1 ISTEP+ Mathematics Item Sampler Updated February 2011 Purpose The purpose of this Item Sampler is to provide teachers and students with examples of the different types of questions on the ISTEP+ Mathematics assessment. The types of questions include multiple-choice, gridded response (grades 6-8 only), constructed-response, and extended-response. Teachers are also encouraged to use this information as a resource to help create other assessments and activities. Constructed-response (CR) and Extended-response (ER) Items The Applied Skills Assessment contains constructed-response and extended-response items. Each CR and ER item assesses Problem Solving and one Content Standard. The Content Standards that may be assessed on the Applied Skills Assessment are listed below. Grades (3-5): Number Sense, Computation, Geometry, and Measurement Grades (6-8): Number Sense, Computation, Measurement, Algebra and Functions Important note: ALL STANDARDS are assessed on the Multiple-Choice Assessment. Constructed-response and extended-response items require students to show their work. It is critical for students to show their work when responding to these questions as full credit will NOT be awarded if no work is shown. Also, incorrect responses may receive partial credit if a correct process or other correct work is shown. Both CR and ER items may require students to provide an explanation or justification within the item. Both item types also require a high level of thinking; however, the ER items may be slightly more complex. Extended-response items may also take students longer to respond. Students should be given several opportunities throughout the year to communicate their knowledge and understanding of mathematics on problems similar to the sample items and released items from previous years. Students must also learn to show their work in a concise and organized manner and to provide valid explanations and justifications when necessary. One goal for all educators should be to challenge students to solve problems that require a high level of critical thinking and reasoning in order to help them develop a broad range of problem-solving skills. Scoring Rubrics The Scoring Rubrics used for the CR and ER items were developed in such a way as to score items more holistically and report student scores more accurately. Prior to 2009, ISTEP+ mathematics rubrics were more analytic in nature and reported scores for problem solving, but not the associated content standard. Utilizing a more comprehensive approach, our current scoring rubrics now provide separate scores for problem solving and the content standard for each CR and ER item.
Transcript
1
ISTEP+ Mathematics Item Sampler
Updated February 2011
Purpose
The purpose of this Item Sampler is to provide teachers and students with examples of the different types of questions on the ISTEP+ Mathematics assessment. The types of questions include multiple-choice, gridded response (grades 6-8 only), constructed-response, and extended-response. Teachers are also encouraged to use this information as a resource to help create other assessments and activities.
Constructed-response (CR) and Extended-response (ER) Items
The Applied Skills Assessment contains constructed-response and extended-response items. Each CR and ER item assesses Problem Solving and one Content Standard. The Content Standards that may be assessed on the Applied Skills Assessment are listed below.
Grades (3-5): Number Sense, Computation, Geometry, and Measurement Grades (6-8): Number Sense, Computation, Measurement, Algebra and Functions
Important note: ALL STANDARDS are assessed on the Multiple-Choice Assessment.
Constructed-response and extended-response items require students to show their work. It is critical for students to show their work when responding to these questions as full credit will NOT be awarded if no work is shown. Also, incorrect responses may receive partial credit if a correct process or other correct work is shown. Both CR and ER items may require students to provide an explanation or justification within the item. Both item types also require a high level of thinking; however, the ER items may be slightly more complex. Extended-response items may also take students longer to respond.
Students should be given several opportunities throughout the year to communicate their knowledge and understanding of mathematics on problems similar to the sample items and released items from previous years. Students must also learn to show their work in a concise and organized manner and to provide valid explanations and justifications when necessary. One goal for all educators should be to challenge students to solve problems that require a high level of critical thinking and reasoning in order to help them develop a broad range of problem-solving skills.
Scoring Rubrics The Scoring Rubrics used for the CR and ER items were developed in such a way as to score items more holistically and report student scores more accurately. Prior to 2009, ISTEP+ mathematics rubrics were more analytic in nature and reported scores for problem solving, but not the associated content standard. Utilizing a more comprehensive approach, our current scoring rubrics now provide separate scores for problem solving and the content standard for each CR and ER item.
