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**Supervisor of K – 5 Mathematics & ALPS**

Welcome Matthew Finacchio Supervisor of K – 5 Mathematics & ALPS 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**

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 drawings Connect to real world Informal and formal math language/vocabulary Link drawings to math talk and written math notation Know WHY, not just HOW 4

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

Math Mountains Partner/Addend 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**

1 78 +23 New Groups Above Traditional Method Steps: 8 + 3 = 11 Place the one and Regroup the Ten Add 101

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**Accessible Algorithms**

New Groups Below Steps: Add the ones Place ten on line below tens Add = 140 78 +65 1 3 13 14

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**Accessible Algorithms**

Show All Totals Steps: Add tens OR ones Add separate totals together to find answer

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Proof Drawings

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**Accessible Algorithms**

Multi-Digit Subtraction Expanded Method Need to Ungroup = 189 347 -158 130 200 140 17

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**X Subtraction Proof Drawing 300 + 40 + 7 100 + 50 + 8 x**

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. X x When doing a subtraction proof drawing you only draw the larger number. You still need to look at each place value and regroup before you do any subtraction. You are left with = 189 Remember in a Subtraction Proof Drawing X stands for ungrouping and – (crossing out) stands for subtraction

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**Accessible Algorithms**

Multi-digit Subtraction Ungroup, then subtract across Left to Right Right to Left

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**Accessible Algorithms**

MULTIPLICATION

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**Background Knowledge 7 X 8**

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, 7 X 7 = 49 and 7 X 1 = 7,

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30 27 3 - Count-bys 1 group of 3 24 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 / 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 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 21 18 15 12 9 6 3

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

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**Always represent in groups of 10’s first**

2 Always represent in groups of 10’s first 10 1

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

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**Multiplication 12 = 10 + 2 11 = 10 + 1 100 20 10 2 10 X 10 = 100**

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

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**Multiplication 100 20 10 2 Algebraic Notation Method**

12 X 11 = (10 + 2) X (10 + 1) = 10 2 = 132

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**Accessible Algorithms Division**

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Problem To Solve 192 / 6 =

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**Rectangle Sections Method**

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

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**Expanded Notation Form**

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

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**Accessible Algorithm Division Digit by Digit Method 3 2 6 192 - 18 1 2**

12 Traditional

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Extra Practice

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**Accessible Algorithms**

Area Model 78 X36 2100 240 420 2808 2,100 240 30 420 48 6

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Multiplication Expanded Notation 78 = x 36 = x 8 = x 70 = 2,100 6 x 8 = 48 6 x 70 = 420 2,808 Short Cut Method 78 X ,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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