ISAT Sample Book Gr 8

GRADE

8ILLINOIS STATE BOARD OF EDUCATION

2009ISAT

Sample Book

999-8738-94-6

Sample Items for Reading and Mathematics

ACKNOWLEDGMENTS

“The Mystery and History of Soap”, from The Christian Science Monitor, June 3, 2003, copyright © 2002 by Sharon Huntington and used by permission.

“They Might Be Giants” copyright © 1988 by Dave Barry. Reprinted with the author’s permission. Cartoon by Jeff MacNelly, copyright © 1988, Tribune Media Services, Inc. Reprinted with permission.

Copyright © 2009 by NCS Pearson, Inc. Copyright © 2009 by the Illinois State Board of Education. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright owner. Pearson and the Pearson logo are trademarks, in the U.S. and/or other countries, of Pearson Education, Inc. or its affi liate(s). Portions of this work were previously published. Printed in the United States of America.

Printed by the authority of the State of Illinois, 20000, IL00002889.

2009 ISAT Grade 8 Sample Book

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Table of Contents

Introduction ............................................................................................................................ 5

READING

Structure of the Grade 8 Reading ISAT ................................................................................. 9Item Formats ...................................................................................................................................................9Reading Sessions ...........................................................................................................................................9

Shorter Passage Followed by Multiple-Choice Sample Items .......................................... 11

Answer Key with Assessment Objectives Identified .......................................................... 14

Longer Passage Followed by Multiple-Choice Sample Items ........................................... 15


Longer Passage Followed by Extended-Response Sample Item ...................................... 21

Extended-Response Scoring Rubric .................................................................................... 25

Annotated Extended-Response Student Samples ............................................................. 27

MATHEMATICS

Structure of the Grade 8 Mathematics ISAT ....................................................................... 41Item Formats .................................................................................................................................................41Answer Document for Grade 8 Mathematics ISAT ..........................................................................41Mathematics Sessions ...............................................................................................................................42Calculator Use for Grade 8 Mathematics ISAT ...................................................................................42Rulers for Grade 8 Mathematics ISAT ...................................................................................................42Scratch Paper for Grade 8 Mathematics ISAT ....................................................................................42Reference Sheet for Grade 8 Mathematics ISAT ...............................................................................43

Multiple-Choice Sample Items ............................................................................................ 44


Short-Response Scoring Rubric ........................................................................................... 60

Using Short-Response Samples .......................................................................................... 60

Blank Short-Response Template ......................................................................................... 61

Short-Response Sample Items and Annotated Student Samples .................................... 62

Extended-Response Scoring Rubric .................................................................................... 72


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Using Extended-Response Samples .................................................................................... 73

Blank Extended-Response Template .................................................................................. 74

Extended-Response Sample Items and Annotated Student Samples ............................. 77


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Introduction

Th is sample book contains sample ISAT items classifi ed with an assessment objective from the Illinois Assessment Frameworks. Th ese samples are meant to give educators and students a general sense of how items are formatted for ISAT. All 2009 ISATs will be printed in color. Th is sample book does not cover the entire content of what may be assessed. Please refer to the Illinois Assessment Frameworks for complete descriptions of the content to be assessed at each grade level and subject area. Th e Illinois Assessment Frameworks are available online at www.isbe.net/assessment/IAFindex.htm. Th e Student Assessment website contains additional information about state testing (www.isbe.net/assessment).

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Illinois Standards Achievement Test

Reading Samples

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Structure of the Grade 8 Reading ISAT

ISAT Reading testing in spring 2009 will consist of 30 norm-referenced items, as well as criterion-referenced items. Th e 30 norm-referenced items are an abbreviated form of the Stanford 10 Reading assessment, developed by Pearson, Inc. Th e criterion-referenced items are all written by Illinois educators and pilot tested with Illinois students.

Item FormatsAll items are aligned to the Illinois Reading Assessment Framework, which defi nes the elements of the Illinois Learning Standards that are suitable for state testing.

Multiple-choice items require students to read and refl ect, and then to select the alternative that best expresses what they believe the answer to be. A carefully constructed multiple-choice item can assess any of the levels of complexity, from simple procedures to sophisticated concepts.

Extended-response items require students to demonstrate an understanding of a passage by explaining key ideas using textual evidence and by using this information to draw conclusions or make connections to other situations. Th e extended-response items are scored with a holistic rubric and count as 10% of the scale score of the test.

Reading SessionsAll standard time administration test sessions are a minimum of 45 minutes in length. Any student who is still actively engaged in testing when the 45 minutes have elapsed will be allowed up to an additional 10 minutes to complete that test session. More details about how to administer this extra time will appear in the ISAT Test Administration Manual. Th is policy does not aff ect students who already receive extended time as determined by their IEP.

Reading ISAT Grade 8

Session 145 minutes 6 shorter passages—30 multiple-choice items total

Session 245 minutes

Two longer passages consisting of:1 expository passage with 10 multiple-choice items1 literary passage with 10 multiple-choice items1 extended-response item

Session 345 minutes

Two longer passages consisting of:1 expository passage (or paired passage) with 10 multiple-choice items1 literary passage (or paired passage) with 10 multiple-choice items1 extended-response item

(Some items will be pilot items.)

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Shorter Passage Followed byMultiple-Choice Sample Items

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GO ON

ReadingXEJ231 Passage XEJ231.AR1

School Photographerby

Kristine O’Connell George

When I am behind my camera lensI can make people stand closer,wrap their arms around each other,even get them to smile.

5 When I am behind my camera lensI see things others don’t.I can record a single momentThat distorts or tells the truth.

When I am behind my camera lens10 I can see everything

Except my own self, hiding behind my camera.

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XEJ2374If you did not know themeaning of distorts in stanza 2,you should —

A look for other words in the poemthat begin with “d”

B say the word over and over toyourself

≥ C read on, looking for cluesD decide on the word’s part of

speech

GO ON

Reading

XEJ2311The poet most likely took theidea for this poem from —

A a book on photographyB a volume of poetryC her camera’s owner’s manual

≥ D her own experience

XEJ2322Why does the speaker feelhidden?

A No one can see her.

≥ B She is looking through thecamera.

C There is no one around.D Other people are standing in

front of her.

XEJ2343In line 6, when the speaker says, “I see things others don’t,”she most likely means —

≥ A people often overlook what’saround them

B people don’t pay attention whentheir picture is taken

C cameras are the most accurateform of record keeping

D the camera lens is like amicroscope

XEJ2395In this poem, which point ofview does the poet use?

