LPLC Tier 3 Math Lee Pesky Learning Center

LPLC Tier 3 Math Lee Pesky Learning Center Dr. Evelyn Johnson, Cristianne Lane, M. Ed ejohnson@lplearningcenter. org clane@lplearningcenter. org

Introductions Logistics for the Day Your Materials About Our Center

LPLC Agenda – Day 1 • Factors that impact math performance • Complex learner profile • Teaching principles for working with students with disabilities • Number and Operations within Base 10 • Multiplication and Division

LPLC Agenda – Day 2 • Rational Numbers: – fractions, decimals, ratios, percentages • • Study Skills Algebra Resources Progress Monitoring Action Plan

LPLC YOU ARE HERE

LPLC What Impacts Math Performance?

LPLC Executive Functions Attention/ Organization Behavior/ Activity Level Flexibility & Self. Regulation Emotions Social Interaction

H Information Processing t 6 6 4 x 6= 24 July 4, 177 r N i S 1 JU 7 Y L The cat ran into the 6 stre et.

Information Processing Short-term memory Immediate memory (Phonological loop, Visual spatial sketchpad Working memory Long-term memory – includes retrieval Visual-motor production Language Visual-spatial thinking Fluid reasoning Crystallized knowledge

Information Processing Executive Functions Language Short-term memory Immediate memory Working memory Visual-spatial thinking Fluid reasoning Crystallized knowledge Long-term memory (LTM) Visual-motor production Long-term retrieval

Subtypes of Math Disability Retrieval Short-term Memory (Verbal) Short-Term Memory (Visual) Processing Speed Semantic Memory Working Memory Fluid Reasoning Language Visual-Spatial Thinking Magnitude/Quotity Retrieval Visual-Spatial Thinking Procedural Number Sense Executive Function Source: Geary, Hoard & Bailey (2010). How SLD Manifests in Mathematics.

LPLC Teaching Principles • Provide opportunities for success • Use multisensory instruction • Provide scaffolded, guided practice through structured task analysis – CRA progression • Practice and review with “relentless consistency” to achieve automaticity • Provide models – CRA progression • Include students in the learning process – opportunities to verbalize reasoning • Teach diagnostically

rti C-R-A Progression Abstract Representational Concrete

LPLC What Impacts Math Performance?

Targeted Assessments • Handout, page 1 • Video of student assessments – Hiding Assessment by K. Richardson – Making Tens by K. Richardson (Place Value) – Math Reasoning Inventories by M. Burns • Whole Numbers • Fractions • Decimals

Where is the breakdown in understanding? K 1 2 3 4 5 6 7 8 HS Counting & Cardinality Number and Operations in Base Ten Number and Operations – Fractions Ratios and Proportional Relationships Number & Quantity The Number System Expressions and Equations Algebra Operations and Algebraic Thinking Functions Geometry Measurement and Data Functions Geometry Statistics and Probability Statistics & Probability

Chris Woodin, Landmark School

LPLC Number Sense & Operations in Base 10 • Key Concepts • Creating durable, consistent images to represent numbers 1 – 10 – Consistent images address deficits in working memory, visual-spatial thinking, retrieval – Create a foundational system for all other operations Source: Woodin, C. (2000)

LPLC Number Sense & Operations in Base 10 Source: Woodin, C. (2000)

LPLC Number Sense & Operations in Base 10 Source: Woodin, C. (2000)

LPLC Number Sense & Operations in Base 10 • Activity: Teaching and Making Icons • Handout, pages 2 -7 Source: Woodin, C. (2012)

LPLC Teaching and Making Icons – Base Five Source: Woodin, C. (2012)

PL Number Sense & Operations in Base 10 • Page 2 Tracking automaticity of icon recognition • Video Clip #1: Building to 5 – You. Tube: “LBLD Math: Icon Card Addition • Page 3: Moving to the X, writing equations for numbers greater than 5 • Page 4: Missing addends (prerequisite for regrouping with subtraction) Source: Woodin, C. (2012)

