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Illinois Standards Achievement Test
Mathematics SamplesForm LM
Grade 8
2010
Illinois State Board of Education
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GO ON
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1
A Point P
B Point Q
C Point RD Point S
0 1 2 3 4 5 6
P Q R S
210
3484856
2
8 6 4 3
A B C D
18
34
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3
8 81 88 90
A B C D
3349312 3349312_AR1
4
Use 3.14 for p.
A 14 inches C 28 inchesB 20 inches D 63 inches
4.5 in.
Which point best represents ?
Amy has of a yard of string
to make bracelets.
She needs of a yard of string
for each one.
What is the most number ofbracelets Amy can make?
A school had 80 students last year.
There are 10% more this year.
How may students are
there this year?
Which is closest to the
circumference of the circle?
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3484864
9
Look at the addition patterns below.
1 3 4
1 3 5 9
1 3 5 7 16
1 3 5 7 9 25
6 7 8 9
A B C D
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8
Use your inch ruler to help you
answer this question.
A 10 feet
B feet
C feet
D 15 feet
121
2
101
2
height
1 inch represents 5 feet.
What is the height of the tree?
The picture is a scale drawing ofa tree.
Using this pattern, how
many numbers must be
added to equal 64?
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3400149 3400149_AR1 to AR4
10
A C
B D
x
y
5 10
-5
5
-10
10
-5-10x
y
5 10
-5
5
-10
10
-5-10
x
y
5-5 10-10
-5
5
-10
10
x
y
5 10
-5
5
-10
10
-5-10
Which graph showsy = 3?
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3484871
12
The graph of a line contains the
points (5, 3) and (5,-1).
A The line intersects the x-axis.B The slope of the line
is negative.
C The line intersects the y-axis.
D The slope of the line is positive.
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Aless than 70 F.
Bgreater than 80 F.
C
between 70 F and 80 F.
D
less than 70 F or greater
than 80 F.
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14
24 49 54 59
A B C D
(x 5)
70
56
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11
A y 2x
B y x 2
C y 5x
D y 3x 2
0
1
2
3
4
2
5
8
11
14
x y
5
Which equation shows the
relationship betweenx andy?
Which must be true about thegraph of this line?
The inequality 70
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Line l intersects parallel lines
m and n as shown.
Which list contains all the
angles that are congruent
to 1?
A 3, 5, 7B 3, 6, 8
C 2, 3, 4
D 2, 7, 8
m n
l14 58
23 67
3349355 3349355.AR1 to .AR5
16
Which drawing represents the
top view of this solid?
A
B
C
D
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3484902 3484902_AR1
17
XYZ is similar to RST.
What is the length of ?
10 cm 9 cm 8.5 cm 7.5 cmA B C D
ST
8 cm6 cm
12 cm
10 cm
R
S TZY
X
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18
8 20 30 72
A B C D
240 Animals at a Zoo
Monkeys30
The circle graph represents a
total of 240 animals.
The shaded area represents thenumber of monkeys.
How many of the animals
are monkeys?
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Answer Key with Assessment Objective Identified
ItemNumber
CorrectAnswer
Assessment Objective
16 D 9.8.10 Identify front, side, and top views of a threedimensional solid builtwith cubes.
17 B 9.8.11 Solve problems involving congruent and similar figures.
18 B
10.8.01 Read, interpret (including possible misleading characteristics), andmake predictions from data represented in a bar graph, line (dot) plot, Venndiagram (with two or three circles), chart/table, line graph, scatterplot, circlegraph, stemandleaf plot, or histogram.
19 $10.8.04 Identify or draw a reasonable approximation of the line of best fit froma set of data or a scatterplot, and use the line to make predictions.
20 A
10.8.06 Solve problems involving the probability of an event composed of
repeated trials, compound events (including independent events), or futureevents with or without replacement.
21 A
6.8.12 Describe the effect of multiplying and dividing by numbers, includingthe effect of multiplying or dividing a rational number by: a number less than zero; zero; a number between zero and one; and a number greater than one.
22 A6.8.14 Estimate the square or cube root of a number less than 1,000 betweentwo whole numbers (e.g., 200 3 is between 5 and 6).
23 C
8.8.10 Identify, graph, and interpret up to two inequalities with a single
variable (including the intersection or union of these inequalities) on anumber line.
24 A
7.8.02 Solve problems involving perimeter/circumference and area ofpolygons, circles, and composite figures using diagrams, models, and grids orby measuring or using given formulas (may include sketching a figure from itsdescription).
