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Welcome Matthew Finacchio Supervisor of K – 5 Mathematics & ALPS mfinacchio@hamilton.k12.nj.us 609-631-4100 ext 3004

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Agenda Welcome and Introductions Online Support Background of Concept Building Developing Fluency of Basic Facts Overview of Accessible Algorithms Practice Accessible Algorithms

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Free Online Support www.hamilton.k12.nj.us www.eduplace.com www.hamilton.k12.nj.us www.eduplace.com Math Background Access to Algorithms Visual Support Math Mountain Cards Product cards Secret Code Cards Etc…

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Building Concepts Use a variety of accessible algorithms (strategies), manipulatives, and math drawingsUse a variety of accessible algorithms (strategies), manipulatives, and math drawings –Connect to real world Informal and formal math language/vocabularyInformal and formal math language/vocabulary Link drawings to math talk and written math notationLink drawings to math talk and written math notation Know WHY, not just HOWKnow WHY, not just HOW

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4 2 2 - - + Math Mountains Adding & Subtracting 2 + 2 = 4 Total/Sum Partner/Addend

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Unique Resources Math Mountain Cards Students can add and subtract with one set of cards Reinforce addition and subtraction as inverse operations

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Understanding to Fluency Count-on Cards Keep the larger number in your head Dots provide “conceptual support”

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Addition Algorithms

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Accessible Algorithms New Groups Above Traditional Method Steps: 1.8 + 3 = 11 2.Place the one and Regroup the Ten 3.Add 1 + 7 + 2 1 78 +23 101

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Accessible Algorithms New Groups Below Steps: 1.Add the ones 2.Place ten on line below tens 3.Add 70 +60 + 10 = 140 78 +65 1 3 13 14

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Accessible Algorithms Show All Totals Steps: 1.Add tens OR ones 2.Add separate totals together to find answer 78 + 13 80 + 11 91

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Proof Drawings

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Accessible Algorithms Expanded Method 300 + 40 + 7 - 100 + 50 + 8 Need to Ungroup 300 + 40 + 7 - 100 + 50 + 8 100 + 80 + 9 = 189 200 130 140 17 347 -158 Multi-Digit Subtraction

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300 + 40 + 7 -100 + 50 + 8 You can subtract 100 from 300 You can’t subtract 50 from 40 You can’t subtract 8 from 7 You need to ungroup. After you ungroup you can subtract. Remember in a Subtraction Proof Drawing X stands for ungrouping and – (crossing out) stands for subtraction X x You are left with 100 + 80 + 9 = 189 Subtraction Proof Drawing

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Accessible Algorithms Multi-digit Subtraction Ungroup, then subtract across Left to Right Right to Left 13 13 2 14 17 2 3 17 3 4 7 3 4 7 - 1 5 8 - 1 5 8 1 8 9 1 8 9

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Accessible Algorithms MULTIPLICATION

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Background Knowledge 7 X 8 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 7 X 2, 7 X 2, 7 X 2, 7 X 2 (7 X 4) + (7 X 4) 7 X 5 = 35 and 7 X 3 = 21, 35 + 21 7 X 7 = 49 and 7 X 1 = 7, 49 + 7

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3 - Count-bys 3 = 1 * 3 6 = 2 * 3 9 = 3 * 3 12 = 4 * 3 15 = 5 * 3 18 = 6 * 3 21 = 7 * 3 24 = 8 * 3 27 = 9 * 3 30 =10 * 3 3 / 1 = 3 6 / 2 = 3 9 / 3 = 3 12 / 4 = 3 15 / 5 = 3 18 / 6 = 3 21 / 7 = 3 24 / 8 = 3 27 / 9 = 3 30 /10 = 3 3 6 9 12 15 18 21 24 27 30 3 / 3 = 1 6 / 3 = 2 9/ 3 = 3 12 / 3 = 4 15 / 3 = 5 18 / 3 = 6 21 / 3 = 7 24 / 3 = 8 27 / 3 = 9 30 / 3 = 10 1 group of 3

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Please use the dot array paper in the back of your packet to draw a 12 by 11 box. Dot Drawings

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Always represent in groups of 10’s first 102 1

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Multiplication 12 11 X 10 100 1 + 2 + 20 10 2 2 132 Area Model/Rectangle Sections Method +

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Multiplication 100 20 10 2 12 = 10 + 2 11 = 10 + 1 X 10 X 10 = 100 10 X 2 = 20 1 X 10 = 10 1 X 2 = 2 132 Expanded Notation

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Multiplication 100 20 10 2 12 X 11 = (10 + 2) X (10 + 1) = 100 + 10 Algebraic Notation Method + 20 + 2 = 132

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Accessible Algorithms Division

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Problem To Solve 192 / 6 =

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Accessible Algorithm Division Rectangle Sections Method 6 192 30 - 180 12 + 2 - 12 0 = 32

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Accessible Algorithm Division Expanded Notation Form 6 192 30 - 180 12 2 -12 0 32

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Accessible Algorithm Division Digit by Digit Method 6 192 3 - 18 1 2 -12 0 2 Traditional

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Extra Practice

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Accessible Algorithms Area Model 78 X36 2100 240 420 + 48 2808 70 8 30 6 2,100 240 42048

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Multiplication Expanded Notation 78 = 70 + 8 x 36 = 30 + 6 30 x 8 = 240 30 x 70 = 2,100 6 x 8 = 48 6 x 70 = 420 2,808 Short Cut Method 78 X36 468 +2,340 2,808

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Equal Shares Drawing Ben arranged his soccer trophies into 3 equal rows. If he has 12 trophies, how many trophies are in each row? Draw a picture to show your answer.

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Thank you!

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