ILLINOIS STATE BOARD OF EDUCATION

2009 ISAT Sample Book GRADE 5 Sample Items for Reading and Mathematics ILLINOIS STATE BOARD OF EDUCATION 999-8738-91-1 ACKNOWLEDGMENTS “Animals...
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2009

ISAT Sample Book

GRADE

5 Sample Items for Reading and Mathematics

ILLINOIS STATE BOARD OF EDUCATION

999-8738-91-1

ACKNOWLEDGMENTS “Animals ‘Speak’ Many Strange Languages”, from The Christian Science Monitor, May 21, 2002, copyright © 2002 by Sharon Huntington and used by permission. “Buildings in Disguise” by Joan Marie Arbogast, from Buildings in Disguise by Joan Marie Arbogast. Reprinted with permission of Boyds Mills Press, Inc. Text copyright © 2004 by Joan Marie Arbogast. Photo of Lucy the Elephant © 2004 by Donata Burger. The photograph of the dog building, Dog Bark Park Inn, by Frances Conklin and used by 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 affiliate(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, IL00002885.

2009 ISAT Grade 5 Sample Book

Table of Contents Introduction ............................................................................................................................ 5 READING Structure of the Grade 5 Reading ISAT ................................................................................. 9 Item Formats ...................................................................................................................................................9 Reading 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 Answer Key with Assessment Objectives Identified .......................................................... 21 Longer Passage Followed by Extended-Response Sample Item ...................................... 23 Extended-Response Scoring Rubric .................................................................................... 29 Annotated Extended-Response Student Samples............................................................. 32 MATHEMATICS Structure of the Grade 5 Mathematics ISAT ....................................................................... 50 Item Formats .................................................................................................................................................50 Answer Document for Grade 5 Mathematics ISAT ..........................................................................50 Mathematics Sessions ...............................................................................................................................51 Calculator Use for Grade 5 Mathematics ISAT ...................................................................................51 Rulers for Grade 5 Mathematics ISAT ...................................................................................................51 Scratch Paper for Grade 5 Mathematics ISAT ....................................................................................51 Multiple-Choice Sample Items ............................................................................................ 52 Answer Key with Assessment Objectives Identified .......................................................... 64 Short-Response Scoring Rubric ........................................................................................... 68 Using Short-Response Samples .......................................................................................... 68 Blank Short-Response Template ......................................................................................... 69 Short-Response Sample Items and Annotated Student Samples .................................... 70 Extended-Response Scoring Rubric .................................................................................... 80

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Using Extended-Response Samples.................................................................................... 81 Blank Extended-Response Template .................................................................................. 82 Extended-Response Sample Items and Annotated Student Samples ............................. 85

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Introduction This sample book contains sample ISAT items classified with an assessment objective from the Illinois Assessment Frameworks. These 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. This 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. The Illinois Assessment Frameworks are available online at www.isbe.net/assessment/IAFindex.htm. The 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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2009 ISAT Grade 5 Sample Book

Structure of the Grade 5 Reading ISAT ISAT Reading testing in spring 2009 will consist of 30 norm-referenced items, as well as criterion-referenced items. The 30 norm-referenced items are an abbreviated form of the Stanford 10 Reading assessment, developed by Pearson, Inc. The criterion-referenced items are all written by Illinois educators and pilot tested with Illinois students.

Item Formats All items are aligned to the Illinois Reading Assessment Framework, which defines the elements of the Illinois Learning Standards that are suitable for state testing. Multiple-choice items require students to read and reflect, 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. The extended-response items are scored with a holistic rubric and count as 10% of the scale score of the test.

Reading Sessions All 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. This policy does not affect students who already receive extended time as determined by their IEP.

Reading ISAT Grade 5 Session 1 45 minutes

6 shorter passages—30 multiple-choice items total

Session 2 45 minutes

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

Session 3 45 minutes

Two longer passages consisting of: 1 expository passage (or paired passage) with 10 multiple-choice items 1 literary passage (or paired passage) with 10 multiple-choice items 1 extended-response item (Some items will be pilot items.)

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Shorter Passage Followed by Multiple-Choice Sample Items

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Reading XEG212 Passage

XEG212.AR1

A Candlelit Holiday by Elaine Masters

canals for outdoor dinners. Adults sit on mats and visit with their neighbors while children play tag or hide-and-seek. In some cities, blazing fireworks and dancers in shining silk costumes entertain the crowd. Many men and women sell things. People sell floats to those who have not made them at home. Other people sell balloons in various shapes and colors or clever toys made of bamboo. Food sellers offer noodle soup, dried fish, candy, little cakes, roasted chicken, and bamboo tubes filled with sticky rice cooked in coconut milk. They pour soft drinks into small plastic bags, whirl a rubber band around the top, and stick in a short straw. Then, when the full moon rises, families light the candles and set their little boats afloat. The waterway soon twinkles like a fairyland with candles bobbing in their floats and fireworks reflecting in the water.

On one full-moon night every fall, the rivers and lakes of Thailand are dotted with twinkling candles. The Thais are celebrating "Loi Krathong," or "Floating Leaf Cup Day." No one knows for sure how this lovely custom got started. Some say it was started 700 years ago by a wife of a king who wanted to surprise and please her husband. Others say it started even longer ago as a special religious ceremony. But however it began, it is delightful. Families always used to make their floats, or little boats, from banana leaves torn into strips and woven into the shape of a bowl. Then they beautifully decorated them with flowers. Now, while many families still make their own floats, others simply buy them. Modern floats may be made of banana leaves or plastic. All of them still hold a lighted candle, a flower, a stick or two of sweet-smelling incense, and a coin. On the holiday evening, families gather at parks near lakes, rivers, or

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Paragraph 2 of this selection is mainly about —

After reading the title, what should you expect to learn from this selection?

