Whole Numbers and their Values Assessment information
Page Overview:
 Rote counting to 100
 Rote counting by multiples, 2, 5, 10, & 3
 Counting back from 10, 8, 20, 100
 Counting to and from 1 000
 Numeral recognition
 Writing or forming numerals
 Subitizing or instant recognition of values
 Onetoone correspondence or synchrony
 Assessment for Onetoone correspondence with matching
 Cardinality matching
 More, less, or the same
 Hierarchical inclusion to five
 Cardinality match numeral and number word
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
 Rote counting to 100
 Rote counting by multiples, 2, 5, 10, & 3
 Counting back from 10, 8, 20, 100
 Counting to and from 1 000. Counting to 0nethousand requires memory of the necessary words, but also a conceptual understanding of ten repeated 100's.
 Numeral recognition
 Writing or forming numerals
 Subitizing or instant recognition of values
 Onetoone correspondence or synchrony [Synchrony information]
 Assessment for Onetoone correspondence with matching
 Cardinality matching subitizing or visual pattern recognition
 More, less, or the same number value
 Hierarchical inclusion to five
 Cardinality match numeral and number word
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:
Ask
 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.
Notes, comments, and suggestions
 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
Ask
 Can you count by 5's?
 Count for me
Stop the child at 100 or as appropriate.
Notes, comments, and suggestions
 Orally counts by 5's to 100 from memory. Doesn't reference intermediate numbers.
Ask
 Can you count by 10's?
 Count for me
Stop the child at 100 or as appropriate.
Notes, comments, and suggestions
 Orally counts by 10's to 100 from memory. Doesn't reference intermediate numbers.
Ask
 Can you count by 2's?
 Count for me
Stop the child at 20 or as appropriate.
Notes, comments, and suggestions
 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.
Ask
 Can you count by 3's?
 Count for me
Stop the child at 21 or as appropriate.
Notes, comments, and suggestions
 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
Ask
 Can you count backward from 10?
 Count for me
Stop the child at 0.
Notes, comments, and suggestions
 Orally counts backwards from 10 to 1 from memory.
Ask
 Can you count backward from 8?
 Count for me
Stop the child at 0.
Notes, comments, and suggestions
 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.
Ask
 Can you count backwards from 12?
 Count for me
Stop the child at 0.
Notes, comments, and suggestions
 Orally counts backwards from 12 to 1 from memory.
Ask
 Can you count backwards from 20?
 Count for me
Stop the child at 0.
Notes, comments, and suggestions
 Orally counts backwards from 24 to 1 from memory.
Ask
 Can you count backwards from 24?
 Count for me
Stop the child at 0.
Notes, comments, and suggestions
 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 1100, 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 6070, 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.
Ask
 Can you count to 1 000?
Notes, comments, and suggestions
 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 twentyone, and so forth. Do NOT include an and, one hundred and one. Source.
Ask
 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
Random number prompt sheets with directions
Ask
 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
Notes, comments, and suggestions
 Quickly recognized numbers 15.
 Quickly recognized numbers 110.
 Identified all numbers 110, except 3 for 8.
Repeat the same procedure for the next number sheet. 12, 17, 19, 16, 18, 13, 15, 11, 14, 20
Notes, comments, and suggestions
 Easily recognized numerals 1115.
 Easily recognized numerals 1120.
 Identified all numbers 1120 except 16 for 19.
Correctly forms numerals
Materials
Writing implement and paper.
Ask
 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.
 A line down one is fun.
 Around and back on a railroad track; two, two, two.
 Around a tree, around a tree, that is how we make a three.
 Down and over and down some more, that is how we make a four.
 Fat old five goes down and around, put a flag on top and see what we've found.
 Down to a loop, a six rolls a loop.
 Across the sky and down low you're headen, that is how we make a seven.
 Make a S, do not wait, come back up and make an eight.
 A loop and a line make number nine.
Notes, comments, and suggestions
 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
 Objects or bean to make groups of 2, 3, 4, 5, [6, 7, 8, 9, 10]
 Or use dot plates or dot flash [15] & [110] See also addition and subtraction assessment
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.
Ask
How many objects do you think are in the group.
Child must instantly (2 seconds) tell the number of objects in a group.
Notes, comments, and suggestions
 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 Onetoone 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:
 Counts a group of 4,
 Counts a group of 8, and
 Counts a group of 12.
Ask
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.
Notes, comments, and suggestions
 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 onetoone 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 onetoone correspondence when the the counting sequence is done in an accurate onetoone 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 onetoone correspondence to touching and move to count ___
 Uses onetoone correspondence by pointing to count ___
 Uses onetoone correspondence to mentally point and count ____
 Use pattern to recognize ___ and ___ , then add count ___
 Uses onetoone correspondence to count groups less than 8 and synchrony above 8.
 Uses onetoone correspondence to count groups to 24
 Count by twos to ___
Assessment for Onetoone 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.
Ask
The student to put as many objects on the plate as there are dots on the card.
Notes, comments, and suggestions
 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 19.
Ask
Match the cards.
Notes, comments, and suggestions
 Subitize or match patterns with a quick look or glance.
 Count with synchrony with some and some not accurate.
 Counting dots using onetoone 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 (110).
Directions
Divide the cards into two piles. Have the student and teacher turn a card over.
Ask
 Who has more or less.
 Repeat for cards of value from 1020.
Notes, comments, and suggestions
 Counts each card using syncope and inconsistently identifies more, less, and same for dot card pairs of values ____
 Counts each card using oneonone 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.
Ask
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.
Notes, comments, and suggestions
 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 19.
Ask
Match the cards.
Notes, comments, and suggestions
 Subitize or match patterns with a quick look or glance.
 Count with synchrony with some and some not accurate.
 Counting dots using onetoone correspondence accurately.
 Student randomly selects cards.
 Students matched dots of ______ and counted dots of _______
 Cardinality score guide, rubric, & score sheet
[Additional assessment materials: Place value and operations of addition and subtraction]
Number Value Summary Sheet
Child's Name:
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.
Ideas for comments.
Rote counting:  Completed √, *,  
Comments 

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


Backwards  Completed √, *,  
Comments 
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


Multiple counting  Completed √, *,  
Comments 
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


Synchrony or Onetoone correspondence  Completed √, *,  
Comments 
1. Onetoone correspondence for group of four (counts a group of 4 objects)  
2. Onetoone correspondence for group of eight (counts a group of 8 objects)  
3. Onetoone correspondence for group of twelve (counts a group of 12 objects)  
4. Onetoone correspondence for group of twentyfour (counts a group of 24 objects)  
5. Generalizes onetoone correspondence for counting all values.  
Summary


Subitize Instant recognition of number value  Completed √, *,  
Comments 
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


Numeral recognition  Completed √, *,  
Comments 
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


Forms numerals
 t Top to bottom and left to right 
Completed √, *,  
Comments 
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


Combinations of addends to 12: hierarchical inclusion  Completed √, *,  
comments 
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 √, *,  
Comments 
Rows of objects onetoone, then spread  
Equal groups of different sizes and shapes  
Summary