≥ A First person (one person whodescribes her own thoughts)

B Third person (a person outsidethe story who describes thethoughts of one other person)

C Third person omniscient (aperson outside the story whodescribes the thoughts of severalcharacters)

D Third person objective (a personoutside the story who describesevents objectively)


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Answer Key with Assessment Objectives Identifi ed

ItemNumber

CorrectAnswer

Assessment Objective

Sho

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Pas

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1 D 2.8.04 Compare stories to personal experience, prior knowledge, or other stories.

2 B 1.8.19 Draw inferences, conclusions, or generalizations about text and support them with textual evidence and prior knowledge.

3 A 2.8.10 Identify literary devices: (e.g., figurative language, hyperbole, understatement, symbols, dialogue).

4 C 1.8.03 Determine the meaning of an unknown word using word, sentence, and cross-sentence clues.

5 A 2.8.05 Recognize points of view in narratives (e.g., first person).

To view all the reading assessment objectives, download the Illinois Reading Assessment Framework for Grades 3–8 online at www.isbe.net/assessment/IAFindex.htm .

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Longer Passage Followed byMultiple-Choice Sample Items

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RG8Soap0807E-V1 Soap0807E_AR1

The mystery & history of SOAPIt has the most unlikely ingredients. For centuries, no one knew how it worked.

But it did — and still does.by Sharon J. Huntington

1 What’s the best substance to clean your clotheswith? Fat or oil, of course! That doesn’t sound right?Well, how about adding some ashes to the oil?Sounds worse, doesn’t it? But that’s the basis of soap,and people have been using it to clean themselvesand their belongings for thousands of years.

2 No one knows who first started using soap. Thereare recipes for soap on Sumerian clay tablets datingfrom 2500 BC, but the recipes don’t say what thesoap was used for. Later cultures used a similarmixture — as hair gel.

3 One story has it that Roman women were doinglaundry in the Tiber River some 4,000 years agowhen some fat and ashes from animal sacrificesupstream washed into the water and then seepedinto the clay of the riverbank. Women found thattheir clothes cleaned more easily with the ashes-fatmixture in the clay.

4 The sacrifices were performed at Mt. Sapo, whichresulted in the word “soap.” It’s a nice story, though probably not true. It is likely,however, that soap’s discovery was accidental. Who would think of using ashes and oil toget things clean? People knew it worked long before they could explain why.

5 One way that soap cleans is by reducing water’s surface tension. What’s that? Watermolecules are attracted to one another. On the surface of the water, the molecules areattracted to the water, not to the air. They are pulled toward the rest of the water. Thispull is called surface tension. It’s why water beads up on surfaces.

6 Surface tension makes it hard for water to wash away dirt. The water tends to stick toitself, not to the dirt.

7 Soaps are made from fats and oils. More specifically, they are made from the fatty acidsin fats and oils. This is done by treating them with a strong alkali, which causes achemical reaction. That’s where the ashes come in. (An alkali is the opposite of an acid.Just as lemon juice is slightly acidic, plant ashes are slightly alkaline.) Plant ashes firstprovided the alkali needed to make soap. Today the alkalis can be made commercially.

8 If you look at the ingredients for a bar of soap, you might see potassium hydroxide orsodium hydroxide. These are the alkalis that react with fatty acid molecules. Themolecules that are formed are called “surface active agents” or surfactants. Surfactantsbreak down water’s surface tension to make the water “wetter,” so it can react with dirtmore easily.

GO ON

Reading

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9 One side of each soap molecule is attracted to water. It is called the hydrophilic (water-loving) end. The other side of the molecule is attracted to oil and grease and is repelled bywater. It is the hydrophobic (water-hating) end. The water-hating end “grabs” the grease,and the water-loving end pulls the grease away from whatever you’re trying to clean andtoward the water. The soap holds the grease in the water until it is rinsed away.

10 Soapmaking was an established business in Europe by the 600s. In the Americancolonies, the first soapmakers arrived in 1608 on the second ship from England to reachJamestown, Va. But for a long time many colonists and pioneers made their own soap.They boiled fat with wood-ash lye. (Lye was made by letting rainwater trickle through abarrel of wood ashes.) Lye soap was smelly and scratchy. By the 1850s, soapmaking wasone of America’s fastest-growing industries.

11 Then, in the early 1900s, the first detergents were created. Instead of using fat or oil,detergents are made synthetically, created chemically from a variety of raw materials. By1953, detergents outsold soaps in the United States and now can be found in soap bars as well as laundry and dishwashing agents. Each person in the US uses an average of 30-1⁄2 pounds of detergents and soaps each year. About 10 million tons of soaps anddetergents were produced globally in 1998.

12 Mostly, soap is for cleaning. But it can be for fun, too. Check out the activities below.

Have some good clean funBubble forecasts

Bubbles are a good example of surface tension. The water molecules are drawn together.They form into the shape that gets them as close together as possible around the air insidethe bubble. That shape is a sphere.

If you want to impress your friends, tell them that you can predict when a bubble willpop. Here’s how: Watch the top of the bubble closely. When a black band begins to formon top of the bubble, announce that it is ready to pop! Blow several bubbles and tellwhich one will pop first. The black band forms because the bubble wall becomes thinnerbefore it pops. Gravity is pulling the moisture downward. Less light is being reflected atthe top, and this results in a black band.

Here’s a bubble-liquid recipe from the Soap and Detergent Association: Combine 4-1⁄2 cupswater with 1⁄2 cup of hand dishwashing detergent and 1⁄2 cup of corn syrup or glycerin.Magic moving toothpicks

You need a straw, some sugar, and soap to make two toothpicks move in water. Fill abowl with water and have two toothpicks ready. Then take a drinking straw and dip oneend in a little sugar. (The sugar sticks better if you get that end of the straw wet first.) Dipthe other end in a few drops of dishwashing detergent. Float the two toothpicks on thewater. Leave enough space between them so you can dip the straw in the gap. First, dip inthe end of the straw that’s coated with sugar. The toothpicks will move together. Then putin the soapy end, and the toothpicks will move apart. Why? The sugar absorbs water. Not much, but enough to move the toothpicks toward each other as water moves into thesugar. The soap on the other end of the straw lowers the surface tension of the water sothat it moves away from the straw and pushes the toothpicks outward.

RG8Soap0807E-V1 Soap0807E_AR1_continued

GO ON

Reading

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35279911Why does the author includethis text from paragraph 1 inthe passage?

