Operations of addition and subtraction
Assessments with record sheets and scoring guides

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

• Subitize, pattern recognition, or quick addition. Dot plates with one and two colors
• Five as an anchor for addition
• Ten plus leftovers with ten frames and ten as anchor
• Addition and Subtraction: Kinds Of Problems Assessment and Scoring Guide combine, separate, part-part-whole, compare
• Combinations of addends to 12: hierarchical inclusion
• Addition and Subtraction Algorithm Scoring Guide

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] & [place value]

Background information on the development of

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

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

Subitize, pattern recognition, or quick addition for number value -

Dot plates with one color of dots

Materials

Dot plates with one color of dots with dots 1-10. or Electronic [1-5] [1-10] file.

Directions

Show students dot plates of one color 1-10. Tell them you will flash each plate for a second and they are to tell you the number of dots on each plate.

Ask

Flash plate, wait ... repeat ...

Notes, comments, and suggestions

Students recognize the following patterns of dots two seconds or less.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Dot plates with two colors of dots

Materials

Dot plates with two colors of dots with dots 2+1, 3+1, 4+1, 4+2, 4+3, 5+1, 5+2, 5+3, 5+4, 5+5, 6+1, 6+2, 6+3, 7+1, 8+1, 9+1

Directions

Show students dot plates of two colors with sums 3 -10. Tell them you will flash each plate for a second and they are to tell you the number of dots on each plate.

Ask

Flash plate, wait ... repeat ...

Notes, comments, and suggestions

Students recognize the following patterns or sums of dots two seconds or less.

2+1, 3+1, 4+1, 4+2, 4+3, 5+1, 5+2, 5+3, 5+4, 5+5, 6+1, 6+2, 6+3, 7+1, 8+1, 9+1

Hierarcial 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 suggestion.

Shows that knows hierachial 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

Five as anchor for addition and subtraction

Put nine OBJECTS on the table. Arrange five into a pattern that the students would recognize as five. If the student does not recognize a pattern of five have the student count out five and set them aside. Cover the five OBJECTS with your hand or a bowl and ask the student how many objects there are all together.
Response
Can’t do the task Moves hand or bowl and counts by ones Counts on to nine Adds five and four
Summary
Uses counting on strategy
 
Put eight OBJECTS on the table. Ask the student how many objects there are on the table. Cover five OBJECTS with your hand or a bowl and ask the student how many objects you have under your hand or bowl.
Response
Can’t do the task Moves hand or bowl and counts by ones Counts back from eight to five Subtracts three from eight
Summary
Uses counting back strategy
 
Pick up a number of OBJECTS, with out the students seeing how many. Hide them in your hand. Put four or five on a plate. Tell the student that there are NUMBER of OBJECTS in your hand.

Ask

how many are there in your hand and on the plate.
Response
Student can count on for
Summary
Uses counting on strategy

Ten plus leftovers with Ten frames and anchor of ten

Give students a ten frames plus cards or a complete ten frame and partial ten frame (10-20) and ask them to sequence them from least to most.
Response
Student counts most cards and has inaccuracies. Student counts some, uses visual pattern for some, and sequences cards. Student mostly uses visual pattern and sequences cards quickly and accurately.
Other
Summary
 Assessment for Number Value (Inclusiveness)

Combinations of addends to 12: hierarchical inclusion

Directions

• Start with a practice session with combinations of numbers 3 and 4.
• Use the number of beans as the sum.
• Count that number of 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 (6, 7, 8, 9, 10, 11, & 12) in a random order. E.g. for five beans (2 + 3, 0 + 5, 1 + 4, 5 + 0, 3 + 2, 4 + 1).
• If a student misses one, you can try it again and if they get it right the second time, then it can count as right with a prompt.

Ask

How many beans are in this hand (hold up the other hand).

• Repeat for all possible combinations of whole numbers (6, 7, 8, 9, 10, 11, & 12) in a random order. E.g. for five beans (2 + 3, 0 + 5, 1 + 4, 5 + 0, 3 + 2, 4 + 1).
• If a student misses one, you can try it again and if they get it right the second time, then it can count as right with a prompt.

Yes means all right on first or second attempt.

• Combinations of 5
• Combinations of 6
• Combinations of 7
• Combinations of 8
• Combinations of 9
• Combinations of 10
• Combinations of 11
• Combinations of 12

Kinds of addition and subtraction problems

Child's Name:

Name of Evaluator:

Assessors note 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 √.

Comments might unclude: used join, separate, part-part whole, compare, count on, count all...

Materials 20 pennies

Addition and Subtraction Whole Number
Calculation Algorithmic Scoring Guide

Dr. Robert Sweetland's notes
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