≥A

how this holiday might have begun B what the floats are made of C when the holiday takes place D what people eat during the holiday



A How to make your own candles B Ideas for new recipes C Why we celebrate the Fourth of July D Where a candlelit holiday is celebrated

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2 To understand more about the meaning of the floating leaf cups, the reader should ask —



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4 Which detail in the selection shows that this is a relaxing holiday?

A how the floats are kept from being burned by the flame B why a coin is placed in the float C what happens to all the floats when the holiday is over D how much store-bought floats cost

≥A

Families spend the evening eating, playing, and visiting. B People spend hours making floats. C There are many different kinds of food to buy. D It is held in autumn.

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Shorter Passage

Answer Key with Assessment Objectives Identified

Item Number

Correct Answer

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1.5.12 Identify explicit and implicit main ideas.

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2.5.05 Compare stories to personal experience, prior knowledge, or other stories.

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1.5.08 Identify probable outcomes or actions.

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1.5.17 Distinguish the main ideas and supporting details in any text.

Assessment Objective

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 by Multiple-Choice Sample Items

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Reading RG5Languages0507E-v1

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This passage is about different ways animals communicate, from scratching to tapping to howling.

Animals ‘speak’ many strange languages by Sharon J. Huntington 1

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If you’re sitting around a lonely campfire at night, the howl of a wolf can sound pretty scary. But the wolf isn’t trying to scare anyone, it’s just letting other wolves know where it is. This helps members of its pack find it and tells other wolves to stay out of the pack’s territory. Animals use communication to tell others about their territory, find a mate, make friends, let others know how they feel, start and stop fights, and warn others of danger. Here are some of the more unusual ways that animals talk. SOUND Dogs bark, cats meow, birds chirp. We’re pretty familiar with these forms of communication. But animals use sounds in other ways, too. To find a mate, the male ruffed grouse stands on a hollow log and beats his wings, making a drumming sound. The hollow log amplifies* the sound so that it can be heard for up to a quarter of a mile. Mole rats use a banging sound for the opposite reason. They like to live alone. So they warn other mole rats to stay out of their way by banging their heads on the top of their tunnels. Anyone who has used a dog whistle knows that dogs can hear sounds pitched so high that humans can’t hear them. Elephants, on the other hand, can hear sounds too low for humans to detect. These low rumblings, or infrasounds, can be heard across long distances. They help elephants keep track of one another when they’re too far away to see or smell each other. TOUCH Animals use touch to communicate in many ways. Biting, kicking, and hitting *amplifies — makes louder

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Reading RG5Languages0507E-v1

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send obvious messages, but touch can also be used in friendly ways. Chimpanzees will touch hands to greet each other. Many primates groom each other as a way to show friendship, removing bits of dirt or insects from each other’s fur. Elephants may touch trunks in greeting.

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SIGHT Elephants also use their trunks for signals. A baby elephant will raise its trunk in the air when it wants attention from its mother. Body language is important to other creatures, too. When a gorilla is startled, it may stand still and shake its head back and forth. This means it does not intend to harm you. A chimpanzee will wear a special “play face” when it wants to let you know it’s friendly. Dancing is another way to “talk.” When a bee wants to tell other bees where to find a good stash of nectar, it performs a special dance, waggling its body and moving in ways that tell the other bees which direction to go and how far to fly. Some creatures even put their message in lights. Each type of firefly has its own flashing code. This helps males and females find mates of the same species. The lights not only tell what kind of firefly it is, they also guide the insects to each other. Color can also be important. The cuttlefish turns different colors to show how it feels. When it’s ready to fight, it turns a dark color. Its colors change quickly when it is agitated. Some animals have been taught to use human sign language to communicate with humans and even with each other. You may have heard of Koko, the gorilla who learned to form simple sentences with sign language. Other primates have also been taught to use such signals. And in another experiment in Thailand in 1994, elephants were taught to “sign” with their trunks and to use them to point to objects as they “talked.” Some bears and tigers leave visual signs. They put scratch marks on a tree as high up as they can. When another bear or tiger comes along, it may discover it can’t make marks that high. That tells the visiting animal that the tiger or bear that made the marks is bigger and should be left alone.

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SMELL Another way to communicate without actually being there is through smell. A gazelle has special scent glands near its eyes that it rubs on branches to mark its territory. When other gazelles pick up the smell, they realize that this territory has already been claimed. Many animals mark territory by smell, including domestic cats and their wild cousins. Queen ants can communicate with their workers by smell. The queen produces different chemicals, which rub off on her workers. As the ants rub antennas, the message travels to more ants, telling them what to do. The chemicals can tell the ants to march across the forest or to camp for the night. The ways animals communicate are as varied as the creatures and the messages they want to send. By observing carefully, we can learn more about what they mean. Try it with your own pets: Notice how many ways they tell you what they want and how they feel. They probably have you trained better than you realize.

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Which word is closest in meaning to the word territory as used in the passage?



A B C D

Which of these would most likely cause a mole rat to bang its head on its tunnel?

Food Family Chemicals Neighborhood



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A Another mole rat is looking for a mate. B Another mole rat changes to a dark color. C Another mole rat makes a high-pitched sound. D Another mole rat attempts to enter its territory.

What is the first thing a male ruffed grouse does to find a mate?



