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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 • 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=blogca tegory&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 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 Add facts SLOW AND FEW ERRORS Subtract facts Multiply facts Division facts Using End-of-Year Benchmarks 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 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. Write answers on back. Your partner is someone sitting next to you. STEP 1: GET READY 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. SAY answer if no answer or mistake. Trade jobs when timer rings Do new job for another 3 minutes Demonstration Math 2 Practice Test 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. 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 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 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 rings Do 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. 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. To assess if knows strategies even with inadequate facts 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 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 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 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) • Missing addends 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. STEP 1: GET READY 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. Trade jobs when timer rings Demonstration MATH 5 : Practice test 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. MATH COMPUTATION COACHES 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 written SHOW 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. 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 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 - 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. 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 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