Sample Book 3 GRADEsolvingmathwordproblems.weebly.com/uploads/2/4/5/4/...ILLINOIS STATE BOARD OF...

ILLINOIS STATE BOARD OF EDUCATION

2006ISAT

Sample Book

999-8334-40-3

Sample Items for Reading and Mathematics

GRADE

3

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Copyright © 2006 by the Illinois State Board of Education. Copyright © 2003 by Harcourt Assessment, Inc. 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 publisher and the Illinois State Board of Education, except for the printing of complete pages for instructional use and not for resale. Printed in the United States of America.


2006 ISAT Grade 3 Sample Book

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Table of Contents

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

READING

Structure of the Grade 3 Reading ISAT ................................................................................. 9Item Formats ...................................................................................................................................................9Reading Sessions ...........................................................................................................................................9Passage Selection ........................................................................................................................................10

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

Long Passage Followed by Multiple-Choice Sample Items and Extended-Response Sample Item ....................................................................................... 15

Functional Passage Followed by Multiple-Choice Sample Items ..................................... 23

Answer Key with Assessment Objectives Identified .......................................................... 26

Extended-Response Scoring Rubric .................................................................................... 29

Annotated Extended-Response Student Samples ............................................................. 31

MATHEMATICS

Structure of the Grade 3 Mathematics ISAT ....................................................................... 37Item Formats .................................................................................................................................................37Mathematics Sessions ...............................................................................................................................38Calculator Use for Grade 3 Mathematics ISAT ...................................................................................38Rulers for Grade 3 Mathematics ISAT ...................................................................................................38

Multiple-Choice Sample Items ............................................................................................ 39

Answer Key with Assessment Objectives Identified .......................................................... 45

Short-Response Sample Item and Scoring Rubric ............................................................. 46

Annotated Short-Response Student Samples ................................................................... 48

Extended-Response Sample Item and Scoring Rubric ...................................................... 51

Annotated Extended-Response Student Samples ............................................................. 54


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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 2006 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 3 Reading ISAT

ISAT Reading testing beginning in spring 2006 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 Harcourt, 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 new policy does not aff ect students who already receive extended time as determined by their IEP.

Reading ISAT Grade 3

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

Session 245 minutes

1 longer passage with 15–18 multiple-choice items1 extended-response item1 functional passage with 3–5 multiple-choice items

Session 345 minutes

1 longer passage with 15–18 multiple-choice items1 extended-response item1 functional passage with 3–5 multiple-choice items

(Some items will be pilot items.)



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Passage SelectionPassages for state tests should be of the highest quality. Passages on the state assessment should be selected from published works of literature or literary nonfi ction. While the selection of such passages must take into account the appropriateness of the material for the age of the students, as well as for the assessment context, the chosen passages should not be simplifi ed or tampered with. On any given test, the passages should include works by both classic and contemporary writers and address a range of cultures.


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Short Passage Followed byMultiple-Choice Sample Items


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GO ON

ReadingXED176 Passage XED176.AR1

Being a Fishby

Russell E. Erickson

Would it be fun to be afish? They are, after all,quite different from us.

Fish have no ears as wedo. Their bodies arecovered with thin, flatplates called scales. Theonly sounds they knoware what they feel usingcertain scales along theirsides. These are specialscales called lateral lines.

We get oxygen from the air by using our lungs. Fish getoxygen from the water by using the gills on the sides oftheir heads. We can play in water and on land, but fishmust stay in the water all the time.

Fish never get hot or cold. They are called cold-bloodedbecause they are always the same temperature as thewater around them. That means they have no need for hot soup, or cold lemonade, or cozy blankets, or cool sandals.

All in all, it’s probably more fun being us.


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Reading

XED1761This story mainly tells —

≥ how fish are different frompeoplehow many kinds of fish therearewhere fish can be foundhow fish swim

XEE0772Which question does thearticle answer?

Do fish have teeth?How can I catch a fish?Do fish sleep?

≥ What does cold-blooded mean?

XEE0813You would most likely find anarticle like this in a bookabout —

farm animalswater fun

≥ sea lifefishing

XED1784How do fish hear?

With ears≥ By feeling

By tastingBy smelling


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Long Passage Followed byMultiple-Choice Sample Items and Extended-Response Sample Item


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GO ON

ReadingPigs0305L PIGS0305L_AR1 and AR2

This is an article about the unknown talents of pigs. These animals have helpedhumans for millions of years.

1 Pigs have been on our planetfor about 40 million years andthere has been very little changein them during that time. Eventheir habit of eating almostanything has stayed the same.