“What’s the best substance toclean your clothes with? Fat oroil, of course!”

A To explain how soap is made

≥ B To draw the reader into thepassage

C To explain how fat and oil worktogether

D To make the reader skip to thenext section

GO ON

Reading

35279802What is the meaning of tensionin paragraph 5?

A Suspense

≥ B StretchingC Emotional strainD A measuring device

35279783In paragraph 9, one end of amolecule of soap is hydrophilicand one end is hydrophobic.What does hydro– mean?

A SideB Agent

≥ C WaterD Grease

35279794Based on the etymology of theword synthesis [from Gk.synthesis “composition”; fromsyntithenai “put together”], whatdoes synthetic mean?

A Produced in large quantitiesB Found naturally on the earth

≥ C Formed by combining materialsD Manufactured by small

companies

35279855Which of these is the bestsummary of “The Mystery andHistory of Soap”?

A Adding ashes to oil is still themethod for producing soap.

B Every year, tons of soaps anddetergents are manufactured and sold.

≥ C Soap has been useful andimportant to people forthousands of years.

D Soap is important because itreduces bacteria, and it keepspeople healthier.

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35279878In the section titled “Magicmoving toothpicks,” whichof these steps must be donebefore toothpicks will move“magically”?

A Dipping two toothpicks in waterat the same time

B Dipping one end of a toothpickin sugar and water

≥ C Dipping one end of a straw insugar and one in soap

D Dipping both ends of a straw ina mixture of sugar and soap

STOP

Reading

35279906What is the most likely reasonthe section “Have some goodclean fun” is included in thepassage?

A To help people produce bettersoap bubbles

B To show how easily people canmake their own soap

≥ C To give ideas for entertainingothers with soap

D To learn how to performimportant scientific experimentswith soap

35279867In the section titled “Bubbleforecasts,” what happens beforea soap bubble pops?

A Hot air pushes the moistureupward.

≥ B Gravity pulls the moisturedownward.

C The walls of the bubble becomethicker.

D The top of the bubble reflectsmore light.

35279959What literary device is used inthe text below?

“You need a straw, some sugar,and soap . . .”

A Symbolism

≥ B AlliterationC PersonificationD Understatement

352799310What genre is “The Mystery andHistory of Soap”?

A MythB Short storyC Legend

≥ D Nonfiction

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ItemNumber

CorrectAnswer


Lon

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Item

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1 B 1.8.24 Determine the author’s purpose as represented by the choice of genre, and literary devices employed.

2 B 1.8.05 Determine the meaning of a word in context when the word has multiple meanings.

3 C1.8.01 Determine the meaning of an unknown word or content-area vocabulary using knowledge of prefixes, suffixes, and word roots (see Roots and Affixes list).

4 C 1.8.02 Use etymologies to determine the meanings of words.

5 C 1.8.16 Summarize a story or nonfiction passage, or identify the best summary.

6 C 1.8.24 Determine the author’s purpose as represented by the choice of genre, and literary devices employed.

7 B 1.8.18 Identify the causes of events in a story or nonfiction account.

8 C 1.8.18 Identify the causes of events in a story or nonfiction account.

9 B 2.8.10 Identify literary devices: (e.g., figurative language, hyperbole, understatement, symbols, dialogue).

10 D

2.8.13 Identify various subcategories of genres: poetry, drama (comedy and tragedy), science fiction, historical fiction, myth or legend, drama, biography/autobiography, short story, poem, fairy tale, folktale, fable, nonfiction, and essay.

To view all the reading assessment objectives, download the Illinois Reading Assessment Framework for Grades 3–8 online at www.isbe.net/assessment/IAFindex.htm .

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Longer Passage Followed byExtended-Response Sample Item

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Giants0805I Giants0805I_AR1

This is a story about one parent’s experiences with Little League baseball. His descriptions ofthese games show how exciting and unpredictable a baseball game can be.

They Might Be Giantsby Dave Barry

1 OK, fans. Time for Great Moments in Sports. The situation is this: The Giants areplaying a team whose name we did not catch in the hotly contested Little League Ages 6 and 7 Division, and the bases are loaded. The bases are always loaded in this particularDivision for several reasons.

2 First off, the coach pitches the ball to his own players. This is because throwing is notthe strong suit of the players in the Ages 6 and 7 Division. They have no idea, when theylet go of the ball, where it’s headed. They just haul off and wing it, really try to hurl thatbaby without getting bogged down in a lot of picky technical details such as whether ornot there is now, or has ever been, another player in the area where the ball is likely toland. Generally there is not, which is good, because another major area of weakness, inthe Ages 6 and 7 Division, is catching the ball.

3 Until I became a parent, I thought children just naturally knew how to catch a ball,that catching was an instinctive biological reflex that all children are born with, likeknowing how to operate a remote control or getting high fevers in distant airports. But itturns out that if you toss a ball to a child, the ball will just bonk off the child’s body andfall to the ground. So you have to coach the child. I go out in the yard with my son, and I give him helpful tips such as:“Catch the ball!” And: “Don’t justlet the ball bonk off your body!”Thanks to this coaching effort, myson, like most of the players onthe Giants, has advanced his gameto the point where, just before theball bonks off his body, he winces.

4 So fielding is also not the strongsuit of the Giants. They standaround the field, chattering toeach other, watching airplanes,picking their noses, thinkingabout dinosaurs, etc. Meanwhileon the pitchers’ mound, the coachof the opposing team tries tothrow the ball just right so that itwill bounce off the bat of one ofhis players, because hitting isanother major area of weakness inthe Ages 6 and 7 Division.

GO ON

Reading

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5 The real athletic drama begins once the opposing coach succeeds in bouncing the balloff the bat of one of his players, thus putting the ball into play and causing the fielders toswing into action. It reminds me of those table-hockey games, where you have a bunchof little men that you activate with knobs and levers, except that the way you activate theGiants is, you yell excitedly in an effort to notify them that the ball is headed their way.Because otherwise they’d probably never notice it.

6 “Robby!” I’ll yell if the ball goes near my son. “The ball!” Thus activated, Robby goes onFull Red Alert, looking around frantically until he locates the ball, which he picks up and — eager to be relieved of the responsibility — hurls in some random direction. Then,depending on where the ball is headed, some other parent will try to activate his child,and the ball will be hurled again and again, pinball-style, around the field, beforeultimately bonking off the body of the first baseman. Of course at this point the batterhas been standing on the base for some time. Fortunately, in this league, he is required tostop there; otherwise, he could easily make it to Japan.