A B C D

Beats his wings Amplifies his sound Stands on a hollow log Makes a drumming sound

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In paragraph 6, the word primates refers to —



A B C D

What is the main idea of the passage?

bees. moles. elephants. chimpanzees.



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What is the most likely reason cats mark their space by smell?



A B C D

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What is the author’s purpose for writing this passage?

To start a fight To clean their fur To leave a message To attract their prey

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To inform B To entertain C To persuade D To convince

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A Animals show anger through sound. B Animals use their senses to communicate. C Animals show emotions through touch. D Animals put their messages in lights.

In what order are the senses discussed in this passage?



A B C D

Touch, Sight, Sound, Smell Sound, Touch, Smell, Sight Sight, Sound, Smell, Touch Sound, Touch, Sight, Smell

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Reading 3527501

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Which of these is an opinion about the passage?



Which type of writing is this passage?

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A Animals use sounds in many ways. B Animal communication is interesting. C Animal territory can be marked by scent. D Animals use body movements to communicate.

Expository B Biography C Persuasive D Narrative

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2009 ISAT Grade 5 Sample Book

Longer Passage with Multiple-Choice Items

Answer Key with Assessment Objectives Identified Item Number

Correct Answer

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1.5.03 Use synonyms to define words.

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1.5.20 Identify or summarize the order of events in a story or nonfiction account.

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1.5.21 Identify the causes of events in a story or nonfiction account.

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1.5.02 Determine the meaning of an unknown word using word, sentence, and cross-sentence clues.

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

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1.5.20 Identify or summarize the order of events in a story or nonfiction account.

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1.5.17 Distinguish the main ideas and supporting details in any text.

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1.5.27 Determine the author’s purpose for writing a fiction or nonfiction text (e.g., to entertain, to inform, to persuade).

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1.5.23 Differentiate between fact and opinion.

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2.5.15 Identify whether a given passage is narrative, persuasive, or expository.

Assessment Objective

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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Reading RG5Buildings0507E-v1

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People seem to love buildings that look like animals or picnic baskets or milk bottles. This passage is about buildings that look like other things, and one especially that looks like an elephant.

Buildings in Disguise by Joan Marie Arbogast

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Some buildings don’t look like buildings. They look like oversize elephants, beagles, or ducks. These buildings are meant to grab your attention, and they usually do. Architects1 call these structures mimetic because they mimic other objects. As engineer and landdeveloper James V. Lafferty Jr. admired his very unusual building, he knew people would come to see it. But that was only part of his plan. The other was to convince people to purchase parcels of his land along the Atlantic coast. That was back in 1881 — and his idea worked! His plan, after all, had been simple. Make it big. Make it fun. Make it in disguise. And that’s exactly what he did. With the help of an architect and a crew of burly builders, Mr. Lafferty constructed a one-of-a-kind, sixty-five-foot-tall elephant-shaped building near the growing seaside resort of Atlantic City, New Jersey. People came from miles around to see his extraordinary building. Curious customers climbed the spiral staircases to the howdah, or canopied2 carrier, on the elephant’s back. There they viewed the lots for sale. Some eager land-buyers even sealed their deals inside the elephant’s belly. To prevent others from copying his idea, Mr. Lafferty applied for and received a patent on his building in 1882.

1architects 2canopy

— people who design buildings — a protective rooflike covering

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Two years later, Lafferty built Elephantine Colossus in Coney Island, New York — the amusement park of its time. This spectacular building towered 122 feet, nearly twice the height of Lucy [the name given to the original elephant building]. Visitors paid to view its innards of seven floors and thirty-one rooms. But in 1896, a fire leveled the mammoth pachyderm.3 In 1887, Mr. Lafferty sold his original elephant to Anton Gertzen, who’d helped construct the unusual building. The Gertzen family owned and operated the elephant as a tourist attraction for nearly eighty years. During the early 1900s, tourists paid ten cents to enter the awesome structure. People traveled the states and sailed the sea to examine this remarkable building. Though Lucy survived severe storms along the Atlantic coast for eighty years, the terrible storm of 1962 left her tattered and torn. Years of saltwater mists had already weakened her wooden “bones.” Years of sandy winds had worn her tin “skin” thin. No longer safe for curious tourists, Lucy’s doors were locked to the public. Afraid that their unusual landmark would be toppled to make room for condominiums, concerned citizens formed the Save Lucy Committee, which sprang into action in 1969. Even children pitched in to protect the aging elephant. The group raised enough money to move their beloved pachyderm to a safe spot in a city park farther from the water’s edge. Though Lucy moved only two short blocks, it took nearly seven hours to inch her down the road. Once secured in her new location, lengthy repairs and restorations began. Then, in 1976, Lucy was honored as a National Historic Landmark. Today Lucy welcomes guests through her doors as she did when she was young. People still climb to the howdah on Lucy’s back, where they can view the seascape and the city of Margate, New Jersey, that Lucy helped to create. Lucy is our nation’s oldest functioning example of mimetic architecture. She’s also our oldest zoomorphic (animal-shaped) structure. Both are designed to grab your attention. And Lucy has for more than 120 years! The Future of Mimetic Architecture

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Sweet Willy is one of the youngest buildings to enter the mimetic scene. His construction was completed in 2003. This thirty-foot beagle stands in Cottonwood, Idaho, among fields of canola and prairie wheat. Designed and built by husband and wife Dennis J. Sullivan and Frances Conklin, the beagle serves as a three-dimensional billboard for their chainsaw art studio.

