Whole Numbers and their Values Assessment information

Examples of how to assess student's rote memory and conceptual understanding of ideas necessary to attain number value literacy. The examples include suggestions, sample scripts, and summary comments or outcomes for the following categories:

Assessments

A summary record sheet can be used to summarize information for each student. Includes categories for yes, no, and comments for each assessment task.

Stop any of the individual assessments if a child is not able to respond or responds with random answers.

Background information on the development of

Assessments for rote counting to 100:

• How far do you think you can count?
• Count for me.
• Count to 5.
• Can you continue to [10, 20, 50, 100] 1000 below

Stop the child when they stop or appear to not know what number comes next.

• Says numbers, from memory, in a random order.
• Says numbers, from memory, to 5, then random numbers, and stops with eight. Eight appears to have highest value.
• Orally counts by 1's to 10 from memory.
• Orally counts by 1's to 20 from memory.
• Orally counts by 1's to 50 from memory.
• Orally counts by 1's to 100 from memory.

Assessments for rote counting by multiples

• Can you count by 5's?
• Count for me

Stop the child at 100 or as appropriate.

• Orally counts by 5's to 100 from memory. Doesn't reference intermediate numbers.

• Can you count by 10's?
• Count for me

Stop the child at 100 or as appropriate.

• Orally counts by 10's to 100 from memory. Doesn't reference intermediate numbers.

• Can you count by 2's?
• Count for me

Stop the child at 20 or as appropriate.

• Says numbers, from memory, by counting by ones in head and saying even numbers aloud.
• Orally counts by 2's to 20 from memory. Doesn't reference intermediate numbers.

• Can you count by 3's?
• Count for me

Stop the child at 21 or as appropriate.

• Says numbers, from memory, by counting by one, two in head and saying every third number aloud.
• Orally counts by 3's to 21 from memory. Doesn't reference intermediate numbers.

Assessments for rote counting backwards

• Can you count backward from 10?
• Count for me

Stop the child at 0.

• Orally counts backwards from 10 to 1 from memory.

• Can you count backward from 8?
• Count for me

Stop the child at 0.

• It may seem that if a child can count back from ten, they should be able to count back from numbers less than ten. However, some students who are able to count backward from 10, bu t may not be able to count back from numbers below ten. They may mentally start with 10, count back till they get to the starting number, and then speak out. This can be comment as: started at 10, dropped back to 8 and continued (for example counting back from 8).
• Orally counts backwards from 8 to 1 from memory.

• Can you count backwards from 12?
• Count for me

Stop the child at 0.

• Orally counts backwards from 12 to 1 from memory.

• Can you count backwards from 20?
• Count for me

Stop the child at 0.

• Orally counts backwards from 24 to 1 from memory.

• Can you count backwards from 24?
• Count for me

Stop the child at 0.

• Orally counts backwards from 24 to 1 from memory.

Assessments for rote counting to and from 1 000:

Directions

If you know the student has memorized the sequence of whole numbers from 1-100, then ask the student to count by tens to 100, Then let them count from 100 by ones for awhile to double check. When confident they can, then stop them and tell them you will give them a number and you want them to count from it and you will repeat the process till 1 000. Vary the following numbers as you think necessary. For example, if you know the student has stumbled counting from 60-70, then be sure to stop and start in the 50's to make certain the stumble has been overcome.

Possible stop and start numbers: stop 101, start 125, stop 138; 186, 210; 489, 508; 798, 803; 989, 1 000.

• Can you count to 1 000?

• Can count to 1 000. Has memorized all the necessary numbers needed to combine to make the numbers 1 - 1 000 and has a conceptual and systematic procedural method to count to 1 000.
• Correctly said one hundred one, one hundred two, ... one hundred eleven, ... one hundred twenty-one, and so forth. Do NOT include an and, one hundred and one. Source.

• Can you count backwards from 1000?