LPLC Preparing for Regrouping • Page 5 -7: adding 5 (horizontal, vertical) • Video Clip #2 – You. Tube: “Kinesthetic Learning: Doing Math with Semiconcrete Diagrams” Two Questions: Are both numbers at least 5? Which number is bigger? Source: Woodin, C. (2012)

LPLC Contextualized Problem Solving • Where do you begin with contextualized problems? “Hiding Assessment” video • Problem Types – Common Core Learning Progressions document (handout page 8) • Story Mats – Contextualized problems – “There are _____. Then _____”

Remember the math posters from Gildo Rey… (refer to “Tier 2 training)

LPLC Teaching Principles • Provide opportunities for success • Use multisensory instruction • Provide scaffolded, guided practice through structured task analysis – CRA progression • Practice and review with “relentless consistency” to achieve automaticity • Provide models – CRA progression • Include students in the learning process – opportunities to verbalize reasoning • Teach diagnostically

Let’s Try It! 5 + 3 8 + 5

LPLC Place Value • Develop place value concepts through counting collections – “Skip Counting with Counting Collections” video clip from the Teaching Channel (https: //www. teachingchannel. org/videos/skipcounting-with-kindergarteners)

LPLC Place Value • Developing conceptual understanding – Pattern of 0 -9 repeating (Scrolling) – Building a hundreds chart – Number lines • These activities allow students to ‘see’ numbers and patterns • 10 x 10 blocks – connect to 100’s and 10’s

LPLC Place Value - CRA Source: http: //moodle. rockyview. ab. ca

LPLC Place Value Hundreds Tens Source: http: //moodle. rockyview. ab. ca Ones

Regrouping: Two Examples • Video: Chris Woodin (see next slide) • Making Math Real

LPLC Multi-Digit Subtraction Involving Regrouping • Page 9 b Making tens sticks and “X’s” Displaying the place value objects in icon formation • Page 11: prerequisite activities • Video clip #3: “diagramming” subtraction • Page 12 -15: practice pages

Let’s Try It! 10 - 3 - 12 5

We do…. then you do! 17 +24 26 + 34 28 + 17

Subtracting with regrouping 27 - 14 32 - 18

Regrouping: Two Examples • Video: Chris Woodin (see next slide) – You. Tube: “Kinesthetic Learning: Subtraction Math Using Diagrams” • Making Math Real

LPLC Teaching Principles • Provide opportunities for success • Use multisensory instruction • Provide scaffolded, guided practice through structured task analysis – CRA progression • Practice and review with “relentless consistency” to achieve automaticity • Provide models – CRA progression • Include students in the learning process – opportunities to verbalize reasoning • Teach diagnostically

LPLC Operations: Multiplication & Division • Whole to part, then part to whole fact models • Developing fluency with math facts • Integration of division and multiplication • Please note that slides are from Woodin, C. L. (2012) Multiplication and Division Facts for the Whole-to-Part, Visual Learner (used here with permission from the author)

LPLC Create the Reference Source: Woodin, C. (2012)

LPLC Move to Establish Part to Whole Source: Woodin, C. (2012)

LPLC Create the Reference Source: Woodin, C. (2012)

LPLC Part to Whole Multiplication 2 Source: Woodin, C. (2012)

LPLC Moving to the next step: Area Models Source: Woodin, C. (2012)

LPLC Moving to the next step: Area Models Source: Woodin, C. (2012)

LPLC Moving to the next step: Area Models Source: Woodin, C. (2012)

LPLC Moving to the next step: Area Models Source: Woodin, C. (2012)

LPLC Moving to the next step: Area Models Source: Woodin, C. (2012)

LPLC Moving to the next step: Area Models Source: Woodin, C. (2012)

LPLC Area Models to Matrix Diagrams Source: Woodin, C. (2012)

Resource for Practice Activities…and More! (O’Connell and San. Giovanni)

LPLC Integrating Division Source: Woodin, C. (2012)

LPLC Integrating Division Source: Woodin, C. (2012)