3pachyderm

— a hoofed mammal, such as an elephant

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“The initial drawing for Sweet Willy was made on a napkin at a restaurant in 1998, when Dennis and I were brainstorming possible billboard designs,” explained Conklin. “One idea led to another, and before dinner was cold, we had decided to make this giant billboard not only wordless, but also large enough to be a lodging.” Inside this pup’s belly is the main bedroom; a loft is tucked in his head. Wooden two-by-four studs form Willy’s “skeleton.” Wire mesh forms his “hide.” Stucco and shingles form his “fur.” Why would the artists choose a beagle for their billboard? Because they sculpt and paint their canine friends. One of their favorite subjects to carve is Seaman, the Newfoundland that accompanied explorers Lewis and Clark through this area years ago. But Sweet Willy won’t be one of the youngest mimetic buildings for long. Somewhere, someone will construct another eye-catching, head-turning building to lure potential customers through its doors.

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Reading

Assessment Objective: 1.5.22 Draw inferences, conclusions, or generalizations about text, and support them with textual evidence and prior knowledge.

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Extended-Response Scoring Rubric

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2009 ISAT Grade 5 Sample Book

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

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Criteria

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• 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).

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• 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.

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• 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.

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• Reader’s response is absent or does not address the task. • Reader’s response is insufficient to show that criteria are met.

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.

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Grade: 5

DIRECTIONS

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.

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*The reader demonstrates an accurate understanding of information in the text by focusing on some key ideas presented explicitly and implicitly. The response uses information from the text to interpret significant concepts through inference (I think everyone would be sad if Lucy fell because they have had this building along time. . . . I think it would be bad for Sweet Willy to fall because thats one speacil buliding of the country gone). The response contains some gaps when attempting to use information from the text to make interpretations that are not correct (As the author says in the book it woud’nt be good for Sweet Willy to fall down because it’s been loved for years) or interpretations that are thin (People should save buildings because people have alot of love for buildings . . . The author says buildings are good. I think buildings are loved because what they have done for our young contury). The response contains attempted connections that are not credited because they are not tied back to significant concepts (My connection is my family dosen’t want a vase to break because it means alot to us. . . . My connection is my family dosen’t want my great grandma to die because she is part of the family. . . . My connection is I built a lego structure when I was 3 and I still have it in my room).

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Grade: 5

DIRECTIONS

Sample: 2

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.

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*The reader demonstrates an accurate understanding of information in the text by focusing on some key ideas presented explicitly and implicitly. The response uses information from the text to interpret significant concepts through inference (. . . people would save because its histroy and really old and it still makes you go see it all the time because its something you don’t see everyday. . . . wouldn’t you save a building that is fun and unsually and extrodinary I would save just because its a great building. . . .), with some gaps (Wouldn’t you save a building if it had that beatiful view I know I would. Moreover, I mean something this beatiful would you tare it down). The response attempts connections that are not credited (I connect this to myself because if I really like something and there going out of business or something I would try to save it. . . . I connect this to myself because I would not tare bone something if it had an ocean view). The response uses relevant and accurate references; all are specific, but not fully supported (. . . its a historic land mark. . . . The text says that it is extraordinary building because people would climb the spiral staircases to the howdah or canopied to the back and look at the Alanta ocean. . . .). Some of the text references are inaccurate (In the text it also mentions that people go there to stay rooms and purchase pracols to fly along the ocean. . . .).

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2009 ISAT Grade 5 Sample Book

Grade: 5

DIRECTIONS

Sample: 3

Score: 4

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.

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*The reader demonstrates an accurate understanding of important information in the text by focusing on the key ideas presented explicitly and implicitly. The response focuses on three reasons why people would want to save structures like Lucy and Sweet Willy: beauty, people care about historical landmarks, and the structures are used as a tourist attraction. The response also uses information from the text to make connections to other situations, as seen in these “text to world” connections (I once read an article where the citizens of Pisa stop the Leaning Tower of Pisa from falling and saved it. I can see how the people must have felt and worked to save Lucy. . . . This is just like the time I watched a National Geographic episode. In it a zoo in China was trying to capture a tiger and put it in a cage. They wanted to do this so they would have more people coming to see the animals in the zoo. All of these people wanted to have something beautiful to attract costumers). The response contains several very strong text references that are specific and fully supported, as seen by the following excerpt (The story says, “Afraid that their unusual landmark would be toppled to make room for condominiums, concerned citizens formed the Save Lucy Committee, which sprang into action in 1969. Once secured in her new location, lenghtly repairs and restorations began. Then, in 1976, Lucy was honored as a National Historic Landmark”). The response integrates interpretation of the text with text-based support, resulting in a balanced response.

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2009 ISAT Grade 5 Sample Book

Grade: 5

DIRECTIONS

Sample: 4

Score: 4

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.

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*The reader demonstrates an accurate understanding of important information in the text by focusing on the key ideas presented explicitly and implicitly. The response uses information from the text to interpret significant concepts through inference and evaluation (. . . they are very interesting building. . . . I think it is special that people raised enough money to save her. . . . People say that we should never destroy history. We should save structures like Sweet Willy because, as the author described, he is the future of mimetic Architecture. . . . there probably aren’t many buildings shaped like animals in the world). The response contains relevant and accurate references; most are specific and fully supported. These references are often embedded within statements containing interpretations to help respond to the prompt (People would want to save Lucy because she was the first building to be shaped like an animal. “She survived severe storms along the Atlantic coast for eighty years” said the author. . . . That is part of why she is a historical landmark. . . . They have historical significance). At first glance, this response seems heavy on interpretation; however, with embedded text referencing, the response integrates interpretation of the text with text-based support, resulting in a balanced response.

