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

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

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…

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

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

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

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

Addition Algorithms

Accessible Algorithms 1 78 +23 New Groups Above Traditional Method Steps: 8 + 3 = 11 Place the one and Regroup the Ten Add 1 + 7 + 2 101

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

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

Proof Drawings

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

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 100 + 80 + 9 = 189 Remember in a Subtraction Proof Drawing X stands for ungrouping and – (crossing out) stands for subtraction

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

Accessible Algorithms MULTIPLICATION

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

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

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

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

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

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

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

Accessible Algorithms Division

Problem To Solve 192 / 6 =

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

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

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

Extra Practice

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

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

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.

Thank you!