2 Farmers have raised pigs formany thousands of years. Bonesof tame pigs have been found inhouses from the New Stone Age.This was the time between 5,000and 10,000 years ago, whenpeople began to settle down toraise crops and live in smallcommunities.

3 The pig is a hoofed animal, anungulate, and belongs to a largegroup that scientists call theeven-toed ungulates. Cattle, deer,goats, sheep, and camels are alsoin this group. These animals havekept the two largest toes—the

second and third—to run on. Theweight of the animal comes downbetween these two toes, whichhave grown into hoofs. The othertoes have become weak andstopped growing. In some casesthey have disappeared.

4 Perhaps one reason the pig hasstayed alive through all theseyears is that it is a fighter. It has aset of sharp tusks and a deadlybite. It often fights rather thanrunning away. Even a tame pig isconsidered a risky animal toapproach in an unfriendly way.

5 The pig is so popular as a sourceof food that only now and thenhas it been used in other ways.The ancient Egyptians used thepig to help in their planting.Their little hoofs made holes justthe right size and depth for the

40 Million Years of Pigsby Alice L. Hopf


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Reading

seeds, and the animals weremoved back and forth over theland to be planted. This wascalled “treading the seed.”

6 Later, other people found usefulwork for pigs. In England longago, there were laws againsthunting. Deer were thought of asthe property of the lord whoruled the area. Peasants wereforbidden to hunt anythingexcept small animals. For thisreason they could not keep largedogs. Instead, they trained thepig as a hunting companion. Pigshave a good sense of smell. Theyare very smart animals—some saysmarter than dogs.

7 In France, pigs are also used tolook for truffles, a kind of blackmushroom that growsunderground. Truffles are veryexpensive and delicious to eat.Pigs use their snouts to dig uproots to eat, and they have beentrained to smell out this treasure.Usually the pig has a ring aroundits snout to keep it from eatingthe truffles before the collectorcan put them in a basket.

8 Pigs have also been trained ascircus animals. They can doanything that dogs can do. Theycan jump through hoops, dance,pull a cart, and walk a tightrope.They can even do things dogs


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Reading

would not figure out, like openingthe bar on a door.

9 Even though pigs have so muchtalent, people still have some badopinions of them. To call anotherperson a pig is a serious insult in almost every language. Our day-to-day language is full ofsayings like “dirty as a pig,”“greedy as a pig,” and “don’t be apig.” All of this is more an insultto the pig than to the person. Pigsare not naturally dirty. A domesticpig becomes dirty when it is shutup in a pen full of garbage. And a

pig is no greedier than any otheranimal. A cat or a dog willovereat—but not a pig. If it digsaround in its food, it is to find thesmall pieces it especially likes,rather than simply eatingeverything in sight. And the pig isa good-natured animal. If it istreated with kindness, it will doalmost anything that is asked of it.

10 The pig has come a long way.But it is still independent, curious,and brave—as well as smart. Thisis why it has lived for millions ofyears.

“40 Million Years of Pigs” by Alice Lightner Hopf, is adapted by permission from 40 MILLION YEARS OF PIGSfrom the May 1982 issue of Cricket Magazine as adapted from “PIGS Wild and Tame” copyright © 1979 by Alice Lightner Hopf.


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Reading

33470561According to the article, which of the following is true about pigs?

They have a poor sense of smell.They are used for hunting deer.

≥ They have changed little overtime.They are born with five toes.

33470472How do scientists know thatpeople raised pigs thousandsof years ago?

There are old stories about circus acts with pigs.Scientists know cattle and pigshave the same kinds of feet.The way people hunt for truffles has not changed inyears.

≥ Scientists have found the bonesof pigs in very old ruins.

33470483Which of the followinganimals has toes like a pig?

BirdLizard

≥ CamelSquirrel

33470594What will a pig probably do ifsomeone threatens it?

Run≥ Fight

DigJump

33470445A pig is a risky animal toapproach in an unfriendlyway. Which of the followingmeans the same as risky?

LargeUnpopularGreedy

≥ Unsafe


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Reading

33470456“Pigs use their snouts to dig uproots to eat, and they havebeen trained to smell out thistreasure.” Which of thefollowing is most like a snout?

≥ A noseA footA tuskA tail

33470537In France, why is a ring placedaround the pig’s snout?

To protect the collector from the pig’s sharp tusksTo show the area where the pigis supposed to hunt

≥ To keep the pig from opening its mouth very wideTo give the collector somethingto tie the pig’s leash to

33470578According to the article, wheremight a person see a pigjumping through a hoop?

On a farm≥ At a circus

In a fieldIn a forest

33470629Which sentence from thestory tells how the author feelsabout pigs?

