### Spring 2024 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 somewhere 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 possible substitutions are found in the table below.
- 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 common materials used in ELA testlets.
- Lists by grade of common materials that may be used to administer testlets to students who are blind or have visual impairments. Some ELA testlets are special forms designed for these students, while others are general testlets that have been adapted to make them accessible for students who are blind or have visual impairments.

Grade 3

**Common Materials Used to Administer Testlets for Grade 3**

1 book

1 crumpled piece of paper

1 large cube

1 large piece of paper

1 large plate

1 large tube sock

1 long pencil

1 long ribbon

1 long, thin crayon

1 long, thick crayon

1 paper clip

1 pen

1 piece of notebook paper

1 piece of string that is 1 foot in length

1 piece of string that is 2 feet in length

1 piece of string that is 3 feet in length

1 rubber band (or piece of string)

1 short pencil

1 short ribbon

1 short, thick crayon

1 small ankle sock

1 small cube

1 small piece of paper

1 small plate

1 smooth piece of paper

2 gloves

2 identical, 16-count boxes of crayons

2 identical blocks

2 identical glue sticks

2 identical puzzles with 4 or more pieces

2 markers with caps

40 objects to use as counters

5 erasers

6 glue sticks

6 index cards

8 dominoes

8 erasers

a container to hold all of the counters

cards numbered 1 to 30

unit cubes

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 2 unequal parts

1 circle divided into 3 unequal parts

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 container with 10 compartments

1 equal sign

1 five-inch object

1 four-inch object

1 hexagon

1 hundred

1 large rectangle

1 large rhombus

1 large right triangle

1 large square

1 medium isosceles triangle

1 medium right triangle

1 oval

1 parallelogram

1 pentagon

1 rectangle divided into 2 unequal parts

1 rectangle divided into 4 unequal parts

1 rectangle divided into halves

1 rectangle divided into thirds

1 rhombus divided into halves

1 set of 60 objects

1 six-inch object

1 small rectangle

1 small square

1 star divided into 4 unequal parts

1 star divided into 6 unequal parts

1 subtraction sign

1 tactile material to create groups

1 tactile picture graph

1 tactile ruler

1 thousand

1 three-inch object

1 trapezoid

1 triangle divided into halves

1 two-inch object

1 whole star

18 containers

18 ones

2 containers with 7 compartments

2 medium objects

2 small objects

2 tactile bar graphs

20 object As

20 object Bs

3 containers with 6 compartments each

3 large congruent circles

3 large congruent equilateral triangles

3 medium congruent circles

3 medium congruent equilateral triangles

3 medium congruent rectangles

3 medium congruent squares

3 sets of 2 objects where the objects within each set vary in length

3 small congruent circles

3 small congruent equilateral triangles

3 tactile number charts

4 dimes

5 large objects

5 large triangles

5 ten-dollar bills

8 tens

tactile numbersGrade 4

**Common Materials Used to Administer Testlets for Grade 4**

1 additional container (if the scale doesn't have a pan)

1 bag

1 balance scale

1 big bowl

1 book

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 paper plate

1 rubber band (or piece of string)

