Classwide Instruction

Individual Instruction

Models for selecting interventions

Supporting MATH skills

Models 1. Won’t Do or Can’t Do

Can’t do reasons: Accuracy, Fluency, Too hard

2. Powerful Effective teaching

Solving standard word problems

ComputationTool Skills Math Vocabulary Conversation

3. Morningside Big 5 Math Targets

Generic Problem solving

Tool skills

• Reading numbers quickly– 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

• Addition, subtraction, Multiplication and 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: http://www.rti4success.org/index.php?option=com_content&task=blogcategory&id=10&Itemid=56

Concepts and Applications

– 18–25 problems– year-long.– Timed– Score: total

number of correct blanks

Grade Time limit

2 8 minutes

3-4 6 minutes

5-6 7 minutes

Early Skills

3. orally identify the missing number3 4 __ 6

2. orally identify the larger number3

7

1. orally identify the number ( 0 thru100).

13

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

Single CBM Tools skills

Tool Skill Single probes

Correct Errors

Reading numbers

Writing numbers

Place value

Add facts

Subtract facts

Multiply facts

Division facts

ACCURACY PROBLEM SLOW AND MANY ERRORS

FLUENCY PROBLEM SLOW AND FEW ERRORS

To assess TOOL Skills

Grade Probe Maximum score

Benchmark

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

Using End-of-Year Benchmarks

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

STEP 1: GET READY

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

Move to math partner seating.

MATH FLASHCARD PARTNERS

Demonstration Math 1: Flashcards

Tear to make 6 flashcards. Write answers on back. Your partner is someone sitting next to you.

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

Partner 2 SHOWS FLASHCARDS for 3 seconds. SAY answer if no answer or mistake.

Trade jobs when timer ringsDo new job for another 3 minutes

STEP 3: GET READY

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.

Demonstration Math 2 Practice Test

STEP 5: GRADE and CORRECT ERRORS

Mark answers right or wrong with colored pen using overhead answer key.

Write correct answers to missed problems.

Answers on overhead

ANSWER KEY 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 8x 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 5x 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 4x 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 2x 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 9x 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 9x 3 x 5 x 3 x 1 x 3 x 3 x 3

9 15 6 3 6 0 27

0

5

10

15

20

25

30

35

40

45

50

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

Practice day

Num

ber o

f dig

its c

orre

ct p

er 2

min

utes

Score Errors

RECORDDemonstration MATH 3

STEP 1: GET READY 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. SAY answer if no answer or mistake.

Trade jobs when timer ringsDo new job for another 3 minutes

STEP 3: GET READYTurn 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 overhead answer key. Write correct answers to missed problems.

STEP 6: RECORD Write score on progress graph. Pass paper to teacher.

MATH FLASHCARD PARTNERS

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

To assess if knows strategieseven with inadequate facts

1) 21+ 43

2) 125+721

3) 26+ 5

4) 92+18

5) 215+495

6) 54 -12

7) 367-121

8) 51-22

9) 40- 11

10) 932-167

11) 34x 2

12) 12x 24

13) 67x 2

14) 523 x 5

15) 37x 25

•(other similar probes with decimal, fractions, rounding, place value)

SKILL TEST #

JOHN TIM JANE TINA

ADDITION          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 YesMultiply 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

3RD GRADE 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

30

Fuchs Math: 17 Scripted Topics

• Identifying and writing numbers to 99

• Identifying more, less, and equal with objects

• Sequencing numbers • Using <, >, and = symbols• Skip counting by 10s, 5s,

and 2s• Understanding place value

(introduction) • Identifying operations • Place value (0-50)

• Writing number sentences (story problems)

• Place value (0-99)• Addition facts (sums to 18)• Subtraction facts (minuends

to 18)• Review of addition and

subtraction facts• Place value review• 2-digit addition (no regrouping)• 2-digit subtraction (no

regrouping)• Missing addends

How to…Computation Class-wide Math Intervention

Teacher first reviews steps and write SKILL STEPS on board.

1) 21+ 43

2) 125+721

3) 26+ 5

4) 92+18

5) 215+495

6) 54 -12

7) 367-121

8) 51-22

9) 40- 11

10) 932-167

11) 34x 2

12) 12x 24

13) 67x 2

14) 523 x 5

15) 37x 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

1. Look at the ones column. 5 3- 3 8

2. Is top number is smaller than bottom? YES So need to make top bigger.

5 3 - 3 8

3. Burrow a 10 from the tens column. Cross out the top number in tens column. Subtract 1 from top number 5 – 1 = 4 Write the number on top.

5 3 - 3 8

4. Add the 10 to the one column. 10 + 4 = 14Write in the 1 next to the top number.

5 4 - 3 8

5. Subtracted ones column correctly. (14 – 8= 6)

5 4 - 3 8 6

6. Subtracted tens column correctly. ( 4 - 3 = 1)

5 4 - 3 8 1 6

4

41

41

4

Tens Ones

STEP 1: GET READY

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

Write name on passed out worksheet.

MATH COMPUTATION COACHES

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

STEP 2: GUIDED PEER PRACTICE for 3 minutes

Partner 1 WRITES as many answers as possible Partner 2 LOOKS at answers as writtenSHOW how to redo missed or stuck answers.

Trade jobs when timer rings

STEP 3: GET READY

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.

Demonstration MATH 5 : Practice test

STEP 1: GET READY 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 writtenSHOW how to redo missed or stuck answers.Trade jobs when timer rings

STEP 3: GET READYTurn 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.

MATH COMPUTATION COACHES

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

answer. – 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!”

• Scan students’ answers.

– 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 - CompareSTEP 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.

Cover the correct answer.

Do the problems on your own paper.

Uncover the correct answer.

Compare your answer with the correct answer.

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:

http://www.interventioncentral.org/htmdocs/tools/mathprobe/addsing.php

Recommended computer fluency building program:

Quarter Mile Math http://www.thequartermile.com/

· Race format to motivate students · > 70,000 problems for K through pre-algebra (K-9th grade)

For Problem solving ideas:

See Interventioncentral.org by Jim Wright

PROBLEM Tools skills Computation Problem Solving

Accurate Peer tutor flashcard

1. Mini skill step 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

KEEP IT SIMPLE