2010 Illinois Standards Achievement Test Mathematics Samples Form LM Grade 6 Illinois State Board of Education _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 2 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Structure of the Grade 6 Mathematics ISAT ISAT Mathematics testing in spring 2010 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 6 Mathematics ISAT Students in grade 6 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. 3 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 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. ISAT Mathematics Form LM Grades 3-8 Session 1 45 minutes Session 2 45 minutes Session 3 45 minutes 40 linguistically modified multiple-choice items (30 of these are an abbreviated form of the Stanford 10.) 30 linguistically modified multiple-choice items 3 short-response items with 2 options: 1. Short-response items in plain English 2. Side-by-side English/Spanish format from original ISAT text 2 extended-response items with 2 options: 1. Extended-response items in plain English 2. Side-by-side English/Spanish format from original ISAT text (Some sessions include pilot items.) Calculator Use for Grade 6 Mathematics ISAT All students in grade 6 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 6 Mathematics ISAT All students in grade 6 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 6 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. 4 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 XIH110 1 3484196 3 There are 50 beans in a bag. Twenty percent (20%) are red. Anna runs 100 meters in ten and sixty-two hundredths seconds. How many are red? How is her time written as a number? A ≥B 5 10 20 30 A ≥B C D 1.62 seconds C 10.62 seconds 100.62 seconds D 1062.00 seconds 3528353 3528353.AR1 4 Use your centimeter ruler to answer the question. 3484192 2 What number goes in the ? 10 16 y 2 4 12 42 52 72 A ≥B C D About how long and wide in centimeters is the rectangle? A 5.0 cm by 3.0 cm B 5.5 cm by 3.5 cm ≥C 5.5 cm by 3.0 cm D 6.0 cm by 3.5 cm GO ON 5 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484200 5 3484200_AR1 to AR4 3484203 6 Which rectangle has an area of 24 square units and a perimeter of 20 units? 3484203_AR1 Which is closest to the measure of ∠XYZ? 12 A X 2 Y 8 B 3 5 C 4 20° 90° 130° A B C 160° ≥D 3484221 7 Mike has x baseball cards. Tyrone has 3 times as many baseball cards as Mike. Frank has 20 baseball cards. 6 ≥D Z 4 Which expression represents how many cards they have in all? ≥A x ⫹ 3x ⫹ 20 B 20 ⫹ 3x ⫺ x C x ⫹ 3 ⫹ 20 D 20 ⫺ 3x ⫹ x GO ON 6 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484224 8 3349428 10 What value of n makes the equation below true? What is the value of the expression below when x = 6 and y = 2? 4n ⫽ 220 8x ⫺ y 84 A ≥ 46 12 4 B C D 3484225 9 50 55 A ≥B 220 C D 3484229 11 3484225_AR1 216 3484229_AR1 What should be the value for x in the triangle shown? Which correctly describes the rule between x and y ? x x y 4 9 5 11 6 13 7 15 A y⫽x⫹6⫺1 B y⫽x•x⫺1 C y⫽x⫹x⫺1 ≥D y⫽x•2⫹1 50° 60° 10° 40° A B ≥ 70° 90° C D GO ON 7 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484232_AR1 XIJ321.AR1 13 Lines w and x intersect lines y and z to make a rectangle. Ta ll Fra nk lin 3484232 12 ey Holloway Pierce w Starlight x y z Which streets do not intersect? Which is true? A Line x is parallel to line y. A Talley and Franklin B Line x is parallel to line z. B Starlight and Pierce Line w is perpendicular to line y. C Franklin and Holloway ≥D Holloway and Starlight ≥C D Line w is perpendicular to line x. GO ON 8 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484235 14 3484235_AR1 3349454 15 3349454_AR1 Triangle RST is similar to triangle XYZ. What solid figure will this pattern make when it is folded along the dotted lines? Y X R Z S T RS corresponds to which side of triangle XYZ? A Rectangular pyramid B Square pyramid SR YZ XZ C Triangular prism A B C ≥D XY ≥D Cube GO ON 9 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 XJE380 16 XJE380_AR1 Students voted for their favorite books. 7 Football 6 5 4 26 3 2 7 1 ts or te ys M Sp ry sy ta Fa n al im An ve nt ur e 0 Ad Number of Votes 3349380_AR1 The Venn diagram shows how many students play baseball and football. Books We Like 8 3349380 17 32 Kinds of Books Baseball How many more students voted for books about adventures than books about sports? How many students play baseball but not football? 0 1 2 3 A B C ≥D 39 33 ≥ 32 26 A B C D GO ON 10 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349383 18 3349383_AR1 to AR5 Carl has 16 books. The bar graph shows the number of each type of book. Number of Books Carl’s Books 10 8 6 4 2 0 Biography Art Fiction Mystery Type of Book Which circle graph best shows the types of books Carl has? Carl’s Books Carl’s Books Biography Art Art Mystery Fiction Fiction Biography A Mystery C Carl’s Books Carl’s Books Art Art Fiction Fiction Biography Biography Mystery Mystery ≥B D GO ON 11 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484236 19 3484240 20 Greg took five tests. Each test is worth 100 points. 