1 set of 20 objects

1 short pencil

1 small bowl

1 small cup

1 straw

1 tactile material to create groups

2 identical, 12-count boxes of colored pencils

2 identical erasers

2 identical folders

2 identical glue sticks

2 identical large cups

2 identical long pencils

2 identical markers

2 identical notebooks

2 identical pens

2 pots

2 re-sealable sandwich bags with different amounts of rice inside

2 towels

20 marbles to use as informal units

3 cut-up pieces from a second identical straw

50 cotton balls to use as informal units

6 erasers

6 paperclips

food coloring

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 4 unequal parts

1 circle divided into 6 unequal parts

1 circle divided into eighths

1 circle divided into fourths

1 circle divided into halves

1 circle divided into sixths

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 circle representing 1/6

1 circle representing 1/8

1 circle representing 2/4

1 circle representing 3/4

1 circle representing 4/6

1 circle with a radius of 1 unit

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 dollar bill

1 heart divided into 2 unequal parts

1 hexagon

1 nickel

1 object about 2 times the size of the small object

1 object about 4 times the size of the small object

1 object with a heavier weight than 3 cube weights

1 object with a lighter weight than 1 cube weight

1 object with a lighter weight than 18 cube weights

1 object with an equal weight to 10 cube weights

1 oval

1 penny

1 quarter

1 rectangle divided into 2 unequal parts

1 rectangle divided into 3 unequal parts

1 rectangle divided into 4 unequal parts

1 rectangle divided into fourths

1 rectangle divided into halves

1 rectangle divided into sixths

1 rectangle divided into thirds

1 rectangle measuring 1 x 2

1 rectangle measuring 2 x 5

1 rectangle measuring 3 x 1

1 rectangle measuring 4 x 6

1 rectangle measuring 7 x 3

1 rectangle measuring 8 x 5

1 rectangle representing 1/2

1 rectangle representing 1/4

1 rectangle representing 2/3

1 rectangle representing 3/6

1 rectangle representing 4/4

1 rectangle representing 9/10

1 rectangle representing fourths

1 rectangle representing halves

1 rectangle representing sixths

1 rectangle representing thirds

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 10 x 5

1 rectangle with discernible square units measuring 5 x 3

1 rectangle with discernible unit squares measuring 5 x 4

1 round object

1 small acute angle

1 small container

1 small object

1 square divided into 3 unequal parts

1 square divided into fourths

1 square divided into halves

1 square divided into thirds

1 square measuring 1 x 1

1 square measuring 2 x 2

1 square measuring 3 x 3

1 square object

1 square representing 1/2

1 square representing 1/4

1 square representing 1/8

1 square representing 2/4

1 square representing 3/4

1 square representing eighths

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 triangle divided into 2 equal parts

1 triangular object

10 object Cs

2 large congruent acute angles

2 sets of 8 objects

2 whole rectangles

3 acute angles of varying measures

3 balance scales

3 obtuse angles of varying measures

3 right angles

3 tactile analog clocks

31 cube weights

4 rhombi

4 trapezoids

6 identical containers

6 non-money objects

6 squares

6 triangles

7 acute angles

7 circles

8 tactile digital clocks

9 object As

9 object Bs

tactile letters and numbers for labelingGrade 5

**Common Materials Used to Administer Testlets for Grade 5**

1 big index card

1 box

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 3" x 4" x 2"

1 empty rectangular container measuring 6" x 5" x 2"

1 empty rectangular container measuring 5" x 4" x 2"

1 empty water bottle

1 full water bottle with a colored liquid

1 rubber band

1 small index card

1 towel

2 identical, 12-count packs of pens

2 identical cards

2 identical cups

2 identical erasers

2 identical number cubes

2 markers

2 plastic cups

5 blocks

5 checkers

5 paintbrushes

6 envelopes

7 number cubes

8 pencils

8 snap cubes

more than enough unit cubes to fill the largest container**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 fourths

