an introduction to the power of 10 - visual strategies for learning basic addition facts presented...

An Introduction to the Power of 10 - Visual Strategies For Learning

Basic Addition FactsPresented by: Ms. Paula Thompson

Requested by: SETSA

On: Monday, February 28, 2011 1 PM - 2 PM

Welcome & Introductions

Ms. Paula Thompson, Mathematics ConsultantYukon Education

1000 Lewes BoulevardWhitehorse, Yukon Y1A 3H9

Paula.Thompson@yesnet.yk.cawww.yukon-education-mathematics.wikispaces.com/

Goals For The Session

• Touch on some of the Big Ideas that are related to addition with 10-frames

• Describe the Power of Ten system for addition

• Consider the conceptual understanding pentagon as it relates to the big ideas and the Power of 10 system.

Big Ideas

• Counting tells how many things are in a set. When counting a set of objects, the last word in the counting sequence names the quantity for that set.

http://www.yesnet.yk.ca/schools/wes/projects/counting_book_K/

counting_book.html

My Favourite Two Examples

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are needed to see this picture.

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Conceptual Understanding Pentagon

• Consider the movie clip in terms of the conceptual understanding pentagon. (Think/Pair/Share)

Big Ideas (continued)

• #s are related to each other through a variety of # relationships. The number 7 is 2 more than 5, 3 less than 10, 3+4, 5+2, can quickly be recognized in several patterned arrangements etc.• These ideas further extend to an

understanding of 17, 57, & 370.

• Five-Frame Tell-About• Ten-Frame Tell-About

• Let’s play!

• Ten-Frame Flash Cards• How many?

• How many more to make ten?

• Say one more, two more, one less, two less.

• Say the ten fact - 6+4=10

Conceptual Understanding Pentagon

• Consider the conceptual understanding pentagon as it relates to the big ideas and the game 10-Frame Tell-About

Big Ideas (cont’d)

• Models can be used to solve contextual problems to figure out what operation is involved in a problem regardless of the size of the #s. Models can also be used to give meaning to # sentences.

The Power of Ten System

• The Power of Ten is a set of specially designed cards (model), games, follow-up worksheets and teaching strategies that encourage children to visualize numbers, making it easier to add.

• It is suitable for children as young as 3 and has been used for remedial purposes at the high school level.

Trevor Calkins’ “Aha!” Moment

• Learning Our Facts -Pg. 4

• More people buy circular watches with hands

• The brain can tell the time quicker because it is using the spatial/visual brain

• The logical brain is required to interpret digital watches

• 1 more step seems to be involved in telling the time so it happens more slowly

What Does Telling Time Have To Do, Have To Do With It?

• The Issue For Mr. Calkins• Some students have

trouble learning the basic facts

• The Calkins’ Way - The Power of 10• Part of the answer to

this concern may lie in the way that the spatial/visual brain is utilized

Changing To A Visual Strategy

• Changing Strategies for Changing Times - Pg. 5

• “Easy facts” first• +ing facts to 10

• 0, 1 or 2 in addends

• Reasons:• Many workbooks go from

easy to difficult• Way I was taught in

school

• Issue• Learning the “easy

facts” first reinforces a counting strategy than the brain tries to generalize for all facts

What Is The Problem?

• Replacing Counting Strategies With Visual Strategies - Pg. 6

• Adults can keep 5 - 9 chunks of information in their short term memory.

• A young student adding by 6, 7, 8 or 9 by counting may actually overload the short term memory.• Lose their place• Give a random answer

• The counting strategy breaks down but students keep trying to use it.

What Do I Do About It?

• Mr. Calkins suggests teaching the difficult facts, such as those that involve an addend of 9, using a non-counting visual strategy

• Generalize the same strategy to all the other facts

• In the book, a visual strategy for adding 10, 9, 8 & 5, in that order, is suggested.

• Next comes the facts involving addends of 6, 7 & 4.

• Finally, facts with addends of 3, 2, 1 & 0 are considered.

• Borrowing on ideas from an article by Roberta Flexer, Mr. Calkins designed a special deck of cards called ten frames in order to harness the power of the spatial brain

• The shape of each number from one to ten could be used to visualize the number

10-Frame Playing Cards - 6-Frame & 4-Frame

• Note how the “four” shape fits with the “six” shape to make a “ten”

• Since 10 plays such a large role in our numeration system and because two fives make up 10, it is very useful to develop relationships for the numbers 1-10 to the important anchors of 5 and 10.

