front end estimation to determine the total amount spent for all items.

Total ____________

2. Use compatible numbers and determine how much Mary would spend if she purchases
the following:

1 notebook, 1 pack of paper, and 1 pen _________________

3. Use compatible numbers and give the amount each person would pay if the total bill is
split between Jim, Mary, and Kim. __________________

4. If the bill is split evenly between just Jim and Mary, how much would each pay to the
nearest cent? ___________________

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7 Grade Est. & Computation   Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 1 of 5
5. Round each item bought to the nearest ten cents. After rounding to the nearest ten
cents, how much would the total bill be? ____________

Computation: The student accurately solves problems (including real-world
situations) involving:

[7] E&C-3 Adding or subtracting fractions or mixed numbers with unlike
denominators, or decimals to the thousandths place (M3.3.3)

2                        1                               1
George ran 4   miles on Monday and 2   miles on Tuesday. Gracie ran 3 miles on
3                        4                               2
3
Monday and 3    miles on Tuesday.
4

1. Who ran more miles? Show your work and explain your thinking.

2. If George and Gracie started running together Tuesday, how much farther did Gracie
run that day than George? Show your work and explain your thinking.

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7 Grade Est. & Computation   Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 2 of 5
[7] E&C-4 Multiplying or dividing decimals to hundredths, or multiplying or
dividing by powers of ten, or multiplying or dividing fractions or mixed numbers
(M3.3.4)

These shapes represent decimal values.

a.                       b.            c.                d.

*The "FLAT" (a) represents 1 whole

*The "Strip" (b) represents .1 (one tenth)

*The "Cube" (c) represents .01 (one hundredth)

*The "Tiny Tot" (d) represents .001 (one thousandth)

1. Using the shapes and their values from above, solve the following problems by writing
the decimal number represented by:

a. 4 A's, 7 B's, 3 C's, and 2 D's. What is the decimal number? __________________

b. 145 A's, 8 B's, and 6 D's. What is the number? _____________________

c. Which shape represents the largest place value?______________________

d. How many tiny tots make a cube? ___________

2. Using information from above, construct a diagram of the following decimal numbers:
(Place the model you construct inside the box provided.)

a.         2.58                                             b.              0 .952

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7 Grade Est. & Computation    Alaska GLE Formative Assessments for Classroom Use, Feb. 2006    Page 3 of 5

[7] E&C-5 Converting between equivalent fractions, terminating decimals, or
percents (10% = 1/10 = 0.1) (M3.3.5)

1. Complete the equivalency table. Simplify.

Percent           Fraction              Decimal

1.      210%

3
2.
8

3.                                           .075

4.      .8%
2
5.                    5

[7] E&C-6 Solving proportions using a given scale (M3.3.6)

1. Give the unit rate of each of the following:

a. If 15 lbs. of chicken cost \$56.85, what is the cost of one pound?

______________________________________________________

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7 Grade Est. & Computation   Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 4 of 5
b. If Helen travels 567 miles in 9 hours, how far does she travel in one hour?

______________________________________________________

c. If Mitch types 275 words in 5 minutes, how many words can he type in one
minute?

______________________________________________________

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7 Grade Est. & Computation   Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 5 of 5

Estimation: The student solves problems (including real-world situations) using
estimation by:

[7] E&C-1 Identifying or using [a variety of L] strategies, including truncating,
rounding, front-end estimation, and compatible numbers, to check for
reasonableness of solutions (M3.3.1) and

[7] E&C-2 (L) Comparing results of different strategies (M3.3.1)

Solve problems 1- 5 using a variety of estimation techniques to determine various
solutions when using the same data.

Mary and Jim bought the following items at a school supply store:

Item purchased           Number purchased          Cost of each item
Pencils                      2                           \$1.49
Pens                         4                             2.74
Puzzles                      6                             3.25
Posters                      2                             4.19
Packs of paper               4                              .79
Notebooks                    2                           12.95

1. Use front end estimation to determine the total amount spent for all items.

Total \$72.40

2. Use compatible numbers and determine how much Mary would spend if she purchases
the following:

1 notebook, 1 pack of paper, and 1 pen \$16.50

3. Use compatible numbers and give the amount each person would pay if the total bill is
split between Jim, Mary, and Kim. \$24.00

4. If the bill is split evenly between just Jim and Mary, how much would each pay to the
nearest cent? \$38.65

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7 Gr. Est. & Comp. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 1 of 4
5. Round each item bought to the nearest ten cents. After rounding to the nearest ten
cents, how much would the total bill be? \$77.80

Computation: The student accurately solves problems (including real-world
situations) involving:

[7] E&C-3 Adding or subtracting fractions or mixed numbers with unlike
denominators, or decimals to the thousandths place (M3.3.3)

2                        1                               1
George ran 4   miles on Monday and 2   miles on Tuesday. Gracie ran 3 miles on
3                        4                               2
3
Monday and 3    miles on Tuesday.
4

1. Who ran more miles? Show your work and explain your thinking.

George ran 6 11/12 miles and Gracie ran 7 1/4 miles, so Gracie ran the farthest.

2. If George and Gracie started running together Tuesday, how much farther did Gracie
run that day than George? Show your work and explain your thinking.

Gracie ran 1 1/2 miles farther than George on Tuesday.

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7 Gr. Est. & Comp. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 2 of 4
[7] E&C-4 Multiplying or dividing decimals to hundredths, or multiplying or
dividing by powers of ten, or multiplying or dividing fractions or mixed numbers
(M3.3.4)

These shapes represent decimal values.

a.                       b.          c.                d.

*The "Flat" (a) represents 1 whole

*The "Strip" (b) represents .1 (one tenth)

*The "Cube" (c) represents .01 (one hundredth)

*The "Tiny Tot" (d) represents .001 (one thousandth)

1. Using the shapes and their values from above, solve the following problems by writing
the decimal number represented by:

a. 4 A's, 7 B's, 3 C's, and 2 D's. What is the decimal number? 4.732

b. 145 A's, 8 B's, and 6 D's. What is the number? 145.806

c. Which shape represents the largest place value? A. The flat

d. How many tiny tots make a cube? 10

2. Using information from above, construct a diagram of the following decimal
numbers: (Place the model you construct inside the box provided.)

a.           2.58                                          b.              0 .952

Drawings should have 2 flats, 5                            Drawings should have 9 strips
strips, and 8 cubes.                                       and 5 cubes, and 2 tiny tots.

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7 Gr. Est. & Comp. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 3 of 4

4.732 x 145.806 = 689.953992

[7] E&C-5 Converting between equivalent fractions, terminating decimals, or
percents (10% = 1/10 = 0.1) (M3.3.5)

1. Complete the equivalency table. Simplify.

Percent            Fraction            Decimal

1.      210%            2 1/10*             2.1*

3
2.      37.5%*                               .375*
8

3.      7.5%*          3/40*                .075

4.      .8%*           1/125*               .008*

2
5.      40%*                                .4
5

[7] E&C-6 Solving proportions using a given scale (M3.3.6)

1. Give the unit rate of each of the following:

a. If 15 lbs. of chicken cost \$56.85, what is the cost of one pound?

\$3.79 / lb

b. If Helen travels 567 miles in 9 hours, how far does she travel in one hour?

63 miles / hour

c. If Mitch types 275 words in 5 minutes, how many words can he type in one
minute?

55 words/minute

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7 Gr. Est. & Comp. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 4 of 4

Describing Patterns and Functions: The student demonstrates conceptual
understanding of functions, patterns, or sequences including those represented in
real-world situations by:

[7] F&R-1 Describing or extending patterns (linear), up to ten terms, represented in
tables, sequences, or in problem situations (M4.3.1)

1. Consider these patterns, choose the correct pattern description, and find the next five
terms of each.

_____     323, 330, 337, 344, 351, _______, _______, _______, _______, ________

_____     .4x, .8x, 1.6x, 3.2x, 6.4x, _______, _______, _______, _______, ________

_____     .0001, .001, .01, .1, 1, 10, _______, _______, _______, _______, ________

_____     108, 96, 84, 72, 60, _______, _______, _______, _______, ________

a. multiply each previous term by 10

b. subtract 12 from each previous term

c. add 7 to each previous term

d. multiply each previous term by 2

2. Figure out the pattern used and complete the table below. Use 18, 54, and 27 for the

108                 9
108             10.8
108             13.5
108              a.
108              b.
108              c.