1 circle divided into halves

1 circle divided into sixths

1 circle divided into tenths

1 circle divided into thirds

1 circle representing 1/3

1 circle representing 1/4

1 circle representing 2/3

1 circle representing 2/8

1 circle representing 3/3

1 circle representing 3/4

1 container packed with unit cubes

1 cube measuring 1 x 1 x 1

1 heart

1 isosceles triangle

1 large cone

1 large cube

1 large cylinder

1 large rectangle

1 large sphere

1 obtuse scalene triangle

1 parallelogram

1 pyramid

1 rectangle divided into 3 unequal parts

1 rectangle divided into 4 unequal parts

1 rectangle divided into eighths

1 rectangle divided into fourths

1 rectangle divided into halves

1 rectangle divided into sixths

1 rectangle divided into tenths

1 rectangle divided into thirds

1 rectangle representing 1/10

1 rectangle representing 1/3

1 rectangle representing 2/10

1 rectangle representing 2/3

1 rectangle representing 2/5

1 rectangle representing 2/8

1 rectangle representing 3/8

1 rectangle representing 4/10

1 rectangle representing 6/10

1 rectangle representing 6/8

1 rectangle representing 7/10

1 rectangle representing 8/10

1 rectangle representing 9/10

1 rectangular prism measuring 2 x 2 x 1

1 rectangular prism measuring 3 x 2 x 1

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 rhombus

1 right triangle

1 set of 20 objects

1 small cube

1 small cylinder

1 small rectangle

1 small sphere

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 divided into thirds

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

17 connecting cubes

2 circles divided into 3 unequal parts

2 congruent cubes

2 congruent ellipses

2 congruent hexagons

2 congruent stars

2 congruent trapezoids

2 equilateral triangles

2 identical cylinders

2 identical rectangular prisms

2 large squares

2 medium circles

2 medium triangles

2 small circles

2 small congruent cones

2 small triangles

2 squares divided into 4 unequal parts

3 tactile bar graphs

3 tactile number lines

3 tactile picture graphs

4 tactile line plots

5 large circles

6 large triangles

8 ones

8 tensGrade 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

2 dry sponges varying in size

2 hard cover books

2 packs of gum

2 plastic cups

2 soft cover books

2 wet sponges varying in size

200 one-inch unit cubes

3 blocks that vary in size

3 empty rectangular containers of any size

3 pencils that vary in length

4 markers

4 pencils

5 cups

6 erasers

6 glue sticks

7 pieces of chalk

7 wooden craft sticks

8 folders

8 pens

9 crayons

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 2 equal parts

1 circle divided into fourths

1 circle representing 1/10

1 circle representing 1/2

1 circle representing 1/3

1 circle representing 2/3

1 circle representing 3/4

1 circle representing 3/6

1 circle representing 4/10

1 circle representing 8/10

1 container with 10 compartments

1 container with 4 compartments

1 continuous substance

1 rectangle divided into halves

1 rectangle measuring 1/3 x 3

1 rectangle measuring 6 x 10

1 rectangle measuring 6 x 4

1 rectangle representing 2/3

1 rectangle representing 3/4

1 rectangle with 1 half shaded

1 rectangle with discernible square units measuring 2 x 3

1 rectangle with discernible square units measuring 4 x 6

1 rectangle with discernible square units measuring 4 x 7

1 rectangle with discernible square units measuring 5 x 3

1 rectangle with discernible square units measuring 6 x 4

1 rectangle with the area shaded

1 rectangle with the border shaded

1 rectangular prism with discernible cube 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 set of 28 objects

1 square divided into 4 equal parts

1 square measuring 1 x 1

1 square measuring 2 x 2

1 square measuring 5 x 5

1 square representing 1/2

1 square representing 1/3

1 square representing 1/4

1 square with discernible square units measuring 3 x 3

1 tactile material to create groups

1 tactile number line

1 tactile picture graph

14 object Bs

2 circles divided into 2 unequal parts

2 circles divided into 4 unequal parts

2 circles representing 1/4

2 rectangles divided into 2 unequal parts

2 squares divided into 4 unequal parts

2 tactile line plots

25 object As

3 containers with 3 compartments each

3 tactile line graphs

3 tactile thermometers

6 identical containers

6 tactile bar graphsGrade 7

**Common Materials Used to Administer Testlets for Grade 7**

1 ball

1 dry sponge

1 large cup

1 long pencil

1 long ribbon

1 rubber band

1 short pencil

1 short ribbon

1 small cup

1 smooth piece of paper

1 wet sponge

1 crumpled piece of paper

2 identical, 12-count boxes of colored pencils

2 identical, 7-count packs of toy cars

2 identical cups

2 identical decks of playing cards in their boxes

2 identical notecards

5 crayons

5 markers

5 notebooks

7 dominoes

8 glue sticks**Common Materials Used to Administer Testlets for Grade 7 Students Who Are Blind or Have Visual Impairments**

1 acute isosceles triangle

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 cone

1 cylinder

1 hexagon

1 large circle

1 large cube

1 line segment

1 medium circle

1 object with the measurable attributes of height, length, and weight

1 octagon

1 oval

1 parallelogram

1 pentagon

1 rectangle divided into tenths

1 rectangle measuring 4 x 2

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 area indicated

1 rectangle with the length of the bottom side indicated

1 rectangle with the length of the top side indicated

1 rectangle with the length, width, and diagonal indicated

1 rectangle with the perimeter indicated

1 rectangular object

1 rhombus

1 right isosceles triangle

1 right scalene triangle

1 small circle

1 small cube

1 small sphere

1 square measuring 2 x 2

1 square with discernible square units measuring 3 x 3

1 star

1 tactile material to create groups

1 tactile number line

1 trapezoid

1 triangular prism

2 circles divided into 2 unequal parts

2 congruent equilateral triangles

2 congruent pyramids

2 object Bs

2 objects without the measurable attribute of height

2 rectangles representing 4/10

2 rectangular prisms

3 circles representing 1/4

3 congruent rectangles

3 tactile coordinate grids

4 sets of objects where each set contains 1 whole object and 1 part of an identical object (objects A-D)

40 object As

5 number cubes

5 squares

6 circlesGrade 8

**Common Materials Used to Administer Testlets for Grade 8**

1 blank piece of paper

1 clear pencil case or plastic bag

1 dry sponge

1 flat piece of paper

1 folded piece of paper

1 large block

1 large bowl

1 large closed box

1 large eraser

1 large open box

1 large piece of construction paper

1 large plastic cup

1 large plate

1 small block

1 small bowl

1 small eraser

1 small open box

1 small piece of construction paper

1 small plastic cup

1 small plate

1 thick book

1 thin book

1 wet sponge

2 bent chenille stems

2 closed containers

2 glue sticks

2 identical, 20-count sheets of stickers

2 identical long ribbons

2 identical short ribbons

2 large rectangles

2 long pencils

2 open containers

2 short pencils

2 small rectangles

2 straight chenille stems

3 books that vary in size

3 circles that vary in size

3 craft sticks that vary in size

3 crayons that vary in length

3 cups

3 pencils that vary in length

3 pom-poms that vary in size

3 triangles that vary in size

5 markers

5 paint brushes

5 pens**Common Materials Used to Administer Testlets for Grade 8 Students Who Are Blind or Have Visual Impairments**

