1. Supervisor of K – 5 Mathematics & ALPS
Welcome
Matthew Finacchio
Supervisor of K – 5 Mathematics & ALPS
ext 3004

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

3. 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…

4. 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

5. 4 2 2 + 2 = 4 Adding & Subtracting Total/Sum - + Partner/Addend
Math
Mountains
Partner/Addend
Partner/Addend

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

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

8. Addition Algorithms

9. Accessible Algorithms1 78
+23
New Groups Above
Traditional Method
Steps:
8 + 3 = 11
Place the one and Regroup the Ten
Add
101

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

11. Accessible Algorithms
Show All Totals
Steps:
Add tens OR ones
Add separate totals together to find answer

12. Proof Drawings

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

14. 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

15. Accessible Algorithms
Multi-digit Subtraction
Ungroup, then subtract across
Left to Right Right to Left

16. Accessible Algorithms
MULTIPLICATION

17. 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,

18. 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

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

20. Always represent in groups of 10’s first2
Always represent in groups of 10’s first 10 1

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

22. 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

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

24. Accessible Algorithms Division

25. Problem To Solve
192 / 6 =

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

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

28. Accessible Algorithm Division Digit by Digit Method 3 2 6 192 - 18 1 212
Traditional

29. Extra Practice

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

31. 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

32. 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.

33. Thank you!