Note and comment suggestions:

• Don't have to count all numbers. Have them start and stop with various numbers until confidence in their ability is found. Could use the possible stop and start numbers above by reversing them.
• Can count back from 1 000 to one. Has memorized all the necessary numbers needed to combine to make the numbers 1 - 1 000 and has a conceptual and systematic procedural method to count backwards from 1 000 - o.

Numeral recognition

Materials

• I am going to point to a number and you can tell me what it is.
• Point to 2. (wait and record response).
• Then repeat for 7, 9, 6, 8, 3, 5, 1, 4, 10

• Quickly recognized numbers 1-5.
• Quickly recognized numbers 1-10.
• Identified all numbers 1-10, except 3 for 8.

Repeat the same procedure for the next number sheet. 12, 17, 19, 16, 18, 13, 15, 11, 14, 20

• Easily recognized numerals 11-15.
• Easily recognized numerals 11-20.
• Identified all numbers 11-20 except 16 for 19.

Correctly forms numerals

Materials

Writing implement and paper.

• Write the number as I say it.
• Say a random number and wait for the child to write it.
• Random numbers (2, 7, 9, 6, 8, 3, 5, 1, 4, 10).

Numbers need to be made from top to bottom and left to right. The following rhymes can be used to help students memorize the patterns for numeral writing.

1. A line down one is fun.
2. Around and back on a railroad track; two, two, two.
3. Around a tree, around a tree, that is how we make a three.
4. Down and over and down some more, that is how we make a four.
5. Fat old five goes down and around, put a flag on top and see what we've found.
6. Down to a loop, a six rolls a loop.
7. Across the sky and down low you're headen, that is how we make a seven.
8. Make a S, do not wait, come back up and make an eight.
9. A loop and a line make number nine.

• Correctly forms numeral 1
• Correctly forms numeral 2
• Correctly forms numeral 3
• Correctly forms numeral 4
• Correctly forms numeral 5
• Correctly forms numeral 6
• Correctly forms numeral 7
• Correctly forms numeral 8
• Correctly forms numeral 9
• Correctly forms numeral 10
• Correctly writes numerals 1 - 10.

Subitizing Instant recognition

Materials

Directions

For each number randomly arrange a group of that many objects. Keep them hidden from the student. Tell the student you will show them a group of objects for a short period of time (2 seconds) and you want them to guess or tell you the number of objects.

Display objects arranged randomly on a tray or mat.

How many objects do you think are in the group.

Child must instantly (2 seconds) tell the number of objects in a group.

• Instantly counts (subitizes) a group of 2.
• Instantly counts (subitizes) a group of 3.
• Instantly counts (subitizes) a group of 4.
• Instantly counts (subitizes) a group of 5.
• Instantly counts (subitizes) a group of 6.
• Instantly counts (subitizes) a group of 7.
• Instantly counts (subitizes) a group of 8.
• Instantly counts (subitizes) a group of 9.
• Instantly counts (subitizes) a group of 10.

Assessment for One-to-one correspondence or synchrony

Materials

Objects or beans to make groups or 4, 8, 12, and 24.

Directions

Put 3 groups of beans on a work mat:

1. Counts a group of 4,
2. Counts a group of 8, and
3. Counts a group of 12.

The child to count a group of beans. If the child counts 12 comfortably then move all the beans together (24) and ask them to count the larger group. If the child can't count the chosen group, then ask the child to count a smaller group.

• Note if the student touches and moves the objects, points, moves head & lips, mentally counts, uses skip counting, stares or looks up and tells final number.
• Synchrony is when the student tries to use one-to-one correspondence, but doesn't totally get it because of focus or not knowing the purpose of one counting number being assigned to each object.
• Student knows one-to-one correspondence when the the counting sequence is done in an accurate one-to-one manner. For objects of 4, 8, 12, 16, and 24.
• Cardinality (identifies the value of all objects). Often by repeating the last number to emphasize the final number as the groups cardinality.
• Uses synchrony to count groups
• Uses synchrony to count groups above ___
• Uses one-to-one correspondence to touching and move to count ___
• Uses one-to-one correspondence by pointing to count ___
• Uses one-to-one correspondence to mentally point and count ____
• Use pattern to recognize ___ and ___ , then add count ___
• Uses one-to-one correspondence to count groups less than 8 and synchrony above 8.
• Uses one-to-one correspondence to count groups to 24
• Count by twos to ___