1 acute angle

1 arc

1 circle

1 circle representing 3/6

1 circle representing 4/4

1 colon

1 cube

1 cylinder

1 decimal point

1 dollar sign

1 equal to sign

1 exclamation point

1 fraction bar

1 greater than sign

1 hexagon

1 less than sign

1 object with a measurable attribute of weight

1 obtuse angle

1 pair of adjacent angles forming an acute angle

1 pair of complementary angles

1 pair of supplementary angles

1 ray

1 rectangle measuring 10 x 7

1 rectangle measuring 12 x 9

1 rectangle measuring 18 x 9

1 rectangle measuring 4 x 2

1 rectangle measuring 6 x 5

1 rectangle measuring 7 x 6

1 rectangle measuring 9 x 3

1 rectangle representing 1/4

1 rectangle representing 10/10

1 rectangle representing 2/10

1 rectangle representing 3/10

1 rectangle representing 5/10

1 rectangle representing 8/10

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 objects which contains 1 whole object and 2 parts of an identical object

1 square

1 square representing 4/8

1 square representing 6/8

1 square representing 8/8

1 tactile line plot

1 tactile material to create groups

2 circles representing 1/6

2 circles representing 2/6

2 right angles

2 squares representing 2/8

3 congruent rectangles

3 tactile bar graphs

3 tactile function tables

3 tactile materials to indicate part of a number

3 tactile picture graphs

3 tactile tally charts

4 containers with 10 compartments each

40 object As

5 sets of objects where each set contains 1 whole object and 1 part of an identical object (objects A-E)

tactile numbers and decimalsGrades 9–12 (High School)

**Common Materials Used to Administer Testlets for High School**

1 bottle

1 crumpled piece of paper

1 hexagon

1 large cup

1 long string

1 rubber band (or piece of string)

1 short string

1 small cup

1 smooth piece of paper

1 yardstick

2 bent straws varying in size

2 closed boxes

2 empty jars varying in size

2 folded pieces of paper

2 full jars varying in size

2 identical, 6-count packs of glue sticks

2 identical blocks

2 identical bowls

2 identical checkers

2 identical crayons

2 identical cups

2 identical dominoes

2 identical envelopes

2 identical erasers

2 identical flat pieces of paper

2 identical keys

2 identical markers

2 identical notebooks

2 identical number cubes

2 identical pencils

2 identical pens

2 identical plates

2 identical playing cards

2 identical rulers

2 identical sponges

2 long rulers

2 open boxes

2 plates varying in size

2 short rulers

2 squares

2 straight straws varying in size

3 buttons

3 cards

3 containers that vary in size

3 cups varying in size

3 markers

3 number cubes

3 pencils that vary in length

3 pieces of paper that vary in size

3 spoons

5 pencils

6 crayons

6 dominoes

6 erasers

6 pens

7 blocks

7 checkers

7 cotton balls

7 keys

9 coins**Common Materials Used to Administer Testlets for High School Students Who Are Blind or Have Visual Impairments**

1 acute angle

1 arrow

1 circular object

1 cylindrical object

1 equal to symbol

1 heart

1 large circle

1 large cube

1 large isosceles triangle

1 large oval

1 large right triangle

1 large similar trapezoid

1 line

1 line segment

1 number cube

1 obtuse angle

1 octagon

1 pentagon

1 point

1 pyramid

1 quarter

1 ray

1 rectangle divided into triangular halves

1 rectangular object

1 rhombus

1 right angle

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 sixteen-inch length of yarn

1 small cube

1 small isosceles triangle

1 small oval

1 small right triangle

1 small trapezoid

1 sphere

1 tactile material to create groups

1 tactile spinner

1 thousand block

18 ones

2 congruent cones

2 congruent cylinders

2 congruent ovals

2 congruent parallelograms

2 congruent rectangles

2 congruent rectangular prisms

2 congruent right scalene triangles

2 congruent squares

2 congruent triangular prisms

2 four-inch craft sticks

2 identical trapezoids

2 identical triangles

2 large rectangles

2 sets of non-perpendicular intersecting lines

2 similar circles

2 similar cones

2 similar hexagons

2 similar rectangular prisms

2 similar right triangles

2 small rectangles

2 small squares

2 small triangles

3 addition signs

3 division signs

3 multiplication signs

3 subtraction signs

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

3 tens

39 object As

4 playing cards

4 six-inch craft sticks

4 tactile function tables

4 tactile less than and greater than symbols

65 objects

7 tactile function graphs

tactile letters and numbers