Mathematics Materials Collections
Year End
Spring 2016
DLM testlets sometimes call for the use of specific materials or manipulatives. Materials are identified in
the Testlet Information Page (TIP) for each testlet. Sometimes materials are required and cannot be
substituted, but substitutes are allowed in most cases. Each TIP states whether materials are needed for a
testlet. If materials are to be used in a testlet, 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 objects, see the TEST ADMINISTRATION MANUAL section titled TeacherAdministered Tests.
Since the DLM system uses dynamic routing to assign a linkage level for each testlet, the TIP is provided
when each testlet is assigned. That means the materials needed in order to assess each student are
unknown before the test window opens.
To give test administrators more opportunity to prepare for the math assessment before the testing
window opens, DLM has compiled a list of materials commonly needed in math testlets. 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. When materials are described in parentheses, these are
examples of objects that can be used in some of the testlets. Again, materials may be substituted unless
the TIP specifically states “No substitutions allowed.”
Hints for using this list:
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Find things that already exist in the classroom or are easily found somewhere in the building.
Pick materials that are familiar to the student.
Look at the whole list for each grade and find objects that can meet multiple purposes. What types
of objects are mentioned more than once?
Remember that in most cases it will be okay to substitute materials as long as they are like the ones
on the list. Examples of possible substitutions are found in the table below.
Example Materials Description
2 sets of identical objects packaged together
(packs of crayons, pencils, markers)
2 objects that are the same size, and one
object that is smaller than the other two
Possible Substitution
use two identical packs of flash cards
use two flash cards that are the same size and a
playing card
DLM Common Mathematics Materials – Spring 2016
Page 1 of 9
Grade
3
Grade
3
Common Materials Used to Administer Testlets
• 2 containers (plastic container, jar, etc.)
• 2 identical objects separated into parts (pens, markers, etc.)
• 2 packages of identical objects (crayons, flash cards, gum, etc.)
• 2 sets of 7 identical objects (buttons, crayons, etc.)
• 3 objects to measure length
• 3 sets of 2 identical objects (buttons, crayons, etc.)
• 3 similar objects that vary by one attribute (buttons, crayons, etc.)
• 50 counters (plastic chips, checkers, etc.)
• Ruler
• Yardstick
Common Materials Used to Administer Testlets for Students Who Are Blind or Who
Have Visual Impairments
• 2 cones (wooden blocks, cardboard, etc.)
• 2 containers (plastic container, jar, etc.)
• 2 fraction sets with fractional parts up to tenths (fraction pizzas, fraction circles, etc.)"
• 2 identical packages of items (crayons, flash cards, gum, etc.)
• 2 objects to measure
• 2 rhombuses (pattern blocks, construction paper, etc.)
• 2 sets of tactile numbers 0-9 (magnetic, cardboard, etc.)
• 2 trapezoids (pattern blocks, construction paper, etc.)
• 3 objects that vary in length
• 3 stars: 1 whole, 1 divided into 6 parts, 1 divided into four parts (pattern blocks,
construction paper, etc.)
• 11 squares: 2 large, 2 medium, 3 small, 1 of each square divided into 2 equal parts, 4
equal parts, 2 unequal parts, 3 unequal parts (pattern blocks, construction paper, etc.)
• 13 triangles: 9 equilateral: 3 large, 3 medium, 3 small, 1 scalene triangle divided into
parts, 2 right triangles (pattern blocks, construction paper, etc.)
• 14 rectangles: 3 large, 2 medium, 3 small, 1 of each rectangle divided into 2 equal parts,
3 equal parts, 4 equal parts, 2 of each circle divided into 2 unequal parts, 3 unequal
parts, and 4 unequal parts. (pattern blocks, construction paper, etc.)
• 16 circles: 3 large, 3 medium, 3 small, 1 of each circle divided into 2 equal parts, 4 equal
parts, 2 unequal parts, and 3 unequal parts (pattern blocks, construction paper, etc.)
• 100's grid
• Material for bundling (string, rubber band, etc.)
• Materials to create tactile graphs (bar, line, & picture) and charts
• Scale (2 pan balance, digital, etc.)
• Tactile clocks: 1 analog, 3 digital
• Tactile symbols: 6 symbols (3 identical, 3 different) 6 letters (3 identical, 3 different)
DLM Common Mathematics Materials – Spring 2016
Page 2 of 9
Grade
4
Grade
4
Common Materials Used to Administer Testlets
• 1 pair of identical objects (buttons, blocks, etc.)
• 1/2 Gallon Pitcher
• 2 containers (plastic container, jar, etc.)