LPLC Integrating Division Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

Images (Woodin… and Van de Walle too) • • • 2’s= anything in pairs (shoes) 3’s= tricycles 4’s= legs 5’s= fingers on one hand 6’s= 6 pack

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Extending the 10 facts Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Developing Fluency Source: Woodin, C. (2012)

LPLC Moving on to multidigit multiplication Distributive Property Source: Woodin, C. (2012)

LPLC Define multidigit factors with expanded notation. 1 3 x 2 = 10 + 3 81

LPLC Define the problem using a compound matrix. The bottom factor defines the width, the top factor defines the height. 2 1 3 x 2 10 + Source: Woodin, C. (2012) 3 82

LPLC Define the composite areas. 2 1 3 x 2 10 2 0 + Source: Woodin, C. (2012) 3 6 83

The multiplication problem is solved procedurally by the teacher. 1 3 x 2 2 6 2 10 2 0 + Source: Woodin, C. (2012) 3 6 2 6

2 6 10 2 0 3 6 2 x 3=6 3 x 2=6 2 685

Organize the matrix so that the width is defined by the bottom factor. 10 Source: Woodin, C. (2012) 9 86

Compute the composite areas. 10 Source: Woodin, C. (2012) 9 300 270 20 18 87

Solve the problem procedurally. Compare the 1 st row and right column. 10 2 8 9 8 300 270 20 18 288√ 88

Solve the problem procedurally. Compare the 2 nd row and left column. 10 9 2 8 8 3 2 0 300 270 20 18 320√ 89

Add Subproducts. 10 9 2 8 3 8 2 0 6 08 Source: Woodin, C. (2012) 300 270 20 18 90

Templated single step division Matching procedure done in parallel: 2 2 6 Put 6 Shoes on a rectangular desk: Source: Woodin, C. (2012) 91

Templated single step division How many whole pairs of shoes? 3. It takes 2 to make 1 whole. 2 Source: Woodin, C. (2012) Matching procedure done in parallel: 2 3 6 92

Templated single step division 2 2 How many shoes are in 3 pair? 6. 3 6 6 3 x 2=6 Source: Woodin, C. (2012) 93

Templated single step division 2 2 After the 3 pair or 6 shoes are taken away and boxed, how many are left? (subtract 6). Source: Woodin, C. (2012) 3 6 6 0 94

Templated single step division Matching procedure done in parallel: 2 2 7 Put 7 Shoes on a rectangular desk: Source: Woodin, C. (2012) 95

Templated single step division How many whole pairs of shoes ? 3. It takes 2 to make 1 whole. 2 Source: Woodin, C. (2012) Matching procedure done in parallel: 2 3 7 96

Templated single step division 2 2 How many shoes are in 3 pair? 6. Source: Woodin, C. (2012) 3 7 6 97

Templated single step division 2 2 After the 3 pair or 6 shoes are taken away and boxed, how many are left? (subtract 6). Source: Woodin, C. (2012) 1 shoe is left on the rectangular table. 3 7 6 1 98

Templated single step division 2 2 After the 3 pair or 6 shoes are taken away and boxed, how many are left? (subtract 6). Source: Woodin, C. (2012) Box the 1 shoe remaining on rectangular table. 3 7 6 1 99

Templated single step division 1 2 2 There is one shoe remaining. It takes 2 to make 1 whole pair Source: Woodin, C. (2012) Record the remainder as a fraction. 3 7 6 1 100 2

Templated single step division Write four related facts Source: Woodin, C. (2012) 101

• Define each step. Compare Divide Multiply Subtract Check Subtraction Bring down • Execute each step using gross motor /kinesthetic processing – if needed. • Verbalize each step to integrate language with each production step. 103

Video Example: You. Tube: LBLD Math - Kinesthetic Learning: Long Division

Check subtraction by adding UP. 0 +2= 2 2 6 2 4 0 0 +4= 4 105

5 x 9 = 45 45 ÷ 9 = 5 9 x 5 = 45 45 ÷ 5 = 9 9 4 5 0 106

LPLC Agenda – Day 2 • Rational Numbers: – Fractions, Decimals, Ratios, Percentages • • Study Skills Algebra Resources Progress Monitoring Action Plan

LPLC YOU ARE HERE

LPLC Rational Numbers: Fractions • “Big Ideas” – handout, page 1 • Developing Effective Fractions Instruction for Kindergarten Through 8 th Grade – IES Practice Guide (September 2010) – Handout of 5 Recommendations, page 2

LPLC Recommendation #1 “Build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts. ” • Problem type sort – page 3

It is the day after Halloween. A friend gives you and your best friend 12 of her candies to split equally.