25 B 8.8.04 Recognize and generate equivalent forms of algebraic expressions.
To view all the mathematics assessment objectives, download the Illinois Mathematics AssessmentFramework for Grades 38 online at www.isbe.net/assessment/IAFindex.htm.
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Using Short-Response Samples
Beginning with the spring 2008 ISA, the sample short-response question and answer (shown below) that
appeared in the 2006 and 2007 ISA test directions will no longer be included in the directions immediatelyprior to session 2. ISBE encourages educators to practice these types of items with students during the courseof the school year so they are familiar with them prior to ISA testing.
Please refer to the 2006 and 2007 ISA sample books for additional short-response items and studentsamples (online at www.isbe.net/assessment/htmls/sample_books.htm).
SAMPLE SHORT-RESPONSE QUESTION
SAMPLE SHORT-RESPONSE ANSWER
50+90+35=$1.75
foreachday1.751.751.751.75
+1.75___$8.75
32
Myanswer
$8.75forfivedays
Sam can buy his lunch at school. Each day, he wants to buy juice that costs 50,
a sandwich that costs 90, and fruit that costs 35.
Exactly how much money does Sam need to buy lunch for 5 days?
Show your work and label your answer.
Short-Response SampleItems
Followed by Scoring RubricStudent Samples
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GO ON
Use your centimeter ruler to draw a rectangle with a perimeter of 24 centimeters.
Label the length and width.
DO NOT WRITE HERE.
USE PAGE __ IN YOURANSWER
DOCUMENTTO ANSWER QUESTION 2.
2
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3349327 3349327_AR1
STOP
Five pieces of this pizza are gone.
What fraction of the pizza is gone?
Change this fraction into a percent.
DO NOT WRITE HERE.
USE PAGE __ IN YOURANSWER
DOCUMENTTO ANSWER QUESTION 3.
3
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3484897
Using each digit only once, list all possible 3-digit numbers that can be made
using the digits 2, 4, and 7.
Utilizando cada dgito solamente una vez, enumera todos los posibles nmeros de 3 dgitos que
se pueden hacer, usando los dgitos 2, 4 y 7.
NO ESCRIBAS AQU.USA LA PGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTARLA PREGUNTA 1.
1
1
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3349330
Using your centimeter ruler, draw a rectangle with a perimeter of 24 centimeters.
Label the length and width.
3349330
Utilizando la regla de centmetros, dibuja un rectngulo con un permetro de 24 centmetros.
Seala el largo y ancho.
NO ESCRIBAS AQU.
USA LA PGINA __ EN TU DOCUMENTODE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 2.
2
2
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3349327 3349327_AR1
In the pizza shown, five pieces have been eaten.
What fractional part of the pizza was eaten?
Convert this fraction into a percent.
GO ON
DO NOT WRITE HERE.USE PAGE __ IN YOURANSWER
DOCUMENTTO ANSWER QUESTION 3.
3
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3349327 3349327_AR1
STOP
En la pizza que se muestra, cinco pedazos han sido comidos.
Qu fraccin de la pizza fue comida?
Convierte esta fraccin en porcentaje.
NO ESCRIBAS AQU.USA LA PGINA __ EN TU DOCUMENTODE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 3.
3
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Mathematics Short-Response Scoring Rubric
Te following rubric is used to score the short-response items for all grade levels.
SCORE
LEVEL DESCRIPTION
2Completely correct response, including correct work shown and/or correct labels/units if called
for in the item
1 Partially correct response
0 No response, or the response is incorrect
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Short-Response Student Sample 1B
Rubric Score Point = 2
Note: Te student correctly identified all possible combinations.
Short Response Student Sample1B
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Short-Response Student Sample 2A
Rubric Score Point = 2
Note: Te student accurately drew a square (special type of rectangle) with a side length of 6 cm, whichdoes have a perimeter of 24 cm.
Short Response Student Sample2A
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Short-Response Student Sample 2C
Rubric Score Point = 1
Note: Te student accurately drew a rectangle with dimensions 3 cm by 8 cm, which has perimeter of22 cm, not 24 cm. Te student computed area, not perimeter.
Short Response Student Sample2C
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Extended-ResponseSampleItems
Followed by Scoring Rubric
and Student Samples
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Using Extended-Response Samples
Beginning with the spring 2008 ISA, the sample extended-response problem and solution (shown below)that appeared in the 2006 and 2007 ISA test directions will no longer be included in the directionsimmediately prior to session 3. ISBE encourages educators to practice these types of items with studentsduring the course of the school year so they are familiar with them prior to ISA testing.
Please refer to the 2006 and 2007 ISA sample books for additional extended-response items and studentsamples (online at www.isbe.net/assessment/htmls/sample_books.htm).
