Mathematics Materials Collections for Year-End States

Spring 2026 Assessment Window: Year-End Model

Download the Mathematics Materials Collections List for Year-End States (pdf)

Dynamic Learning Maps® (DLM®) testlets sometimes call for the use of specific materials. The Testlet Information Page (TIP) for each testlet identifies these materials. Sometimes materials are required and cannot be substituted, but substitutions are allowed in most cases. If a testlet requires materials, the TIP will state the specific materials mentioned in the testlet and describe their attributes so that test administrators can find appropriate substitutions. For more information about substituting materials, see the TEST ADMINISTRATION MANUAL sections titled Teacher-Administered Testlets and Retrieve the Testlet Information Page and Gather Materials. .

Since the DLM system uses adaptive delivery to assign a linkage level for each testlet, the system provides the TIP when each testlet is assigned. Therefore, the exact materials needed to assess each student are unknown prior to the opening of the spring assessment window. 

The following list contains materials commonly needed in mathematics testlets and gives test administrators more opportunity to prepare for the mathematics alternate assessment prior to the opening of the assessment window. The tables in this document summarize lists of materials per grade level for general testlets and, where appropriate, for students who are blind or have visual impairments.

Materials may be substituted unless the TIP specifically states, “No substitutions allowed.” 

Hints for using this list

  • Look at the whole list for each grade and find materials that can meet multiple purposes. 
    Note the types of materials mentioned more than once.
  • Find materials that already exist in the classroom or are easily found in the school building.
  • Pick materials that are familiar to the student.
  • Remember that in most cases, materials can be substituted if they have the same attributes as those on the list. Examples of substitutions are found in Table 1.
  • Materials substitutions are listed for individual testlets on the corresponding TIP.
  • The student’s safety should be the primary concern when choosing materials or substitutions.

Example Materials Description

Possible Solution

Two sets of identical objects packaged together (packs of crayons, pencils, and markers)

Two identical packs of flash cards

Two objects that are the same size, and one object that is smaller than the other two

Two flash cards that are the same size and a smaller playing card

12 object As

12 congruent triangles

The following information is contained in the accordions below:
  • Lists by grade of materials commonly used in mathematics testlets.
  • Lists by grade of materials that may be used to administer testlets to students who are blind or have visual impairments. These mathematics testlets are general testlets adapted to be more accessible for students who are blind or have visual impairments.
Grade 3

Common Materials Used to Administer Testlets for Grade 3
1 book (less than a foot long)  
1 box  
1 container (one foot or longer)  
1 crayon box  
1 crumpled piece of paper  
1 cup  
1 large piece of paper  
1 large tube sock  
1 piece of notebook paper  
1 rubber band (or piece of string)  
1 ruler  
1 small ankle sock  
1 small piece of paper  
1 smooth piece of paper  
2 gloves  
2 identical blocks  
2 identical checkers  
2 identical pens  
2 paper plates of which 1 is whole and 1 is in parts  
2 plates of which 1 is large and 1 is small  
2 ribbons of which 1 is one foot or longer and 1 is short  
2 sponges of which 1 is whole and 1 is in parts  
3 pieces of string of which 1 is 1 foot, 1 is 2 feet, and 1 is 3 feet  
5 glue sticks of which at least 2 are identical  
5 pencils of which at least 1 is long and 1 is short  
7 erasers of which at least 2 are identical  
8 craft sticks  
8 crayons of which at least 1 is long & thin, 1 is long & thick, and 1 is short & thick  
8 markers  
9 dominoes  
10 connecting cubes  
10 index cards  
10 paper bowls  
16 circles  
30 cubes of which at least 1 is large and 1 is small  
40 objects to use as counters in a container  
cards numbered 1 to 30  
enough unit cubes to measure the length of the notebook paper  
yardstick with feet clearly marked