LPLC Recommendation #2 • “Cover Up” from MTI (handout, pages 4 -5) – Ordering basic unit fractions – Writing equations that equal 1 – Equivalency activities = • Making a chart to order fractions (reference tool) – Fraction War – V Math example, page 6 • Equivalence activity (“simplifying fractions”) – Ratio tables to show equivalency (recipes, etc. ) • Using number lines – Measuring with strips – Using tenths to link to decimals, page 7 – Hundreds charts (decimals, percentages, fractions page 8

Use of number lines to teach equivalence of fractions in a Japanese curriculum

LPLC Teaching Principles • Provide opportunities for success • Use multisensory instruction • Provide scaffolded, guided practice through structured task analysis – CRA progression • Practice and review with “relentless consistency” to achieve automaticity • Provide models – CRA progression • Include students in the learning process – opportunities to verbalize reasoning • Teach diagnostically

LPLC Recommendations #3 - #4 • Math Vids – Using a number line to understand why procedures work (next slide) • Ratios the Landmark Way – page 9 • Sorts for practice (Jennifer Sauriol) – page 10 • Two column notes (study skills) – page 11 • “Flapper cards” (study skills) – pages 12 a-c

Math. Vids. com

Why do we invert and multiply? Use the number line to explain to your partner why we invert and multiply? Example: 2 ÷ 1/3

Close up of “flapper cards”

LPLC Teaching Principles • Provide opportunities for success • Use multisensory instruction • Provide scaffolded, guided practice through structured task analysis – CRA progression • Practice and review with “relentless consistency” to achieve automaticity • Provide models – CRA progression • Include students in the learning process – opportunities to verbalize reasoning • Teach diagnostically

LPLC Algebra Resources • DMT website (MTI) • Math. Vids • Solving Equations: An Algebra Intervention by Brad Witzel and Paul Ricommini – handout, page 13 - 16 • KUTA software – handout, page 17 • Jennifer Sauriol from Landmark – Algebra “make it and take it” activities

LPLC Teaching Principles • Provide opportunities for success • Use multisensory instruction • Provide scaffolded, guided practice through structured task analysis – CRA progression • Practice and review with “relentless consistency” to achieve automaticity • Provide models – CRA progression • Include students in the learning process – opportunities to verbalize reasoning • Teach diagnostically

LPLC Error Analysis • Handout page 18

LPLC Progress Monitoring • For students with disabilities, we want a General Outcome Measure to gauge progress relative to grade level performance standards • However, we also want individualized progress monitoring tools to determine growth in the taught skill.

LPLC Progress Monitoring GOM and Mastery Measures • Handout page 1

LPLC Progress Monitoring – Mastery Measures • Mastery Measures tell us whether students are learning the skills we are teaching them • They are generally not norm referenced or standardized • Important to set MASTERY targets – remember, we want kids to ‘overlearn’ a skill

LPLC Developing and Charting Mastery Measures • Ensure you have sufficient number of problems reflecting current skill • Typically mastery measures are not timed • Establish baseline • Review performance to inform teaching • Compare performance on skill to GOM measures • Over time, you may want to create ‘mixed skill’ measures to determine retention of performance on specific concepts

Two Free Tools • Intervention Central – Math Worksheet Generator • CBM Focus (PM Focus)

Progress Monitoring Focus

LPLC Improving the lives of people who learn differently through prevention, evaluation, treatment, and research. 3324 Elder Street • Boise, ID 208 -333 -0008 www. LPLearning. Center. org