18
54
27

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7 Gr. Functions & Relationships Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 1 of 5
[7] F&R-2 Generalizing relationships (linear) using a table of ordered pairs, a
function, or an equation (M4.3.4)

1. Melvin owns a snow machine shop and sells 5 different models of sleds. Melvin pays
for the cost of the machines and shipping and then sells them at a higher price. The table
below shows the cost and the selling price of each machine. What rule does Melvin use
to calculate the selling price?

Cost of machine                     Selling price
Model #1                             \$2,500                             \$3,500
Model #2                             \$3,200                             \$4,480
Model #3                             \$3,800                             \$5,320
Model #4                             \$4,200                             \$5,880
Model #5                             \$4,800                             \$6,720

a. \$1000 + the cost = the selling price

b. (The cost x 10%) + the cost = the selling price

c. (The cost x 20%) + the cost = the selling price

d. (The cost x 40 %) + the cost = the selling price

2. Consider this equation and the unfinished ordered pairs. Then answer true or false to
the questions below.

X+Y=9
X                      Y
3                      a
b                      5
c                     -1

True             False             a = -6

True             False             a=6

True             False             b =-4

True             False            b=4

True             False             c = 10

True             False             c=8

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7 Gr. Functions & Relationships Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 2 of 5
[7] F&R-3 Describing in words how a change in one variable in a formula affects the
remaining variables (how changing the length affects the area of a quadrilateral)
(M4.3.2)

1. Consider this formula and then answer the true and false questions below.

1
A = bh
2

True             False             When you double the height, the area is doubled.

True             False            When you divide the base by 2, the area is doubled.

True             False             When the base is divided by 2, the area is divided by 2.

2. Describe in writing how the area of a triangle is affected when this variable is
changed.

1
A = bh when the height is 5 centimeters and then is changed to 10 centimeters.
2

______________________________________________

______________________________________________

3. Describe in writing how the area of a rectangle is affected when this variable is
changed.

A=lw when the length is 3 centimeters and is changed to 1.5 centimeters.

______________________________________________

______________________________________________

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7 Gr. Functions & Relationships Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 3 of 5
[7] F&R-4 (L) Using a calculator as a tool when describing, extending, or
representing patterns (M4.3.3)

1. Use a calculator to extend these patterns, then describe the pattern and what functions
you performed on your calculator to find the next terms.

a. 1, 4, 9, 16, 25, 36, 49, _______ , ________ , ________ , ________ , ________ …

b. 1, 8, 27, 64, 125, 216, _______ , _______ , ________ , ________, __________ ...

Modeling and Solving Equations and Inequalities: The student demonstrates
algebraic thinking by:

[7] F&R-5 Evaluating algebraic expressions (M4.3.5)

1. If t = 11 and s = 5, evaluate the following expression: 3t – 5s

a. 8

b. 4

c. –11

d. 23

2. Evaluate this expression if x = 7 and y = 3:

7y – 2x

a. 42

b. 14

c. 7

d. 5

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7 Gr. Functions & Relationships Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 4 of 5
3. Evaluate this expression if p=0 and s = -4:

2s + 3p – 4(p-s)

a. 16

b. -32

c. –12

d. 32

[7] F&R-6 Solving or identifying solutions to one-step linear equations of the form
x ± a=b or ax=b, where a and b are whole numbers, translating a story problem into
an equation of similar form, or translating a story problem into an equation of
similar form and solving it (M4.3.5)

1. Solve this equation, show your work, and choose the best answer: 5x + 8 = 18

a. x = 2

b. x = 5 1/5

c. x = 5

d. x = 1/2

2. Dennis has decided to save his money since he just got a job cleaning fish for the
summer. He currently has \$157 in his account. He plans to work at the docks for 6 hours
each day. He charges \$1/fish and he cleans 12 fish each hour on the average. Using this

a. How much will Dennis make (on average) each hour?

b. How much will Dennis make (on average) each day?

c. At the end of one week how much will he have made?

d. If he deposits his earnings at the end of each week, how much will he have in the
bank at the end of the first week?

e. If the summer fish season lasts 6 weeks, how much will he have in his savings at
the end of each week and at the end of the summer? Make a table to figure out the
values.

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7 Gr. Functions & Relationships Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 5 of 5

Describing Patterns and Functions: The student demonstrates conceptual
understanding of functions, patterns, or sequences including those represented in
real-world situations by:

[7] F&R-1 Describing or extending patterns (linear), up to ten terms, represented in
tables, sequences, or in problem situations (M4.3.1)

1. Consider these patterns, choose the correct pattern description, and find the next five
terms of each.

c         323, 330, 337, 344, 351, 358, 365, 372, 379, 386

d         .4x, .8x, 1.6x, 3.2x, 6.4x, 12.8, 25.6, 51.2, 102.4, 204.8

a         .0001, .001, .01, .1, 1, 10, 100, 1000, 10,000, 100,000, 1,000,000

b         108, 96, 84, 72, 60, 48, 36, 24, 12, 0

a. multiply each previous term by 10

b. subtract 12 from each previous term

c. add 7 to each previous term

d. multiply each previous term by 2

2. Figure out the pattern used and complete the table below. Use 18, 54, and 27 for the

108                 9
108              10.8
108              13.5
108               a. 18
108               b. 27
108               c. 54
18
54
27

The pattern is: Divide 108 by 12, then 10, then 8, then by each descending even
number.

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7 Gr. Funct. & Rels. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 1 of 5
[7] F&R-2 Generalizing relationships (linear) using a table of ordered pairs, a
function, or an equation (M4.3.4)

1. Melvin owns a snow machine shop and sells 5 different models of sleds. Melvin pays
for the cost of the machines and shipping and then sells them at a higher price. The table
below shows the cost and the selling price of each machine. What rule does Melvin use
to calculate the selling price?

Cost of machine                     Selling price
Model #1                             \$2,500                             \$3,500
Model #2                             \$3,200                             \$4,480
Model #3                             \$3,800                             \$5,320
Model #4                             \$4,200                             \$5,880
Model #5                             \$4,800                             \$6,720

a. \$1000 + the cost = the selling price

b. (The cost x 10%) + the cost = the selling price

c. (The cost x 20%) + the cost = the selling price

d. (The cost x 40 %) + the cost = the selling price*

2. Consider this equation and the unfinished ordered pairs. Then answer true or false to
the questions below.

X+Y=9
X                      Y
3                      a
b                      5
c                     -1

True             False*            a = -6

True*            False             a=6

True             False*            b =-4

True*            False             b=4

True*            False             c = 10

True             False*            c=8

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7 Gr. Funct. & Rels. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 2 of 5
[7] F&R-3 Describing in words how a change in one variable in a formula affects the
remaining variables (how changing the length affects the area of a quadrilateral)
(M4.3.2)

1. Consider this formula and then answer the true and false questions below.

1
A = bh
2

True*            False             When you double the height, the area is doubled.

True             False*            When you divide the base by 2, the area is doubled.

True*            False             When the base is divided by 2, the area is divided by 2.

2. Describe in writing how the area of a triangle is affected when this variable is
changed.

1
A = bh when the height is 5 centimeters and then is changed to 10 centimeters.
2

The area of the triangle is doubled.

3. Describe in writing how the area of a rectangle is affected when this variable is
changed.

A=lw when the length is 3 centimeters and is changed to 1.5 centimeters.

The area of the rectangle is half of the original.