Common Materials Used to Administer Testlets for Grade 3 Students Who Are Blind or Have Visual Impairments
1 addition sign  
1 circle divided into 4 unequal parts  
1 circle divided into fourths  
1 circle divided into halves  
1 circle divided into thirds  
1 circle representing 1/10  
1 circle representing 1/2  
1 circle representing 1/3  
1 circle representing 1/4  
1 continuous substance  
1 eight-inch object  
1 ellipse  
1 equal sign  
1 five-inch object  
1 four and a half-inch object  
1 hexagon divided into halves  
1 hundreds block  
1 long object D  
1 medium right scalene triangle  
1 medium trapezoid  
1 octagon  
1 one-inch object  
1 parallelogram  
1 pentagon  
1 rectangle divided into 2 equal columns  
1 rectangle divided into 2 equal rows and 2 equal columns  
1 rectangle divided into 2 equal rows and 4 unequal columns  
1 rectangle divided into 2 unequal columns  
1 rectangle divided into 2 unequal rows and 2 unequal columns  
1 rectangle divided into 3 equal rows and 2 equal columns  
1 rectangle divided into 3 unequal parts  
1 rectangle divided into thirds  
1 rectangle representing 1/10  
1 rectangle representing 1/2  
1 rectangle representing 1/3  
1 rectangle representing 1/4  
1 seven-inch object  
1 short object C  
1 six-inch object 
1 square divided into halves  
1 subtraction sign  
1 tactile material to create groups  
1 tactile number chart  
1 tactile picture graph  
1 ten-inch object  
1 thousands cube  
1 three-inch object  
1 triangle divided into halves  
1 two-inch object  
2 circles divided into 2 unequal parts  
2 circles divided into 3 unequal parts  
2 four-inch objects  
2 hexagons of which 1 is large and 1 is small  
2 medium isosceles triangles of which 1 is right and 1 is acute  
2 medium objects  
2 rhombi of which 1 is medium & whole and 1 is divided into halves  
2 small objects  
2 stars of which 1 is whole and 1 is divided into halves  
2 tactile bar graphs  
3 medium congruent rectangles  
3 tactile rulers  
5 large objects  
9 circles of which 3 are large, 3 are medium, and 3 are small  
9 equilateral triangles of which 3 are large & congruent, 3 are medium & congruent, and 3 are small & congruent  
9 squares of which 3 are large & congruent, 3 are medium & congruent, and 3 are small & congruent  
12 object Bs of which at least 1 is long and 1 is short  
12 ten-dollar bills  
13 tens  
18 containers of which at least 6 are identical  
19 dimes  
20 ones  
63 object As of which at least 1 is long and 1 is short

Grade 4

Common Materials Used to Administer Testlets for Grade 4
1 bag  
1 balance scale  
1 ball  
1 clear 1/2-gallon pitcher  
1 clear 4-cup measuring cup with the number of cups clearly marked  
1 empty coffee can  
1 glove  
1 plastic bottle  
1 rubber band (or piece of string)  
2 baskets  
2 bowls of which 1 is large and 1 is small  
2 highlighters  
2 identical blocks  
2 identical craft sticks  
2 identical erasers  
2 identical folders  
2 identical markers  
2 identical notebooks  
2 identical pens  
2 paper plates of which 1 is whole and 1 is in parts  
2 pots  
2 re-sealable sandwich bags with different amount of rice inside  
2 sponges of which 1 is whole and 1 is in parts  
2 strings of which 1 is long and 1 is short  
2 towels  
3 cups of which 2 are identical & large cups and 1 is small  
3 small boxes, each with a different volume  
5 number cubes  
6 counters  
6 paperclips  
7 colored pencils  
7 crayons  
10 index cards  
10 paper bowls  
10 pencils  
20 marbles to use as informal units  
50 cotton balls to use as informal units  
cubes to measure volume  
food coloring  
pennies to measure mass 
water