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48

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Illinois Standards Achievement Test

Mathematics Samples

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2009 ISAT Grade 5 Sample Book

Structure of the Grade 5 Mathematics ISAT ISAT Mathematics testing in spring 2009 will consist of 30 norm-referenced items, as well as 45 criterionreferenced items, some of which will be used for developmental purposes. The 30 norm-referenced items are an abbreviated form of the Stanford 10 Mathematics Problem Solving assessment, developed by Pearson, Inc. The 45 criterion-referenced items are all written by Illinois educators and pilot tested with Illinois students.

Item Formats All 75 items are aligned to the Illinois Mathematics Assessment Framework, which defines the elements of the Illinois Learning Standards that are suitable for state testing. Multiple-choice items require students to read, reflect, or compute and then to select the alternative that best expresses what they believe the answer to be. This 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. They 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. These items reduce the concern about guessing that accompanies multiple-choice items. The 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. These 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). The extended-response items are scored with a rubric and count as 10% of the scale score of the test. Scoring Extended- and Short-Response Items Extended- 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-specific criteria that are used to score all short- and extended-response items consistently and systematically.

Answer Document for Grade 5 Mathematics ISAT Students in grade 5 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. 50

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2009 ISAT Grade 5 Sample Book

Mathematics Sessions All 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. This policy does not affect students who already receive extended time as determined by their IEP.

Mathematics ISAT Grade 5 Session 1 45 minutes

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

Session 2 45 minutes

30 multiple-choice items 3 short-response items

Session 3 45 minutes

2 extended-response items (Some items will be pilot items.)

Calculator Use for Grade 5 Mathematics ISAT All students in grade 5 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 suffer. 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 5 Mathematics ISAT All students in grade 5 will be provided with a ruler to use during all sessions of the mathematics assessment. This ruler will allow students to measure in both inches and centimeters.

5

6 1

2

2 3 4 ISAT GRADES FOUR–EIGHT

Centimeters

3

4

5

6

7

8

9

10

1 11

12

13

Inches

0

0

14

15

Scratch Paper for Grade 5 Mathematics ISAT Students 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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Mathematics XIH110

1 In the 1988 Olympic Games, Florence Griffith Joyner of the United States set an Olympic record for the women’s 100-meter dash. Her time was ten and sixty-two hundredths seconds. How is this time written as a number? A

≥B

1.62 seconds 10.62 seconds

C

100.62 seconds

D

1062.00 seconds

3347610

2 Which letter on the number line below best represents the location of

R

S

T

0

A R

3347610_AR1

3 ? 4

U 1



B S

C T

D U

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Mathematics 3347639

3

3484053

5

The table below shows the area in square miles for 5 different states. Carlos calculated the sum of the areas of 3 states. He found that the total number of square miles for these three states is 119,156 square miles.

3484053_AR1

A pizza was cut into 8 equal pieces. Ben ate 2 pieces, and Sam ate 3 pieces.

State Square Miles State

Square Miles

Illinois

55,593

Hawaii

6,423

Ohio Vermont Wisconsin

40,953 9,249

What fractional part of the pizza did Ben and Sam eat?

54,314

Which 3 states did Carlos include in his total?

≥A

Illinois, Vermont, Wisconsin

B

Vermont, Wisconsin, Hawaii

C

Wisconsin, Ohio, Vermont

D

Ohio, Hawaii, Illinois

3 8

3 5

A

B



5 8

8 5

C

D

3347640

4

Lisa had $40.80. She spent $14.50 for a CD, $9.57 for a shirt, and $8.95 for lunch. Exactly how much money should Lisa have left? A

$1.85

C

$24.07

≥B

$7.78

D

$47.78

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Mathematics 3484054

6

3484054_AR1

3484056

8

All items listed below are on sale for 50% off the regular price.

Anish went to sleep at 9:00 P.M. and woke up at 6:30 A.M.

Items on Sale Item

Regular Price (including tax)

Hat Shirt CD Coat

$ 10.95 $ 21.05 $ 15.95 $ 21.92

What is the total number of hours Anish slept?

Which is closest to the amount of money needed to buy 1 of each item listed, at the sale price?

$30 A

$35

≥B

$60

$70

C

D

A

3

1 hours 2

B

7

1 hours 2

C

8

1 hours 2

≥D

9

1 hours 2

3528134

9

Field Day begins at 8:45 A.M. and ends at 2:20 P.M. How long is Field Day? 3484055

7

Six out of every ten fifth-grade students in a school have a pet. There are 50 fifth-grade students in this school.

A

5 hours and 25 minutes

≥B

5 hours and 35 minutes

C

6 hours and 25 minutes

D

6 hours and 35 minutes

What is the total number of fifth-grade students in this school who have a pet? A

6 students

B

10 students

≥C

30 students

D

66 students

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Mathematics 3484057

10

3484057_AR1

3528387

11

3528387_AR1

Use your centimeter ruler to help you answer this question.

What is the perimeter of the figure below? 6 feet

5 feet

2 feet

10 feet

Which is closest to the perimeter in centimeters of this triangle?

?

?

36 feet

≥A

28 feet

23 feet

13 feet

B

C

D

A

5 cm

B

7 cm

≥C

12 cm

D

15 cm

3408763

12 The scale on Todd’s map is

1 inch ⫽ 200 miles. The distance from his house to his friend’s house 1 on the map is 5 inches. 4 What is the distance in miles from Todd’s house to his friend’s house? A

1,000 miles

≥B

1,050 miles

C

1,500 miles

D

24,000 miles

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Mathematics 3347613

13

3484059

15

Francine is 5 years older than her brother Mark. Mark’s age is m.