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7 Gr. Funct. & Rels. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 3 of 5
[7] F&R-4 (L) Using a calculator as a tool when describing, extending, or
representing patterns (M4.3.3)

1. Use a calculator to extend these patterns, then describe the pattern and what functions
you performed on your calculator to find the next terms.

a. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 …the pattern is n squared.
b. 1, 8, 27, 64, 125, 216, 343, 512 , 729, 1000, 1331 ...the pattern is n cubed

Modeling and Solving Equations and Inequalities: The student demonstrates
algebraic thinking by:

[7] F&R-5 Evaluating algebraic expressions (M4.3.5)

1. If t = 11 and s = 5, evaluate the following expression: 3t – 5s

a. 8*

b. 4

c. –11

d. 23

2. Evaluate this expression if x = 7 and y = 3: 7y – 2x

a. 42

b. 14

c. 7*

d. 5

3. Evaluate this expression if p=0 and s = -4: 2s + 3p – 4(p-s)
a. 16

b. -24*

c. –12

d. 32

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7 Gr. Funct. & Rels. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 4 of 5
[7] F&R-6 Solving or identifying solutions to one-step linear equations of the form
x ± a=b or ax=b, where a and b are whole numbers, translating a story problem into
an equation of similar form, or translating a story problem into an equation of
similar form and solving it (M4.3.5)

1. Solve this equation, show your work, and choose the best answer: 5x + 8 = 18

a. x = 2* 5x+8 -8 =18-8        5x = 10      5x/5 = 10/5      x= 2

b. x = 5 1/5

c. x = 5

d. x = 1/2

2. Dennis has decided to save his money since he just got a job cleaning fish for the
summer. He currently has \$157 in his account. He plans to work at the docks for 6 hours
each day. He charges \$1/fish and he cleans 12 fish each hour on the average. Using this

a. How much will Dennis make (on average) each hour? \$12/hour

b. How much will Dennis make (on average) each day? \$72/day

c. At the end of one week how much will he have made
\$504/WEEK (7 X \$72)

d. If he deposits his earnings at the end of each week, how much will he have in the
bank at the end of the first week?
\$661 (\$504 + \$157)

e. If the summer fish season lasts 6 weeks, how much will he have in his savings at
the end of each week and at the end of the summer? Make a table to figure out the
values.
Week 1             661
Week 2             1165
Week 3             1669
Week 4             2173
Week 5             2677
Week 6             3181

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7 Gr. Funct. & Rels. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 5 of 5

Perimeter, Area, and Volume: The student solves problems (including real-world
situations) by:

[7] G-5 Determining the volume of cubes and rectangular prisms (M5.3.4) and

[7] G-6 Determining the surface area of rectangular prisms (M5.3.4)

1. Find the volume (V) and surface area (S.A.) of the following figures.

Right Rectangular Prism

V = Area of Base*Height
Volume = ________________

S.A. = Sum of all surface areas
Surface Area = ________________
8 in

6 in
3 in

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7 Gr. Geometry   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 1 of 8
Geometric Relationships: The student demonstrates an understanding of geometric
relationships by:

[7] G-1 Using the attributes and properties of polygons (diagonals, number of sides
and angles) to identify and classify regular or irregular polygons (M5.3.1)

Match the following terms with their definitions by writing the correct letter on the blank
line.

Definition                                                Term

1.____3-sided figure with                                         A.   Polygon
two congruent sides                                        B.   Equilateral Triangle
2.____Geometric figure with all sides congruent                   C.   Regular Polygon
and all angles congruent                                   D.   Diagonal
3.____3-sided figure with no congruent sides                      E.   Irregular Polygon
4.____Geometric figure with no congruent sides                    F.   Isosceles Triangle
and no congruent angles                                     G.   Perimeter
5.____3-sided figure with all sides congruent                     H.   Scalene Triangle
and all angles congruent                                   J.   Acute Triangle
6.____3-sided figure with all angles less than 90°                K.   Obtuse Triangle
7.____Line segment that joins two nonadjacent
vertices of a polygon
8.____A 3-sided figure where one angle measures
more than 90°
9.____Three or more line segments in a plane that
form a closed figure
10.____The distance around a figure

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7 Gr. Geometry   Alaska GLE Formative Assessments for Classroom Use, February 2006      Page 2 of 8
[7] G-2 Using the attributes and properties of prisms (vertices, length and alignment
of edges, shape and number of bases, shape of faces) to identify and describe
triangular or rectangular pyramids (M5.3.2)

Given the following rectangular pyramid:

7 ft
7 ft
7 ft
7 ft

2 ft                           7 ft

1. Respond to each statement below with either “true” or “false”

a. ______There are 4 vertices.

b. ______There are 8 edges.

c. ______There are 2 equilateral triangles as faces.

d. ______There are no isosceles triangles as faces.

e. ______There are 5 edges that are each 7 ft. in length.

f. ______Opposite sides of the base are not equal in length.

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7 Gr. Geometry     Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 3 of 8
Transformation of Shapes: The student demonstrates conceptual understanding of
similarity, congruence, symmetry, or transformations of shapes by:

[7] G-3 Using a scale factor to solve problems involving similar shapes (e.g., scale
drawings, maps) (M5.3.3)

1. On a map of Alaska, the scale is 1cm = 80 miles. The actual distance between
Anchorage and Oscarville is 480 miles. On the map, what will be the distance in
centimeters between Anchorage and Oscarville?

a.   38,400 cm
b.   7 cm
c.   6 cm
d.   3,840 cm

[7] G-4 (L) Drawing or describing the results of applying transformations such as
translations, rotations, reflections, or dilations to figures (M5.3.5)

1. Given the original point (x,y) choose the rule for the translation “4 right, 3 down.”

a.   (x-3, y+4)
b.   (x+3, y+4)
c.   (x+4, y-3)
d.   (x-4, y+3)

Perimeter, Area, and Volume: The student solves problems (including real-world
situations) by:

[7] G-5 Determining the volume of cubes and rectangular prisms (M5.3.4)

1. Each side of a cube measures 5 cm in length. What is the cube’s volume?

a.   15 cm3
b.   125 cm3
c.   5 cm3
d.   12.5 cm3

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7 Gr. Geometry    Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 4 of 8
[7] G-7 Determining the circumference of a circle (M5.3.4)

1. Given the circle below:

a. Using your ruler, measure the circle’s diameter (D) to the nearest centimeter.
D = _________________

b. The circumference (C) of a circle is given by C = 2πr, where r = the radius of the
circle. Calculate C in centimeters, using π = 3.14

C = ________________________

2. Given circle P below: Determine the circumference (C) of circle P using the formula
C = 2πr
Let π = 3.14

6m

C = _____________

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7 Gr. Geometry     Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 5 of 8
Geometric Relationships: The student demonstrates an understanding of geometric
relationships by:

[7] G-1 Using the attributes and properties of polygons (diagonals, number of sides
and angles) to identify and classify regular or irregular polygons (M5.3.1)

Constructions: The student demonstrates a conceptual understanding of geometric
drawings or constructions by:

[7] G-9 (L) Drawing or measuring polygons with given dimensions and angles or
circles with given dimensions (M5.3.7)

1. Given pentagon HOUSE: With the aid of your ruler and protractor, respond to each
statement below with either “true” or “false.”

U

O

S

H                                            E

a. _______Side HO measures approximately 2.1 cm.

b. _______Angles HOU and OUS are approximately congruent.

c. _______Side US measures approximately 1.25 in.

d. _______Angles OHE and HES are not congruent.

e. _______Side HE measures approximately 2.75 in.

f. _______Side SE measures approximately 1.5 cm.

g. _______Pentagon HOUSE is a regular polygon.

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7 Gr. Geometry   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 6 of 8
Transformation of Shapes: The student demonstrates conceptual understanding of
similarity, congruence, symmetry, or transformations of shapes by:

[7] G-4 (L) Drawing or describing the results of applying transformations such as
translations, rotations, reflections, or dilations to figures (M5.3.5)

1
1. Given quadrilateral WILD below: Using a ruler, apply a dilation of scale factor          to it,
3
and draw the reduced quadrilateral TINY below it.