Common Materials Used to Administer Testlets for Grade 4 Students Who are Blind or Have Visual Impairments
1 circle divided into 2 unequal parts  
1 circle divided into 3 unequal parts  
1 circle divided into halves  
1 circle divided into thirds  
1 circle representing 1/2  
1 circle representing 1/4  
1 circle representing 2/2  
1 circle representing 2/3  
1 circle representing 4/4  
1 circle representing fourths  
1 container about 2 times the size of the small container  
1 container about 20 times the size of the small container  
1 continuous substance  
1 cube measuring 1 x 1 x 1  
1 dime  
1 nickel  
1 one-dollar bill  
1 penny  
1 pentagon divided into 2 unequal parts  
1 pentagon divided into 3 unequal parts  
1 pentagon divided into halves  
1 quarter  
1 rectangle divided into 2 unequal parts  
1 rectangle divided into 3 unequal parts  
1 rectangle divided into halves  
1 rectangle divided into thirds  
1 rectangle measuring 1 x 2  
1 rectangle measuring 2 x 5  
1 rectangle measuring 7 x 3  
1 rectangle measuring 8 x 5  
1 rectangle representing 1/2  
1 rectangle representing 2/2  
1 rectangle representing 2/3  
1 rectangle representing fourths  
1 rectangle representing sixths  
1 rectangle with a tactile border  
1 rectangle with discernable square units measuring 4 x 3  
1 rectangle with discernable square units measuring 4 x 6  
1 rectangle with discernable square units measuring 4 x 7 
1 rectangle with discernible square units measuring 4 x 2  
1 rectangle with discernible square units measuring 5 x 3  
1 rectangle with discernible square units measuring 5 x 4  
1 rectangle with discernible square units measuring 6 x 2  
1 rectangle with discernible square units measuring 6 x 3  
1 rectangle with the area indicated  
1 rectangle with the length indicated  
1 rhombus  
1 small container  
1 square divided into 3 unequal parts  
1 square divided into halves  
1 square measuring 1 x 1  
1 square measuring 2 x 2  
1 square representing 1/2  
1 square representing 1/3  
1 square representing 1/4  
1 square representing 2/2  
1 square representing 3/4  
1 square representing 4/4  
1 square representing eighths  
1 square representing fourths  
1 square representing thirds  
1 square with a tactile border  
1 square with discernable square units measuring 3 x 3  
1 square with discernable square units measuring 5 x 5  
1 star divided into halves  
1 tactile material to create groups  
1 ten-dollar bill  
1 trapezoid  
1 triangle divided into 2 unequal parts  
2 hearts of which 1 is whole and 1 is in 2 unequal parts  
2 squares divided into 2 unequal parts  
3 balance scales  
3 objects of which 1 is small, 1 is 2 times the size of the small object and 1 is 4 times the size of the small object  
3 objects of which 1 is triangular, 1 is rectangular and 1 is round  
3 tactile analog clocks  
4 ovals of which 1 is whole, 1 divided into halves, 1 is divided into 2 unequal parts and 1 is divided into 3 unequal parts  
5 hexagons of which 1 divided into halves, 1 is divided into 3 unequal parts, 2 are divided into 2 unequal parts, and 1 is whole  
6 identical containers  
6 pentagons  
6 squares  
6 triangles  
7 circles  
7 objects of which 1 is heavier than 2 cube weights, 1 is heavier than 3 cube weights, 1 is heavier than 1 cube weight, 1 is lighter than 8 cube weights, 1 is lighter than 18 cube weights, 1 is lighter than 10 cube weights, and 1 is equal to 10 cube weights  
8 tactile digital clocks  
10 different non-money objects (objects A–J)  
10 object Cs  
13 angles of which 7 are acute, 3 are obtuse, and 3 are right angles  
19 object Bs  
30 object As  
31 cube weights

Grade 5

Common Materials Used to Administer Testlets for Grade 5
1 container measuring 5” x 8” x 2” filled with unit cubes  
1 crayon  
1 empty container measuring 4” x 4” x 3”  
1 empty container measuring 5” x 8” x 2”  
1 empty container measuring 6” x 2” x 3”  
1 empty rectangular container measuring 6” x 5” x 2”  
1 empty rectangular container measuring 5” x 4” x 2”  
1 large basket  
1 rubber band (or piece of string)  
1 small box  
1 towel  
2 identical cards  
2 index cards of which 1 is large and 1 is small  
2 markers  
2 water bottles of which 1 is empty and 1 is filled with a colored liquid  
5 blocks  
5 connecting cubes  
5 paintbrushes  
6 cups of which at least 2 are identical and 2 are plastic  
7 number cubes of which at least 2 are identical  
8 erasers of which at least 2 are identical  
8 glue sticks  
8 pencils  
8 pens  
8 snap cubes

