Math Error Analysis Worksheet by stt79717

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```									Supporting MATH skills
Models
for selecting interventions

Classwide
Instruction

Individual
Instruction
Models
1. Won’t Do or Can’t Do

Can’t do reasons:
Accuracy, Fluency,   Too hard
2. Powerful Effective teaching
3. Morningside Big 5 Math Targets

Tool Skills   Computation            Math Vocabulary
Conversation

Solving standard
word problems

Generic Problem
solving
Tool skills
– 1-9 digit numbers
• Writing numbers quickly and legibly
– 1-9 digit numbers
•   Copying and taking dictation
•   Place value
•   Quickly identifying, explaining, manipulating
•   Math facts fluency
– Number family method
– E.g., 5 9 45 = 5x9 = 45, 9x5= 45, 45~9 + 5, 45~5 + 9
• Number sense of number relationships
Computation
• Working with number combinations
division
• Whole numbers, fractions, decimals, &
simple percentage calculations
• “Mental” arithmetic
• Direct and explicit instruction of algorithms
Solving standard work problems
• Typical story problems involving quantities
• Between 20 to 70 word lengths
• Students learn to
– Write an algebraic equation with one unknown
– Determine the unknown by manipulating the
equation and doing arithmetic
• Direct instruction for 10 types of word
problems
• Fluency building
How To….
1)Select students for intervention
using screening data
1) Identify Can’t do problems
2) Conduct math level of assessment.
3) Set up progress monitoring.
4) Plan for implementation.
Who will do what and when.
CBM- To identify who
• Screen early for struggling students (K-1)
– Number Identification
– Quantity Discrimination
– Missing Number

• On going Screening for basic skills (1-6)
– Computation

• Screen for Solving and Predict end of year test (2-6)
– Concepts and Applications

Fuchs Manual:
tegory&id=10&Itemid=56
Concepts and Applications

–   18–25 problems
–   year-long.
–   Timed
–   Score: total
number of
correct blanks

2       8 minutes
3-4      6 minutes
5-6      7 minutes
Early Skills
1. orally identify the
13
number ( 0 thru100).

2. orally identify the
3        7         larger number

3. orally identify the
3   4 __ 6            missing number
Why CBM?
To identify level for Intervention

Common computation errors:

1. Inadequate tool skills and mastery of facts

2. Ineffective strategy (error in steps in
procedure) but sound facts
3. Inadequate facts but effective strategies
To assess TOOL Skills
Single CBM Tools skills

Tool Skill         Correct   Errors
Single probes                         ACCURACY PROBLEM
Reading numbers                       SLOW AND MANY ERRORS
Writing numbers
Place value
FLUENCY PROBLEM
SLOW AND FEW ERRORS
Subtract facts
Multiply facts
Division facts
Using End-of-Year
Benchmarks
Kindergarten                          Data not yet available
First          Computation                        30            20 digits
First                                 Data not yet available
Second         Computation                        45            20 digits
Second         Concepts and Applications          32            20 blanks
Third          Computation                        45            30 digits
Third          Concepts and Applications          47            30 blanks
Fourth         Computation                        70            40 digits
Fourth         Concepts and Applications          42            30 blanks
Fifth          Computation                        80            30 digits
Fifth          Concepts and Applications          32            15 blanks
Sixth          Computation                       105            35 digits
Sixth          Concepts and Applications          35            15 blanks
How to…Tool skills
Class-wide Math Intervention
Classwide monitoring
of skill acquisition
After classwide instruction
Tool Skill Flashcard Intervention
15 Min per Day
• Model, Guided Practice, Independent Timed
Practice with delayed error correction
MATH FLASHCARD                  PARTNERS

Demonstration Math 1: Flashcards

Tear to make 6 flashcards.
Your partner is someone sitting next to you.

Get out flashcards and a regular pencil and a
colored pen.

Move to math partner seating.
STEP 2: GUIDED PEER PRACTICE for 3 minutes

Partner 1 SAYS flashcard ANSWERS .

Partner 2 SHOWS FLASHCARDS for 3 seconds.

Do new job for another 3 minutes
Demonstration Math 2 Practice Test

Turn passed out practice paper over.
Write name on back.

STEP 4: 2 minute TIMED INDEPENDENT PRACTICE

At “GO!” turn paper over and write answers.

Hold paper in the air when timer rings.
STEP 5: GRADE and CORRECT ERRORS

Mark answers right or wrong with colored pen using

Write correct answers to missed problems.