7 This is why the bases are always loaded, which is what leads us to today’s SportsMoment. Standing on third base is James Palmieri, who is only 5, but who plays for theGiants anyway because his older brother, T.J., is on the team. James got on base via anexciting play: He failed to actually, technically, hit the ball, but the Giants’ wily coach,Wayne Argo, employed a classic bit of baseball strategy. “Let’s let James get on base,” hesaid. And the other team agreed, because at this point the Giants were losing the hotlycontested game by roughly 143 — 57.

8 So here it is: James is standing on third, for the first time in his entire life, thinkingabout dinosaurs, and next to him, ready to activate, is his mom, Carmen. And now CoachWayne is throwing the pitch. It is a good pitch, bouncing directly off the bat. Bedlamerupts as parents on both teams try to activate their players, but none is shouting withmore enthusiasm than Carmen. “Run, James!” she yells, from maybe a foot away. “Run!”

9 James, startled, looks up, and you can almost see the thought forming in his mind: I’msupposed to run. And now he is running, and Carmen is running next to him, cheeringhim on, the two of them chugging toward the plate, only 15 feet to go, James about toscore his first run ever. Then suddenly, incredibly, due to a semi-random hurl somewhereout in the field, there appears of all things: the ball. And — this is a nightmare — anopposing player actually catches it, and touches home plate and little James is OUT.

10 Two things happen:• Carmen stops. She says a bad word. A mom to the core.• James, oblivious, keeps running. Chugs right on home, touches the plate smiling and

wanders off, happy as a clam.

11 You can have your Willie Mays catch and your Bill Mazeroski home run. For me, theultimate mental picture is James and Carmen at that moment: the Thrill of Victory, theAgony of Defeat. A Great Moment in Sports.

GO ON

Reading

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33520501In the story, the author describes the behavior of adults at a little league game. Explainwhy adults behave as they do in this story. Use information from the story and your ownobservations and conclusions to support your answer.

STOP

Reading

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Assessment Objective: 2.8.06 Determine what characters are like by their words, thoughts, and actions, as well as how other characters react to them.


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Extended-ResponseScoring Rubric

Reading Extended-Response Scoring Rubric

Readers identify important information found explicitly and implicitly in the text. Readers use this information to interpret the text and/or make connections to other situations or contexts through analysis, evaluation, or comparison/contrast. A student-friendly version of this extended-response rubric is available online at www.isbe.net/assessment/reading.htm.

Score Criteria

4

• Reader demonstrates an accurate understanding of important information in the text by focusing on the key ideas presented explicitly and implicitly.

• Reader uses information from the text to interpret significant concepts or make connections to other situations or contexts logically through analysis, evaluation, inference, or comparison/contrast.

• Reader uses relevant and accurate references; most are specific and fully supported.

• Reader integrates interpretation of the text with text-based support (balanced).

3

• Reader demonstrates an accurate understanding of information in the text by focusing on some key ideas presented explicitly and implicitly.

• Reader uses information from the text to interpret significant concepts or make connections to other situations or contexts logically (with some gaps) through analysis, evaluation, inference, or comparison/contrast.

• Reader uses relevant and accurate references; some are specific; some may be general and not fully supported.

• Reader partially integrates interpretation of the text with text-based support.

2

• Reader demonstrates an accurate but limited understanding of the text.

• Reader uses information from the text to make simplistic interpretations of the text without using significant concepts or by making only limited connections to other situations or contexts.

• Reader uses irrelevant or limited references.

• Reader generalizes without illustrating key ideas; may have gaps.

1• Reader demonstrates little or no understanding of the text; may be inaccurate.

• Reader makes little or no interpretation of the text.

• Reader uses no references or the references are inaccurate.

• Reader’s response is insufficient to show that criteria are met.

0 • Reader’s response is absent or does not address the task.

• Reader’s response is insufficient to show that criteria are met.


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Grade: 8 Sample: 1 Score: 3

Make sure you— Read the question completely before you start to write your

answer,— Write your answer to the question in your own words,— Write as clearly as you can so that another person can read

your answer and understand what you were thinking,— Read over your answer to see if you need to rewrite any

part of it.

DIRECTIONS


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*Th is response demonstrates a good understanding of the text by focusing on some key ideas, for example, “. . . even if the kids lose, they will be happy”; “Parents on the other hand, want to win.”; and by providing some interpretations, “Even if they get an out, they will not realize it, and they will celebrate”; and “In reality, kids like to have fun.”

*Th e response makes some connections in the last paragraph, but the connections are not well supported. To obtain a higher score, the response needed to better reinforce statements made in the last paragraph and include explicit, text-based support.


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part of it.

DIRECTIONS



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*Th is response demonstrates an accurate understanding of some key ideas presented in the essay; for example, “. . . the moms and dads are more intense then the children.” and “. . . the children as they are playing are very spacy.” Th e writer uses explicit and implicit text-based support to interpret some key points; for example, “. . . a mother is described as a mom to the core. Which obviously means that she is horrifi ed when her son doesn’t score.” and “. . . parents are like this only because they care for their child and want the best for them.”

*Th e response attempts to connect the text to a possible childhood experience, but the connection is weak and not well supported. To obtain a higher score, the response needed to better reinforce statements made to support the connection.

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g




part of it.

DIRECTIONS


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*Th is response demonstrates a strong interpretation of the text by focusing on the key ideas, “It is a parent’s job to encourage their child . . .” and “. . . it is very important to them that their child plays the game and wins. Th ey probably feel that their child’s success refl ects on their abilities as a parent.” Th e writer uses explicit text references, for example, “. . . activate . . .”; “. . . happy as a clam . . .”; “. . . a mom to the core . . .”, along with implicit text references, “. . . Little League team cannot throw and catch well . . .”; “. . . shouting at them to get their attention when the ball is near . . .” In-depth analysis is evident; “Th e adults in this story behave the way they do because it is very important to them that their child plays the game and wins.”; “. . . she displayed tipical behavior for a mom whose child didn’t win. Th e child did his best, and felt over the moon. But the mother, ever the greatest fan, was let down when her son did not get the home run she was hoping for.”

*Th is response is well-balanced with both specifi c text-based references and student interpretations related to the passage.


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g




part of it.

DIRECTIONS



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*Th is response demonstrates a very complete understanding of information in the passage. Th e writer cites numerous passage references to support interpretations; for example, “James got out. James didn’t care however. His mother on the other hand was furious. James’ mom is ‘a mom to the core,’ meaning she wants her baby boy to win. Since he is out, he can no longer win. Th is dissapoints the mother . . .”