“The pig is a hoofed animal, anungulate, and belongs to a largegroup that scientists call theeven-toed ungulates.”“Farmers have raised pigs formany thousands of years.”“Their little hoofs made holesjust the right size and depth forthe seeds, and the animals weremoved back and forth over theland to be planted.”

≥ “All of this is more an insult tothe pig than to the person.”

334706310This passage is an example ofwhat form of writing?

Fairy taleTall tale

≥ NonfictionFable


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334702711How have pigs been useful animals throughout history? Explain your answerusing information in the article and your own ideas.

GO ON

Reading


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Functional Passage Followed byMultiple-Choice Sample Items


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GO ON

ReadingKite0305F R3KITE0305I_AR1.eps

How to Fly a Kite

A windy day in the park could be a perfect dayto fly a kite. Here are the steps to follow whenyou fly a kite.

1. Find a large, open area with no trees orpower lines.

2. Hold the kite in both hands and toss it intothe wind so the wind catches it.

3. If it is a very windy day, the kite may need a tail added to help it flycorrectly.

4. Let out a small length of kite string.5. Holding the string in your hand, run with the kite behind you so

the wind lifts it higher in the sky.6. Begin letting out some string until the kite rises very high in the air.7. Keep an eye on the kite. If it dips, run or pull in the string a bit.8. When you are ready to quit, bring the kite down by slowly winding

the string around a spool or stick.9. Reach out and grab the kite before it hits the ground.


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STOP

Reading

33517801Which words below mean the same as the word dips instep 7?

Flies awayGoes straight upBegins to tear

≥ Starts to fall

33517782In which steps does the kitefly higher in the sky?

Steps 1 and 2Steps 3 and 4

≥ Steps 5 and 6Steps 7 and 8

33517843In step 1, which is the bestexample of a large, open areathat is good for kite flying?

A small, shady yard≥ A grassy field

A city sidewalkA park with many trees

33517774What is happening in step 8?

The kite is caught in a tree.The kite is getting a longer tail.The kite is getting higher in the sky.

≥ The kite is getting closer to theground.



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Answer Key with Assessment Objectives Identifi ed

Item Number

Correct Answer

Assessment Objective

Sho

rt P

assa

ge

1 A 1.3.17 Identify explicit and implicit main ideas.

2 D 1.3.20 Determine the answer to a literal or simple inference question regarding the meaning of a passage.

3 C 2.3.10 Identify the following forms and genres: story, poem, fairy tale, tall tale, fable, nonfiction, and essay.

4 B 1.3.20 Determine the answer to a literal or simple inference question regarding the meaning of a passage.

Lon

g P

assa

ge

1 C 1.3.21 Distinguish the main ideas and supporting details in informational text.


3 C 1.3.21 Distinguish the main ideas and supporting details in informational text.

4 B 1.3.13 Identify probable outcomes or actions.

5 D1.3.01 Determine the meaning of an unknown word using knowledge of common prefixes, suffixes, and word roots (see Roots and Affixes List) (e.g., use knowledge of the prefix dis- to determine the meaning of disrespect).

6 A 1.3.07 Determine the meaning of unknown words using within-sentence clues.

7 C 1.3.20 Determine the answer to a literal or simple inference question regarding the meaning of a passage.

8 B 1.3.24 Draw inferences, conclusions, or generalizations about text, and support them with textual evidence and prior knowledge.

9 D 2.3.05 Identify author’s message.

10 C 2.3.10 Identify the following forms and genres: story, poem, fairy tale, tall tale, fable, nonfiction, and essay.

11Extended-Response

Item

1.3.21 Distinguish the main ideas and supporting details in informational text.



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Item Number

Correct Answer


Fun

ctio

nal

Pas

sag

e

1 D 1.3.08 Determine the meaning of an unknown word using word, sentence, and cross-sentence clues.

2 C1.3.27 Determine whether a set of simple instructions or procedures is complete and, therefore, clear (e.g., if incomplete, identify what is missing).

3 B1.3.27 Determine whether a set of simple instructions or procedures is complete and, therefore, clear (e.g., if incomplete, identify what is missing).


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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Extended-ResponseScoring Rubric



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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: 3 Sample: 1 Score: 3

*Th is response demonstrates an accurate understanding of the text by focusing on several specifi c facts from the report that show how pigs have been useful to humans. However, the student fails to do little more than make a list. Th e student does make a connection beyond the text to his dog and notes, “Dog and pig are both smart and have very good sense of smell.” Th is general interpretation connects logically to the report. However, to move to a higher score, more explanation of the textual references would be needed. Furthermore, a more detailed connection to a reference beyond the text would be required. Th is student response is a good example of one that just gets a score of 3.



