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

• 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 0ne-thousand 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
• One-to-one correspondence or synchrony [Synchrony information]
• Assessment for One-to-one 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

• Pre number sense
• Number sense
• Conservation
• Place value, &
• Addition and subtraction

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 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.

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 twenty-one, 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 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

Notes, comments, and suggestions

• 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.

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.

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.

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 [1-5] & [1-10] 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 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.

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 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.

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 1-9.

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 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.

Ask

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

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 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.

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 1-9.

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 one-to-one 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]

Dr. Robert Sweetland's notes
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