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Gridded Response Items (Grades 6-8 only)
Teachers are encouraged to use the Practice Gridded Response Test and Blank Gridded Response Sheets to familiarize students with this item format.
Reference Sheet (Grades 6-8 only)
The ISTEP+ Mathematics Reference Sheet may be used on all Mathematics ISTEP+ tests.
The 1st page of the reference sheet contains information for Grades 6-8. The 2nd page of the reference sheet contains information for Grades 7-8.
Teachers are encouraged to use the reference sheet throughout the year to familiarize students with the structure of and information contained in the reference sheet.
Calculator Policy Students in grades 6-8 are allowed to use a calculator on the Applied Skills Assessment and on one session of the Multiple-Choice Assessment. Students will not be allowed to use a calculator on the other session of the Multiple-Choice Assessment unless specified in the student’s IEP or
Section 504 plan. Please note that the prohibited calculator list is not exhaustive. Changes in technology occur at a rapid pace; thus, it is very difficult to list all of the calculators not permissible. In general, calculators with a QWERTY keyboard, a computer algebra system (CAS), and talking devices are NOT allowed. Be sure to ask your mathematics department chair if you are unsure whether a particular calculator is allowed. You may also contact the Indiana Department of Education at 317-232-9050 for further clarification.
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Grade 3 Sample Items
1. Solve the problem below. 48 + 23 = ____
A. 70
B. 71
C. 61
D. 60
2. Round the number below to the nearest hundred.
873
A. 800
B. 870
C. 900
D. 860
3. What factor should go on the line to make the equation true? 8 x ____ = 27 – 3
A. 7
B. 6
C. 4
D. 3
4
4. Which triangle has a right angle?
A. B.
C. D.
jrummel
Rectangle
jrummel
Polygonal Line
5
5. Teri has a set of flower pots shown below.
Teri gave of the set to a friend. Show the number of pots that Teri gave to her friend by
placing an X on the correct number of pots.
Teri sold the rest of the flower pots for $8 each. How much money did Teri earn from the flower pots she sold?
Show All Work
Answer $ ____________
If Teri had sold all of the flower pots and not given any to her friend, how much money would she have earned?
Write your answer in the form of an addition (or multiplication) number sentence.
7. Joey, Tim, and Carlos have 300 cards IN ALL. Joey has 70 cards. Tim has 100 cards.
On the line below, write a number sentence that can be used to find how many cards Tim and Joey have IN ALL.
Show All Work Answer ___________________________________________ Now write a number sentence that can be used to find how many cards Carlos has. Show All Work Answer ___________________________________________
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8. Jason is doing his math homework. He finishes one math problem every ten minutes. Use the information to complete the chart below.
Time (in minutes)
Number of Problems
10 1
20 2
30 3
40
50
How much time in MINUTES will Jason take to finish 10 math problems?
Show All Work
Answer _________________minutes
How much time in HOURS and MINUTES will Jason take to finish 10 math problems?
Show All Work
Answer ___________hour(s) and ___________minutes
If Jason started his homework at 2:00 p.m., what time would he finish?
Answer _______________ p.m.
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Use words, numbers or pictures to explain how you know what time Jason will finish all 10 math problems.
9. Eleanor’s class took a vote to choose what kind of ice cream to buy for their class party. They created the circle graph below to show their results.
Eleanor’s teacher will buy the 2 most popular kinds of ice cream for the party, and he put
cookie dough and strawberry on his list. On the lines below use words, numbers or symbols to describe how Eleanor would explain that her teacher was incorrect.
How many more students in the class voted for strawberry than vanilla?
Show All Work
Answer_________________ students
chocolate, 9
vanilla, 2cookie
dough, 12
strawberry, 6
10
What is the total number of students in Eleanor’s class? On the line below write a number sentence using information from the circle graph that can be used to find how many students are in the class.