The drawing below is an input-output machine. Input

Which expression represents Francine’s age? A

m⫺5

B

m•5

≥C

3484059_AR1

Add 7 Subtract 3

m⫹5 Output

m⫼5

D

3484058

14

Using this machine, when the input is 5, what is the output?

What is the value of m ⫹ m ⫺ 3 when m ⫽ 4?

1

5

11

13

A

≥B

C

D

2

4

A

B



9

12

C

D

3484060

16

Mr. Jackson is 36 years old. His son is 8 years old. Let n represent the age of Mr. Jackson’s wife. The ages of Mr. Jackson, his wife, and their son total 77. Which correctly represents this information? A

77 ⫹ 36 ⫹ 8 ⫽ n

B

36 ⫺ n ⫹ 8 ⫽ 77

C

77 ⫺ 36 ⫹ 8 ⫽ n

≥D

36 ⫹ n ⫹ 8 ⫽ 77

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Mathematics 3408676

17

3347618

19

What is the value of n?

What is the length of each side of an equilateral triangle that has a perimeter of 18 inches?

50 ⫼ n ⫽ 10 5

10

40

50

18 in.

9 in.

7 in.

≥A

B

C

D

A

B

C

3408628 3408628_AR1

18

6 in.

≥D

3535809 3535809_AR1

20

Which best describes a cube?

What are the new coordinates of point P if ⌬PQR is translated 3 units to the right and 2 units up?

y

10 9

A



8

Eight faces, six vertices, nine edges

7

Q

6

B

Six faces, five vertices, four edges

5

C

Six faces, eight vertices, twelve edges

3

D

Six faces, nine vertices, twelve edges

1

4

P

R

2

0

1

2

3

4

5

6

7

8

9 10

A

(2, 7)

C

(6, 3)

≥B

(3, 6)

D

(6, 6)

x

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Mathematics XIJ321

21

3347619

22

ey

3347619_AR1

Which best describes the type of angle made by the hands on the clock shown below?

Fra nk lin

Ta ll

XIJ321.AR1

Holloway

Pierce

1112 1 2 10 9 3 8 4 76 5

Starlight

≥A

Which streets on this map appear to never intersect? A

Talley and Franklin

B

Starlight and Pierce

C

Franklin and Holloway

≥D

Holloway and Starlight

B

Obtuse

C

Acute

Right

D

Straight

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Mathematics 3347624

23

3347624_AR1

What three-dimensional figure could be made by folding the pattern along the dashed line segments?

A

Cube

B

Rectangular prism

C

Triangular pyramid

≥D

Rectangular pyramid

3484062

24

3484062_AR1

Which figures appear to be congruent?

M

N

P

O

O and M

N and P

A

B

Q

N and R



C

R

P and Q D

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Mathematics 3484061

25

3484061_AR1

3484064

26

3484064_AR1

The graph below shows the average daily temperatures for the town of Jonesboro during a seven-day period.

Which is closest to the distance from point G to point H on the number line below?

Average Daily Temperature G 10

A

3 units

≥B

10 units

C

13 units

D

26 units

35°

20 Temperature (°F)

0

H

30° 25° 20° 15° 10° 5° 0° Sun. Mon. Tues. Wed. Thurs. Fri.

Sat.

Day

Which is closest to the difference in the average daily temperatures for Monday and Wednesday?

0 °F

≥A

5 °F

10 °F

25 °F

B

C

D

GO ON 60

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Mathematics 3347633

27

3347633_AR1

3408731

28

The Venn diagram below shows student participation in Band and Math Club.

The high temperatures each day during the first week of August were 90°, 87°, 95°, 96°, 93°, 88°, and 88°. What was the mean (average) high temperature for the week?

Band

6

Math Club

3

88°

90°

A

B



91°

96°

C

D

5 3484065

29

3484065_AR1

The spinner below is divided into six sections of equal size.

1 6

2

5

3

Exactly how many students participate in Math Club?



A

14

B

8

C

5

D

3

4

What is the probability that the arrow will land in a space labeled with an odd number?

1 6

2 6

A

B



3 6

4 6

C

D

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Mathematics XIF606

30

XIF606.AR1 to AR5

Tim’s mother put these cookies on a plate.

Which kind of cookie would Tim most likely get if he takes one without looking?

A

B



C

D

STOP 62

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2009 ISAT Grade 5 Sample Book

Answer Key with Assessment Objectives Identified Item Number

Correct Answer

1

B

6.5.05 Read, write, recognize, and model decimals and their place values through thousandths.

2

C

6.5.10 Identify and locate whole numbers, halves, fourths, and thirds on a number line.

3

A

6.5.12 Solve problems and number sentences involving addition, subtraction, multiplication, and division using whole numbers.

4

B

6.5.13 Solve problems and number sentences involving addition and subtraction of decimals through hundredths (with or without monetary labels).

5

C

6.5.14 Model situations involving addition and subtraction of fractions.

6

B

6.5.16 Make estimates appropriate to a given situation with whole numbers, fractions, and decimals.

7

C

6.5.18 Solve problems involving proportional relationships, including unit pricing (e.g., one apple costs 20¢, so four apples cost 80¢).

8

D

7.5.01 Solve problems involving elapsed time in compound units.

9

B

7.5.01 Solve problems involving elapsed time in compound units.

A

7.5.03 Solve problems involving the perimeter and area of a triangle, rectangle, or irregular shape using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).