• 2 identical packages of items (crayons, flash cards, gum, etc.)
• 2 sets of 3 similar objects that vary by one attribute (buttons, blocks, etc.)
• 2 sets of 7 objects (pattern blocks, toys, etc.)
• 20-30 objects to use as weights (cubes, pennies, etc.)
• 4 C measuring cup
• 4 objects that can be measured
• Food coloring
• Fraction set with fractional parts up to tenths (fraction pizzas, fraction circles, etc.)
• Scale (2 pan balance, digital, etc.)
• Water
Common Materials Used to Administer Testlets for Students Who Are Blind or Who Have
Visual Impairments
• 4 Objects to weigh
• 5 Rectangles: 2 whole, 1 of each rectangle divided into 2 equal parts, 3 equal parts, 4
equal parts, 6 equal parts, 4 unequal parts (paper, cardboard, etc.)
• 6 containers: 2 large, 2 medium, 2 small (plastic container, jar, etc.)
• 6 Triangles: 1 right, 4 equilateral, 1 divided into 2 unequal parts (paper, cardboard,
etc.)
• 8 counters (plastic chips, checkers, etc.)
• 8 Squares: 4 whole, 1 of each divided into 2 equal parts, 4 equal parts, 2 unequal parts,
4 unequal parts (paper, cardboard, etc.)
• 9 Circles: 4 whole, 1 of each circle divided into 2 equal parts, 3 equal parts, 4 equal
parts, 2 unequal parts, 3 unequal parts (paper, cardboard, etc.)
• 9 unit square tiles
• Enough unit cubes to fill each container
• Materials to create tactile symbols: arch, line, point, ray, line segment, line with a
square on it, line with a triangle on it, intersecting lines, parallel lines; 11 angles:5 acute
(3 identical, 2 different), 3 right, 3 obtuse (paper, straws, etc.)
• Money (real or play) (1-$10 bill, 1 each Quarter, Dime, Nickel, Penny.)
• Scale (2 pan balance, digital, etc.)
• Set of weights (ounces & pounds)
DLM Common Mathematics Materials – Spring 2016
Page 3 of 9
Grade
5
Grade
5
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Common Materials Used to Administer Testlets
2 containers (plastic container, jar, etc.)
2 identical packages of items (crayons, flash cards, gum, etc.)
2 sets of 2 identical objects (pattern blocks, toys, etc.)
3 rectangular containers of different sizes
Enough unit cubes to fill largest container
3 sets of 5 objects (buttons, crayons, etc.)
4 similar objects that vary by one attribute (books, papers, etc.)
10 counters (checkers, plastic chips, etc.)
Material to bundle (string, rubber band, etc.)
Ruler
String cut into different lengths
Yardstick
Common Materials Used to Administer Testlets for Students Who Are Blind or Who Have
Visual Impairments
• 3 sets of objects to measure, 1 small, 1 medium, 1 large
• 4 Tactile Clocks - 2 analog, 2 digital
• 5 pencils
• 6 containers: 3 rectangular containers (3x4), (2x3), (2x4), 3 other containers
• 15 Triangles: 12 whole equilateral triangles - 3 small, 6 medium, 3 large; 1 of each
triangle divided into 2 unequal parts, 4 unequal parts, 3 equal parts (paper, cardboard,
etc.)
• 19 Rectangles: 8 whole, 2 small, 6 medium, 2 large; 1 of each rectangle divided into 10
equal parts, 8 equal parts, 6 equal parts, 4 equal parts, 3 equal parts, 2 equal parts, 2
unequal parts (paper, cardboard, etc.)
• 21 Squares: 15 whole - 5 small, 5 medium, 5 large; 1 of each square divided into 2 equal
parts, 3 equal parts, 4 equal parts, 2 unequal parts, 3 unequal parts, 4 unequal parts
(paper, cardboard, etc.)
• 22 Circles: 12 whole, 2 small, 5 medium, 5 large; 2 of each circle divided into 2 unequal
parts, 3 unequal parts, 4 unequal parts; 1 of each circle divided into 2 equal parts, 3
equal parts, 4 equal parts, 8 equal parts, 10 equal parts (paper, cardboard, etc.)
• 25 counters (plastic chips, checkers, etc.)
• 2 Dimensional Objects: 2 of each - star, ellipse, heart, trapezoid, hexagon, sphere
(pattern blocks, construction paper, etc.)
• 3 Dimensional Objects: 2 of each (1 large, 1 small) - cylinder, cone, cube (wooden blocks,
cardboard, etc.)