10. Sara is making birthday cards. She takes 1 hour to make 5 cards. On Tuesday, Sara made 25 cards. How long did Sara spend working on the cards on Tuesday? Show All Work
Answer _______________________
On Wednesday, Sara started at 10:00 a.m. and finished at 2:00 p.m. How many cards did Sara make ALTOGETHER on Tuesday and Wednesday?
Show All Work
Answer ________________________
Use words, numbers or pictures to explain how you found your answer.
1. Jeremy has a diagram of a rectangular garden. The garden has an area of 12 square meters. If the length and width of the rectangle are whole numbers, which of the following perimeters, in meters, will NOT give an area of 12 square meters? A. 14 meters
B. 16 meters
C. 24 meters
D. 26 meters
2. Study the rectangle below.
What is the perimeter, in meters, of the rectangle?
A. 14 meters
B. 18 meters
C. 28 meters
D. 40 meters
3. Michael divided some toy cars among his 5 friends. Each friend received 3 toy cars. Which equation could you use to find the total number of toy cars? A. 3 + k = 5
B. k ÷ 5 = 3
C. 3 x k = 5
D. k – 5 = 3
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4. Use the model to help find the difference. 2.3 – 1.7
A. 0.6
B. 1.4
C. 1.6
D. 2.7
5. Amanda’s line plot shows the number of swimmers absent from swim practice for one week. Which BEST describes the pattern you see in the data?
A. More swimmers were absent during the middle of the week than at the beginning and end of the week.
B. Fewer swimmers were absent at the beginning of the week than at the end of the week.
C. Fewer swimmers were absent at the end of the week than in the middle of the week.
D. More swimmers were absent on Mondays and Fridays than on the other days.
X
X
X
X
X
X
X
X
X
X
X
X
X X
Mon Tues Wed Fri Thu
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6. Which geometric term describes this figure?
A. line segment XZ
B. ray XZ
C. plane XZ
D. line XZ
7. Three friends were comparing the number of crackers they ate from their snack bags. The numbers are listed below.
4
31
10
7
0.25
What is the TOTAL number of crackers the three friends ate in decimal form?
Show All Work
Answer _________________crackers
What is the number as a fraction?
Answer _________________crackers
X
Z
0.25
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8. About 15,090 people live in Crawfordsville; about 16,402 people live in Frankfort; about 18,140 people live in New Castle; and about 15,927 people live in Dyer. Fill in the table. Organize the information from GREATEST to LEAST population.
POPULATION OF SOME INDIANA CITIES
City
Population
Which of these cities in Indiana has the GREATEST population?
Answer ______________________________________
Order the population values from GREATEST to LEAST using the greater than symbol.
Which two cities have the same population if the population values are rounded to the nearest thousand?
Show All Work
Answer _________________________ and _________________________
9. The diagram below shows the three floors Elaine will mop for her summer job.
What is the total area, in square yards, that Elaine will mop if she mops each floor once?
Show All Work
Answer _____________________ square yards
16
This week, Elaine has to mop floor B twice. At the end of the week, she thinks that she mopped a larger area by mopping floor B twice than mopping floors A and C once.
Use words, numbers, or symbols to explain why Elaine is NOT correct. Be sure to indicate the areas to support your answer.
9. Blueberry muffins are on the menu every morning in the school cafeteria. The cook keeps track of the number of pints of blueberries she uses each day.
Pints of Blueberries Used
Monday 4 pints
Tuesday 3 pints
Wednesday 5 pints
Thursday 3 pints
Friday 4 pints
The cook had 25 pints of blueberries at the beginning of the week. How many pints were left at the end of the week?
On the lines below, describe a method you could use to solve this problem. How many steps are there in your method?
10. Edward is having a pizza party for his birthday. What fraction of a pizza will each person get when 3 pizzas are divided among 8 people?
Show all work.