W

I

L

D

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7 Gr. Geometry   Alaska GLE Formative Assessments for Classroom Use, February 2006       Page 7 of 8
Constructions: The student demonstrates a conceptual understanding of geometric
drawings or constructions by:

[7] G-9 (L) Drawing or measuring polygons with given dimensions and angles or
circles with given dimensions (M5.3.7)

1. Draw a circle below with a diameter of 4 inches.

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7 Gr. Geometry   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 8 of 8

Perimeter, Area, and Volume: The student solves problems (including real-world
situations) by:

[7] G-5 Determining the volume of cubes and rectangular prisms (M5.3.4) and

[7] G-6 Determining the surface area of rectangular prisms (M5.3.4)

1. Find the volume (V) and surface area (S.A.) of the following figures.

Right Rectangular Prism

V = Area of Base*Height
Volume = 144 in3

S.A. = Sum of all surface areas
Surface Area = 180 in2
8 in

6 in
3 in

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 1 of 8
Geometric Relationships: The student demonstrates an understanding of geometric
relationships by:

[7] G-1 Using the attributes and properties of polygons (diagonals, number of sides
and angles) to identify and classify regular or irregular polygons (M5.3.1)

Match the following terms with their definitions by writing the correct letter on the blank
line.
Definition                                           Term

1. F 3-sided figure with                                            A.    Polygon
two congruent sides                                           B.   Equilateral Triangle
2. C Geometric figure with all sides congruent                      C.   Regular Polygon
and all angles congruent                                      D.    Diagonal
3. H 3-sided figure with no congruent sides                         E.   Irregular Polygon
4. E Geometric figure with no congruent sides                       F.   Isosceles Triangle
and no congruent angles                                       G.    Perimeter
5. B 3-sided figure with all sides congruent                        H.    Scalene Triangle
and all angles congruent                                      J.   Acute Triangle
6. J  3-sided figure with all angles less than 90°                  K.    Obtuse Triangle
7. D Line segment that joins two nonadjacent
vertices of a polygon
8. K A 3-sided figure where one angle measures
more than 90°
9. A Three or more line segments in a plane that
form a closed figure
10.G The distance around a figure

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 2 of 8
[7] G-2 Using the attributes and properties of prisms (vertices, length and alignment
of edges, shape and number of bases, shape of faces) to identify and describe
triangular or rectangular pyramids (M5.3.2)

Given the following rectangular pyramid:

7 ft
7 ft
7 ft
7 ft

2 ft                            7 ft

1. Respond to each statement below with either “true” or “false”

a. False    There are 4 vertices.

b. True     There are 8 edges.

c. True     There are 2 equilateral triangles as faces.

d. False There are no isosceles triangles as faces.

e. False    There are 5 edges that are each 7 ft. in length.

f. False              Opposite sides of the base are not equal in length.

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 3 of 8
Transformation of Shapes: The student demonstrates conceptual understanding of
similarity, congruence, symmetry, or transformations of shapes by:

[7] G-3 Using a scale factor to solve problems involving similar shapes (e.g., scale
drawings, maps) (M5.3.3)

1. On a map of Alaska, the scale is 1cm = 80 miles. The actual distance between
Anchorage and Oscarville is 480 miles. On the map, what will be the distance in
centimeters between Anchorage and Oscarville?

a.   38,400 cm
b.   7 cm
c.   6 cm*
d.   3,840 cm

[7] G-4 (L) Drawing or describing the results of applying transformations such as
translations, rotations, reflections, or dilations to figures (M5.3.5)

1. Given the original point (x,y) choose the rule for the translation “4 right, 3 down.”

a.   (x-3, y+4)
b.   (x+3, y+4)
c.   (x+4, y-3)*
d.   (x-4, y+3)

Perimeter, Area, and Volume: The student solves problems (including real-world
situations) by:

[7] G-5 Determining the volume of cubes and rectangular prisms (M5.3.4)

1. Each side of a cube measures 5 cm in length. What is the cube’s volume?

a.   15 cm3
b.   125 cm3*
c.   5 cm3
d.   12.5 cm3

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 4 of 8
[7] G-7 Determining the circumference of a circle (M5.3.4)
1. Given the circle below:

a. Using your ruler, measure the circle’s diameter (D) to the nearest centimeter.
D = Measure and check student answer.

b. The circumference (C) of a circle is given by C = 2πr, where r = the radius of the
circle. Calculate C in centimeters, using π = 3.14

C = Calculate circumference based

2. Given circle P below: Determine the circumference (C) of circle P using the formula
C = 2πr
Let π = 3.14

6m

C = 37.68 m

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 5 of 8
Geometric Relationships: The student demonstrates an understanding of geometric
relationships by:

[7] G-1 Using the attributes and properties of polygons (diagonals, number of sides
and angles) to identify and classify regular or irregular polygons (M5.3.1)

Constructions: The student demonstrates a conceptual understanding of geometric
drawings or constructions by:

[7] G-9 (L) Drawing or measuring polygons with given dimensions and angles or
circles with given dimensions (M5.3.7)

1. Given pentagon HOUSE: With the aid of your ruler and protractor, respond to each
statement below with either “true” or “false.”

U

O

S

H                                           E

a. F       Side HO measures approximately 2.1 cm.

b. T       Angles HOU and OUS are approximately congruent.

c. F       Side US measures approximately 1.25 in.

d. F       Angles OHE and HES are not congruent.

e. F       Side HE measures approximately 2.75 in.

f. T       Side SE measures approximately 1.5 cm.

g. F       Pentagon HOUSE is a regular polygon.

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 6 of 8
Transformation of Shapes: The student demonstrates conceptual understanding of
similarity, congruence, symmetry, or transformations of shapes by:

[7] G-4 (L) Drawing or describing the results of applying transformations such as
translations, rotations, reflections, or dilations to figures (M5.3.5)

1
1. Given quadrilateral WILD below: Using a ruler, apply a dilation of scale factor              to it,
3
and draw the reduced quadrilateral TINY below it.

W

I

L

D

Measure to check student results: Sides should be 1/3 length of WILD with same
orientation.

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 7 of 8
Constructions: The student demonstrates a conceptual understanding of geometric
drawings or constructions by:

[7] G-9 (L) Drawing or measuring polygons with given dimensions and angles or
circles with given dimensions (M5.3.7)

1. Draw a circle below with a diameter of 4 inches.

Measure to check student results.

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7 Gr. Geometry Answer Key Alaska GLE Formative Assessments for Classroom Use, February 2006 Page 8 of 8

Measurable Attributes: The student demonstrates understanding of measurable
attributes by:

[7] MEA-1 (L) Estimating length to the nearest sixteenth of an inch or millimeter,
volume to the nearest cubic centimeter or milliliter or angle to the nearest 30
degrees (M2.3.1)

Measurement Techniques: The student uses measurement techniques by:

[7] MEA-4 Measuring various dimensions to one-sixteenth of an inch or millimeter
(M2.3.1)

1. Estimate the length of this key to the nearest sixteenth of an inch. Select the answer
that is in simplest terms.

inches
5
a. 3
8
3
b. 3
4
13
c. 3
16
15
d. 3
16

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7 Grade Measurement   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 1 of 8
2. Estimate the height of this penguin to the nearest millimeter.

a.   5.3 mm
b.   53 mm
c.   53.3 mm
d.   54 mm

Measurable Attributes: The student demonstrates understanding of measurable
attributes by:

[7] MEA-1 (L) Estimating length to the nearest sixteenth of an inch or millimeter,
volume to the nearest cubic centimeter or milliliter or angle to the nearest 30
degrees (M2.3.1)

1. Estimate the volume of the liquid in the cylinder to the nearest cm3.

a.   0.36 cm3
b.   3.6 cm3
c.   36 cm3
d.   360 cm3

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7 Grade Measurement   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 2 of 8
2. Estimate the measure of this angle to the nearest whole number degree.

a. 50 0
b. 80 0
c. 120 0
d. 130 0

[7] MEA-2 Identifying or using equivalent English (square inches, square feet,
square yards) or metric systems (square centimeters, square meters) (M2.3.2)

1. If the length of a rectangular portrait is 9 inches and the width is 1 foot, what is the
area of the portrait?

a.   9 inches2
b.   9 feet2
c.   108 inches2
d.   108 feet2

2. If the length of a pocket mirror is 7.5 cm and the width is 5 cm, what is the surface area
of the pocket mirror?

a.   37.5 cm
b.   3.75cm
c.   37.5cm2
d.   3.75 cm2

3. Match the equivalent units.

_____a.      144 in2                                         1.   .00001 km2
_____b.      9 ft2                                           2.    1 ft2
_____c.      100 cm2                                         3.    1 yd2
_____d.      1 m2                                            4.    .01 m2

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7 Grade Measurement     Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 3 of 8
Measurement Techniques: The student uses measurement techniques by:

[7] MEA-3 Applying a given scale factor to find missing dimensions of similar
figures (M2.3.4)

1. Taipei, Taiwan celebrated the opening of the world’s tallest skyscraper recently. It is
known as “Taipei 101,” named after the number of floors it has. The building is 1,679
feet tall. A souvenir model of this building will be designed using a scale factor of 1 inch
= 100 ft. How tall will the model be?

a.   1.679 inches
b.   16.79 inches
c.   1.679 feet
d.   16.79 feet

2. If figure A is similar to Figure B, what is the length of side x?

a.   0.5
b.   1
c.   1.25
d.   1.5

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7 Grade Measurement      Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 4 of 8
[7] MEA-3 Applying a given scale factor to find missing dimensions of similar
figures (M2.3.4)

[7] MEA-4 Measuring various dimensions to one-sixteenth of an inch or millimeter
(M2.3.1)

1. Below is a scale drawing of a basketball court. Measure the sides of the drawing in
inches to determine the scale used. The scale used is:

a.   1”=50’
b.   1:50
c.   1”=20’
d.   1:20

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7 Grade Measurement   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 5 of 8
2. Below is a photo of Zachar Bay that has been reduced in size. If the original photo is
3.5 times as large. What is the length (the longer side) of the original photo?