• Base 10 pieces
• Material to bundle (string, rubber band, etc.)
• Materials to create tactile graphs (bar, line, & picture) and charts
• Money (real or play) - 1 Quarter, 1 dime, 1 nickel, 20 pennies
DLM Common Mathematics Materials – Spring 2016
Page 4 of 9
Grade
6
Grade
6
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Common Materials Used to Administer Testlets
3 different size rectangular containers
Enough unit cubes to fill largest rectangular container
7 familiar objects (pattern blocks, toys, etc.)
2 sets of 5 similar objects that vary by one attribute (buttons, crayons, etc.)
2 sets of 2 identical objects (buttons, crayons, etc.)
2 identical packages of items (crayons, flash cards, gum, etc.)
Common Materials Used to Administer Testlets for Students Who Are Blind or Who Have
Visual Impairments
• 3 Rectangles: 1 of each (2x4), (3x4), (5x4) (paper, cardboard, etc.)
• 5 Containers: 1 divided into 8 parts, 1 divided into 10 parts, 1 small, 1 medium, 1 large
(plastic container, jar, etc.)
• 10 Circles: 2 whole, 1 of each circle divided into 2 equal parts, 3 equal parts, 4 equal
parts, 6 equal parts, 10 equal parts, 3 unequal parts, 4 unequal parts, 6 unequal parts
(paper, cardboard, etc.)
• 50 counters (plastic chips, checkers, etc.)
• Enough unit cubes to fill the largest container
• Materials to create tactile graphs (bar, line, & picture) and charts
• Set of 17 identical objects, Set of 5 identical objects (erasers, pencils, markers, etc.)
DLM Common Mathematics Materials – Spring 2016
Page 5 of 9
Grade
7
Grade
7
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Common Materials Used to Administer Testlets
2 sets of 2 identical objects (pattern blocks, toys, etc.)
2 identical packages of items (crayons, flash cards, gum, etc.)
Set of 7 identical objects, set of 3 identical objects (pattern blocks, toys, etc.)
2 sets of 3 similar objects that vary by one attribute (buttons, crayons, etc.)
15 counters (plastic chips, checkers, etc.)
Common Materials Used to Administer Testlets for Students Who Are Blind or Who Have
Visual Impairments
• 2 sets of tactile numbers 0-9 (magnetic, cardboard, etc.)
• 3 containers (plastic container, jar, etc.)
• 3 Dimensional shapes: 3 of each (1 small, 1 medium, 1 large)- cylinder, pyramid, cube,
sphere (wooden blocks, cardboard, etc.)
• 3 objects to measure weight and length
• 4 pairs of identical objects (pattern blocks, toys, etc.)
• 4 Triangles: 2 medium equilateral triangles, 1 large right triangle, 1 small right triangle
• 6 Circles: 2 large, 2 medium, 2 small (pattern blocks, construction paper, etc.)
• 6 Rectangles: 1 large; 1 of each (3x2) and (4x2); 1 of each rectangle divided into 2 equal
parts, 2 unequal parts, 4 unequal parts (pattern blocks, construction paper, etc.)
• 12 Squares: 9 whole - 3 small, 3 medium, 3 large; 1 of each (3x3) and (2x2) (pattern
blocks, construction paper, etc.)
• 30 counters (plastic chips, checkers, etc.)
• Ruler
• Scale (2 pan balance, digital, etc.)
• Tactile coordinate grid - 8x8
• Tactile symbols: 3 of each - line, ray, line segment, arrow, point; 2 of each angle (acute,
right, obtuse), 2 hearts, pentagon (construction paper, straws, etc.)
DLM Common Mathematics Materials – Spring 2016
Page 6 of 9
Grade
8
Grade
8
Common Materials Used to Administer Testlets
• 2 identical packages of items (crayons, flash cards, gum, etc.)
• 2 pairs of identical objects (buttons, crayons, etc.)
• 2 pattern blocks
• 3 sets of 3 objects (buttons, crayons, etc.)
• 4 similar objects that vary by one attribute (buttons, crayons, etc.)
• 7 familiar objects (pattern blocks, toys, etc.)
Common Materials Used to Administer Testlets for Students Who Are Blind or Who Have
Visual Impairments
• 1 Cube (wooden block, cardboard, etc.)
• 3 containers: 1 small, 1 medium, 1 large
• 5 Rectangles: 1 of each rectangle (3x5), (5x10), (12x9), (18x9), (6x5) (paper, cardboard,
etc.)
• 9 Squares: 3 large, 3 medium, 3 small (pattern blocks, construction paper, etc.)