SAMPLE EXTENDED-RESPONSE PROBLEM
Mrs. Martin wants to put tiles on the floor by the front door of her house. She wants
to use 3 different colors of tiles in her design.
She also wants
of the tiles to be blue,
of the tiles to be gray, and
of the tiles to be red.
Use the grid below to design a floor for Mrs. Martin. Label each tile with the first
letter of the color that should be placed there.
Show all your work. Explain in words how you found your answer. Tell why you
took the steps you did to solve the problem.
B B B B B B
R R R R R R
First, I know that there are 4 equal rows, so 2 rows is halfand
1 row is . So I made 2 rows B for blue because she wantshalf the tiles blue. Then I made 1 row G for gray because she
wants ofthe tiles to be gray. Since she wants gray and red
to be the same amount of tiles, I made the last row R for red.
14
14
14
14
blue
gray
red
12
B B B B B B
G G G G G G
SAMPLE EXTENDED-RESPONSE SOLUTION
12
14
1
4
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Blank Extended-Response Template
Make sure you show all your work in solving the problem, clearly label your answer, write in words how you solved the problem, write in words why you took the steps you did to solve the problem, and write as clearly as you can.
DIRECTIONS
Mathematics - Session 3
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Mathematics - Session 3
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3484898 3484898_AR1
POOL
DECK
GO ON
Extended-Response Items Reactivos de Respuesta Larga
Plain English-Usepages -
Englishand Spanish-Usepages-Ingls y Espaol-Usalaspginas-
The pool is a rectangle 10 feet wide and 20 feet long.
The deck around the pool is 2 feet wide.
What is the area of the deck?
Show all your work. Explain in words how you found your answer.
Tell why you took the steps you did to solve the problem.
DO NOT WRITE HERE.USE PAGE __ IN YOURANSWER
DOCUMENTTO ANSWER QUESTION .
1
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3484898 3484898_AR1
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NO ESCRIBAS AQU.USA LA PGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTARLA PREGUNTA .
Una alberca rectangular tiene un ancho de 10 pies y un largo de 20 pies. a plataforma
que rodea la alberca tiene un ancho de 2 pies.
PATAFRMA
ABERCA
Cul es el rea de la plataforma que rodea la alberca?
Demuestra tu trabajo. Explica con palabras cmo llegaste al resultado. Relata por qu
seguiste esos pasos para solucionar el problema.
1
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3349284
The Prairie Land Baseball Conference has 6 teams. The team names are listed below.
Aces
Broncos
Cougars
WildcatsEagles
Mustangs
How many games must be played so that every team plays each other once?
Show all your work. Explain in words how you found your answer. Tell why you took
the steps you did to solve the problem.
3349284
STOP
a Conferencia de Bisbol Prairie and tiene 6 equipos. os nombres son los siguientes.
Aces
Broncos
Cougars
Wildcats
Eagles
Mustangs
Cuntos juegos deben disputarse para que cada equipo se enfrente entre s una vez?
Demuestra tu trabajo. Explica con palabras cmo llegaste al resultado. Relata por qu
seguiste esos pasos para solucionar el problema.
NO ESCRIBAS AQU.
USA LA PGINA __ EN TU DOCUMENTODE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 2.
2
2
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Mathematics Extended-Response Scoring Rubric
Te following rubric is used to score the extended-response items for all grade levels. A student-friendlyversion of this extended-response scoring rubric is available online at www.isbe.net/assessment/math.htm.
SCORE
LEVEL
MATHEMATICAL KNOWLEDGE:
Knowledge of mathematical principles andconcepts which result in a correct solution toa problem.
STRATEGIC KNOWLEDGE:
Identification and use of importantelements of the problem that representand integrate concepts which yield thesolution (e.g., models, diagrams, symbols,algorithms).
EXPLANATION:
Written explanation of the rationales andsteps of the solution process. A justificationof each step is provided. Though important,the length of the response, grammar, andsyntax are not the critical elements of thisdimension.