*Th is response is well-balanced with both specifi c, text-based references and interpretations related to the passage.

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Illinois Standards Achievement Test

Mathematics Samples

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Structure of the Grade 8 Mathematics ISAT

ISAT Mathematics testing in spring 2009 will consist of 30 norm-referenced items, as well as 45 criterion-referenced items, some of which will be used for developmental purposes. Th e 30 norm-referenced items are an abbreviated form of the Stanford 10 Mathematics Problem Solving assessment, developed by Pearson, Inc. Th e 45 criterion-referenced items are all written by Illinois educators and pilot tested with Illinois students.

Item FormatsAll 75 items are aligned to the Illinois Mathematics Assessment Framework, which defi nes the elements of the Illinois Learning Standards that are suitable for state testing.

Multiple-choice items require students to read, refl ect, or compute and then to select the alternative that best expresses what they believe the answer to be. Th is format is appropriate for quickly determining whether students have achieved certain knowledge and skills. Well-designed multiple-choice items can measure student knowledge and understanding, as well as students’ selection and application of problem-solving strategies. A carefully constructed multiple-choice item can assess any of the levels of mathematical complexity from simple procedures to sophisticated concepts. Th ey can be designed to reach beyond the ability of students to “plug-in” alternatives or eliminate choices to determine a correct answer. Such items are limited in the extent to which they can provide evidence of the depth of students’ thinking.

Short-response items pose similar questions as multiple-choice items and provide a reliable and valid basis for extrapolating about students’ approaches to problems. Th ese items reduce the concern about guessing that accompanies multiple-choice items. Th e short-response items are scored with a rubric and count as 5% of the scale score of the test.

Extended-response items require students to consider a situation that demands more than a numerical response. Th ese items require students to model, as much as possible, real problem solving in a large-scale assessment context. When an extended-response item poses a problem to solve, the student must determine what is required to “solve” the problem, choose a plan, carry out the plan, and interpret the solution in terms of the original situation. Students are expected to clearly communicate their decision-making processes in the context of the task proposed by the item (e.g., through writing, pictures, diagrams, or well-ordered steps). Th e extended-response items are scored with a rubric and count as 10% of the scale score of the test.

Scoring Extended- and Short-Response ItemsExtended- and short-response items are evaluated according to an established scoring scale, called a rubric, developed from a combination of expectations and a sample of actual student responses. Such rubrics must be particularized by expected work and further developed by examples of student work in developing a guide for scorers. Illinois educators play a substantial role in developing these guides used for the scoring of the short- and extended-response items. Committees of mathematics educators from throughout the state attend a validation meeting, during which they use the mathematics scoring rubrics to establish task-specifi c criteria that are used to score all short- and extended-response items consistently and systematically.

Answer Document for Grade 8 Mathematics ISATStudents in grade 8 respond to all test items in a separate answer document. Test administrators should monitor students carefully during testing to make sure students are using the appropriate pages of the answer document, especially for the short- and extended-response items.


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Mathematics SessionsAll standard time administration test sessions are a minimum of 45 minutes in length. Any student who is still actively engaged in testing when the 45 minutes have elapsed will be allowed up to an additional 10 minutes to complete that test session. More details about how to administer this extra time will appear in the ISAT Test Administration Manual. Th is policy does not aff ect students who already receive extended time as determined by their IEP.

Mathematics ISAT Grade 8

Session 145 minutes

40 multiple-choice items(30 of these are an abbreviated form of the Stanford 10.)

Session 245 minutes

30 multiple-choice items3 short-response items

Session 345 minutes 2 extended-response items

(Some items will be pilot items.)

Calculator Use for Grade 8 Mathematics ISATAll students in grade 8 are allowed to use a calculator during all sessions of the mathematics assessment.Students are allowed to use any calculator they normally use in their mathematics classes. Schools, teachers, and parents should be advised that when students attempt to use calculators with which they are unfamiliar, their performance may suff er. In a like manner, students who are not taught when and how to use a calculator as part of their regular mathematics instructional program are also at risk.

Rulers for Grade 8 Mathematics ISATAll students in grade 8 will be provided with a ruler to use during all sessions of the mathematics assessment. Th is ruler will allow students to measure in both inches and centimeters.

Inches0 1 2 3 4 5 6

Centimeters0123456789101112131415

ISAT GRADES FOUR–EIGHT

Scratch Paper for Grade 8 Mathematics ISATStudents must be provided with blank scratch paper to use during only session 1. Only session 1 contains norm-referenced items, which were normed under such conditions. Students may not use scratch paper during session 2 or session 3, but they may use the test booklet itself as scratch paper. However, students must show their work, when required, for each short-response item in session 2 on the appropriate page in the answer document. Students must show their work for each extended-response item in session 3 on the appropriate pages in the answer document.


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ISAT MATHEMATICS REFERENCE SHEETGrades 7 and 8

Reference Sheet for Grade 8 Mathematics ISATAll students in grade 8 will be provided with a reference sheet to use during all sessions of the mathematics assessment. Th is reference sheet is shown below.

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Mathematics

3484834 3484834_AR11Which point on the numberline below best represents thevalue ?

A Point PB Point Q

≥ C Point RD Point S

0 1 2 3 4 5 6

P Q R S

210

34848562

Amy has of a yard of string to

make bracelets. Each bracelet

requires of a yard of string.

What is the greatest number ofbracelets Amy can make withthis length of string?

8 6 4 3

A ≥ B C D

18

34

34848625Last year there were 80 studentsenrolled in the eighth-grade class.This year the number of studentsenrolled in the eighth-grade classincreased by 10%.

How many students areenrolled in the eighth-gradeclass this year?

8 81 88 90

A B ≥ C D

33493054Between which two consecutiveintegers is ?

≥ A 6 and 7B 17 and 18C 75 and 76D 100 and 101

23 300

33568443Paula multiplied a number by16. Her result is a positivenumber less than 16. Which ofthese did Paula multiply by 16?

≥ A A number between zero andone

B A number greater than oneC A number less than zeroD Zero

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34848638A company packs its coffee intocylindrical containers. The height ofeach container is 6 inches, and theradius of the container is 3 inches.

Which is closest to the volumeof one of these cylindricalcontainers? (Use 3.14 for �.)

A 36 cubic inchesB 54 cubic inchesC 113 cubic inches

≥ D 170 cubic inches

3349312 3349312_AR16

Which is closest to thecircumference of this circle?(Use 3.14 for p.)