• 13 Circles: 2 large, 2 medium, 2 small; 1 of each circle divided into 3 unequal parts, 3
equal parts, 4 unequal parts, 4 equal parts (pattern blocks, construction paper, etc.)
• 18 Triangles: 2 of each small, medium and large right triangles, 2 of each small, medium
and large equilateral triangles, 2 of each small, medium and large scalene triangles
(pattern blocks, construction paper, etc.)
• 50 counters (plastic chips, checkers, etc.)
• Enough unit cubes to fill the largest container
• Materials to create tactile graphs (bar, line, & picture) and charts
• Objects to measure length, height, and volume
• Tactile symbols: 2 of each - line, ray, line segment, pentagon, hexagon, ellipse, star, oval;
2 of each angle (acute, right, obtuse) (construction paper, straws, etc.)
DLM Common Mathematics Materials – Spring 2016
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Grade
9
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Grade
9
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Grade
10
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Grade
10
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Common Materials Used to Administer Testlets
2 identical packages of items (crayons, flash cards, gum, etc.)
2 pairs of identical objects (pattern blocks, buttons, etc.)
3 sets of 7 objects (pattern blocks, toys, etc.)
3 similar objects that vary by one attribute (buttons, crayons, etc.)
6 straws
25 paperclips
Common Materials Used to Administer Testlets for Students Who Are Blind or
Who Have Visual Impairments
2 Dimensional Shapes: 1 octagon, 1 hexagon (pattern blocks, construction paper, etc.)
3 Dimensional Shapes: 1 rectangular prism, 1 pyramid, 1 cone, 1 cylinder (wooden
blocks, cardboard, etc.)
6 Circles: 2 small, 2 medium, 2 large (pattern blocks, construction paper, etc.)
6 Squares: 2 small, 2 medium, 2 large (pattern blocks, construction paper, etc.)
9 Rectangles: 3 small, 3 medium, 3 large (pattern blocks, construction paper, etc.)
Base Ten Pieces - 10 10's, 17 1's
Materials to create tactile graphs (bar, line, & picture), grids and charts
Money (real or Play) - 30 pennies
Tactile symbols: 2 of each - parallel line, intersecting line, perpendicular line, ray, line
segment, arrow, different size angles (construction paper, straws, etc.)
Common Materials Used to Administer Testlets
2 identical packages of items (crayons, flash cards, gum, etc.)
2 sets of 7 objects (pattern blocks, buttons, etc.)
4 sets of 3 similar objects that vary by one attribute (buttons, crayons, etc.)
Common Materials Used to Administer Testlets for Students Who Are Blind or
Who Have Visual Impairments
2 Dimensional Shapes: 2 pentagons (pattern blocks, construction paper, etc.)
2 sets of tactile letters (magnetic, cardboard, etc.)
2 sets of tactile numbers 0-9 (magnetic, cardboard, etc.)
3 Dimensional Shapes: 1 cone, 1 cube, 1 cylinder (wooden blocks, cardboard, etc.)
4 Circles: 2 small, 2 large (pattern blocks, construction paper, etc.)
4 Triangles: 2 right, 2 equilateral (pattern blocks, construction paper, etc.)
6 Rectangles: 2 small, 2 medium, 2 large (pattern blocks, construction paper, etc.)
6 Squares: 2 small, 2 medium, 2 large (pattern blocks, construction paper, etc.)
Materials to create tactile graphs (bar, line, pie, & picture), coordinate planes, & charts
DLM Common Mathematics Materials – Spring 2016
Page 8 of 9
Grade
11
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Grade
11
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Common Materials Used to Administer Testlets
2 pairs of identical objects (pattern blocks, buttons, etc.)
2 sets of 7 objects (pattern blocks, buttons, etc.)
4 set of 3 objects (pattern blocks, buttons, etc.)
4 similar objects that vary by one attribute (pattern blocks, crayons, etc.)
Common Materials Used to Administer Testlets for Students Who Are Blind or
Who Have Visual Impairments
3 Dimensional Shapes: 1 cone, 1 cube, 1 cylinder, 1 rectangular prism (wooden blocks,
cardboard, etc.)
6 Squares: 2 small, 2 medium, 2 large (pattern blocks, construction paper, etc.)
9 Rectangles: 3 small, 3 medium, 3 large (pattern blocks, construction paper, etc.)
9 Triangles: 3 scalene, 3 right, 3 equilateral (pattern blocks, construction paper, etc.)
Materials to create tactile graphs (bar, line, pie, & picture), coordinate planes, & charts
DLM Common Mathematics Materials – Spring 2016
Page 9 of 9