3484240_AR1 to AR4 Which spinner is most likely to have the arrow stop on B? Here are Greg’s scores: 85, 87, 87, 89, 97 What is Greg’s mean (average) score for these five tests? 89 88 87 12 ≥A B C D B R G Y B R Y B A ≥B B C Y B R B R Y D G B R Y GO ON 12 3349451 3349451_AR1 to AR4 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349080 22 21 3349080_AR1 Tom's Work List Work Time Read Book 3 hour 4 Cut Grass 1 1 hours 4 B C D Key: 1cm = 5 feet ! 1 2 hours 4 Fix Car 3 Tree 1 hour 2 Clean Room A Swing 6 hours 14 3 3 hours 4 1 4 hours 2 3 4 hours 4 ≥ A 4 feet B 5 feet C 20 feet D 25 feet ≥ 3349454 GO ON 13 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349423 23 24 !# "best quation? y y=x+4 20 18 16 A x y 14 0 0 12 1 1 2 2 6 3 3 4 10 8 2 B ≥C D x y 0 4 1 4 2 4 3 4 x y 0 4 1 5 2 6 3 7 x y 0 0 1 4 2 8 3 12 0 2 4 6 8 10 12 14 16 18 20 x If x is 8 on the graph, what is y? ≥ 25 A 4 B 14 C 16 D 18 ≥ ≥ Jan has 18 cards. Ray gives her v cards. Jan now has less than 30 cards. Which best describes Jan's cards? A v ⫺ 18 ⬎ 30 ≥B v ⫹ 18 ⬍ 30 C v ⫺ 18 ⬍ 30 D v ⫹ 18 ⬎ 30 STOP 14 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Answer Key with Assessment Objectives Identified Item Number Correct Answer 1 B 6.6.05 Read, write, recognize, and model equivalent representations of decimals and their place values through thousandths. 2 B 6.6.15 Identify and apply order of operations to simplify numeric expressions involving whole numbers. 3 B 6.6.21 Solve number sentences and problems involving percents. 4 C 7.6.01 Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles. 5 D 7.6.02 Solve problems involving the perimeter and area of a triangle, parallelogram, or irregular shape using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description). 6 D 7.6.03 Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0° to 180°) using referents. 7 A 8.6.02 Write an expression using variables to represent unknown quantities. 8 B 8.6.03 Evaluate algebraic expressions with up to two whole number variable values (e.g., evaluate 3m + n + 3 when m = 4 and n = 2). 9 D 8.6.04 Determine a rule having two operations from an input–output table (e.g., multiply by 3 and add 2). 10 B 8.6.09 Solve for the unknown in an equation with one operation (e.g., 8x=24, m÷2=25). 11 C 9.6.03 Solve problems using properties of triangles and quadrilaterals (e.g., sum of interior angles of a quadrilateral is 360°). 12 C 9.6.07 Identify and sketch parallel, perpendicular, and intersecting lines. 13 D 9.6.07 Identify and sketch parallel, perpendicular, and intersecting lines. 14 D 9.6.09 Identify a three–dimensional object from its net. 15 D 9.6.12 Determine if figures are similar, and identify relationships between corresponding parts of similar figures. 16 D 10.6.01 Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph. Assessment Objective 15 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Answer Key with Assessment Objective Identified Item Number Correct Answer 17 C 10.6.01 Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, or circle graph. 18 B 10.6.02 Compare different representations of the same data. 19 A 10.6.04 Determine the mode, range, median, and mean, given a set of data or a graph. 20 B 10.6.05 Solve problems involving the probability of a simple event, including expressing the probability as a ratio, fraction, decimal, or percent. 21 D 6.6.14 Solve problems involving addition and subtraction of fractions and mixed numbers, and express answers in simplest form. 22 D 7.6.03 Compare and estimate length (including perimeter), area, volume, weight/mass, and angles (0° to 180°) using referents. 23 C 8.6.03 Evaluate algebraic expressions with up to two whole number variable values (e.g., evaluate 3m + n + 3 when m = 4 and n = 2). 24 C 8.6.04 Determine a rule having two operations from an input–output table (e.g., multiply by 3 and add 2). 25 C 8.6.05 Select a table of values that satisfies a linear equation, and recognize the ordered pairs on a rectangular coordinate system. 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. 16 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Sample Items Followed by Scoring Rubric Student Samples 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). 17 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Items Reactivos de Respuesta Corta Plain English - Use pages English and Spanish - Use pages - Inglés y Español - Usa las páginas - 3484241 1 3484241_AR1 What is the location of point A? What is the location of point B? A 0 B 1 2 3 Label your answers. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION 1. 