A 14 inches ≥ C 28 inchesB 20 inches D 63 inches

4.5 in.

3407469 3407469_AR19What is the surface area of thisrectangular prism?

A 135 square feetB 155 square feetC 180 square feet

≥ D 198 square feet

3 feet

15 feet3 feet

3533987 3533987.AR17Quadrilateral KLMN is an isoscelestrapezoid with a perimeter of 32 cm.

What is the area of quadrilateralKLMN?

≥ A 44 cm2

B 55 cm2

C 88 cm2

D 112 cm2

K N

ML 8 cm

14 cm

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3528416 3528416_AR111Use your inch ruler to help youanswer this question.

The picture shows the scale drawingof a tree.

Which is closest to the heightin feet of the actual tree?

A 10 feet

B feet

≥ C feet

D 15 feet

1212

1012

height

1 inch represents 5 feet.

334920410When filled to capacity, acontainer holds 4.6 liters ofliquid. How many milliliters(mL) is this?

A 0.46 mLB 46 mLC 460 mL

≥ D 4600 mL

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348486412Look at the addition patterns below.

1 � 3 � 41 � 3 � 5 � 91 � 3 � 5 � 7 � 161 � 3 � 5 � 7 � 9 � 25

How many consecutive oddintegers starting with 1 must be added to produce 64?

6 7 8 9

A B ≥ C D

335685614Which is equivalent to theexpression below?

A C x � 1

≥ B D x � 2x � 2

2

x � 12

x2

� 1

3400068 3400068_AR113Which expression satisfies thepattern below?

A 4n2 � 3 C n3

B 3n2 ≥ D n2

n ?

0 0

1 1

2 4

3 9

4 16

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3400149 3400149_AR1 to AR415Which represents the graph of y � 3?

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

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348487117The graph of a line contains thepoints (5, 3) and (5, -1).

Which of the following mustbe true about the graph of this line?

≥ 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.

3484869 3484869_AR116Which of the followingequations represents therelationship between x and yin the table?

A y � 2xB y � x � 2C y � 5x

≥ D y � 3x � 2

0

1

2

3

4

2

5

8

11

14

x y

348487318The inequality 70° � x � 80°represents the range of the idealwater temperature, in degreesFahrenheit, for Sammy’s fish.

Which statement is true aboutthe situation?

A The ideal water temperature isless than 70 °F.

B The ideal water temperature isgreater than 80 °F.

≥ C The ideal water temperature isbetween 70 °F and 80 °F.

D The ideal water temperature isless than 70 °F or greater than 80 °F.

3530136 3530136_AR1-419Which graph best represents thesolution to the inequalitybelow?

-4x � 10 � -6

A

B

C

≥ D -4 -3 -2 -1 0 1 2 3 4 5

-4 -3 -2 -1 0 1 2 3 4 5

-4 -3 -2 -1 0 1 2 3 4 5

-4 -3 -2 -1 0 1 2 3 4 5

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3484900 3484900_AR121What is the value of x in thetriangle shown?

24 49 54 59

A B C ≥ D

(x – 5)°

70°

56°

335610820

Malia has times more tennis

balls than Jolie. Together they

have 20 tennis balls. How many

tennis balls does Malia have?

8 10 12 15

A B ≥ C D

112

3349352 3349352.AR122

What is the circumference ofthis circle in terms of p?

A 65p cm ≥ C 13p cmB 42.25p cm D 6.5p cm

6.5 cm

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3484901 3484901_AR123Line l intersects parallel lines m and n as shown.

Which list contains all theangles that are congruent to ∠1?

≥ A ∠3, ∠5, ∠7B ∠3, ∠6, ∠8C ∠2, ∠3, ∠4D ∠2, ∠7, ∠8

m n

l14 58

23 67

3349355 3349355.AR1 to .AR524

Which drawing represents thetop view of this solid?

A

B

C

≥ D

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3484902 3484902_AR125�XYZ is similar to �RST.

What is the length of ?

10 cm 9 cm 8.5 cm 7.5 cm

A ≥ B C D

ST

8 cm6 cm

12 cm

10 cm

R

S TZY

X

3349325 3349325_AR126

The following pairs of numbers can be graphed on this number line.

Which numbers have the same absolute value?

≥ A -3 and 3B 5 and 10C 4 and -8D -2 and -4

-5-6-7-8-9-10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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3484896 3484896_AR127The circle graph below represents atotal of 240 animals at a zoo. Theshaded sector represents the numberof monkeys at this zoo.

How many monkeys are at this zoo?

8 20 30 72

A ≥ B C D

240 Animals at a Zoo

Monkeys30º

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3356854 3356854.AR1 to .AR428Which scatter plot shows the line that best fits the data points given?

≥ A C

B D

y

x

y

x

y

x

y

x

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Mathematics

334924429Mike has only 2 red apples and 3 green apples in a bowl. Withoutlooking he chooses an apple andgives it to his sister. Then he chooses an apple for himself.

What is the probability that he and his sister will each get a red apple?

10% 30% 40% 60%

≥ A B C D

353012630The student council is making snackbags for a class trip. Each snack bagwill contain:

• 1 type of drink• 1 type of cookie• 1 type of fruit

To make each snack bag, they willchoose from 2 types of drinks, 4 types of cookies, and 2 types of fruit.

How many combinations of 1 type of drink, 1 type ofcookie, and 1 type of fruit are possible?

A 3B 8

≥ C 16D 48

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ItemNumber

CorrectAnswer


1 C 6.8.07 Identify and locate rational and irrational numbers (e.g., π, 2 , 5 ) on a number line.

2 B 6.8.09 Solve problems and number sentences involving addition, subtraction, multiplication, and division using rational numbers, exponents, and roots.

3 A

6.8.12 Describe the effect of multiplying and dividing by numbers, including the 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.

4 A6.8.14 Estimate the square or cube root of a number less than 1,000 between two whole numbers (e.g., 2003 is between 5 and 6).

5 C6.8.18 Solve number sentences and problems involving fractions, decimals, and percents (e.g., percent increase and decrease, interest rates, tax, discounts, tips).

6 C

7.8.02 Solve problems involving perimeter/circumference and area of polygons, circles, and composite figures using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).

7 A

7.8.02 Solve problems involving perimeter/circumference and area of polygons, circles, and composite figures using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).

8 D7.8.04 Solve problems involving the volume or surface area of a right rectangular prism, right circular cylinder, or composite shape using an appropriate formula or strategy.

