Illinois Standards Achievement Test Mathematics Samples 35 2011 ISAT Grade Sample Book Structure of the Grade Mathematics ISAT ISAT Mathematics testing in spring 2011 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 multiplechoice 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 largescale 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 decisionmaking 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 Mathematics ISAT Students in Grade 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 36 2011 ISAT Grade 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 Session 45 minutes 40 multiple-choice items (30 of these are an abbreviated form of the Stanford 10.) Session 45 minutes 30 multiple-choice items short-response items Session 45 minutes extended-response items (Some items will be pilot items.) Calculator Use for Grade Mathematics ISAT All students in Grade are allowed to use a calculator during all sessions of the mathematics assessment Students are allowed to use a calculator as long as the calculator does not have any prohibited features as noted in the Calculator Use Policy for the ISAT Mathematics Tests (http://www.isbe.net/assessment/pdfs/2010/calculator_ISAT.pdf) 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 Mathematics ISAT All students in grade 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 2 ISAT GRADES FOUR–EIGHT Centimeters 10 11 12 13 Inches 0 14 15 Scratch Paper for Grade Mathematics ISAT Students must be provided with blank scratch paper to use during only session Only session contains norm-referenced items, which were normed under such conditions Students may not use scratch paper during session 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 on the appropriate page in the answer document Students must show their work for each extendedresponse item in session on the appropriate pages in the answer document 37 Mathematics 2011 ISAT Grade Sample Book 3483412 What is the value of the in 5,360? A 60 ≥B 600 6,000 C D Which shows the standard form of the number written in words below? three hundred eighty-six thousand, seven hundred four 308,674 368,704 386,704 386,740 A B C D GO ON 38 Mathematics 2011 ISAT Grade Sample Book 3349018 A farmer has different types of farm animals Information about the number of each type of animal is shown below Which expression is equal to ϫ 8? A B ≥C D 7ϩ7ϩ7ϩ7ϩ7ϩ7ϩ7 7ϫ7ϫ7ϫ7ϫ7ϫ7ϫ7ϫ7 8ϩ8ϩ8ϩ8ϩ8ϩ8ϩ8 8ϫ8ϫ8ϫ8ϫ8ϫ8ϫ8 3349037 • of the animals are cows 50 • 27 of the animals are chickens 50 • 11 of the animals are pigs 50 • of the animals are horses 50 Which inequality is correct? A ≥B C D 71,255 Ͻ 71,215 64,948 Ͻ 64,984 45,382 Ͻ 45,328 20,663 Ͻ 20,336 Which lists the number of animals on this farm from least to greatest? A B C Which number has a value greater than 2.3? A B C D D Horses, cows, pigs, chickens Chickens, pigs, horses, cows Horses, pigs, cows, chickens Cows, chickens, pigs, horses 2.2 2.09 2.9 2.29 GO ON 39 Mathematics 2011 ISAT Grade Sample Book 3349039 3349039_AR1 to AR5 Which shape on the number line best represents the location of ? ≥B A C XIE112 ≥A 479 589 379 B C D D Josh built 10 toy houses He used 12 blocks to build each toy house George collected 489 rocks for his science project Matthew collected 100 fewer than George How many rocks did Matthew collect? 389 What is the total number of blocks Josh used to build these 10 houses? 12 22 120 1200 A B C D GO ON 40 Mathematics 2011 ISAT Grade Sample Book 3348990 10 3348988 13 Ms Fields wants to buy 30 cupcakes for her class There are cupcakes in each package The 4th-grade class has 32 students There are 13 girls in the class What fractional part of the class is boys? What is the least number of packages she will have to buy? 19 32 13 32 32 19 32 13 ≥A B C D A B 3348992 11 C ≥D D What time did the airplane land in New Orleans? A B 3483413 12 C An airplane left Chicago at 1:15 P.M and landed in New Orleans hours and 15 minutes later 15 ϫ ϭ (10 ϫ 3) Ϭ (5 ϫ 3) 15 ϫ ϭ (10 ϫ 3) ϫ (5 ϫ 3) 15 ϫ ϭ (10 ϫ 3) Ϫ (5 ϫ 3) 15 ϫ ϭ (10 ϫ 3) ϩ (5 ϫ 3) B 14 Which number sentence is true? A ≥ C D The average length of a song on a CD is minutes 5:45 P.M 6:15 P.M 6:30 P.M 6:45 P.M Which is closest to the number of songs that can be played in 16 minutes? 19 13 A B ≥ C D GO ON 41 Mathematics 3528352 15 2011 ISAT Grade Sample Book 3528352_AR1 16 Use your inch ruler to help you answer this question M What is the area of the rectangular sign in the picture below? N 40 feet Which is closest to the length in inches of line segment MN? 20 feet A B C ≥D in 1 in 2 in in A B C D 60 square feet 80 square feet 120 square feet 800 square feet GO ON 42 Mathematics 2011 ISAT Grade Sample Book 3348993 17 3348993_AR1 3483414 18 Which is closest to the area of this figure in square units? 