Assessment for One-to-one correspondence with matching

Materials

Dot pattern cards or dot plates, collection of 12 objects or beans, cup, plate or mat

Directions

Show students a pattern of six. Give them a collection of at least 12 objects in a cup and a plate or mat placed beside the dot pattern.

The student to put as many objects on the plate as there are dots on the card.

• Has no strategy to proceed.
• Counts objects on dot card and counts out same number of objects onto the plate.
• Subitizes or recognizes patterns of _ and counts out same number of objects onto the plate.
• Subitizes or recognizes patterns smaller than six, counts on, and counts out same number onto plate.

Cardinality match subitizing or visual pattern recognition

Materials

Two sets of Dot pattern cards

Directions

Give students two sets of dot cards 1-9.

Match the cards.

• Subitize or match patterns with a quick look or glance.
• Count with synchrony with some and some not accurate.
• Counting dots using one-to-one correspondence accurately.
• Student randomly selects cards.
• Students matched dots of ______ and counted dots of _______
• Cardinality score guide, rubric, & score sheet

Number Value (More, Less, and Same)

Materials

Two sets of Dot pattern cards (1-10).

Directions

Divide the cards into two piles. Have the student and teacher turn a card over.

• Who has more or less.
• Repeat for cards of value from 10-20.

• Counts each card using syncope and inconsistently identifies more, less, and same for dot card pairs of values ____
• Counts each card using one-on-one correspondence and correctly identifies the values and which is more, less, and same for dot card pairs to 10.
• Uses subitize or pattern recognition to correctly identify and add dots to accurately find values on cards and correctly identify more, less, and same for dot card pairs of ____

Hierarchal inclusion for five

Materials

Five objects, cup,

Directions

Put five objects in a cup. Ask the student if they could use the objects in the cup to show someone what four objects would look like.

What other numbers could you show a person using the objects in the cup.

Dump the objects out and place the empty cup in front of the student.

• Shows that knows hierarchical inclusion: Knows that a number of objects can make a set of objects from zero to and including the number of objects.
• Can show objects of five, four, three, two, one, zero

Cardinality match numeral and number word

Materials

Two sets of cards. Dot pattern cards, numeral cards, number word cards

Directions

Give students two sets of dot cards 1-9.

Match the cards.

• Subitize or match patterns with a quick look or glance.
• Count with synchrony with some and some not accurate.
• Counting dots using one-to-one correspondence accurately.
• Student randomly selects cards.
• Students matched dots of ______ and counted dots of _______
• Cardinality score guide, rubric, & score sheet

Assessor's Name:

See notes, comments, and suggestions in directions.

Scoring suggestions

• The child can either do it or not do it. It's important to give prompts to help the child feel successful, but if the task is completed correctly, the appropriate column must be recorded. The child must be able to complete the task without a prompt to receive a √. with a prompt *, and not at all -.
• If you want to use the chart for triangulation data, then use numbers along with comments and other marks. For example. √1, √2, √3. Comments - Did ... 1, 2, 3.