9 D7.8.04 Solve problems involving the volume or surface area of a right rectangular prism, right circular cylinder, or composite shape using an appropriate formula or strategy.

10 D7.8.05 Solve problems involving unit conversions within the same measurement system for length, weight/mass, capacity, square units, and measures expressed as rates (e.g., converting feet/second to yards/minute).

11 C

7.8.06 Solve problems involving scale drawings, maps, and indirect measurement (e.g., determining the height of a building by comparing its known shadow length to the known height and shadow length of another object).

12 C 8.8.01 Analyze, extend, and create sequences or linear functions, and determine algebraic expressions to describe the nth term of a sequence.


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ItemNumber

CorrectAnswer


13 D 8.8.01 Analyze, extend, and create sequences or linear functions, and determine algebraic expressions to describe the nth term of a sequence.

14 B 8.8.04 Recognize and generate equivalent forms of algebraic expressions.

15 D8.8.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph.

16 D 8.8.08 Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions.

17 A 8.8.09 Interpret the meaning of slope and intercepts in linear situations.

18 C 8.8.11 Represent and analyze problems with linear equations and inequalities.

19 D 8.8.12 Solve linear equations and inequalities in one variable over the rational numbers (e.g., 5x+7= –13, 4x–3= –7x+8, –2x+3>–5).

20 C 8.8.13 Solve word problems involving unknown quantities.

21 D 9.8.02 Solve problems that require knowledge of triangle and quadrilateral properties (e.g., triangle inequality).

22 C 9.8.04 Identify, describe, and determine the radius, diameter, and circumference of a circle and their relationship to each other and to pi.

23 A9.8.08 Identify or analyze relationships of angles formed by intersecting lines (including parallel lines cut by a transversal) and angles formed by radii of a circle.

24 D 9.8.10 Identify front, side, and top views of a three–dimensional solid built with cubes.

25 B 9.8.11 Solve problems involving congruent and similar figures.

26 A 9.8.12 Relate absolute value to distance on the number line.

27 B

10.8.01 Read, interpret (including possible misleading characteristics), and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two or three circles), chart/table, line graph, scatter plot, circle graph, stem–and–leaf plot, or histogram.

28 A 10.8.04 Identify or draw a reasonable approximation of the line of best fit from a set of data or a scatter plot, and use the line to make predictions.

29 A10.8.06 Solve problems involving the probability of an event composed of repeated trials, compound events (including independent events), or future events with or without replacement.

30 C 10.8.08 Solve simple problems involving the number of ways objects can be arranged (permutations and combinations).

To view all the mathematics assessment objectives, download the Illinois Mathematics Assessment Framework for Grades 3–8 online at www.isbe.net/assessment/IAFindex.htm.

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Mathematics Short-ResponseScoring Rubric

Followed by Student Samples


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Mathematics Short-Response Scoring RubricTh e following rubric is used to score the short-response items for all grade levels.

SCORELEVEL DESCRIPTION

2 Completely 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

Using Short-Response SamplesBeginning with the spring 2008 ISAT, the sample short-response question and answer (shown below) that appeared in the 2006 and 2007 ISAT test directions will no longer be included in the directions immediately prior to session 2. ISBE encourages educators to practice these types of items with students during the course of the school year so they are familiar with them prior to ISAT testing.

Please refer to the 2006 and 2007 ISAT sample books for additional short-response items and student samples (online at www.isbe.net/assessment/htmls/sample_books.htm).

SAMPLE SHORT-RESPONSE QUESTION

SAMPLE SHORT-RESPONSE ANSWER

50¢ + 90¢ + 35¢ = $1.75for each day

1.751.751.751.75

+ 1.75___$8.75

3 2

My answer$8.75

for five days

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.


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Blank Short-Response Template

Mathematics - Session 2 Question 1

Write your response to question 1 on this page. Only what you write on this page will be scored.


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Mathematics Short-Response Sample Item 1

Below is a short-response sample item, followed by 3 samples of student responses.

This short-response sample item is classified to assessment objective 9.8.09, “Solve problems involving vertical, complementary, and supplementary angles.”

3403483 3403483_AR11The lines shown intersect at point P.

If the measure of ° and the measure of °, what is the value of x?

Show your work.

�2 � (4x � 36)�1 � 60

1

2P


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Short-Response Student Sample 1A


Rubric Score Point = 2

Note: Th e student sets the equation equal to 60° and correctly solves for x (6=x).


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Short-Response Student Sample 1B



Note: Th e student sets the expression 4�6�36 equal to 60 and correctly solves for x (x=6).


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Short-Response Student Sample 1C



Note: Th e student sets the expression 4x�36 equal to 60 but, due to a computation error, arrived at an incorrect answer (x=8).


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Mathematics Short-Response Sample Item 2

Below is a short-response sample item, followed by 3 samples of student responses.

This short-response sample item is classified to assessment objective 8.8.13, “Solve word problems involving unknown quantities.”

34000472There are 24 students in Mr. Reyna’s class. Each student is wearing either a hat, or gymshoes, or both a hat and gym shoes.

• 16 students are wearing hats.• 20 students are wearing gym shoes.

How many students in Mr. Reyna’s class are wearing both a hat and gym shoes?

Show your work.


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Note: Th e student provides a drawing with the correct number of students, hats, and gym shoes to depict the strategy used to reach the answer. Th e student correctly draws circles connecting those who wear both hats and gym shoes. Th e student correctly states the answer as, “12 students are wearing both.”


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Note: Th e student correctly represents the data using a Venn diagram to show the number of students wearing only hats, only shoes, and both. Th e student correctly states the answer as, “12 students in Mr. Reyna’s class are wearing both a hat and gym shoes.”


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Note: Th e student provides a correct algorithm for solving the problem (20�16�24). Due to a computation error (20�16�26), the student arrives at an incorrect answer of 2.

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Mathematics Extended-ResponseScoring Rubric

Followed by Student Samples


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Mathematics Extended-Response Scoring Rubric

Th e following rubric is used to score the extended-response items for all grade levels. A student-friendly version of this extended-response scoring rubric is available online at www.isbe.net/assessment/math.htm.

SCORELEVEL

MATHEMATICAL KNOWLEDGE:Knowledge of mathematical principles and concepts which result in a correct solution to a problem.

STRATEGIC KNOWLEDGE:Identification and use of important elements of the problem that represent and integrate concepts which yield the solution (e.g., models, diagrams, symbols, algorithms).