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Grade: 3 Sample: 2 Score: 4



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*Th is response demonstrates a strong understanding of the important information in the text by focusing on the key ideas presented explicitly and implicitly. Th e reader interprets the text accurately and uses a signifi cant amount of text-based support. For example, in the fi rst paragraph, the response focuses on the historical time span and the uses of pigs in diff erent countries.

*Th e relevant references are supported, and the information is clearly understood as presented. Th is discussion eff ectively incorporates and articulates information from the article and makes an eff ective connection between the reader’s outside knowledge and the interpretation of the text regarding the intelligence of pigs. For example, “I once heard of a pet pig who saved someone’s life.”


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Illinois Standards Achievement Test

Mathematics Samples


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Structure of the Grade 3 Mathematics ISAT

ISAT Mathematics testing beginning in spring 2006 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 Harcourt, 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.



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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 new policy does not aff ect students who already receive extended time as determined by their IEP.

Mathematics ISAT Grade 3

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 3 Mathematics ISATIn grade 3, students are not allowed to use calculators on any session of the mathematics assessment, unless it is a documented accommodation for a student with an Individualized Education Program (IEP). Th is policy was developed in light of the continued work on the development of algorithms and the basic facts of whole numbers in grade 3 and the general lighter use of technology in classrooms at this level.

Rulers for Grade 3 Mathematics ISATAll students in grade 3 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 GRADE THREE

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Mathematics

GO ON

3483398 3483398_AR1 to AR41

Which of these has of the figure shaded?

≥

13

XIE1122George collected 489 rocks forhis science project. Matthewcollected 100 fewer thanGeorge. How many rocks didMatthew collect?

389 479 589 379≥

34833993Ed has 19 eggs. He has 2 empty eggcartons that can hold 12 eggs ineach carton.

How many more eggs does Edneed to fill the 2 egg cartons?

5 7 24 33≥


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Mathematics

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3483402 3483402_AR16Use your centimeter ruler to helpyou answer this question.

How many centimeters long isthe drawing of this crayon?

4 cm5 cm

≥ 6 cm7 cm

CRAYON

34834004John bought 2 notebooks. Eachnotebook costs $1.80. John gavethe clerk $5.00 to pay for thenotebooks.

How much change shouldJohn receive?

≥ $1.40$2.40$3.20$3.60

XJE121 XJE121.AR15

If a month ends on a Tuesday,on what day does the nextmonth begin?

MondayTuesday

≥ WednesdayThursday


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Mathematics

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3483401 3483401_AR17What is the perimeter of this square?

25 m≥ 20 m

15 m5 m

5 m

34834038What is the missing numberin this repeating pattern?

82, 88, 94, ____, 106, 112

102 100 98 96≥

34834049What number goes in the box to make this numbersentence true?

12 � � 3

4 7 9 15≥

348340510How many sides does ahexagon have?

5 6 7 8≥


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Mathematics

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3483406 3483406_AR111What number pair shows thelocation of the ?

≥ (2, 4)(3, 2)(1, 3)(4, 2)

1

2

3

4

5

6

0 1 2 3 4 65

y

x

3483407 3483407_AR112Which shapes below appear to be congruent?

1 and 4 2 and 4 2 and 3 1 and 3≥

1 42 3


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Mathematics

GO ON

XJE380 XJE380_AR114Mrs. Robbins’ class voted for theirfavorite kinds of books to read.

How many more studentsvoted for books aboutadventures than books aboutsports?

0 1 2 3≥

0

1

2

3

4

5

Num

ber

of V

otes

Kind of Book

Books We Like

Adve

ntur

e

Anim

al

Fant

asy

Myster

y

Spor

ts

6

7

8

3483408 3483408_AR113A class of 24 students recordedinformation on the tally chartbelow about what type of pet they have.

According to the tally chart, how many students have a cat for a pet?

7 8 9 24≥

Type ofPet

Numberof Students

Students' Pets

FishDogCat


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Mathematics

STOP

3483409 3483409_AR115Dan will spin the arrow shownbelow many times.

In which colored space is thearrow least likely to land?

RedBlueGreen

≥ Yellow

Red

Green

Yellow

Blue



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Answer Key with Assessment Objectives Identifi ed

Item Number

Correct Answer


1 D 6.3.03 Recognize a fraction represented with a pictorial model.

2 A6.3.08 Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., odd/even, factors/multiples, greater than, less than).

3 A 6.3.09 Solve problems and number sentences involving addition and subtraction with regrouping.

4 A 6.3.10 Solve problems involving the value of a collection of bills and coins whose total value is $10.00 or less, and make change.

