Place Value Prerequisite Skills Test

Directions: The past module presented five different prerequisite skills students need in order to develop a solid understanding of place value. Use your notes to help you answer the following questions. There is no time limit. You will receive your score at the end of the test.

Question 1 of 5

Value: 5 Points

1. The teacher asks a student to count a small group of objects (less than 10) that are on the table in front of him/her. What prerequisite skill (or skills) could the teacher be assessing? (select all answers that apply)

a. Cardinalityb. Decompositionc. Unitizingd. Subitizing

Correct Combination= a, b, and d

Answer Choice

Feedback

a. Correct- Cardinality; The teacher may be trying to determine if the student is able to count the number of objects correctly by saying the correct number for each object and knowing that the last number that he/she says is the total number of objects for the set.

b. Correct- Decomposition; Although more challenging, the teacher may be trying to determine if the student is able to break the objects into two or more groups to determine the total number of objects.

c. Incorrect- Unitizing; Since the number of objects is less than 10, the teacher could not be assessing if the student puts objects together into a group of 10 in order to count. (We are consistently working in base 10, however if we were working in a different base, this answer could be true).

d. Correct- Subitizing; The teacher may be trying to determine if the student will simply look at the total number of objects and know the answer without counting one by one.

Question 2 of 5

Value: 5 Points

2. The teacher gives the student a bag of tiles to use, then asks the student to use two different colors of tiles to show all of the different combinations (or ways to make) the number 8. What specific prerequisite skill (or skills) is the teacher assessing? (select all answers that apply)

a. Hierarchical Inclusionb. Compositionc. Cardinalityd. Unitizinge. Decomposition

Correct Combination: b, e

Answer Choice

Feedback

a. Incorrect- Hierarchical Inclusion; Hierarchical inclusion means that the student recognizes that all numbers preceding the selected number are included in the value of the selected number. Although understanding hierarchical inclusion is required in order to do this activity, the activity is not specifically assessing this skill.

b. Correct- Composition; Compose means putting the sub-parts together to make a whole number. The activity given to the student is assessing whether the student is able to put the sub-parts of the number 8 together to make the whole number.

c. Incorrect- Cardinality; Cardinality means counting items in sequence and knowing the number applied to the last item represents the total amount for the group. Although understanding cardinality is required in order to do this activity, the activity is not specifically assessing this skill.

d. Incorrect- Unitizing; Unitizing means treating an object or a collection of objects as one unit. The activity given to the student is not specifically assessing this skill.

e. Correct- Decomposition; Decomposition means breaking numbers apart into their sub-parts. The activity given to the student is assessing whether the student is able to break the number 8 into its sub-parts.

Question 3 of 5

Value: 5 Points

3. True or False. (choose one)One way to assess if students understand cardinality is to give the student a bag of blocks and ask the student to show you all of the ways to make the number 38 using the blocks.

a. True

b. False

Answer Choice

Feedback

a. True Incorrect; Cardinality means counting items in sequence and knowing the number applied to the last item represents the total amount for the group. If the student knows the total number of blocks after counting the group, then he/she understands the concept of cardinality. This is an example of unitizing. In this example, the student is asked to construct the number 38 using blocks. Unitizing includes treating an object or set of objects as a one unit. In a base-10 system, this would mean the student puts objects into groups of ten with the left over cubes demonstrating the “ones.”

b. False Correct; Cardinality means counting items in sequence and knowing the number applied to the last item represents the total amount for the group. If the student knows the total number of blocks after counting the group, then he/she understands the concept of cardinality. This is an example of unitizing. In this example, the student is asked to construct the number 38 using blocks. Unitizing includes treating an object or set of objects as a one unit. In a base-10 system, this would mean the student puts objects into groups of ten with the left over cubes demonstrating the “ones.”

Question 4 of 5

Value: 5 Points

4. True or False. (Choose one)A student is asked to count seven blocks and put them in a container. The teacher takes out three blocks for the child to see and covers the container holding the remaining blocks so the child cannot see inside. When asked how many are inside of the container, the child responded four. This is an example of an informal assessment for hierarchical inclusion.

Answer Choice

Feedback

a. True Correct; Hierarchical Inclusion means recognizing that all numbers preceding the selected number are included in the value of the selected number. Thus, the child’s ability to recognize that there were four blocks still in the cup shows that she has developed this skill.

b. False Incorrect; Hierarchical Inclusion means recognizing that all numbers preceding the selected number are included in the value of the selected number. Thus, the child’s ability to recognize that there were four blocks still in the cup shows that she has, in fact, developed this skill.

Question 5 of 5

Value: 5 Points

(1 point for each correct response)

5. Match each of the following prerequisite skills with its definition (write the letter that’s next to the definition onto the line next to the correct term):

____ 1. Hierarchical Inclusion

____ 2. Decomposition/Composition

____ 3. Unitizing

____ 4. Cardinality

____ 5. Subitizing

a. Counting items in sequence and knowing the number applied to the last item represents the total amount for the group.

b. Treating an object or a collection of objects as one unit.

c. Recognizing that all numbers preceding the selected number are included in the value of the selected number.

d. Putting the sub-parts together to make a whole number or breaking numbers apart into their sub-parts.

e. Identifying the number of objects in a small group of objects without counting

Answers:

__c.__ 1. Hierarchical Inclusion

__d.__ 2. Decomposition/Composition

__b.__ 3. Unitizing

__e.__ 4. Subitizing

__a.__ 5. Cardinality

a. Counting items in sequence and knowing the number applied to the last item represents the total amount for the group.

b. Treating an object or a collection of objects as one unit.

c. Recognizing that all numbers preceding the selected number are included in the value of the selected number.

d. Putting the sub-parts together to make a whole number or breaking numbers apart into their sub-parts.

e. Identifying the number of objects in a

small group of objects without counting