Answer_____________ pizza
Izzie was hungry and said that she would rather have 25% of a pizza because that would be more. On the lines below show why Izzie was incorrect and explain your answer.
Edward ended up having 1½ pizzas left over from the party. How many friends can have 25% of a pizza each?
Show all work
Answer_____________ friends
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11. Joan needs to paint the cardboard triangle shown in the diagram below for a school project.
Joan has a bottle of paint that covers an area of 8 square feet. She thinks she will have to buy another bottle of paint to paint the front of the cardboard triangle.
Use words, numbers, or symbols to prove that Joan is correct.
If Joan also wants to paint the back of the cardboard triangle, what is the total area, in square feet, that she will have left to paint AFTER using one bottle of paint?
Show All Work
Answer ___________________square feet
How many bottles of paint will she need to paint the entire front AND back of the cardboard triangle?
Show All Work
Answer ___________________bottles of paint
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12. Dean is painting a wall that is 16 feet long and 9 feet high. One small can of paint will cover an area of 50 square feet. How many cans of paint will Dean need to paint the wall?
Show All Work
Answer ______________cans
Dean needs to paint a 2nd wall that measures 25 feet long and 5 feet high. He decides to buy 5 small cans of paint.
Use words, numbers, or symbols to verify if Dean has purchased enough paint to completely paint BOTH walls.
Any combination of Xs that represents 2/5 of the flower pots $24 ($8 + $8 + $8 = $24) or ($8 x 3 = $24) or other valid response $8 + $8 + $8 + $8 + $8 = $40 or 5 x $8 = $40
I know that it took Jason 100 minutes to do 10 math problems. 100 minutes = 1 hr. and 40 mins. 2:00 p.m. plus 1 hr. and 40 mins. Is 3:40 p.m.
Other Valid Response
Sample Process:
The circle graph shows that 12 students voted for cookie dough, 6 voted for strawberry, 9 voted for chocolate, and 2 voted for vanilla. Since 12 and 9 are the 2 highest votes, cookie dough and chocolate were the 2 most popular kinds of ice cream.
6 students voting for strawberry – 2 students voting for vanilla = 4 students
9 chocolate votes + 2 vanilla votes + 12 cookie dough votes + 6 strawberry votes = 29 total students
Any valid response explaining that Katie needs to use multiplication (or repeated addition) to find the number of balloons in 4 packages.
No, 4 packages are not enough balloons. 5 packages 30 balloons 3/6 or ½
Sample Process:
Floor A = 2 x 8 = 16 square yards Floor B = 3 x 5 = 15 square yards Floor C = 4 x 7 = 28 square yards
16 + 15 + 28 = 59 square yards
Floor B twice is 15 x 2 = 30 square yards Floors A and C together is 16 + 28 = 44 square yards
Other Valid Response
Sample Process:
Multiplication, because I need to find out how many balloons there are in 4 medium packages. Then I can compare that amount to see if it is greater than or less than 27.
4 x 6 = 24; 24 < 27, so that is not enough balloons for all the guests
$10 ÷ $2 = 5 packages
5 x 6 = 30 balloons
30 – 27 = 3 balloons 6 balloons in 1 package 3/6 of a package is left over
Other Valid Response
30
Grade 5 Answer Key
1. D (Measurement) 2. D (Problem Solving) 3. B (Number Sense) 4. C (Computation) 5. A (Algebra & Functions) 6. B (Geometry) 7. C (Data Analysis & Probability)
Any valid response explaining the method used and the number of steps to solve the problem using the method.
4 pints
Sample Process:
1,080,000 coins
I could use estimation. I would round 45,000 to 50,000 and 24 to 20; 50 x 2 = 100, so 50,000 x 20 = 1,000,000. My answer is close to the estimate, so it is a reasonable answer.
Other Valid Response
Sample Process:
My method has two steps. First, I would add to find how many pints of blueberries were used during the week. Then I would subtract the total from 25 pints to find how many pints of blueberries were left.