Common Materials Used to Administer Testlets for Grade 5 Students Who Are Blind or Have Visual Impairments
1 circle divided into 2 unequal parts  
1 circle divided into halves  
1 circle representing 1/10  
1 circle representing 1/3  
1 circle representing 1/4  
1 circle representing 10/10  
1 circle representing 2/3  
1 circle representing 2/8  
1 circle representing 3/3  
1 circle representing 3/4  
1 circle representing 5/10  
1 container packed with unit cubes  
1 equal-to sign  
1 heart  
1 irregular pentagon  
1 large pentagon  
1 large rectangle  
1 medium pentagon  
1 obtuse scalene triangle  
1 parallelogram  
1 rectangle divided 3 unequal parts  
1 rectangle divided into 4 equal parts  
1 rectangle divided into 4 unequal parts  
1 rectangle representing 1/10  
1 rectangle representing 1/3  
1 rectangle representing 10/10  
1 rectangle representing 2/3  
1 rectangle representing 2/5  
1 rectangle representing 2/8  
1 rectangle representing 3/3  
1 rectangle representing 3/8  
1 rectangle representing 4/10  
1 rectangle representing 5/10  
1 rectangle representing 6/8  
1 rectangle representing 7/10  
1 rectangle representing 8/10  
1 rectangular prism measuring 3 x 2 x 2  
1 rectangular prism with discernible cubic units measuring 2 x 1 x 2  
1 rectangular prism with discernible cubic units measuring 3 x 1 x 1
1 rectangular prism with discernible cubic units measuring 3 x 1 x 2  
1 rectangular prism with discernible cubic units measuring 4 x 1 x 1  
1 rectangular prism with discernible cubic units measuring 4 x 1 x 2  
1 regular pentagon  
1 rhombus  
1 set of 20 objects  
1 small pentagon  
1 small pyramid  
1 small rectangle  
1 small right triangle  
1 square divided into 2 unequal parts  
1 square divided into 3 unequal parts  
1 square divided into fourths  
1 square divided into halves  
1 square representing 1/2  
1 square representing 1/3  
1 square representing 3/4  
1 tactile material to create groups  
1 tactile table  
1 triangular prism  
2 circles divided into 3 unequal parts  
2 congruent ellipses  
2 congruent hexagons  
2 congruent right triangles  
2 congruent stars  
2 congruent trapezoids  
2 greater than/less than signs  
2 identical rectangular prisms  
2 isosceles triangles of which 1 is acute and 1 is right  
2 large squares  
2 large triangles  
2 medium rectangles  
2 medium squares  
2 similar cones of which 1 is large and 1 is small  
2 similar hexagons  
2 similar rectangular prisms of which 1 is large and 1 is small  
2 small squares  
2 spheres of which 1 is large and 1 is small  
2 squares divided into 4 unequal parts  
3 congruent circles  
3 congruent squares  
3 cubes of which 1 is large and 2 are small & congruent 
3 cylinders of which 2 are small & congruent and 1 is large & similar  
3 large circles  
3 medium circles  
3 tactile bar graphs  
3 tactile number lines  
3 tactile picture graphs  
4 congruent pentagons  
4 congruent rectangles  
4 hexagons of varying sizes  
4 tactile line plots  
6 medium equilateral triangles  
6 small circles  
7 object Bs  
8 ones  
8 tens  
15 object As of which at least 3 are long, 3 are medium length, and 3 are short  
17 connecting cubes  
tactile numbers 

Grade 6

Common Materials Used to Administer Testlets for Grade 6
1 bag  
1 empty box of tea bags  
1 empty shoe box  
1 empty tissue box  
1 rubber band (or piece of string)  
2 packs of gum  
3 blocks that vary in size  
3 empty rectangular containers of any size  
4 books of which 2 are hard cover and 2 are soft cover  
4 markers  
4 sponges varying in size of which 2 are dry and 2 are wet  
6 erasers  
6 glue sticks  
6 pencils of which at least 3 vary in length  
7 cups of which 2 are plastic and 5 are paper  
7 pieces of chalk  
7 wooden craft sticks  
8 folders  
8 index cards  
8 pens  
9 crayons  
200 one-inch unit cubes  
more than enough unit cubes to fill the largest container