Length: inches

a. 1.66 inches
b. 15 inches
c. 17.5 inches
d. 20.5 inches

[7] MEA-4 Measuring various dimensions to one-sixteenth of an inch or millimeter
(M2.3.1)

1. Measure the length of this nail to the nearest mm.

The length of the nail is ______________mm.

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7 Grade Measurement   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 6 of 8
2. Measure the length of this nail to the nearest one sixteenth of an inch.

The length of the nail is ______________inches.

[7] MEA-5 Accurately measuring a given angles using a protractor to the nearest
plus or minus 2 degrees (M2.3.1)

1. Measure this angle to nearest 20 .

a.   490
b.   530
c.   1270
d.   1310

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7 Grade Measurement     Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 7 of 8
[7] MEA-6 Solving real-world problems involving elapsed time between world time
zones (M2.3.5)

1. Jon lives in Alaska, which uses Alaska Standard Time. He wants to call his
Grandmother to wish her a ‘Happy Birthday.’ She lives in Chicago, Illinois, which uses
Central Standard Time. If he calls his grandmother at 11:15 AM Alaska time, what time
will his grandmother receive the call in Chicago?

a.   2:15 AM
b.   11:15 AM
c.   1:15 PM
d.   2:15 PM

2. Chris lives in Alaska. He is leaving Alaska on a flight for Venice, Italy at 9:00 AM
Alaska time on Sunday morning. If the flight takes a total of 12 hours including
connections, what local time and day will Chris arrive in Venice? (The time in Venice is

a.   7:00 PM on Sunday
b.   9:00 PM on Sunday
c.   7:00 AM on Monday
d.   9:00 AM on Monday

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7 Grade Measurement   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 8 of 8

Measurable Attributes: The student demonstrates understanding of measurable
attributes by:

[7] MEA-1 (L) Estimating length to the nearest sixteenth of an inch or millimeter,
volume to the nearest cubic centimeter or milliliter or angle to the nearest 30
degrees (M2.3.1)

Measurement Techniques: The student uses measurement techniques by:

[7] MEA-4 Measuring various dimensions to one-sixteenth of an inch or millimeter
(M2.3.1)

1. Estimate the length of this key to the nearest sixteenth of an inch. Select the answer
that is in simplest terms.

inches
5
a. 3
8
3
b. 3 *
4
13
c. 3
16
15
d. 3
16

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 1 of 8
2. Estimate the height of this penguin to the nearest millimeter.

a.   5.3 mm
b.   53 mm*
c.   53.3 mm
d.   54 mm

Measurable Attributes: The student demonstrates understanding of measurable
attributes by:

[7] MEA-1 (L) Estimating length to the nearest sixteenth of an inch or millimeter,
volume to the nearest cubic centimeter or milliliter or angle to the nearest 30
degrees (M2.3.1)

1. Estimate the volume of the liquid in the cylinder to the nearest cm3.

a.   0.36 cm3
b.   3.6 cm3*
c.   36 cm3
d.   360 cm3

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 2 of 8
2. Estimate the measure of this angle to the nearest whole number degree.

a. 50 0
b. 80 0 *
c. 120 0
d. 130 0

[7] MEA-2 Identifying or using equivalent English (square inches, square feet,
square yards) or metric systems (square centimeters, square meters) (M2.3.2)

1. If the length of a rectangular portrait is 9 inches and the width is 1 foot, what is the
area of the portrait?
a. 9 inches2
b. 9 feet2
c. 108 inches2 *
d. 108 feet2

2. If the length of a pocket mirror is 7.5 cm and the width is 5 cm, what is the surface area
of the pocket mirror?

a.   37.5 cm
b.   3.75cm
c.   37.5cm2*
d.   3.75 cm2

3. Match the equivalent units.

2     a.    144 in2                               1.   .00001 km2
3     b.    9 ft2                                 2.    1 ft2
4     c.    100cm2                                3.    1 yd2
1     d.    1 m2                                  4.    .01 m2

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 3 of 8
Measurement Techniques: The student uses measurement techniques by:

[7] MEA-3 Applying a given scale factor to find missing dimensions of similar
figures (M2.3.4)

1. Taipei, Taiwan celebrated the opening of the world’s tallest skyscraper recently. It is
known as “Taipei 101,” named after the number of floors it has. The building is 1,679
feet tall. A souvenir model of this building will be designed using a scale factor of 1 inch
= 100 ft. How tall will the model be?

a.   1.679 inches
b.   16.79 inches*
c.   1.679 feet
d.   16.79 feet

2. If figure A is similar to Figure B, what is the length of side x?

a.   0.5
b.   1*
c.   1.25
d.   1.5

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 4 of 8
[7] MEA-3 Applying a given scale factor to find missing dimensions of similar
figures (M2.3.4)

[7] MEA-4 Measuring various dimensions to one-sixteenth of an inch or millimeter
(M2.3.1)

1. Below is a scale drawing of a basketball court. Measure the sides of the drawing in
inches to determine the scale used. The scale used is:

a.    1”=50’
b.    1:50
c.    1”=20’*
d.    1:20

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 5 of 8
2. Below is a photo of Zachar Bay that has been reduced in size. If the original photo is
3.5 times as large. What is the length (the longer side) of the original photo?

Length: inches

a. 1.66 inches
b. 15 inches
c. 17.5 inches*
d. 20.5 inches

[7] MEA-4 Measuring various dimensions to one-sixteenth of an inch or millimeter
(M2.3.1)

1. Measure the length of this nail to the nearest mm.

The length of the nail is 155 mm.

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 6 of 8
2. Measure the length of this nail to the nearest one sixteenth of an inch.

The length of the nail is 6 ½ inches.

[7] MEA-5 Accurately measuring a given angles using a protractor to the nearest
plus or minus 2 degrees (M2.3.1)

1. Measure this angle to nearest 20 .

a.   490
b.   530*
c.   1270
d.   1310

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 7 of 8
[7] MEA-6 Solving real-world problems involving elapsed time between world time
zones (M2.3.5)

1. Jon lives in Alaska, which uses Alaska Standard Time. He wants to call his
Grandmother to wish her a ‘Happy Birthday.’ She lives in Chicago, Illinois, which uses
Central Standard Time. If he calls his grandmother at 11:15 AM Alaska time, what time
will his grandmother receive the call in Chicago?

a.   2:15 AM
b.   11:15 AM
c.   1:15 PM
d.   2:15 PM*

2. Chris lives in Alaska. He is leaving Alaska on a flight for Venice, Italy at 9:00 AM
Alaska time on Sunday morning. If the flight takes a total of 12 hours including
connections, what local time and day will Chris arrive in Venice? (The time in Venice is
a. 7:00 PM on Sunday
b. 9:00 PM on Sunday
c. 7:00 AM on Monday*
d. 9:00 AM on Monday

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7 Gr. Measurement Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 8 of 8

Understanding Numbers: The student demonstrates understanding of rational
numbers (fractions, decimals, percents, or integers) by:

[7] N-1 Ordering rational numbers (M1.3.1)

1. Arrange the following integers from least to greatest:

-1, -2, -3

a.   -1 < -2 < -3
b.   -3 < -1 < -2
c.   -3 < -2 < -1
d.   -1 < -3 < -2

2. Which of the following lists of decimal numbers is displayed in order, from the least
to the greatest?

a.   0.068, 0.086, 0.68, 0.86
b.   0.086, 0.068, 0.68, 0.86
c.   0.068, 0.68, 0.086, 0.86
d.   0.86, 0.68, 0.086, 0.068

3
3. On the number line,        lies between which of the following fractions?
4

5      13
a.    and
8      16
12       13
b.     and
16       16
7       12
c.    and
8       16
7       15
d.    and
8       16

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 1 of 7
4. Which of the following lists of fractions is displayed in order, from greatest to
smallest?