Learning Your Facts By Playing Games Pg. 8

• Saying, seeing, hearing, as well as the movement in the game allows each child’s brain to experience the card in four different ways.

• It is important to highlight this for students so they understand the value of saying the numerals as games are played.

• Later, when children want the logical brain to manipulate these #s in math sentences, it is much easier to remember the shape because they have created several different paths in the brain to help them find the memory.

Learning Facts By Playing Games Pg. 7 (continued)

• Concentration or Memory: Turn the 20 cards face down and try to turn over matching pairs (C-2).

• Face Off: This is the same as war only a tie is broken by simply turning over another card and stating the value (C-1).

• 10-Frame Bingo

Fish: This is the traditional game (C-3).

Teaching Addition Pg. 13Adding 10

• “Power of 10” Game• Reinforce• Addition Grid (D-1)

• Fill in both ten rows

• Complete 1 column of Visual Tables for Learning the Patterns Involving 10 (G-1)

• “Power of Ten” Game• Each player places a ten

card in front of them.• Each player flips a

second card and says the total.

• The player with the greatest sum wins but only removes the card in the “units place,” leaving the ten for the next round.

• Play continues until the whole deck is used

+ 0 1 2 3 4 5 6 7 8 9 10

0 10

1 11

2 12

3 13

4 14

5 15

6 16

7 17

8 18

9 19

10 10 11 12 13 14 15 16 17 18 19 20

Adding 9

• “Power of 9” Game• Reinforce• Addition Grid (D-1)

• Fill in the grid for 9

• Complete one column of the Visual Table for Learning The Patterns Involving 9 (G-2)

• Do an “All The Facts You Need To Know” sheet (Appendix H)• Scaffolding• Other ?s• Timing

• Graph results on the Addition Graph (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 9 10

1 10 11

2 11 12

3 12 13

4 13 14

5 14 15

6 15 16

7 16 17

8 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Adding 8

• “Power of 8” Game• Reinforce• Addition Grid (D-1)

• Fill in the grid for 8

• Complete one column of the Visual Table For Learning The Patterns Involving 8 (G-3)

• Do an “All The Facts You Need To Know” sheet (Appendix H)

• Graph results on the Addition Grid (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 8 9 10

1 9 10 11

2 10 11 12

3 11 12 13

4 12 13 14

5 13 14 15

6 14 15 16

7 15 16 17

8 8 9 10 11 12 13 14 15 16 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Adding 5

• “Power of 5” Game• Often makes another one

of the #s like 5+4=9• Can be positioned to make

ten like in 5+8=5+5+3 or 10+3

• Reinforce• Addition Grid (D-1)

• Fill in the grid for 5

• Complete one column of the Visual Table For Learning The Patterns Involving 5 (G-4)

• Do an “All The Facts You Need To Know” sheet (Appendix H)

• Graph results on the Addition Grid (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 5 8 9 10

1 6 9 10 11

2 7 10 11 12

3 8 11 12 13

4 9 12 13 14

5 5 6 7 8 9 10 11 12 13 14 15

6 11 14 15 16

7 12 15 16 17

8 8 9 10 11 12 13 14 15 16 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Doubles

• Doubles• 7+7=5+5+4• 6+6=5+5+2• 5+5=10• 4+4=8• 3+3=6• 2+2=4• 1+1=2• 0+0=0• (Doubles Challenge C-8)

• Doubles Plus 1• 6+7=6+6+1

• Nearly Doubles• 7+9=7+7+2

• Addition Grid (D-1)• Do an “All The Facts

You Need To Know” sheet (Appendix H)

• Graph results on the Addition Grid (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 0 1 2 5 8 9 10

1 1 2 3 6 9 10 11

2 2 3 4 5 6 7 10 11 12

3 4 5 6 7 8 11 12 13

4 6 7 8 9 10 12 13 14

5 5 6 7 8 9 10 11 12 13 14 15

6 10 11 12 13 14 15 16

7 12 13 14 15 16 17

8 8 9 10 11 12 13 14 15 16 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Adding 0, 1, 2 & 3

• By now many children will already know how to add 0, 1, 2 and 3

• Discuss methods• Counting• Visualization

• Many students will use visualization rather than counting strategies.