18 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349370 2 B 10 in. A 1 in. 3 in. C 8 in. 4 in. 5 in. 3349370_AR1 12 in. 12 in. 6 in. D 6 in. 6 in. 3 in. Which rectangular prism has the greatest volume? Volume of a rectangular prism ⫽ length ⫻ width ⫻ height Show your work. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION 2. 19 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349372 3 3349372_AR1 Julio made a pattern of equilateral triangles out of toothpicks. Number of Triangles Made 1 2 3 4 5 Number of Toothpicks Used 3 5 7 9 11 How many toothpicks would Julio use to make a figure with 10 equilateral triangles? Show your work. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION 3. 20 STOP _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 1 3484241 3484241_AR1 3484241 3484241_AR1 Use the number line below to answer the following questions. What number best represents the location of point A? What number best represents the location of point B? A 0 B 1 2 3 Label your answers. 1 Usa la línea numerada de abajo para responder a las siguientes preguntas. ¿Qué número representa mejor la ubicación del punto A? ¿Qué número representa mejor la ubicación del punto B? A 0 B 1 2 3 Marca tus respuestas. NO ESCRIBAS AQUÍ. USA LA PÁGINA __ EN TU DOCUMENTO DE RESPUESTAS PARA CONTESTAR LA PREGUNTA 1. 21 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349370 2 B 10 in. A 1 in. 3 in. C 8 in. 4 in. 12 in. 6 in. D 6 in. 12 in. 5 in. 3349370_AR1 6 in. 3 in. Which rectangular prism has the greatest volume? Volume of a rectangular prism ⫽ length ⫻ width ⫻ height Show your work. 3349370 2 B 10 in. A 1 in. 3 in. C 8 in. 4 in. 5 in. 12 in. 12 in. 3349370_AR1 6 in. D 6 in. 6 in. 3 in. ¿Qué prisma rectangular tiene el mayor volumen? Volumen de un prisma rectangular = largo x ancho x altura Demuestra tu trabajo. NO ESCRIBAS AQUÍ. USA LA PÁGINA __ EN TU DOCUMENTO DE RESPUESTAS PARA CONTESTAR LA PREGUNTA 2. 22 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349372 3 3349372_AR1 Using toothpicks, Julio made a pattern of equilateral triangles. He recorded the number of triangles made and the number of toothpicks used in a chart. Number of Triangles Made 1 2 3 4 5 Number of Toothpicks Used 3 5 7 9 11 Using this chart, how many toothpicks would Julio use to make a figure with 10 equilateral triangles? Show your work. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION 3. 23 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349372 3 3349372_AR1 Usando escarbadientes, Julio hizo un patrón de triángulos equiláteros. En un gráfico, registró la cantidad de triángulos hechos y la cantidad de escarbadientes utilizados. Cantidad de triángulos hechos 1 2 3 4 5 Cantidad de escarbadientes utilizados 3 5 7 9 11 ¿Cuántas latas deben poner en cada caja? Demuestra tu trabajo. Explica con palabras cómo llegaste al resultado. Relata por qué seguiste esos pasos para solucionar el problema. NO ESCRIBAS AQUÍ. USA LA PÁGINA __ EN TU DOCUMENTO DE RESPUESTAS PARA CONTESTAR LA PREGUNTA 3. 24 STOP _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 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 25 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 1A Short Response Student Sample1A Rubric Score Point = 2 Note: The student correctly identified the location of both points. 26 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 1B Short Response Student Sample1B Rubric Score Point = 2 Note: The student correctly identified the location of both points. 27 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 1C Short Response Student Sample1C Rubric Score Point = 1 Note: The student correctly identified the location of one point. 28 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 2A Short Response Student Sample2A Rubric Score Point = 2 Note: The student correctly chose “D” as having the most volume, and supporting work, including the volumes of the other three rectangular prisms, is present. 29 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 30 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 2B Short Response Student Sample 2B Rubric Score Point = 2 Note: The student correctly chose “D” as having the most volume, and supporting work is present. 31 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 2C Short Response Student Sample 2C Rubric Score Point = 1 Note: The student correctly calculated the volume of each rectangular prism but incorrectly chose “C” as their answer. 32 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 3A Short Response Student Sample3A Rubric Score Point = 2 Note: The student provided the correct answer of 21 toothpicks and showed supporting work (counting by 2s). 33 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 3B Short Response Student Sample3B Rubric Score Point = 2 Note: The student provided the correct answer of 21 toothpicks and showed supporting work (# of triangles ⫻ 2 ⫹ 1). 