Place Value
Assessments with record sheets and scoring guides
Examples of how to assess student's 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:
- Pre-place value, Number sequence to 100 with a 100 chart
- Multiple groupings, number sequences, counting, addition, conservation, pre-place value
- Groups of tens and ones set A, place value or bust
- Groups of tens and ones set B, place value or bust
A summary record sheet can be used to summarize information for each student. Includes categories for yes, no, and comments for each assessment task.
Assessment of [number sense] & addition and subtraction
Background information on the development of
Stop any of the individual assessments if a child is not able to respond or responds with random answers.
Pre-Place Value
Number sequence to 100, Tens and ones,
Child's Name:
Assessor's Name:
Materials
32 objects, 100 chart puzzle pieces. Two complete 100 chart puzzles, hundred chart with only numbers 1 & 100, and five pieces from a 100 chart.
Directions
Complete 100 chart puzzle:
- Give the child the puzzle pieces for a complete 100 chart puzzle and ask them to put the puzzle together.
- Ask how they knew where the pieces went.
- Record their response on the record sheet.
- Repeat with second 100 chart.
Ask
- Can yoi make this puzzle?
- How did you know where the pieces went?
Hundred chart with only numbers 1 & 100 and puzzle pieces with one number.
- Give the child a hundred chart with only numbers 1 & 100
- Give the child one puzzle piece and ask them where the puzzle together would go.
- Ask how they knew where the piece went.
- Ask them to write or tell you what other numbers would be on the piece.
- Record their response on the record sheet.
- Repeat with other puzzle pieces.
Ask
- Can you put this piece where it belongs on the mostly blank 100 chart?
- How did you know where the piece went?
- What are the rest of the numbers on the piece?
- How did you know?
Notes, comments, and suggestions
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 √.
- 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 - Completed all puzzles correctly referencing top to bottom counting ones and tens. 1, 2, 3.
Ideas for comments.
- Watch how the child decides where to place the pieces. Is the placement based on the number value of the numbers in the pieces and the number values required to complete the puzzle with lowest values in the top left to highest values in the bottom right. Or is the stragegy of using the shape of the pieces more employed. Are number values systematically used.
| Place value |
|
Comments | 100 chart puzzle. There are patterns to the way numbers
are sequenced. |
|---|---|---|
| Give the child the 100 chart puzzle pieces and ask them to put the puzzle together. | ||
| Ask how they knew where the pieces went. | ||
| Give the child an incomplete puzzle piece for a hundred chart (100 chart puzzle ) and ask them place it on a completed 100 chart. If successful, then ask them to complete the piece by saying or writing the missing numbers. | ||
| Ask how they knew what number to put into each box. | ||
Multiple Groups
Child's Name:
Assessor's Name:
Materials
Directions
- Put 32 objects in front of the student in three groups of ten and one group of two.
Ask
- How many objects are there all together?
- How do you know?
- Group the objects in different ways.
- How many objects are there all together?
- How do you know?
- Repeat the procedure.
- Record their response on the record sheet.
Notes, comments, and suggestions
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 √.
- 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 - Completed all puzzles correctly referencing top to bottom counting ones and tens. 1, 2, 3.
Ideas for comments.
- Watch how the child decides and counts the objects to put them into groups.
- Child is dependent on ones. Not comfortable with other ways of counting.
- Counts by ones, twos, ...
- Use groups to count and visually represents the total? Groups objects in twos or fives or tens and uses as anchors.
| Place value |
|
Comments |
|---|---|---|
| Groupings of ones and tens can be combined in different ways | ||
| Place a set of 32 objects onto the table with three groups of ten and one group of two. Ask the child how many objects there are all together. (32) | ||
| How did you know? (counted by ... ) | ||
| Ask the child if they can group the objects in a different way. Ask him/her to show you. Ask how they know there are 32. (group by fives, count 5, 10 ... , 31, 32.) | ||
| Ask if they can group them a third way. Ask him/her to show you. Ask how they know there are 32. (group by 2's ... 2, 4, ... 32 | ||
Groups of tens and ones
Pre-Place Value
Place values of tens and ones
Conservation of numbers
Unitize
Child's Name:
Assessor's Name:
Materials
27 objects (beans ... ), paper, pencil
Directions
- Put 24 objects in front of the student and ask how many objects.
Ask
- How many objects?
- Write that number.
- With the objects show me what (point to 4) that number represents.
- The three, show me what (point to 2) that number represents.
- If there are objects left over, then ask what should be done with the left over objects.
- How many objects are there all together now?
- Repeat the procedure with 27 objects.
Notes, comments, and suggestions
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 √.