5 5 1 1
a.     , , ,
3 8 3 4
7 3 5 2
b.      , , ,
16 4 8 3
4 2 2 1
c.     , , ,
6 4 5 2
8 7 6 5
d.     , , ,
5 4 3 2

[7] N-2 (L) Modeling (place value blocks) or identifying place value positions of
whole numbers and decimals (M1.3.2)

1. What is the value of the 3 in 25.309?

a.   Ones
b.   Tenths
c.   Hundredths
d.   Thousandths

2. What is the value of the 4 in 57.004?

a.   Tenths
b.   Hundredths
c.   Thousandths
d.   Ten thousandths

3. In 68, what number is in the tens place?

a.   8
b.   5
c.   6
d.   0

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 2 of 7
[7] N-3 Converting between expanded notation (multiples of ten) and standard form
for decimal numbers (M1.3.3)

1. Which of these is another way to write 24,810.79?

a.   (2 x 100) + (4 x 100) + (8 x 10) + (1 x 10) + (7 X .1) + (9 x .01)
b.   (2 x 10,000) + (4 x 1000) + (8 x 100) + (1 X 10) + (7 x .1) + (9 x .01)
c.   (24 x 1000) + (81 x 100) + (79 x .01)
d.   (2 x 10,000) + (4 x 1,000) + (81 x 100) + (7 x .1) + (9 x .01)

2. Which of these numbers shows the value of 5000 + 700 + .8 + .09 + .001?

a.   5,078.091
b.   5,007.891
c.   5,700.891
d.   570.891

3. Write this number in expanded form: 5,280

________________________________________________________________________

Understanding Numbers: The student demonstrates understanding of positive
fractions, decimals, or percents by:

[7] N-4 Identifying or representing equivalents of numbers (M1.3.4 & M3.3.5)

2
1. What is       as a decimal number?
3

a.   .33333…
b.   .22222…
c.   .66666…
d.   .2323…

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 3 of 7
2. 0.48 is what equivalent to what fraction?

12
a.
25
4
b. 4
5
6
c.
125
2
d.
5

3. Write 0.27 as a fraction.

_____________________________

4
4.         is what percent?
100

a.   400%
b.   40%
c.   4%
d.   .4 %

5. .89 is what percent?

a.   .89%
b.   8.9%
c.   89%
d.   890%

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 4 of 7
Understanding Meaning of Operations: The student demonstrates conceptual
understanding of mathematical operations by:

[7] N-5 Using models, explanations, number lines, real-life situations, describing or
illustrating the effects of arithmetic operations on rational numbers (fractions,
decimals) (M1.2.3)
7    2
1. Which of these models best describes the difference of – ?
8    4

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 5 of 7
Number Theory: The student demonstrates conceptual understanding of number
theory by:

[7] N-6 Using commutative, [associative L], inverse, or identity properties with
rational numbers (M1.3.6)

1. Which is an example of the Commutative Property?

a.   2 + 6 + 4 = 14 – 2
b.   3 x 3 = 12 – 3
c.   (3 + 2) + 7 = 7 + (3 + 2)
d.   14/2 = 21 /3

2. Which is the multiplicative inverse of 5?
5
a.
1
b. -5
c. 5
1
d.
5

3. Which is the additive inverse of .5?

5
a.
10
b. -.5
c. .5
d. 1

[7] N-7 Applying rules of divisibility to whole numbers (M1.3.5)

1. In which list of numbers are all numbers divisible by 8?

a.   56, 104, 128
b.   8, 18, 88
c.   8, 57, 74
d.   16, 52, 118

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 6 of 7
2. In which list of numbers are all numbers divisible by 3?

a.   183, 72, 393
b.   134, 42, 132
c.   137, 711, 16
d.   136, 36, 21

[7] N-8 Identifying prime and composite numbers (M1.3.5)

1. Which of the following numbers is not composite?

a.   51
b.   69
c.   91
d.   121

2. Label each number below as either “prime” or “composite.”

25 _______________                  51 __________________

17 _______________                  38 __________________

97 _______________                  11 ___________________

[7] N-9 (L) Using distributive property with rational numbers (M1.3.6)

5
1. Show two ways to multiply the sum of n and            by 8.
6

2. 14 – 1.6 may also be expressed as which of the following?

a. 14 ( 7 – 1.6 )

b. 2 ( 7 – 0.8 )

c. 2 ( 7 – 1.6 )

d. 2 ( 7 – 0.08 )

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7 Grade Numeration Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 7 of 7

Understanding Numbers: The student demonstrates understanding of rational
numbers (fractions, decimals, percents, or integers) by:

[7] N-1 Ordering rational numbers (M1.3.1)

1. Arrange the following integers from least to greatest:

-1, -2, -3

a.   -1 < -2 < -3
b.   -3 < -1 < -2
c.   -3 < -2 < -1*
d.   -1 < -3 < -2

2. Which of the following lists of decimal numbers is displayed in order, from the least
to the greatest?

a.   0.068, 0.086, 0.68, 0.86*
b.   0.086, 0.068, 0.68, 0.86
c.   0.068, 0.68, 0.086, 0.86
d.   0.86, 0.68, 0.086, 0.068

3
3. On the number line,       lies between which of the following fractions?
4

5       13
a.    and     *
8       16
12       13
b.     and
16       16
7       12
c.    and
8       16
7       15
d.    and
8       16

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 1 of 7
4. Which of the following lists of fractions is displayed in order, from greatest to
smallest?

5 5 1 1
a.     , , , *
3 8 3 4
7 3 5 2
b.      , , ,
16 4 8 3
4 2 2 1
c.     , , ,
6 4 5 2
8 7 6 5
d.     , , ,
5 4 3 2

[7] N-2 (L) Modeling (place value blocks) or identifying place value positions of
whole numbers and decimals (M1.3.2)

1. What is the value of the 3 in 25.309?

a.   Ones
b.   Tenths*
c.   Hundredths
d.   Thousandths

2. What is the value of the 4 in 57.004?

a.   Tenths
b.   Hundredths
c.   Thousandths*
d.   Ten thousandths

3. In 68, what number is in the tens place?

a.   8
b.   5
c.   6*
d.   0

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 2 of 7
[7] N-3 Converting between expanded notation (multiples of ten) and standard form
for decimal numbers (M1.3.3)

1. Which of these is another way to write 24,810.79?

a.   (2 x 100) + (4 x 100) + (8 x 10) + (1 x 10) + (7 X .1) + (9 x .01)
b.   (2 x 10,000) + (4 x 1000) + (8 x 100) + (1 X 10) + (7 x .1) + (9 x .01)*
c.   (24 x 1000) + (81 x 100) + (79 x .01)
d.   (2 x 10,000) + (4 x 1,000) + (81 x 100) + (7 x .1) + (9 x .01)

2. Which of these numbers shows the value of 5000 + 700 + .8 + .09 + .001?

a.   5,078.091
b.   5,007.891
c.   5,700.891*
d.   570.891

3. Write this number in expanded form: 5,280

(5 x 1,000) + (2 x 100) + (8 + 10)

Understanding Numbers: The student demonstrates understanding of positive
fractions, decimals, or percents by:

[7] N-4 Identifying or representing equivalents of numbers (M1.3.4 & M3.3.5)

2
1. What is       as a decimal number?
3

a.   .33333…
b.   .22222…
c.   .66666…*
d.   .2323…

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 3 of 7
2. 0.48 is what equivalent to what fraction?