11

C

7.5.03 Solve problems involving the perimeter and area of a triangle, rectangle, or irregular shape using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description).

12

B

7.5.07 Solve problems involving map interpretation (e.g., one inch represents five miles, so two inches represent ten miles).

13

C

8.5.03 Write an expression using variables to represent unknown quantities.

14

B

8.5.04 Evaluate algebraic expressions with a whole number variable value (e.g., evaluate m ⫹ m ⫹ 3 when m ⫽ 4)

15

C

8.5.05 Demonstrate, in simple situations, how a change in one quantity results in a change in another quantity (e.g., input–output tables).

16

D

8.5.07 Represent problems with equations and inequalities.

10

Assessment Objective

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2009 ISAT Grade 5 Sample Book

Item Number

Correct Answer

17

A

8.5.08 Solve for the unknown in an equation with one operation (e.g., 2 + n = 20, n ⫼ 2 = 6).

18

C

9.5.02 Identify and describe three–dimensional shapes (cubes, spheres, cones, cylinders, prisms, and pyramids) according to their characteristics (faces, edges, vertices).

19

D

9.5.03 Solve problems using properties of triangles (e.g., sum of interior angles of a triangle is 180°).

20

B

9.5.07 Identify, describe, and predict results of reflections, translations, and rotations of two–dimensional shapes.

21

D

9.5.08 Identify and sketch parallel, perpendicular, and intersecting lines.

22

A

9.5.09 Identify and sketch acute, right, and obtuse angles.

23

D

9.5.11 Identify a three–dimensional object from its net.

24

C

9.5.13 Identify congruent and similar figures by visual inspection.

25

B

9.5.15 Determine the distance between two points on a horizontal or vertical number line in whole numbers.

26

A

10.5.01 Read, interpret, and make predictions from data represented in a pictograph, bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph.

27

B

10.5.01 Read, interpret, and make predictions from data represented in a pictograph, bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph.

28

C

10.5.03 Determine the mode, range, median (with an odd number of data points), and mean given a set of data or a graph.

29

C

10.5.04 Solve problems involving the probability of a simple event, including representing the probability as a fraction between zero and one.

30

C

10.5.04 Solve problems involving the probability of a simple event, including representing the probability as a fraction between zero and one.

Assessment Objective

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 Scoring Rubric Followed by Student Samples

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2009 ISAT Grade 5 Sample Book

Mathematics Short-Response Scoring Rubric The following rubric is used to score the short-response items for all grade levels. SCORE LEVEL

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 Samples Beginning 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.

SAMPLE SHORT-RESPONSE QUESTION 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.

SAMPLE SHORT-RESPONSE ANSWER

$1.75 50¢ + 90¢ + 35¢ =each day for

My answer

$8.75

3 2

1.75 1.75 1.75 1.75 5 1.7_ +_ _ $8.75 for five days

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). 68

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2009 ISAT Grade 5 Sample Book

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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2009 ISAT Grade 5 Sample Book

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 8.5.02, “Construct and identify a rule that can generate the terms of a given sequence.”

3408750

1 The first two numbers in a pattern are 1 and 3.

1, 3, ___, ___, ___ • Explain a rule you could use to continue the pattern. • Use your rule to find the next three numbers in the pattern.

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2009 ISAT Grade 5 Sample Book

Short-Response Student Sample 1A

Short-Response Student Sample 1A Rubric Score Point = 2 Note: The student provides the rule “multiply by 2 and add 1” to continue the pattern and correctly applies this rule to find the next three numbers: 7, 15, and 31.

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2009 ISAT Grade 5 Sample Book

Short-Response Student Sample 1B

Short-Response Student Sample 1B Rubric Score Point = 2 Note: The student provides the rule “Multiply by 3” to continue the pattern and correctly applies this rule to find the next three numbers: 9, 27, and 81.

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Short-Response Student Sample 1C

Short-Response Student Sample 1C Rubric Score Point = 1 Note: The student provides the rule “it could be odd numbers” to continue the pattern and correctly applies this rule to find only the next two numbers: 5 and 7.

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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 10.5.05, “Apply the fundamental counting principle in a simple problem (e.g., How many different combinations of one-scoop ice cream cones can be made with 3 flavors and 2 types of cones?).”

3408981 3408981_AR1

2

The volleyball team is selling gift sets that include 1 type of soap and 1 type of shampoo. The chart below lists the different types of soap and shampoo available.

Soap

Shampoo

• Bar • Liquid

• Rose • Lilac • Melon • Vanilla

How many different combinations of 1 type of soap and 1 type of shampoo are possible for each gift set? Show your work.

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2009 ISAT Grade 5 Sample Book

Short-Response Student Sample 2A

Short-Response Student Sample 2A Rubric Score Point = 2 Note: The student provides the correct answer of 8 and shows work using an organized chart.

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2009 ISAT Grade 5 Sample Book

Short-Response Student Sample 2B

Short-Response Student Sample 2B Rubric Score Point = 2 Note: The student provides the correct answer of 8 and shows work of 4 ⫻ 2.

76

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Short-Response Student Sample 2C

Short-Response Student Sample 2C Rubric Score Point = 1 Note: The student provides an incorrect answer of 16 but shows some correct work using tree graphs.

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Mathematics Extended-Response Scoring Rubric Followed by Student Samples

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2009 ISAT Grade 5 Sample Book

Mathematics Extended-Response Scoring Rubric The 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.