Common Materials Used to Administer Testlets for Grade 6 Students Who Are Blind or Have Visual Impairments
1 circle divided into 3 unequal parts  
1 circle divided into halves  
1 circle representing 1/10  
1 circle representing 1/3  
1 circle representing 1/4  
1 container with 10 compartments  
1 container with 4 compartments  
1 continuous substance  
1 hexagon  
1 rectangle divided into 4 equal parts  
1 rectangle measuring 1 x 2  
1 rectangle measuring 1/3 x 3  
1 rectangle measuring 10 x 12  
1 rectangle measuring 5 x 7  
1 rectangle measuring 6 x 10  
1 rectangle measuring 6 x 4  
1 rectangle measuring 8 x 9  
1 rectangle representing 1/2  
1 rectangle with 1 half shaded  
1 rectangle with discernable area  
1 rectangle with discernable perimeter  
1 rectangle with discernible square units measuring 2 x 3  
1 rectangle with discernible square units measuring 2 x 6  
1 rectangle with discernible square units measuring 3 x 4  
1 rectangle with discernible square units measuring 3 x 5  
1 rectangle with discernible square units measuring 4 x 5  
1 rectangle with discernible square units measuring 4 x 6  
1 rectangle with discernible square units measuring 4 x 7  
1 rectangle with the area shaded  
1 rectangle with the border shaded  
1 rectangular prism measuring 4 x 3 x 2  
1 rectangular prism measuring 5 x 4 x 3  
1 rectangular prism with discernible cubic units measuring 2 x 2 x 1  
1 rectangular prism with discernible cubic units measuring 3 x 2 x 1  
1 rectangular prism with discernible cubic units measuring 4 x 3 x 1  
1 rectangular prism with discernible cubic units measuring 6 x 4 x 1  
1 rectangular prism with discernible cubic units measuring 8 x 2 x 4  
1 square divided into 3 unequal parts  
1 square divided into halves 
1 square measuring 1 x 1  
1 square measuring 2 x 2  
1 square representing 1/3  
1 square representing 1/4  
1 square representing 3/4  
1 square with discernible square units measuring 3 x 3  
1 square with discernible square units measuring 5 x 5  
1 tactile material to create groups  
1 tactile number line  
1 tactile picture graph  
1 unit cube  
2 circles divided into 2 unequal parts  
2 rectangles divided into 4 unequal parts  
2 squares divided into 2 unequal parts  
2 squares of which 1 is small and 1 is large  
2 squares representing 1/2  
2 tactile line plots  
3 containers with 3 compartments each  
3 tactile line graphs  
3 tactile thermometers  
6 identical containers  
6 tactile bar graphs  
14 object Bs  
28 objects As

Grade 7

Common Materials Used to Administer Testlets for Grade 7
1 ball  
1 basket  
1 box  
1 large container  
1 long pencil  
1 rubber band (or piece of string)  
1 short pencil  
2 identical 12-count boxes of colored pencils  
2 identical erasers  
2 identical notebooks  
2 identical notecards  
2 identical pencils  
2 pieces of paper of which 1 is smooth and 1 is crumpled  
5 glue sticks  
5 markers  
5 paintbrushes  
5 paper cups of which at least 1 is large, 1 is small, and 2 are identical  
5 pens  
5 sponges  
6 crayons  
7 dominoes  
8 game cards

Common Materials Used to Administer Testlets for Grade 7 Students Who Are Blind or Have Visual Impairments
1 circle divided into 3 unequal parts  
1 circle divided into fourths  
1 circle divided into halves  
1 circle representing 2/4  
1 circle representing 3/4  
1 hexagon  
1 irregular pentagon  
1 large pentagon  
1 line segment  
1 medium isosceles triangle  
1 medium pentagon  
1 medium scalene triangle  
1 medium square  
1 medium trapezoid  
1 object with the measurable attributes of height, length, and weight  
1 octagon  
1 oval  
1 parallelogram  
1 rectangle divided into tenths  
1 rectangle measuring 5 x 10  
1 rectangle measuring 7 x 3  
1 rectangle representing 3/10  
1 rectangle representing 6/10  
1 rectangle representing 7/10  
1 rectangle with discernible square units measuring 2 x 4  
1 rectangle with discernible square units measuring 3 x 2  
1 rectangle with discernible square units measuring 4 x 3  
1 rectangle with discernible square units measuring 5 x 4  
1 rectangle with the 2 long sides indicated  
1 rectangle with the area indicated  
1 rectangle with the length indicated  
1 rectangle with the perimeter indicated  
1 small cone  
1 small pentagon  
1 square with discernible square units measuring 5 x 5  
1 star  
1 tactile material to create groups  
1 tactile number line  
2 circles divided into 2 unequal parts 
2 medium rectangles  
2 rectangles representing 4/10  
2 regular pentagons  
2 rhombi of which at least 1 is medium  
2 right triangles of which at least 1 is medium  
2 small cubes  
2 small cylinders  
2 small pyramids  
2 small spheres  
2 subtraction signs  
2 tetrahedrons  
2 triangular prisms  
3 circles of which 1 is large, 1 is medium, and 1 is small  
3 circles representing 1/4  
3 equilateral triangles of which 2 are medium and 1 is small  
3 object Bs  
3 rectangular prisms of which 2 are small and 1 is a different size  
3 tactile coordinate grids  
4 addition signs  
4 sets of objects where each set contains 1 whole object and 1 part of an identical object (objects A-D)  
5 number cubes  
55 object As