3483414_AR1 What is the volume of this shape? Represents cubic unit A ‫ ؍‬1 sq unit A B ≥C D B ≥C 24 sq units 32 sq units 34 sq units 36 sq units D 10 cubic units 11 cubic units 12 cubic units 18 cubic units 3483415 19 Ben is years old How many months are equal to years? A B ≥C D 10 months 12 months 18 months 24 months GO ON 43 Mathematics 2011 ISAT Grade Sample Book 3349002 22 20 If b equals 5, which equation is true? Which rule was used to make this increasing number pattern? 11, 22, 44, 88, 176, A B C D ϩ b ϭ 15 Ϫ b ϭ 15 Ϭ b ϭ 15 ϫ b ϭ 15 A B Add 11 Add 22 Multiply by Multiply by 11 C ≥D 3483417 23 Tom has been saving his money for three weeks The chart below shows his total savings each week 3483416 21 Raj earns points for each question he answers correctly Tom‘s Savings Let p represent the number of questions Raj answers correctly B C D Total Amount Saved Week Which expression could be used to find the total number of points Raj earns? ≥A 3483417_AR1 pϫ5 pϩ5 pϬ5 pϪ5 $2.25 $4.50 $6.75 If Tom continues to add the same amount to his savings each week, what should be the total amount saved by week 4? $3.50 $5.50 $8.00 A B C $9.00 ≥D GO ON 44 Mathematics 2011 ISAT Grade Sample Book 3349010 24 26 Exactly how many right angles and vertices does a rectangle have? Which sentence describes the information in the table below? ≥A Number of Tables Number of People 0 2 10 right angles and vertices right angles and vertices right angles and vertices right angles and vertices A B C D 3483419 27 3483419_AR1 Exactly how many faces does a rectangular prism have? There are people at each table There are people at each table There are people at each table There are people at each table B C D 3483418 25 10 A B ≥ C D What is the value of M in the number sentence? M Ϭ ϭ 20 40 22 18 10 ≥A B C D GO ON 45 Mathematics 2011 ISAT Grade Sample Book 3349020 28 3349023 30 Which statement is true? A ≥B C D 29 Which of the following figures shows only a flip of the shaded figure across line m? All polygons have angles All polygons are closed figures All polygons are 4-sided figures All polygons have lines of symmetry 3483420 3349023_AR1 to AR5 m 3483420_AR1 to AR4 ≥A m B m C m D m Which shape has exactly line of symmetry? A B C ≥D GO ON 46 Mathematics 2011 ISAT Grade Sample Book 3349025 31 3483421 33 Which of the following describes the faces of a triangular pyramid? A ≥B C D If the regular hexagon below were cut on the dashed line segment, what would be the shape of each piece? rectangular faces triangular faces triangular faces rectangular faces 3528405 32 3528405_AR1 What solid figure can be made by folding the pattern shown below along the dashed line segments? A ≥B C D ≥A B C D 3483421_AR1 Rectangle Trapezoid Square Pentagon Rectangular prism Triangular prism Cylinder Cube GO ON 47 Mathematics 2011 ISAT Grade Sample Book 34 Which pair of figures appears to be congruent? A B C D GO ON 48 Mathematics 2011 ISAT Grade Sample Book 3483422 35 3483422_AR1 The graph below shows the results of a survey to find the number of students who ride their bicycles to school Students Riding Bicycles to School Beth’s class Miguel’s class Ali’s class Kamilla’s class Each represents one student Whose class has the most students ride their bicycles to school? A B C ≥D Beth’s class Miguel’s class Ali’s class Kamilla’s class GO ON 49 Mathematics XID501 36 2011 ISAT Grade Sample Book XID501.AR1 The tally chart shows how John’s class voted on the games they should play at the class outing Which two games received the most votes? Games |||| Kickball |||| |||| | Freeze Tag A B C ≥D 3349031_AR1 According to this Venn diagram, how many characteristics Bob and Bill have in common? Bob Tally Marks Soccer Relay Races 3349031 37 Boy years old |||| | Likes cats ||| Kickball and Soccer Relay Races and Freeze Tag Soccer and Freeze Tag Kickball and Relay Races Bill Blue eyes Brown hair years old Likes dogs A ≥B C D GO ON 50 Mathematics 2011 ISAT Grade Sample Book 38 What is the mode of the following set of numbers? {3, 8, 5, 8, 7, 8, 4, 6, 8, 3, 8, 7, 3} A B C D XIF606 39 XIF606.AR1-5 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 C ≥B D GO ON 51 Mathematics 2011 ISAT Grade Sample Book 3483423 40 3483423_AR1 Sally put the cubes shown below in a box She chose one cube without looking Gray Gray White White Gray White Gray Gray White What is the probability that she chose a white cube? A ≥B C D out of 4 out of out of out of STOP 52 ... Cylinder Cube GO ON 47 Mathematics 2 011 ISAT Grade Sample Book 34 Which pair of figures appears to be congruent? A B C D GO ON 48 Mathematics 2 011 ISAT Grade Sample Book 348 342 2 35 348 342 2_AR1 The graph... feet 800 square feet GO ON 42 Mathematics 2 011 ISAT Grade Sample Book 3 348 993 17 3 348 993_AR1 348 341 4 18 Which is closest to the area of this figure in square units? 348 341 4_AR1 What is the volume... polygons are 4- sided figures All polygons have lines of symmetry 348 342 0 3 349 023_AR1 to AR5 m 348 342 0_AR1 to AR4 ≥A m B m C m D m Which shape has exactly line of symmetry? A B C ≥D GO ON 46 Mathematics