SCORE LEVEL

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

• gives a complete written explanation of the • identifies all important elements of • shows complete understanding of the solution process; clearly explains what was the problem and shows complete problem’s mathematical concepts and done and why it was done understanding of the relationships among principles elements • may include a diagram with a complete • uses appropriate mathematical terminology explanation of all its elements and notations including labeling answer if • shows complete evidence of an appropriate strategy that would correctly solve the appropriate problem • executes algorithms and computations completely and correctly

3

• shows nearly complete understanding of • identifies most of the important elements the problem’s mathematical concepts and of the problem and shows a general principles understanding of the relationships among them • uses mostly correct mathematical terminology and notations • shows nearly complete evidence of an appropriate strategy for solving the • executes algorithms completely; problem computations are generally correct but may contain minor errors

• 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

• 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

• 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

• no answer attempted

• no apparent strategy

• no written explanation of the solution process is provided

2

1

0

80

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2009 ISAT Grade 5 Sample Book

Using Extended-Response Samples Beginning 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.

SAMPLE EXTENDED-RESPONSE PROBLEM Mrs. Martin wants to put tiles on the floor by the front door of her house. She wants to use 3 different colors of tiles in her design. She also wants 1 — of the tiles to be blue, 2 1 — of the tiles to be gray, and 4 1 — of the tiles to be red. 4 Use the grid below to design a floor for Mrs. Martin. Label each tile with the first letter of the color that should be placed there.

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

SAMPLE EXTENDED-RESPONSE SOLUTION

B B G R

B B G R

B B G R

B B G R

B B G R

B B G R

–1 2 blue –1 gray 4 –1 4 red

First, I know that there are 4 equal rows, so 2 rows is half and 1 row is –41 . So I made 2 rows B for blue because she wants half the tiles blue. Then I made 1 row G for gray because she wants –41 of the tiles to be gray. Since she wants gray and red to be the same amount of tiles, I made the last row R for red. 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). IL09-I2-5SB

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2009 ISAT Grade 5 Sample Book

Blank Extended-Response Template Mathematics - Session 3

Problem 1

82

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2009 ISAT Grade 5 Sample Book

Mathematics - Session 3

IL09-I2-5SB

Problem 1-continued

83

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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 6.5.14, “Model situations involving addition and subtraction of fractions.”

3409738

1

Five friends bought a total of 2 pizzas. Each pizza was cut into 12 equal slices. The amount of one whole pizza each person ate is shown below. Joe:

1 2

Mary:

1 4

Kim:

1 6

Bill:

1 3

Sue:

1 4

How many slices of pizza were not eaten by these 5 friends? Show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem.

IL09-I2-5SB

85

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1A

86

IL09-I2-5SB

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1A Continued

IL09-I2-5SB

87

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1B

88

IL09-I2-5SB

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1B Continued

IL09-I2-5SB

89

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1C

90

IL09-I2-5SB

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1C Continued

IL09-I2-5SB

91

2009 ISAT Grade 5 Sample Book

Scoring Guide for “Pizza for Friends” To solve this problem, the student must determine the amount of pizza not eaten by five friends who shared two whole pizzas. Answers of six slices or half of one whole pizza were accepted.

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 correctly determines the number of pizza slices eaten by each friend and correctly determines the number of slices not eaten by the friends (“I got six which meant ½ of one pizza was not eaten by the five friends”).

The response shows complete evidence of an appropriate strategy that correctly solves this problem. The student correctly changes each friend’s fractional amount of pizza into the number of slices eaten (Joe = ½ = 6…), adds the number of slices together, and subtracts the number of slices eaten from the total number of slices in both pizzas (24 - 18 = 6).

The response provides a complete written explanation of the solution process by clearly explaining what was done and why it was done (“I took down the names of the five friends and what fraction they ate. Then I turned them into whole numbers, so it would be easier to add them instead of adding fractions”).

Extended-Response Student Sample 1B MATHEMATICAL KNOWLEDGE

STRATEGIC KNOWLEDGE

EXPLANATION

4

4

2

The response shows complete understanding of the problem’s mathematical concepts and principles. The student draws two pizzas, correctly shades the number of pizza slices eaten by the friends, and determines the portion of pizza left uneaten (“they didn’t eat ½ a pizza”).

The response shows complete evidence of an appropriate strategy that correctly solves this problem. The student provides a diagram of each pizza to show the correct total number of slices present (2 pizzas each divided into 12 slices) and shades the correct number of slices that have been eaten by the friends. The student counted the unshaded pieces to determine the uneaten portion.

92

The response provides some written explanation of the solution process by explaining only what was done (“I made 2 models of the pizza…I made all the fractions the friends ate into a common denominator…I then shaded the parts they have eaten…I counted the parts they didn’t eat”).

IL09-I2-5SB

2009 ISAT Grade 5 Sample Book

Extended-Response Student Sample 1C MATHEMATICAL KNOWLEDGE

STRATEGIC KNOWLEDGE

EXPLANATION

2

2

3

The response shows some understanding of the problem’s mathematical concepts and principles by correctly modeling the fractional portion each friend ate.

IL09-I2-5SB

The response identifies some of the problem’s important elements and shows some evidence of a strategy for solving the problem. However, the student subtracts the total number of friends (5) from the total number of slices in one pizza (12) to determine the number of slices left uneaten, which shows a limited understanding of the relationship among elements.

93

The response addresses what was done and begins to address why (“I drawed a picture…I figured my answer by subtracting…The #12 came from the number of pizzas, the # 5 came from the pizzas that were eaten”).

IL09-I2-5SB

1 2 3 4 5 6 7 8 9 10 11 12 A B C D E

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