12
a.      *
25
4
b. 4
5
6
c.
125
2
d.
5

3. Write 0.27 as a fraction.

27/100

4
4.         is what percent?
100

a.   400%
b.   40%
c.   4%*
d.   .4 %

5. .89 is what percent?

a.   .89%
b.   8.9%
c.   89%*
d.   890%

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 4 of 7
Understanding Meaning of Operations: The student demonstrates conceptual
understanding of mathematical operations by:

[7] N-5 Using models, explanations, number lines, real-life situations, describing or
illustrating the effects of arithmetic operations on rational numbers (fractions,
decimals) (M1.2.3)
7    2
1. Which of these models best describes the difference of – ?
8    4

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 5 of 7
Number Theory: The student demonstrates conceptual understanding of number
theory by:

[7] N-6 Using commutative, [associative L], inverse, or identity properties with
rational numbers (M1.3.6)

1. Which is an example of the Commutative Property?

a.   2 + 6 + 4 = 14 – 2
b.   3 x 3 = 12 – 3
c.   (3 + 2) + 7 = 7 + (3 + 2)*
d.   14/2 = 21 /3

2. Which is the multiplicative inverse of 5?
5
a.
1
b. -5
c. 5
1
d. *
5

3. Which is the additive inverse of .5?

5
a.
10
b. -.5*
c. .5
d. 1

[7] N-7 Applying rules of divisibility to whole numbers (M1.3.5)

1. In which list of numbers are all numbers divisible by 8?

a.   56, 104, 128*
b.   8, 18, 88
c.   8, 57, 74
d.   16, 52, 118

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 6 of 7
2. In which list of numbers are all numbers divisible by 3?

a.   183, 72, 393*
b.   134, 42, 132
c.   137, 711, 16
d.   136, 36, 21

[7] N-8 Identifying prime and composite numbers (M1.3.5)

1. Which of the following numbers is not composite?

a.   51
b.   69
c.   91*
d.   121

2. Label each number below as either “prime” or “composite.”

25 C                 51 C

17 P                 38 C

97 P                 11 P

[7] N-9 (L) Using distributive property with rational numbers (M1.3.6)

5
1. Show two ways to multiply the sum of n and            by 8.
6

8(n +5/6) or 8n + 20/3 or (n+5/6) * 8

2. 14 – 1.6 may also be expressed as which of the following?

a. 14 ( 7 – 1.6 )

b. 2 ( 7 – 0.8 )*

c. 2 ( 7 – 1.6 )

d. 2 ( 7 – 0.08 )

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7 Gr. Numeration Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 7 of 7

Process Skills: The student demonstrates an ability to problem solve by:

[7] PS-1 Selecting, modifying, and applying a variety of problem-solving strategies
(e.g., working backwards, drawing a picture, Venn diagrams and verifying the
results) (M7.3.2)

1. Three birds have a combined age of 76 years. One bird is 10 years old. The second
bird is twice as old as the third bird. How old are they?

a. _______________         b. ______________         c. _________________

2. The students in a seventh grade math class are given the following information about
the sizes of shoes in Mr. Perkins’ gym class: The smaller sizes are 6, 5, 6.5, and 7.The
range in sizes for all the shoes of the students is 6. The class is asked to predict the largest
shoe size for the class. The students predict that the largest shoe size has to be a size 10.
Explain why this is an incorrect answer.

1
3. Mr. Hill's math class makes up      of the entire student body at Liberty Middle
20
School. There are 27 students in his class. How many students attend Liberty Middle
School?

4. Princess Beauty Shop sells discount hair supplies. Today they are having a clearance
sale on already discounted items. If a clearance shampoo item is already on sale at 25%
off the regular price of \$24.96, and gets an additional 20% off of that sale price, how
much will the shampoo sell for?

a. Is the amount of the final cost of the shampoo more or less than 45% off the regular
cost of \$24.96? ______________

_____________________________________________________

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7 Grade Process Skills   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 1 of 2
2
5. If 2 cups of nuts are needed for a recipe,         of the nuts must be walnuts. How many
3
pounds of walnuts are needed?

1
6. Jessica needs 8     cups of raisins to make 2 fruitcakes. A 12 oz box of raisins contains
4
1
2     cups. How many boxes of raisins should Jessica buy?
3

7. Mike, Paul and Charlie went fishing. Everyone caught salmon and pike. Mike caught 1
pike and 4 salmon; Charlie caught 5 pike and 2 salmon. Paul caught half the number of
pike that both Charlie and Mike caught combined, and 1 less salmon than Charlie caught.
How many of each kind of fish did Paul catch?

_____ Pike

_____ Salmon

What was the total number of fish the three boys caught? __________________

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7 Grade Process Skills   Alaska GLE Formative Assessments for Classroom Use, February 2006   Page 2 of 2

Process Skills: The student demonstrates an ability to problem solve by:

[7] PS-1 Selecting, modifying, and applying a variety of problem-solving strategies
(e.g., working backwards, drawing a picture, Venn diagrams and verifying the
results) (M7.3.2)

1. Three birds have a combined age of 76 years. One bird is 10 years old. The second
bird is twice as old as the third bird. How old are they?

a. 10     b. 44 (second bird)       c. 22 (third bird)

Let X = the age of the third bird.
X + 10+2X = 76
3X+10 = 76
3X =66
X =22

2. The students in a seventh grade math class are given the following information about
the sizes of shoes in Mr. Perkins’ gym class: The smaller sizes are 6, 5, 6.5, and 7.The
range in sizes for all the shoes of the students is 6. The class is asked to predict the largest
shoe size for the class. The students predict that the largest shoe size has to be a size 10.
Explain why this is an incorrect answer.

The students counted 5, 6, 7, 8, 9, and 10 and got 6. They should have added 5 + 6 to
get 11. (Or they needed to be able to subtract 5 from some number in order to get 6.)
Then the range would be from 5 to 11; the difference, 11-5 = 6.

Eleven is the largest shoe size and 5 is the smallest shoe size.

1
3. Mr. Hill's math class makes up      of the entire student body at Liberty Middle
20
School. There are 27 students in his class. How many students attend Liberty Middle
School?

* 540 students

1 X =2720
X = 20(27)
X = 540

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7 Gr. Process Skills Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 1 of 2
4. Princess Beauty Shop sells discount hair supplies. Today they are having a clearance
sale on already discounted items. If a clearance shampoo item is already on sale at 25%
off the regular price of \$24.96, and gets an additional 20% off of that sale price, how
much will the shampoo sell for?

The shampoo will sell for \$ 14.98. You save \$6.24, and then \$3.74; for a total savings
of \$9.98.

a. Is the amount of the final cost of the shampoo more or less than 45% off the regular
cost of \$24.96? More

Explain your answer. 45% off of \$24.96 equals \$11.23. This is the amount you save
at 45% off the regular cost. This means the shampoo will sell for \$13.73.

2
5. If 2 cups of nuts are needed for a recipe,         of the nuts must be walnuts. How many
3
pounds of walnuts are needed?
2
pound. (2 cups = 16 oz; 16 oz = 1 lb)
3

1
6. Jessica needs 8     cups of raisins to make 2 fruitcakes. A 12 oz box of raisins contains
4
1
2     cups. How many boxes of raisins should Jessica buy?
3

Four boxes (3 boxes will give her 7 cups of raisins. Therefore she will need to buy
1
another box in order to have the 8 cups.)
4

7. Mike, Paul and Charlie went fishing. Everyone caught salmon and pike. Mike caught 1
pike and 4 salmon; Charlie caught 5 pike and 2 salmon. Paul caught half the number of
pike that both Charlie and Mike caught combined, and 1 less salmon than Charlie caught.
How many of each kind of fish did Paul catch?

3 Pike

1 Salmon

What was the total number of fish the three boys caught? 16 fish in all.

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7 Gr. Process Skills Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 2 of 2

Data Display: The student demonstrates an ability to classify and organize data by:

[7] S&P-1 [Collecting, L] displaying, organizing, or explaining the classification of
data in real-world problems (e.g., science or humanities, peers or community), using
circle graphs, frequency distributions, stem and leaf, [or scatter plots L] with
appropriate scale (M6.3.1)

1. The following is a list of unit car and truck sales made by the Ford Motor Company in
North America over the past 9 years. Make a scatter plot of the information. Does the
scatter plot show a positive, negative, or no correlation? Draw a trend line. If the trend
continues, make a prediction as to the number of sales that will be made in 2005. Is this
an accurate prediction? What might influence the sales of Ford autos during future years?

Year     1995         1996      1997      1998     1999      2000      2001     2002      2003       2004
Amount 3.1            3.3       4.3       4.4      4.7       5.0       4.0      3.7       3.4        3.3
Millions

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7 Gr. Statistics and Probability Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 1 of 5
[7] S&P-1 [Collecting, L] displaying, organizing, or explaining the classification of
data in real-world problems (e.g., science or humanities, peers or community), using
circle graphs, frequency distributions, stem and leaf, [or scatter plots L] with
appropriate scale (M6.3.1) and

Analysis and Central Tendency: The student demonstrates an ability to analyze
data (comparing, explaining, interpreting, evaluating or making predictions; or
drawing or justifying conclusions) by:

[7] S&P-3 Determining range, mean, median, or mode (M6.3.3)

The following data represent the number of trucks sold during a three-week period at a
large auto dealer in a big city.