5 C 7.3.01 Solve problems involving simple elapsed time in compound units (e.g., hours, minutes, days).

6 C7.3.02 Select and use appropriate standard units and tools to measure length (to the nearest inch or cm), time (to nearest minute), and temperature (to nearest degree).

7 B 7.3.03 Solve problems involving the perimeter of a polygon with given side lengths or a given non–standard unit (e.g., paper clip).

8 B8.3.01 Determine a missing term in a pattern (sequence), describe a pattern (sequence), and extend a pattern (sequence) when given a description or pattern (sequence).

9 C 8.3.04 Solve one–step addition and subtraction equations that have a missing number or missing operation sign (e.g., 3 + = 5, 6 1 = 7).

10 B9.3.01 Identify, describe, and sketch two–dimensional shapes (triangles, squares, rectangles, pentagons, hexagons, and octagons) according to the number of sides, length of sides, and number of vertices.

11 A9.3.03 Locate and identify points using numbers and symbols on a grid, and describe how points relate to each other on a grid (e.g., � is 2 units below ✹, point A is 3 units to the right of point B).

12 D 9.3.10 Identify congruent and similar figures by visual inspection.

13 B 10.3.01 Read and interpret data represented in a pictograph, bar graph, Venn diagram (with two circles), tally chart, or table.

14 D 10.3.01 Read and interpret data represented in a pictograph, bar graph, Venn diagram (with two circles), tally chart, or table.

15 D 10.3.04 Classify events using words such as certain, most likely, equally likely, least likely, possible, and impossible.

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-Response Sample Item

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

This short-response sample item is classified to assessment objective 6.3.04, “Represent multiplication as repeated addition.”

348341016Kari wants to give 8 stickers to each of her 5 friends. To find out how many stickers sheneeds, she writes this number sentence.

8 � 8 � 8 � 8 � 8 �

Write a different number sentence using multiplication that Kari could use torepresent the number of stickers she needs.



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Mathematics Short-Response Scoring Rubric

Th e following rubric is used to score the short-response items for all grade levels.

SCORELEVEL

2 Completely correct response, including correct work shown and/or correct labels/units if calledfor in the item

1 Partially correct response

0 No response, or the response is incorrect



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Short-Response Student Sample 1


Rubric Score Point = 2

Note: Th e student wrote a correct multiplication sentence.



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Note: Th e student did not write a multiplication sentence but did fi gure out the number of stickers needed.



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Note: Th e student wrote a correct multiplication sentence but the response is not completely correct.



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348341117A toy store sells bicycles and tricycles. All of the bicycles have 2 wheels, and all of thetricycles have 3 wheels. There are a total of 19 wheels.

How many bicycles and tricycles could there be in the toy store?

Show all your work. Explain in words how you found your answer. Tell why youtook the steps you did to solve the problem.

Mathematics Extended-Response Sample Item

Below is an extended-response sample item, followed by the extended-response scoring rubric and 3 student samples.

This extended-response sample item is classified to assessment objective 8.3.05, “Solve word problems involving unknown quantities.”


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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 the answer if appropriate

• executes algorithms 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 and answers

• 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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Extended-Response Student Sample 1



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Scoring Guide for “Bicycles and Tricycles”

Th ere are three possible correct answers to this extended-response problem: 8 bicycles and 1 tricycle; 5 bicycles and 3 tricycles; or 2 bicycles and 5 tricycles.


MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION

4 4 4

This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. A correct answer of 5 bikes and 3 tricycles is present.

The response reflects a systematic strategy (drawing wheels and circling groups of 2 and 3) that includes all important elements of the problem.

The response addresses both what was done and why (“…drew 19 wheels…paired them up…so I could find out how many bikes…”).



4 4 4

This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. A correct answer of 8 bikes and 1 trike is present.

The response reflects a systematic strategy (drawing wheels and making bikes until there were only 3 wheels left) that includes all important elements of the problem.

The response addresses both what was done and why (“…made 19 wheels…bike 2 wheels or trike 3 wheels…made bikes but…stopped because…I’d only have 1 wheel left…”).



3 4 3

This response shows a nearly complete understanding of the problem’s mathematical concepts and principles. A correct answer is implied in the drawing on the first page, but the answer is stated incorrectly as 19 wheels.

The response reflects a systematic strategy (drawing pictures of bicycles and tricycles) that includes all important elements of the problem.

The response addresses what was done but only begins to address why (“I drew bikes…I counted to see how many wheels there are…wrote down my answer…”).


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