Grade 8

Common Materials Used to Administer Testlets for Grade 8
1 clear pencil case or plastic bag  
1 rubber band (or piece of string)  
2 baskets of which 1 is large and 1 is small  
2 bowls of which 1 is large and 1 is small  
2 connecting cubes  
2 containers of which 1 is closed and 1 is open  
2 pieces of construction paper of which 1 is large and 1 is small  
2 plastic cups of which 1 is large and 1 is small  
3 books that vary in size  
3 boxes of which 1 is large & closed, 1 is large & open, and 1 is small & open  
3 circles that vary in size  
3 pieces of paper that vary in size  
3 triangles that vary in size  
4 rectangles of which 2 are large and 2 are small  
4 ribbons of which 2 are long & identical and 2 are short & identical  
4 sponges of which 2 are wet and 2 are dry  
5 blocks  
5 colored pencils  
5 crayons of which at least 3 vary in length  
5 highlighters  
5 markers  
5 pencils of which 2 are long, 2 are short, and 1 is a different length  
5 pens  
6 craft sticks of which at least 3 vary in size  
7 paintbrushes  
8 checkers  
8 erasers of which at least 1 is large and 1 is small

Common Materials Used to Administer Testlets for Grade 8 Students Who Are Blind or Have Visual Impairments
1 addition sign  
1 angle measuring 10 degrees  
1 angle measuring 20 degrees  
1 angle measuring 50 degrees  
1 angle measuring 60 degrees  
1 angle measuring 70 degrees  
1 angle measuring 80 degrees  
1 arc  
1 circle  
1 circle representing 1/2  
1 circle representing 1/3  
1 circle representing 4/4  
1 circle representing 6/8  
1 colon  
1 container of 6 object As  
1 cube  
1 cylinder  
1 decimal point  
1 dollar sign  
1 equal-to sign  
1 exclamation point  
1 fraction bar  
1 hexagon  
1 line segment  
1 object A separate from the container  
1 obtuse angle  
1 pair of adjacent angles forming an acute angle  
1 pair of complementary angles  
1 pair of supplementary angles  
1 point  
1 ray  
1 rectangle measuring 10 x 7  
1 rectangle measuring 12 x 9  
1 rectangle measuring 18 x 9  
1 rectangle measuring 3 x 4  
1 rectangle measuring 3 x 7  
1 rectangle measuring 4 x 2  
1 rectangle measuring 6 x 5  
1 rectangle measuring 6 x 7
1 rectangle measuring 9 x 3  
1 rectangle representing 10/10  
1 rectangle representing 3/4  
1 rectangle representing 3/8  
1 rectangle representing 4/4  
1 rectangle representing 4/6  
1 rectangle representing 4/8  
1 rectangle representing 6/8  
1 rectangle representing 8/8  
1 rectangular prism measuring 3 x 3 x 6  
1 rectangular prism measuring 3 x 4 x 8  
1 rectangular prism measuring 6 x 10 x 5  
1 rectangular prism measuring 6 x 4 x 2  
1 rectangular prism measuring 9 x 6 x 8  
1 set of 30 identical objects  
1 square  
1 subtraction sign  
1 tactile coordinate plane  
1 tactile line plot  
1 tactile material to create groups  
2 angles measuring 30 degrees  
2 angles measuring 40 degrees  
2 circles representing 2/8  
2 circles representing 4/8  
2 greater than/less than signs  
2 rectangles representing 1/4  
2 rectangles representing 2/4  
2 rectangles representing 2/8  
2 right angles  
3 congruent rectangles  
3 materials to indicate part of the number  
3 tactile bar graphs  
3 tactile function graphs  
3 tactile function tables  
3 tactile picture graphs  
3 tactile tables  
3 tactile tally charts  
4 containers with 10 compartments each  
5 sets of objects where each set contains 1 whole object and 1 part of an identical object (objects A–E)  
40 object As  
tactile numbers and decimals

Grades 9–12 (High School)