2     3            8        3        2        3        8
x 3   x 2         x   3    x   6    x   3    x   3    x   3
6        6        24       18       6        9        24

7        3        9        3        8        5        8
x   3    x   6    x   3    x   7    x   3    x   3    x   3
21       18       27       21       24       15       24

2        3        5        3        8        3        5
x   3    x   2    x   3    x   7    x   3    x   3    x   3
6        6        15       21       24       9        15

7        3        1        3        0        0        4
x   3    x   0    x   3    x   3    x   3    x   3    x   3
21       0        3        9        0        0        12

4        3        3        3        0        3        2
x   3    x   2    x   3    x   6    x   3    x   3    x   3
12       6        9        18       0        9        6

6        3        1        3        9        5        9
x   3    x   5    x   3    x   8    x   3    x   3    x   3
18       15       3        24       27       15       27

3        3        2        3        2        0        9
x   3    x   5    x   3    x   1    x   3    x   3    x   3
9        15       6        3        6        0        27
RECORD
Demonstration MATH 3
50

45
Number of digits correct per 2 minutes
40

35

30
Score
25
Errors
20

15

10

5

0
1   2   3   4   5   6   7   8   9 10 11 12 13 14 15

Practice day
MATH FLASHCARD     PARTNERS
Get out flashcards and a regular and a colored pen.
Move to math partner seating.

STEP 2: GUIDED PEER PRACTICE for 3 minutes
Partner 1 SAYS flashcard ANSWERS .
Partner 2 SHOWS FLASHCARDS for 3 seconds.

Do new job for another 3 minutes

Turn passed out practice paper over.
Write name on back.

STEP 4: 2 minute TIMED INDEPENDENT PRACTICE
At “GO!” turn paper over and write answers.
Hold paper in the air when timer rings.

STEP 5: GRADE and CORRECT ERRORS
Write correct answers to missed problems.

STEP 6: RECORD
Write score on progress graph.    Pass paper to teacher.
To assess if knows strategies

Computation Error Analysis

Test strategies with “easy” facts to target gaps

Fluency: Time 2 to 5 minutes and mark last problem

Accuracy: Allow to finish untimed
1)              2)              3)              4)            5)
21             125             26              92            215
+ 43            +721            + 5             +18           +495

6)              7)              8)              9)            10)
54             367             51               40           932
-12            -121            -22             - 11          -167

11)             12)             13)             14)           15)
34               12             67               523           37
x 2             x 24            x 2              x 5          x 25

•(other similar probes with decimal, fractions, rounding, place value)
SKILL                                             TEST # JOHN TIM     JANE   TINA
Addition Score > 20 digits per minute?                     Yes   No    No     Yes
Add two columns no regrouping                       1                       
Add three columns no regrouping                     2                       
Add one column regrouping                           3                        
Add two columns regrouping                          4                         
Add three columns regrouping                        5                         

SUBTRACTION
Subtract > 20 digits per minute?                           Yes   No    Yes     No
Subtract two columns no regrouping                 6                         
Subtract three columns no regrouping               7                         
Subtract two columns with regrouping               8                          
Subtract three columns with regrouping and zero    9                          
Subtract three columns with regrouping             10

MULTIPLICATION
Multiplication > 20 digits per minute?                     Yes   No    No     Yes
Multiply one digit no regrouping                    11                       
Multiply two digits no regrouping                   12                        
Multiply one digit with regrouping                13, 14                      
Multiply two digits with regrouping                 15
Sample computation Sequence
1. addition and subtraction facts 0-20                flash cards
2. fact families addition and subtraction 0-20        practice set – same as skill
3. 3 digit addition without and with regrouping       practice set – same as skill
4. 3 digit subtraction without and with regrouping    practice set – same as skill
5. 2 and 3 digit addition and subtraction             practice set – same as skill
with and without regrouping
6.   multiplication facts 0-9                        flash cards
7.   division facts 0-9                              flash cards
8.   fact families multiplication and division 0-9   practice set – same as skill
9.   add/subtract fractions with like denominators   practice set – same as skill
(3rds, 4ths, 8ths, 10ths, no regrouping)
10. single digit multiplied by double/triple digit   practice set – same as skill
without regrouping
11. single digit multiplied by double/triple digit   practice set – same as skill
with regrouping
12. single digit divided into double/triple digit    practice set – same as skill
without remainders
13. add and subtract decimals to the hundredths      practice set – same as skill
Fuchs Math: 17 Scripted Topics

•   Identifying and writing       •   Writing number sentences
numbers to 99                     (story problems)
•   Identifying more, less, and   •   Place value (0-99)
equal with objects            •   Addition facts (sums to 18)
•   Sequencing numbers            •   Subtraction facts (minuends
•   Using <, >, and = symbols         to 18)
•   Skip counting by 10s, 5s,     •   Review of addition and
and 2s                            subtraction facts
•   Understanding place value     •   Place value review
(introduction)                •   2-digit addition (no regrouping)
•   Identifying operations        •   2-digit subtraction (no
•   Place value (0-50)                regrouping)

30
How to…Computation
Class-wide Math Intervention

Teacher first reviews steps and write SKILL STEPS on board.
1)              2)            3)           4)            5)
21           125           26           92            215
+ 43          +721          + 5          +18           +495

6)              7)            8)           9)            10)
54            367           51            40           932
-12           -121          -22          - 11          -167

