Gridded-Response Math Problems on the MCA
Grades 5–6
Starting in 2005, the Minnesota Comprehensive Assessments in grades 5, 6, 7, 8 and 11 have
included gridded-response items. A gridded-response item is similar to a multiple-choice
item, except that no answer choices are given. The student solves the problem and then fills
in a response grid to give the answer. Each gridded-response item is worth one point.
What other tests use gridded-response items? At what grade levels?
Gridded-response items have been used in other states’ assessments for several years. In
addition, the GED and SAT use gridded-response items. Most states use gridded-response
items beginning in grade 5, though some even use them in grade 4.
How are these items scored?
Gridded-response items are scored in a manner similar to multiple-choice items. A scanner
will only read a completed grid.
What are the advantages of a gridded-response item?
Benefits provided by gridded-response items include:
Allowing students to solve the problem with their preferred method (i.e., expressing
probability in fraction or percent format).
Providing more information about the student’s knowledge of a concept; because the
student must produce an answer rather than selecting it, students cannot use a
different skill (i.e., substitution) to arrive at the correct answer.
Assessing a benchmark more effectively because a correct response could be in a
range (i.e., estimation items).
Grades 5–6 Gridded-Response
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Parts of a Response Grid
An example of a response grid for grades 5–6 is shown below.
Area for
writing
Decimals
Numbers
Dollar sign,
fraction
symbols
and percent
symbol
Area for writing: After students solve the problem, they write their answer in the boxes in the
first row.
Dollar sign, fraction symbols and percent symbol: Students fill in the circles under each
symbol of their answer in the first row. The slash rather than a dash is used as the fraction
symbol in order to avoid confusion with the negative sign.
Decimals: The third row has five decimal marks. Students fill in the circle below the decimal
mark, if any, in the answer they wrote in the top row.
Numbers: Students fill in the appropriate circles under each number they wrote in the top
row.
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A Possible Introduction of Gridded-Response Items to Students
Review and discuss Directions for a Gridded-Response Problem page.
Students work first sample problem and complete grid.
Discuss students’ completed grids (student groups could be used in this activity). A
solution page for the first sample problem is provided, showing possible completed
grids.
Students work second sample problem and complete grid.
Discuss students’ completed grids (student groups could be used in this activity). A
solution page for the second sample problem is provided, showing possible completed
grids.
Use items in gridded-response format in future assignments (homework, group work,
class work, tests).
If students need to improve their accuracy in completing a grid, students may grid
numbers without working a math problem first. Students could grid their age,
numbers on the wall around the room, numbers from the newspaper, etc.
The following pages are intended for student use, if desired.
A page with blank grids that teachers may copy is provided at the end of this tutorial.
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Directions for a Gridded-Response Problem
1. Solve the problem.
2. Write the answer in the boxes of the grid.
Write only one digit or one symbol in a box.
Write the decimal point or fraction bar in the answer box if it is part of the
answer.
Mixed numerals must be changed to improper fractions or decimals.
Do not leave spaces between digits or symbols.
Do not include commas.
3. Fill in the correct bubble under each box in which you wrote a number or symbol.
4. The examples below show numbers correctly gridded.
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GRADE 5 SAMPLE PROBLEMS
Gridded-Response Sample Problem 1
Grade 5
Solve problem 1 and record your answer in the response grid.
1. Erica is 38 inches tall. Joanna is 62 inches tall. Marsha is halfway between Joanna
and Erica in height. How many inches tall is Marsha?
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Gridded-Response Sample Problem 1 Solution
Grade 5
The answer key shows some ways the answer to the problem can be correctly filled in
on the response grids.
The correct answer is 50.
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Gridded-Response Sample Problem 2
Grade 5
Solve problem 2 and record your answer in the response grid.
2. The results of the final exam for Mr. Johnson’s class are shown.
88, 80, 75, 94, 97, 91, 87, 81, 87, 83
What is the median of the final exam?
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Gridded-Response Sample Problem 2 Solution
Grade 5
The answer key shows some ways the answer to the problem can be correctly filled in
on the response grids.
The correct answer is 87.
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GRADE 6 SAMPLE PROBLEMS
Gridded-Response Sample Problem 1
Grade 6
Solve problem 1 and record your answer in the response grid.
1. The table shows results of a skiing competition.
SKIING COMPETITION
Number
Country
of Points
Austria
1,702
Denmark
846
Norway
1,096
Switzerland
1,064
United States
932
How many more points did Austria earn than Denmark?
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Gridded-Response Sample Problem 1 Solution
Grade 6
The answer key shows some ways the answer to the problem can be correctly filled in
on the response grids.
The correct answer is 856.
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Gridded-Response Sample Problem 2
Grade 6
Solve problem 2 and record your answer in the response grid.
2. Mr. Hartmann wants to apply a new coat of paint to one side of a shed. He must first
determine how much paint to buy. His shed measures 20 feet wide and 12 feet high.
What is the area, in square feet, of the side of his shed?
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Gridded-Response Sample Problem 2 Solution
Grade 6
The answer key shows some ways the answer to the problem can be correctly filled in
on the response grids.
The correct answer is 240.
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Grades 5–6 Blank Grids
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