- 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 - Completed all puzzles correctly referencing top to bottom counting ones and tens. 1, 2, 3.
Ideas for comments.
- Watch what the child does. Children that don't conserve or are unable to unitize or are not yet comfortable with the idea that something can have two names or values will deal with both numbers as units. Adding 2+4=6 and claim the other numbers as not needed. They will sometimes even say that 24 is really 6.
- Comfortable with composing and decomposing 24 as two tens and four ones, 20-ones and 4-ones, or 24-ones and recognizing all ot them as having the same value.
- Overwhelmed by a comparison as equal 24 objects and the digits 2 and 4.
- Overwhelmed by 2 in the position of 24 being equal to 20 or 20-ones.
| Place value |
|
Comments |
|---|---|---|
| Problem 1 Counting a set of 24. Sets of ten can be pereceived as single entities and used to describe how many. Give the child a set of 34 objects (substitute name of objects for object when talking to child). |
||
| a. Ask how many objects are there? (24) | ||
| b. Ask them to write the numeral for that number. (24) | ||
| c. Ask them how they know. (I counted ... ) | ||
| Point to the numeral 4 and ask how many objects that number means, represents, stands for ... (4) | ||
| Then ask what the three means, represents stands
for ... (20) Some children will say 2 and pull aside or point to three objects. When they do, prompt them by asking them what about the rest of the objects. What should you do with them? |
||
| Problem 2 Making a set of 27. The position of the digits in numerals determines what they represent and the size group they count. |
||
| a. Write the number 27 on a sheet
of paper. Ask the child to put that many objects beside the number.
(27 objects) |
||
| Point to the 7 and ask how many objects it represents. (7) | ||
| Ask the student to put that many objects next to the 7. (7) | ||
| b. Point to the two and ask how many objects that number means, represents, stands for ... (20) | ||
| Ask the child to put those objects
beside the two. (20) If the child answers by placing 2 or another number of objects, then prompt by asking. What should you do with them? |
||
| c. Ask how many objects there are. (27) | ||
Pre-Place Value (set b)
Place values of tens and ones
Conservation of numbers
Unitize
Child's Name:
Assessor's Name:
Materials
37 objects (beans ... ), paper, pencil
Directions
- Put 37 objects in front of the student and ask how many objects.
Ask
- How many objects?
- Write that number.
- With the objects show me what (point to 7) that number represents.
- The three, show me what (point to 3) that number represents.
- If there are objects left over, then ask what should be done with the left over objects.
- How many objects are there all together now?
- Repeat the procedure with 26 objects.
Notes, comments, and suggestions
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 √.
- 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 - Completed all puzzles correctly referencing top to bottom counting ones and tens. 1, 2, 3.
Ideas for comments.
- Watch what the child does. Children that don't conserve or are unable to unitize or are not yet comfortable with the idea that something can have two names or values will deal with both numbers as units. Adding 3+7=10 and claim the other numbers as not needed. They will sometimes even say that 37 is really 10.
- Comfortable with composing and decomposing a two digit number as tens and ones, ones and ones, or all ones and recognizing all ot them as having the same value (3 of 10+7 = 30+7 = 37).
- Overwhelmed by a comparison as equal 37 objects and the digits 3 and 7.
- Overwhelmed by 3 in the position of 37 being equal to 30 or 30-ones.
| Place value |
|
Comments |
|---|---|---|
| Problem 1 Counting a set of 37. Sets of ten can be pereceived as single entities and used to describe how many. Give the child a set of 37 objects (substitute name of objects for object when talking to child). |
||
| a. Ask how many objects are there? (37) | ||
| b. Ask them to write the numeral for that number. (37) | ||
| c. Ask them how they know. (I counted ... ) | ||
| Point to the numeral 7 and ask how many objects that number means, represents, stands for ... (7) | ||
| Then ask what the three means, represents stands
for ... (30) Some children will say 3 and show pull aside or point to three objects. When they do, prompt them by asking them what about the rest of the objects. What should you do with them? |
||
| Problem 2 Making a set of 26. The position of the digits in numerals determines what they represent and the size group they count. |
||
| a. Write the number 26 on a sheet
of paper. Ask the child to put that many objects beside the number.
(26 objects) |
||
| Point to the 6 and ask how many objects it represents. (6) | ||
| Ask the student to put that many objects next to the 4. (6) | ||
| b. Point to the two and ask how many objects that number means, represents, stands for ... (20) | ||
| Ask the child to put those objects
beside the two. (20) If the child answers by placing 2 or another number of objects, then prompt by asking. What should you do with them? |
||
| c. Ask how many objects there are. (26) | ||