EXPLANATION:Written explanation of the rationales and steps of the solution process. A justification of each step is provided. Though important, the length of the response, grammar, and syntax are not the critical elements of this dimension.

4

• shows complete understanding of the problem’s mathematical concepts and principles

• uses appropriate mathematical terminology and notations including labeling answer if appropriate

• executes algorithms and computations completely and correctly

• identifies all important elements of the problem and shows complete understanding of the relationships among elements

• shows complete evidence of an appropriate strategy that would correctly solve the problem

• gives a complete written explanation of the solution 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 of the problem’s mathematical concepts and principles

• uses mostly correct mathematical terminology and notations

• executes algorithms completely; computations are generally correct but may contain minor errors

• identifies most of the important elements of the problem and shows a general understanding of the relationships among them

• shows nearly complete evidence of an appropriate strategy for solving the problem

• gives a nearly complete written explanation of the solution process; clearly explains what was done and begins to address why it was done

• may include a diagram with most of its elements explained

2

• shows some understanding of the problem’s mathematical concepts and principles

• uses some correct mathematical terminology and notations

• may contain major algorithmic or computational errors

• identifies some important elements of the problem but shows only limited understanding of the relationships among them

• shows some evidence of a strategy for solving the problem

• gives some written explanation of the solution process; either explains what was done or addresses why it was done

• explanation is vague, difficult to interpret, or does not completely match the solution process

• may include a diagram with some of its elements explained

1

• shows limited to no understanding of the problem’s mathematical concepts and principles

• may misuse or fail to use mathematical terminology and notations

• attempts an answer

• fails to identify important elements or places too much emphasis on unrelated elements

• reflects an inappropriate strategy for solving the problem; strategy may be difficult to identify

• gives minimal written explanation of the solution process; may fail to explain what was done and why it was done

• explanation does not match presented solution process

• may include minimal discussion of the elements in a diagram; explanation of significant elements is unclear

0 • no answer attempted • no apparent strategy • no written explanation of the solution process is provided


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Using Extended-Response SamplesBeginning with the spring 2008 ISAT, the sample extended-response problem and solution (shown below) that appeared in the 2006 and 2007 ISAT test directions will no longer be included in the directions immediately prior to session 3. ISBE encourages educators to practice these types of items with students during the course of the school year so they are familiar with them prior to ISAT testing.

Please refer to the 2006 and 2007 ISAT sample books for additional extended-response items and student samples (online at www.isbe.net/assessment/htmls/sample_books.htm).

SAMPLE EXTENDED-RESPONSE PROBLEMMrs. Martin wants to put tiles on the floor by the front door of her house. She wantsto 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 firstletter of the color that should be placed there.

Show all your work. Explain in words how you found your answer. Tell why youtook 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 half and1 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 shewants of the tiles to be gray. Since she wants gray and redto be the same amount of tiles, I made the last row R for red.

1–4

1–4

1–41–4

blue

gray

red

1–2B B B B B BG G G G G G

SAMPLE EXTENDED-RESPONSE SOLUTION

1—21—41—4


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Mathematics - Session 3 Problem 1

Blank Extended-Response Template


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Mathematics - Session 3 Problem 1-continued

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34067691In a recent survey, 72 people who like to bake were asked to choose their favorite item to

bake. Of those people, chose cake, chose bread, chose cookies, and the rest chose pie

as their favorite item to bake.

Create a graph to represent this information. Be sure to label all parts of your graphand include a title.

Show all your work. Explain in words how you created your graph. Write why youtook the steps you did to solve the problem.

12

18

14

Mathematics Extended-Response Sample Item 1

Below is an extended-response sample item, followed by 3 student samples.

This extended-response sample item is classified to assessment objective 10.8.03, “Create a bar graph, chart/table, line graph, or circle graph and solve a problem using the data in the graph for a given set of data.”


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Extended-Response Student Sample 1A


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Extended-Response Student Sample 1A Continued


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Extended-Response Student Sample 1B


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Extended-Response Student Sample 1B Continued


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Extended-Response Student Sample 1C


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Extended-Response Student Sample 1C Continued


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Scoring Guide for “People Who Bake”

Any type of pictorial display was accepted as a “graph.” Depending upon the type of graph students choose, students must fi nd the missing number, fraction, or percent of people who chose pie (9, 1/8, or 12.5%, respectively).

Extended-Response Student Sample 1A

MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION

4 4 4

The response shows complete understanding of the problem’s mathematical concepts and principles. The student provides a correctly drawn bar graph with correct labels and titles. The student executes all algorithms and computations completely and correctly.

The response shows complete evidence of an appropriate strategy that correctly solves the problem. The student selects a bar graph to represent the information. The bar lengths correctly identify the relationships between the categories.

The response provides a complete explanation of the solution process, clearly explaining what was done and why it was done (…try to find out how many people were the ones who bake…cake, cookies, Bread, and pie…By that, you would divide…then add the numbers...But then subtract 72-63…So 9 people or 1/8 baked pie). The student further explains what was done to create the scale and why (I ordered it by 6…measure the number of people who baked their favorite item in the bar graph).

Extended-Response Student Sample 1B


4 4 4

The response shows complete understanding of the problem’s mathematical concepts and principles. The student provides a correctly drawn circle graph with correct labels and titles. The student executes all algorithms and computations completely and correctly.

The response shows complete evidence of an appropriate strategy that correctly solves the problem. The student selects a circle graph to represent the information. The circle graph sectors correctly identify the relationships between the categories.

The response provides a complete explanation of the solution process, clearly explaining what was done and why it was done (…I converted the fractions…to find out how many people choose to bake cake, cookies, bread. I then added up…so that I can take the answer away from 72…Next I made a pie chart, because it shows a percentage or fraction of how many people like baking bread, cookies, cake, pie…).


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Extended-Response Student Sample 1C


2 2 2

The response shows some understanding of the problem’s mathematical concepts and principles by correctly calculating the number of people who bake cake, bread, and cookies. However, the student fails to calculate the number of people who bake pies and consequently does not address a major portion of the mathematical concept.

The response shows some evidence of a strategy for solving the problem. The student understands that a pictorial representation can be used to display the data.

The response provides some written explanation of the solution process by explaining what was done (Then I divided 72 by 2 and I came up with 36).

1 2

3 4

5 6

7 8

9 1

0 1

1 1

2 A

B C

D E

IL09-A2-8SB

ISAT Sample Book Gr 8

Documents

Transcript of ISAT Sample Book Gr 8