# 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

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

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.

Flash plate, wait ... repeat ...

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.

Flash plate, wait ... repeat ...

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.

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 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.

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.

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

### 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 Do with no prompts
Do with one prompt
1
Can or can not do with one or less prompts
-
1. Join
Sandra had 8 pennies. George gave her 4 more. How many pennies does Sandra have altogether? (8 + 4 = ?)
Sandra had 7 pennies. George gave her somemore. Now Sandra has 13 pennies. How many did George give her? (7 + ? = 13)
Sandra had some pennies. George gave her 6 more. Now Sandra has 15 pennies. How many did Sandra have to start? (? + 6 = 15)
2. Separate
Sandra had 11pennies. She gave 5 pennies to George. How many pennies does Sandra have now? (11 - 5 = ?)
Sandra had 12 pennies. She gave some to George. Now she has 9 pennies. How many did she give to George?
Sandra had some pennies. She gave 5 to George. Now Sandra has 9 pennies left. How many pennies did Sandra have to begin with?
3. Part-part whole
George has 5 pennies and 10 pennies. How many coins does he have? (5 + 10 = ?)
George has 13 pennies. Five pennies are in his right hand and the rest are in his left. How many pennies are in his left hand?
4. Compare
George have 11pennies and Sandra has 8 pennies. How many more pennies does George have than Sandra? (11 - 8 = ? or 8 + ? = 11)
George have 13 pennies. Sandra has 9 pennies. How many fewer pennies does Sandra have than George? (13 - 9 = ? or 9 + ? = 13)

## Addition and Subtraction Whole Number Calculation Algorithmic Scoring Guide

1
• Counts on for values to 20
• Uses five and ten as anchors

2
• Can tell one more and one less.
• Can tell two more and two less.
• Compose and decompose numbers to 20
• Mentally Adds and subtracts values to 20

3
• Add and subtract from left to right by decomposing double digit numbers to tens and ones.
• Works with tens, then works with ones, and then adds tens and ones.

4
• Adds on or subtracts from a two digit numer
• Mentally Adds and subtracts values to 100 including regrouping for addition and subtraction
• Adds and subtracts money values by composing and decomposing into coin values.

5
• Constructs and deconstructs addition and subtraction problems to 10 000.
• Regroup with addition fairly easily
• Regrouping with subtraction is cumbersome with problems requiring multiple regroupings

6
• Constructs and deconstructs addition and subtraction problems of any size with and without regrouping until confidence in the accuracy of the solution is attained.