34 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Short-Response Student Sample 3C Short Response Student Sample3C Rubric Score Point = 1 Note: The student provided an incorrect answer (20) but showed supporting work (drawing and counting). 35 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Sample Items Followed by Scoring Rubric and Student Samples 36 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 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). 37 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Blank Extended-Response Template Mathematics - Session 3 DIRECTIONS Make sure you – show all your work in solving the problem, – clearly label your answer, – write in words how you solved the problem, – write in words why you took the steps you did to solve the problem, and – write as clearly as you can. 38 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Mathematics - Session 3 39 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Items Reactivos de Respuesta Larga Plain English - Use pages - English and Spanish - Use pages - Inglés y Español - Usa las páginas - 3484244 3484244_AR1 Austin, Ben, Catina, and Darius bring cans from home. The cans go in 4 boxes. Each box gets the same number of cans. Austin Ben 18 cans 25 cans 8 cans 13 cans Box 2 Box 3 Box 4 Box 1 Catina Darius How many cans go in each box? Show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION . 40 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349092 2 Use your centimeter ruler to solve this problem. Make a scale drawing of a straight road that is 24 miles long. Use the scale 1 centimeter represents 3 miles. You must include: • A beginning point • An ending point • A stop sign that is 6 miles from the ending point of the road Label all parts of the road. Show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION 2. 41 STOP _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484244 3484244_AR1 Austin, Ben, Catina, and Darius collected cans for a local food shelter. They will put the same number of cans in each of 4 boxes. The number of cans each student collected is shown. Austin Ben Catina Darius 18 cans 25 cans 8 cans 13 cans Box 1 Box 2 Box 3 Box 4 How many cans should they put in each box? Show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem. DO NOT WRITE HERE. USE PAGE __ IN YOUR ANSWER DOCUMENT TO ANSWER QUESTION 1. 42 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3484244 3484244_AR1 Austin, Ben, Catina y Darius recogieron latas de alimentos para un refugio local. En cada una de 4 cajas colocarán la misma cantidad de latas. Se muestra la cantidad de latas recolectadas por cada estudiante Austin Ben Catina Darius 18 latas 25 latas 8 latas 13 latas Caja 1 Caja 2 Caja 3 Caja 4 ¿Cuántas latas deben poner en cada caja? Demuestra tu trabajo. Explica con palabras cómo llegaste al resultado. Relata por qué seguiste esos pasos para solucionar el problema. NO ESCRIBAS AQUÍ. USA LA PÁGINA __ EN TU DOCUMENTO DE RESPUESTAS PARA CONTESTAR LA PREGUNTA . 43 GO ON _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 3349092 2 Use your centimeter ruler to help you solve this problem. Make a scale drawing of a straight bike path that is 24 miles long. Use the scale 1 centimeter represents 3 miles. You must include: • A beginning point. • An ending point. • A drinking fountain that is 6 miles from the ending point of the path. Label all parts of the path. Show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem. 3349092 2 Utiliza la regla de centímetros para ayudarte a resolver este problema. Dibuja en escala el sendero de una bicicleta que tiene 24 millas de largo. Usa la escala, 1 centímetro representa 3 millas Debes incluir: •· Un punto de partida. •· Un punto de llegada. •· Un bebedero a 6 millas del punto de llegada. Marca todas las partes del sendero. Demuestra tu trabajo. Explica con palabras cómo llegaste al resultado. Relata por qué seguiste esos pasos para solucionar el problema. NO ESCRIBAS AQUÍ. USA LA PÁGINA __ EN TU DOCUMENTO DE RESPUESTAS PARA CONTESTAR LA PREGUNTA . 