Common Materials Used to Administer Testlets for High School
1 bottle  
1 hexagon  
1 large bowl  
1 rubber band (or piece of string)  
1 yardstick  
2 closed containers  
2 counter chips  
2 crumpled pieces of paper  
2 folded pieces of paper  
2 identical bowls  
2 identical cups  
2 identical flat pieces of paper  
2 identical highlighters  
2 identical notebooks  
2 identical number cubes  
2 identical plates  
2 identical rulers  
2 open containers  
2 plates varying in size  
2 playing cards  
2 squares  
2 strings of which 1 is long and 1 is short  
3 containers that vary in size  
3 cups that vary in size  
3 dominoes  
3 pieces of paper that vary in size  
3 pom-poms that vary in size  
3 sponges of which 2 are identical & dry and 1 is wet  
4 boxes of which 2 are open and 2 are closed  
4 jars of which 2 are empty & vary in size and 2 are full & vary in size  
4 straws of which 2 are bent & vary in size and 2 are straight & vary in size  
5 books  
5 colored pencils  
5 index cards  
6 craft sticks of which at least 2 are identical  
6 erasers of which at least 4 are neither too large or too small to easily subitize by touch or sight  
6 glue sticks of which at least 2 are identical  
6 pencils of which at least 2 are identical and 3 vary in length  
6 pens of which at least 2 are identical  
7 blocks of which at least 2 are identical  
7 checkers  
7 cotton balls  
7 folders  
7 keys  
7 markers of which at least 2 are identical  
8 crayons of which at least 2 are identical  
9 coins 

Common Materials Used to Administer Testlets for High School Students Who Are Blind or Have Visual Impairments
1 arrow  
1 circular object  
1 cone net  
1 cube net  
1 cylinder net  
1 cylindrical object  
1 equal-to symbol  
1 hundred  
1 large cylinder  
1 large similar trapezoid  
1 line  
1 line segment  
1 medium similar cylinder  
1 medium trapezoid  
1 number cube  
1 obtuse isosceles triangle  
1 point  
1 quarter  
1 ray  
1 rectangular object  
1 rectangular prism net  
1 right isosceles triangle  
1 set of non-perpendicular intersecting line segments  
1 set of parallel line segments  
1 set of parallel lines  
1 set of perpendicular line segments  
1 set of perpendicular lines  
1 small rhombus  
1 small trapezoid  
1 spherical object  
1 subtraction symbol  
1 tactile material to create groups  
1 tactile spinner  
1 tactile table  
1 ten  
1 thousand  
1 triangular object  
1 triangular prism net  
2 congruent cones
2 congruent cylinders  
2 congruent parallelograms  
2 congruent rectangles  
2 congruent rectangular prisms  
2 congruent rhombi  
2 congruent triangular prisms  
2 ellipses of which 1 is large, 2 are medium & congruent, and 1 is small  
2 large congruent trapezoids  
2 large rectangles  
2 medium congruent right scalene triangles  
2 sets of non-perpendicular intersecting lines  
2 similar cones  
2 similar equilateral triangles of which 1 is medium and 1 is large  
2 similar hexagons of which 1 is large and 1 is medium  
2 similar isosceles triangles of which 1 is large and 1 is small  
2 similar octagons of which 1 is large and 1 is medium  
2 similar right scalene triangles of which 1 is large and 1 is small  
2 similar spheres of which 1 is large and 1 is medium  
2 small congruent hearts  
2 small congruent stars  
2 small congruent triangles  
2 small rectangles  
2 tactile coordinate planes  
3 angles of which 1 is acute, 1 is obtuse, and 1 is right  
3 congruent trapezoids  
3 cubes of which 1 is small, 1 is medium, and 1 is large  
3 tactile bar graphs  
3 tactile coordinate grids  
3 tactile line graphs  
3 tactile line plots  
3 tactile number lines  
3 tactile picture graphs  
3 tactile pie charts  
4 addition signs  
4 circles of which 2 are small & congruent, 1 is medium, and 1 is large  
4 greater/less than signs  
4 pentagons of which 1 is large, 2 are medium & congruent, and 1 is small & similar  
4 playing cards  
4 pyramids of which 1 is tall, 1 is medium, 1 is small & short, and 1 is large, short, & similar  
4 tactile function tables  
5 squares of which 3 are large & congruent and 2 are small & congruent 
7 tactile function graphs  
13 long, thin rectangular prisms  
18 ones  
39 object As  
65 objects  
tactile letters and numbers