Isat Math Grade8lm

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Illinois Standards Achievement Test

Mathematics SamplesForm LM

Grade 8

2010

Illinois State Board of Education


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,6$70DWKHPDWLFV)RUP/06DPSOH%RRN*UDGH


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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

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2

8 6 4 3

A B C D

18

34

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8 81 88 90

A B C D

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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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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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GO ON

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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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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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15

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

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16

Which drawing represents the

top view of this solid?

A

B

C

D



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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?


GO ON


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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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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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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


3



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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.

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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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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


3



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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


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


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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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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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


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


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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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


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


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


4 4 0

This response includes evidence of The response reflects a systematic There is no written explanation of


Isat Math Grade8lm

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