10   3 18 22 24 29 17 6 24 28 15 18 30 26 11

1. Using the following chart, make a frequency distribution of the data.

Interval          Tally         Frequency

0-9

10-19

20-29

30-39

2. Make a stem-and-leaf plot of the data.

Stem            Leaf

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7 Gr. Statistics and Probability Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 2 of 5
3. What is the mode?

4. What is the mean?

5. What is the median?

6. Which is the best representation of the data? Why?

The table below contains the price of a hamburger at several different restaurants.

Restaurant       A        B         C         D         E         F         G         H          I
Price (\$)        1.00     1.25      1.37      2.35      1.99      1.99      1.85      2.60       3.50

6. What is the mean price of a hamburger?

7. What is the mode of this set of data?

8. What is the median price of the number of hamburgers?

9. What is the best indicator (the mean, median, or mode) of the price of a hamburger?
Why is this the best representation of the data?

Probability: The student demonstrates an ability to problem solve by:

[7] S&P-4 Determining the [experimental L] and theoretical probability of a simple
event (M6.3.5)

1. A bag contains eight red marbles, six blue marbles, five yellow marbles, and two green
marbles. One marble is chosen randomly. What is the theoretical probability that the
marble is blue? Write the probability in simplest form.

6
a.
21
2
b.
7
1
c.
21
6
d.
15

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7 Gr. Statistics and Probability Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 3 of 5
[7] S&P-5 Using a systematic approach to finding sample spaces or to making
predictions about the probability of independent events (M6.3.5)

1. Laura orders an ice cream sundae at her favorite snack shop. She could choose from
vanilla, mint, or fudge ripple ice cream; chocolate, strawberry or butterscotch topping;
M&Ms, chopped peanuts, jelly beans. or crushed cookies for a topping. How many
different ice cream sundaes can she chose using these ingredients?

a.   10
b.   36
c.   13
d.   21

2. Dave is making sandwiches. He can choose to use white, rye, or wheat bread. For
meat he can use ham, bologna, salmon, or turkey. For a condiment, he can use
mayonnaise or mustard. Find the number of different sandwiches Dave can make.

a.   24
b.   9
c.   12
d.   10

3. A number cube is rolled once. Find the probability of rolling a number that is more
than four.

1
a.
3
2
b.
3
1
c.
2
1
d.
6

4. The spelling contest awards four prizes. Tim, Sam, Jen, and Kate all made it to the
final round. In how many ways can first, second, third, and fourth place be assigned?

a.   24 ways
b.   16 ways
c.   25 ways
d.   12 ways

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7 Gr. Statistics and Probability Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 4 of 5
[7] S&P-6 (L) Designing and conducting a simulation to study a problem and
communicate the results (M6.3.6)

1. Design and conduct an experiment that uses the basic counting technique and
probability to solve a problem. List all of the possible outcomes.

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7 Gr. Statistics and Probability Alaska GLE Formative Assessments for Classroom Use, Feb. 2006   Page 5 of 5

Data Display: The student demonstrates an ability to classify and organize data by:

[7] S&P-1 [Collecting, L] displaying, organizing, or explaining the classification of
data in real-world problems (e.g., science or humanities, peers or community), using
circle graphs, frequency distributions, stem and leaf, [or scatter plots L] with
appropriate scale (M6.3.1)

1. The following is a list of unit car and truck sales made by the Ford Motor Company in
North America over the past 9 years. Make a scatter plot of the information. Does the
scatter plot show a positive, negative, or no correlation? Draw a trend line. If the trend
continues, make a prediction as to the number of sales that will be made in 2005. Is this
an accurate prediction? What might influence the sales of Ford autos during future years?

Year     1995         1996     1997     1998      1999     2000      2001     2002      2003     2004
Amount 3.1            3.3      4.3      4.4       4.7      5.0       4.0      3.7       3.4      3.3
Millions

There is a negative correlation. Prices may go up or down, gas prices may influence
the consumers’ choices, style may influence the consumers’ purchases, etc.

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7 Gr. Stats & Prob. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 1 of 5
[7] S&P-1 [Collecting, L] displaying, organizing, or explaining the classification of
data in real-world problems (e.g., science or humanities, peers or community), using
circle graphs, frequency distributions, stem and leaf, [or scatter plots L] with
appropriate scale (M6.3.1) and

Analysis and Central Tendency: The student demonstrates an ability to analyze
data (comparing, explaining, interpreting, evaluating or making predictions; or
drawing or justifying conclusions) by:

[7] S&P-3 Determining range, mean, median, or mode (M6.3.3)

The following data represent the number of trucks sold during a three-week period at a
large auto dealer in a big city.

10   3 18 22 24 29 17 6 24 28 15 18 30 26 11

1. Using the following chart, make a frequency distribution of the data.

Interval          Tally        Frequency
0-9              //                2
10-19            ///// /           6
20-29            ///// /           6
30-39            /                 1

2. Make a stem-and-leaf plot of the data.

Stem             Leaf

0         3    6
1         0    1      5    7   8   8
2         2    4      4    6   8   9
3         0

3. What is the mode? 18 and 24

4. What is the mean? 18.7333

5. What is the median? 18

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7 Gr. Stats & Prob. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 2 of 5
6. Which is the best representation of the data? Why?

Median and/or mean because 18 represents the average of all the numbers and it is the
middle number after putting the numbers in order.

The table below contains the price of a hamburger at several different restaurants.

Restaurant      A        B         C         D         E        F         G         H         I
Price (\$)       1.00     1.25      1.37      2.35      1.99     1.99      1.85      2.60      3.50

7. What is the mean price of a hamburger?
\$1.99

8. What is the mode of this set of data?
1.99

9. What is the median price of the number of hamburgers?
\$1.99

10. What is the best indicator (the mean, median, or mode) of the price of a hamburger?
Why is this the best representation of the data?
All are the same, so either one will work.

Probability: The student demonstrates an ability to problem solve by:

[7] S&P-4 Determining the [experimental L] and theoretical probability of a simple
event (M6.3.5)

1. A bag contains eight red marbles, six blue marbles, five yellow marbles, and two green
marbles. One marble is chosen randomly. What is the theoretical probability that the
marble is blue? Write the probability in simplest form.

6
a.
21
2
b.    *
7
1
c.
21
6
d.
15

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7 Gr. Stats & Prob. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 3 of 5
[7] S&P-5 Using a systematic approach to finding sample spaces or to making
predictions about the probability of independent events (M6.3.5)

1. Laura orders an ice cream sundae at her favorite snack shop. She could choose from
vanilla, mint, or fudge ripple ice cream; chocolate, strawberry or butterscotch topping;
M&Ms, chopped peanuts, jelly beans. or crushed cookies for a topping. How many
different ice cream sundaes can she chose using these ingredients?

a.   10
b.   36*
c.   13
d.   21

2. Dave is making sandwiches. He can choose to use white, rye, or wheat bread. For
meat he can use ham, bologna, salmon, or turkey. For a condiment, he can use
mayonnaise or mustard. Find the number of different sandwiches Dave can make.

a.   24*
b.   9
c.   12
d.   10

3. A number cube is rolled once. Find the probability of rolling a number that is more
than four.

1
a.   *
3
2
b.
3
1
c.
2
1
d.
6

4. The spelling contest awards four prizes. Tim, Sam, Jen, and Kate all made it to the
final round. In how many ways can first, second, third, and fourth place be assigned?
a. 24 ways*
b. 16 ways
c. 25 ways
d. 12 ways

th
7 Gr. Stats & Prob. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 4 of 5
[7] S&P-6 (L) Designing and conducting a simulation to study a problem and
communicate the results (M6.3.6)

1. Design and conduct an experiment that uses the basic counting technique and
probability to solve a problem. List all of the possible outcomes.

th
7 Gr. Stats & Prob. Answer Key Alaska GLE Formative Assessments for Classroom Use, Feb. 2006 Page 5 of 5

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