Rote counting: Completed
√, *, -
Count by ones
1. Orally counts by 1's to 10
2. Orally counts by 1's to 20
3. Orally counts by 1's to 50
4. Orally counts by 1's to 100
5. Orally counts by 1's to 1 000
Summary
• Knows the counting words in sequence from 1 to 5, 10, 12, 24, 100, 1000.
Backwards Completed
√, *, -
1.Orally counts backwards from 10 to 1
2. Orally counts backwards from 20 to 1
3. Orally counts backwards from 50 to 1
4. Orally counts backwards from 100 to 1
Summary
• Knows the counting words in sequence from 5, 10, 12, 24, 100, 1000 to 1 or 0.
Multiple counting Completed
√, *, -
1. Orally counts by 2's to 22
2. Orally counts by 5's to 100
3. Orally counts by 10's to 100
4. Orally counts by 3's to 21
Summary
• Knows skip counting words in sequence by 2, 5, 10, 3 to 100.
Synchrony or One-to-one correspondence Completed
√, *, -
1. One-to-one correspondence for group of four (counts a group of 4 objects)
2. One-to-one correspondence for group of eight (counts a group of 8 objects)
3. One-to-one correspondence for group of twelve (counts a group of 12 objects)
4. One-to-one correspondence for group of twenty-four (counts a group of 24 objects)
5. Generalizes one-to-one correspondence for counting all values.
Summary
• Uses synchrony for numbers to (4 / 8 / 12 / 24 / 100).
• Uses one-to-one correspondence (connects the counting sequence in a one-to-one manner) for numbers to (4 / 8 / 12 / 24 / 100).
• Knows cardinality (identifies the value of objects possibly by repeating the last number with emphasis). For numbers to (4 / 8 / 12 / 24 / 100).
Subitize Instant recognition of number value Completed
√, *, -
1. Instantly identifies groups of 2 objects
2. Instantly identifies groups of 3 objects
3. Instantly identifies groups of 4 objects
4. Instantly identifies groups of 5 objects
5. Instantly identifies groups of 6 objects
6. Instantly identifies groups of 7 objects
7. Instantly identifies groups of 8 objects
8. Instantly identifies groups of 9 objects
9. Instantly identifies groups of 10 objects
Summary
• Uses visualization abilities to subitize or visually recognizes patterns for 2, 3, 4, 5, 6, 7, 8, 9, 10 objects to identify cardinality.
Numeral recognition Completed
√, *, -
Instantly recognizes numeral 0
Instantly recognizes numeral 1
Instantly recognizes numeral 2
Instantly recognizes numeral 3
Instantly recognizes numeral 4
Instantly recognizes numeral 5
Instantly recognizes numeral 6
Instantly recognizes numeral 7
Instantly recognizes numeral 8
Instantly recognizes numeral 9
Instantly recognizes numeral 10
Instantly recognizes numeral 11
Instantly recognizes numeral 12
Instantly recognizes numeral 13
Instantly recognizes numeral 14
Instantly recognizes numeral 15
Instantly recognizes numeral 16
Instantly recognizes numeral 17
Instantly recognizes numeral 18
Instantly recognizes numeral 19
Instantly recognizes numeral 20
Summary
• Cannot yet identify numerals one to ten.
• Can identify all numerals in the range of one to ten.
• Can identify all numerals in the range of one to twenty.
• Can identify all numerals in the range of one to one hundred.
• Can identify all numerals in the range of one to one thousand.
Forms numerals - t
Top to bottom and left to right
Completed
√, *, -
Correctly forms numeral 0
Correctly forms numeral 1
Correctly forms numeral 2
Correctly forms numeral 3
Correctly forms numeral 4
Correctly forms numeral 5
Correctly forms numeral 6
Correctly forms numeral 7
Correctly forms numeral 8
Correctly forms numeral 9
Summary
• Forms all numerals top to bottom and left to right.

Combinations of addends to 12: hierarchical inclusion Completed
√, *, -
Task: Use the number of beans as the sum. Count the beans into your hand. Hide the beans behind your back and distribute them into both hands. Show the child one hand and ask how many are in the other hand. Repeat for all possible combinations of whole numbers in a random order. (2 + 3, 0 + 5, 1 + 4, 5 + 0, 3 + 2, 4 + 1)
1. Combinations of 5
2. Combinations of 6
3. Combinations of 7
4. Combinations of 8
5. Combinations of 9
6. Combinations of 10
7. Combinations of 11
8. Combinations of 12

Conservation of numbers Completed
√, *, -