44 STOP _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 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 • shows complete understanding of the • identifies all important elements of • gives a complete written explanation of the problem’s mathematical concepts and the problem and shows complete solution process; clearly explains what was principles understanding of the relationships among done and why it was done elements • uses appropriate mathematical terminology • may include a diagram with a complete and notations including labeling answer if • shows complete evidence of an appropriate explanation of all its elements appropriate strategy that would correctly solve the 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 45 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Student Sample 1A 46 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Student Sample 1B 47 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 48 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Student Sample 1C 49 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 50 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Scoring Guide for “Cans for Food Shelter” The correct answer to this extended-response problem is 16 cans in each box. Extended-Response Student Sample 1A MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION 4 4 4 This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. The correct answer of 16 cans is present. The response reflects a systematic strategy (adding the total number of cans and dividing by 4) that includes all important elements of the problem. The response addresses both what was done and why (“…added to see how many cans there are… divided 64 by 4…have to be put in 4 boxes…”). Extended-Response Student Sample 1B MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION 4 4 4 This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. The correct answer of 16 cans is present. The response reflects a systematic strategy (adding the total number of cans and dividing by 4 then checking with tally marks) that includes all important elements of the problem. The response addresses both what was done and why (“…added to see how many there are all together…divided 64 ÷ 4 because there are 64 cans and 4 boxes…”). Extended-Response Student Sample 1C MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION 4 4 2 This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. The correct answer of 16 cans is present. The response reflects a systematic strategy (adding the total number of cans and dividing by 4 and drawing a picture) that includes all important elements of the problem. 51 The response addresses only what was done (“…first I add…then I divide…”). _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Student Sample 2A 52 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Student Sample 2B 53 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 54 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Extended-Response Student Sample 2C 55 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 56 _____________________________________________________________ 2010 ISAT Mathematics Form LM Sample Book - Grade 6 Scoring Guide for “Bike Path” To solve this problem correctly, students must make a scale drawing of a bike path. Since the scale given is 1 cm=3 miles, their scale drawing must be 8 cm long and have a drinking fountain that is 2 cm from the ending point on their drawing. The drinking fountain could be on the bike path itself or beyond it in any direction, as long as its distance from the ending point is 2 cm. Extended-Response Student Sample 2A MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION 4 4 4 This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. Both the path length and fountain placement are correct. The response reflects a systematic strategy that includes all important elements of the problem. The student divided 24 by 3 to find the correct path length of 8 cm and then drew the path with the fountain correctly placed on the path. The response addresses both what was done and why (“divided 24 by 3 so I would know how many centimeters would equal 24 miles. Next, I draw a line that was 8 centimeters long because that is how many centimeters it takes for 24 miles…After that I divided 6 by 3 to get 2. The reason…to find were the drinking fountain goes…”). Extended-Response Student Sample 2B MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION 4 4 3 This response includes evidence of a complete understanding of the problem’s mathematical concepts and principles. Both the path length and fountain placement are correct. The response reflects a systematic strategy that includes all important elements of the problem. The response addresses what was done and begins to address why (“my path was 8 centimeters long because every 3 centimeters was a mile”). Extended-Response Student Sample 2C MATHEMATICAL KNOWLEDGE STRATEGIC KNOWLEDGE EXPLANATION 2 4 4 The response reflects a systematic strategy that includes all important elements of the problem. The response addresses both what was done and why (“I drew a line that was 8 cm long because 8х3=24. Then I… measured 2 centimeters higher and labeled drinking fountain because I knew 3х2=6”). This response includes some understanding of the problem’s mathematical concepts and principles. The path contains a major error (1 cm off in length). This was a measuring error. 57
© Copyright 2024