4
shows complete understanding of theproblems mathematical concepts and
principles uses appropriate mathematical terminology
and notations including labeling answer ifappropriate
executes algorithms and computationscompletely and correctly
identifies all important elements ofthe problem and shows complete
understanding of the relationships amongelements
shows complete evidence of an appropriatestrategy that would correctly solve theproblem
gives a complete written explanation of thesolution process; clearly explains what was
done and why it was done may include a diagram with a complete
explanation of all its elements
3
shows nearly complete understanding ofthe problems mathematical concepts andprinciples
uses mostly correct mathematicalterminology and notations
executes algorithms completely;
computations are generally correct but maycontain minor errors
identifies most of the important elementsof the problem and shows a generalunderstanding of the relationships amongthem
shows nearly complete evidence of anappropriate strategy for solving the
problem
gives a nearly complete written explanationof the solution process; clearly explainswhat was done and begins to address whyit was done
may include a diagram with most of itselements explained
2
shows some understanding of theproblems mathematical concepts andprinciples
uses some correct mathematicalterminology and notations
may contain major algorithmic orcomputational errors
identifies some important elementsof the problem but shows only limitedunderstanding of the relationships amongthem
shows some evidence of a strategy forsolving the problem
gives some written explanation of thesolution process; either explains what wasdone or addresses why it was done
explanation is vague, difficult to interpret,or does not completely match the solutionprocess
may include a diagram with some of itselements explained
1
shows limited to no understanding of the
problems mathematical concepts andprinciples
may misuse or fail to use mathematicalterminology and notations
attempts an answer
fails to identify important elements or
places too much emphasis on unrelatedelements
reflects an inappropriate strategy forsolving the problem; strategy may bedifficult to identify
gives minimal written explanation of the
solution process; may fail to explain whatwas done and why it was done
explanation does not match presentedsolution process
may include minimal discussion of theelements in a diagram; explanation ofsignificant elements is unclear
0 no answer attempted no apparent strategy no written explanation of the solution
process is provided
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Extended-Response Student Sample A
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Extended-Response Student Sample C
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Scoring Guide for Area of Pool Deck
Te correct answer to this extended-response problem is 136 square feet.
Extended-Response Student Sample A
MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION
4 4 4
This response includes evidence ofa complete understanding of theproblems mathematical conceptsand principles. The correct answerof 136 ft2 is present.
The response reflects a systematicstrategy (subtracting the area ofthe pool from the area of the pooland deck together) that includesall important elements of the
problem.
The response addresses bothwhat was done and why (I took10 + 2 + 2 to find the total widthI subtracted the area of the pool,200 ft2 from the area of the pool
and deck combined to get just thearea of the deck.).
Extended-Response Student Sample B
MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION
4 4 4
This response includes evidence ofa complete understanding of theproblems mathematical conceptsand principles. The correct answerof 136 ft2 is present.
The response reflects a systematicstrategy (subtracting the area ofthe pool from the area of the pooland deck together) that includesall important elements of theproblem.
The response addresses both whatwas done and why (found thearea of the pool by multiplyingsince the deck is 2 ft wide I added2 ft + 2 ft on to the width of thepool).
Extended-Response Student Sample C
MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION
3 3 3
This response shows a nearlycomplete understanding of theproblems mathematical conceptsand principles. An incorrect answerof 64 ft2 is present.
The response identifies mostof the important elements, andthe solution process is nearlycomplete (only added 2 ft to thelength and width).
The response addresses what wasdone and begins to address why(found the area of the pooladded two to the side of each partof the decksubtracted the areaof the pool to find the area of justthe deck).
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Extended-Response Student Sample 2A
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Extended-Response Student Sample 2B
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BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB,6$70DWKHPDWLFV)RUP/06DPSOH%RRN*UDGH
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7/28/2019 Isat Math Grade8lm
57/59
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7/28/2019 Isat Math Grade8lm
58/59
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB,6$70DWKHPDWLFV)RUP/06DPSOH%RRN*UDGH
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7/28/2019 Isat Math Grade8lm
59/59
Scoring Guide for Baseball Games
Te correct answer for this problem is 15 games. Students used a variety of strategies to solve this problem. Some drewdiagrams with lines connecting team names, others made charts with teams paired up to represent each game to beplayed, and others simply used counting techniques.
Extended-Response Student Sample 2A
MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION
4 4 4
This response includes evidence ofa complete understanding of theproblems mathematical concepts
and principles. The correct answerof 15 games is present.
The response reflects a systematicstrategy (listing the initials forthe team names and connecting
them with lines to representgames) that includes all importantelements of the problem.
The response addresses bothwhat was done and why (drew alineto represent a game; one less
gamecontinued to count).
Extended-Response Student Sample 2B
MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION
4 4 2
This response includes evidence ofa complete understanding of theproblems mathematical conceptsand principles. The correct answerof 15 games is present.
The response reflects asystematic strategy (listing thesix team names as headings andassociating the other teams theywould play under this heading)that includes all importantelements of the problem.
The response addresses what wasdone but not why.
Extended-Response Student Sample 2C
MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION
4 4 0
This response includes evidence of The response reflects a systematic There is no written explanation of
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