11)             12)           13)          14)           15)
34             12           67            523           37
x 2           x 24          x 2           x 5          x 25

To subtract two numbers that require regrouping need to know:
1)check ones place (place value)
2)know top number should be bigger
3)know how to take a 10 from tens place to ones place
4)Subtraction facts
MATH COMPUTATION STEP BY STEP COACHES

Tens Ones
1. Look at the ones column.                  53
- 38
2. Is top number is smaller than bottom?           53
YES                                            -38
So need to make top bigger.
4
3. Burrow a 10 from the tens column.                    53
Cross out the top number in tens column.               -38
Subtract 1 from top number  5 – 1 = 4
Write the number on top.                                     4
4. Add the 10 to the one column.                             5 14
10 + 4 = 14                                                 -38
Write in the 1 next to the top number.                              4
5. Subtracted ones column correctly.                                    1
54
(14 – 8= 6)                                                   -38
6        4
6. Subtracted tens column correctly.                                         5 4
( 4 - 3 = 1)                                                             -3 8
16
MATH COMPUTATION COACHES

Demonstration Math 4
Your partner is someone sitting next to you.

Move to math partner seating with folder, regular
pencil and a colored pen

Write name on passed out worksheet.
STEP 2: GUIDED PEER PRACTICE for 3 minutes

Partner 1 WRITES as many answers as possible

Partner 2 LOOKS at answers as written
SHOW how to redo missed or stuck answers.

Demonstration MATH 5 : Practice test

Turn passed out practice paper over.
Write name on back.

STEP 4: 2 minute TIMED INDEPENDENT PRACTICE

At “GO!” turn paper over and write answers.

Hold paper in the air when timer rings.
MATH COMPUTATION COACHES
Move to math partner seating with folder, regular and a colored pen
Write name on passed out worksheet.

STEP 2: GUIDED PEER PRACTICE for 3 minutes
Partner 1 WRITES as many answers as possible
Partner 2 LOOKS at answers as written
SHOW how to redo missed or stuck answers.

Turn passed out practice paper over.
Write name on back.

STEP 4: 2 minute TIMED INDEPENDENT PRACTICE
At “GO!” turn paper over and write answers.
Hold paper in the air when timer rings.

STEP 5: GRADE and CORRECT ERRORS
Mark answers right or wrong with colored pen.
Write correct answers to missed problems.

STEP 6: RECORD score on progress graph.
Computation Coaches Intervention
15 Min per Day
• Teachers encouraged to
– Provide applied practice using mastery-level basic
tool skills
– Have stronger do it first. That person can then show
his or her process on paper if needed.
– Make sure students tell how to do it and not just give
– Scan papers for high error rates
– Do 5-min re-teach for those with high-error rates
Measurement Plan
• Weekly probe of Intervention skill
• Weekly probe of Retention of previously
mastered computational skills
• Monthly probe to monitor progress toward
year-end computational goals
General Findings
• Growth rates and trials to criterion varied
dramatically across skills
• Retention probe was strongest predictor of year-
end SAT-9 performance
• Mastery level performance on early skills
predicted fewer trials to criterion on future
related complex skills
• Fluency scores higher than “mastery” predicted
retention of skill over time (about +20 dc/min)

VanDerHeyden, in preparation
Tier 1 Outcome 2 in math
Response Cards
Guided practice
PREP

• For each student: a laminate board, a dry erase marker,
and paper towel.

• Train until all students respond to cues :
– “Cards write” write problem and answer
– “Cards up” hold card above head towards teacher
– “Cards clean” wipe clean
Response Cards
Small group guided practice
After lecture and skill modeling, give 1 problem at a time.

• Say “Cards write!”
• Wait sufficient time.
• Say “Cards up!”
– All correct  praise, say “Clean cards!”, and move on.
– Two or three wrong  give correct response, instruct
the students to check their answers, move on
– More than 25% wrong  reteach and ask again.
• Increase Pace as students learn skill.
Cover - Copy - Compare
STEP 1: Give a copy of the answers or another student’s 100% paper.
STEP 2: Prompt to do the following 5 steps when working on problems.
Look at the solution of the problem.
Do the problems on your own paper.

STEP 3: After 4 problems correct, try 4 problems without procedure.
STEP 4: Check work. If incorrect, give help and tell the student to redo
the problem 3 times.
STEP 5: Have student complete worksheet, grade and chart.

Website for cover copy and compare worksheets:
Recommended computer fluency building
program:
Quarter Mile Math
http://www.thequartermile.com/

· Race format to motivate students
· > 70,000 problems for K through pre-

For Problem solving ideas:

See Interventioncentral.org by Jim Wright
KEEP IT SIMPLE
PROBLEM    Tools skills   Computation             Problem Solving
Accurate   Peer tutor     1. Mini skill step
flashcard      lessons

PLUS

2. Large group:
Peer tutoring
or
Cover copy Compare

Small group:
Response cards

PLUS

3. Daily fluency test

Fluency    Timed trials   Time trials with goal
setting

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