• Addition Grid (D-1)• Fill in the grid for 0, 1, 2

& 3 using different colours for adjacent rows

• Do an “All The Facts You Need To Know” sheet (Appendix H)

• Graph results on the Addition Grid (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 0 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10 11

2 2 3 4 5 6 7 8 9 10 11 12

3 3 4 5 6 7 8 9 10 11 12 13

4 4 5 6 7 8 9 10 12 13 14

5 5 6 7 8 9 10 11 12 13 14 15

6 6 7 8 9 10 11 12 13 14 15 16

7 7 8 9 10 12 13 14 15 16 17

8 8 9 10 11 12 13 14 15 16 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Friendly Facts For Addition

• Friendly facts are the numbers which add to give 10• Concentration/Memory

(C-2)• Slap-Jack (C-6)• Power of 10 Solitaire (C-

5)• Salute With Different

Rules! Let’s Play! (C-7)

• Connecting to multiplication

• Addition Grid (D-1)• Fill in the friendly facts

• 4+6 and 6+4

• Do an “All The Facts You Need To Know” sheet (Appendix H)

• Graph results on the Addition Grid (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 0 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10 11

2 2 3 4 5 6 7 8 9 10 11 12

3 3 4 5 6 7 8 9 10 11 12 13

4 4 5 6 7 8 9 10 12 13 14

5 5 6 7 8 9 10 11 12 13 14 15

6 6 7 8 9 10 11 12 13 14 15 16

7 7 8 9 10 12 13 14 15 16 17

8 8 9 10 11 12 13 14 15 16 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Last But Not Least . . .

• At this point only one fact has not been taught : 4+7

• Discuss methods• Power of Ten cards• Egg cartons

• Addition Grid (D-1)• Do an “All The Facts

You Need To Know” sheet (Appendix H)

• Graph results on the Addition Grid (E-1)

+ 0 1 2 3 4 5 6 7 8 9 10

0 0 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10 11

2 2 3 4 5 6 7 8 9 10 11 12

3 3 4 5 6 7 8 9 10 11 12 13

4 4 5 6 7 8 9 10 11 12 13 14

5 5 6 7 8 9 10 11 12 13 14 15

6 6 7 8 9 10 11 12 13 14 15 16

7 7 8 9 10 11 12 13 14 15 16 17

8 8 9 10 11 12 13 14 15 16 17 18

9 9 10 11 12 13 14 15 16 17 18 19

10 10 11 12 13 14 15 16 17 18 19 20

Another Game In The Book

• Salute

• Salute With Revised Rules• Two players each hold a card for the

others to see• One player says the sum• The other two players determine what is on

their own card

Celebrate The Mastery of Addition

• Appendix I

Recap of Teaching Addition

• Subitizing Games• Face-Off• Concentration/Memory• Fish• 10-Frame Bingo• 10-Frame Flash• 5-Frame Flash

• Adding 10• “Power of 10” Game• Reinforce• Addition Grid

• Adding 9• “Power of 9” Game• Reinforce• Addition Grid• Visual Table for

Learning The Patterns Involving 9

• All The Facts You Need To Know

• Graph Results

Recap of Teaching Addition (continued)

• Adding 8• “Power of 8” Game• Reinforce• Addition Grid• Visual Table for Learning

The Patterns Involving 8• All The Facts You Need

To Know• Graph Results

• Adding 5• See Adding 8

• Doubles - Reinforce, Addition Grid, All The Facts You Need To Know, Graph Results

• 0, 1, 2 & 3 - See Doubles

• Friendly Facts - See Doubles

• 4+7 - See Doubles• Celebrate!

Conceptual Understanding Pentagon

• Consider the conceptual understanding pentagon as it relates to the Power of 10 system for addition. (Think/Pair/Share)

Increasing Efficiency

• Once students can obtain accurate answers and have demonstrated mastery it is time for increasing efficiency.

• They may now be timed, with the same reservations as discussed previously.

Taking It Further - Graphing The Results

• The % Graph (E-3)• Review results from the Addition Graph (E-

1) and/or the Subtraction Graph (E-2) as fractions, decimals, and percents for older children.

• If appropriate, do this for younger children too!

Other Ideas To Consider

• Other Ideas:• Five Frames• Dot Plates• Index Cards• Dominoes• Rhythms• Box Cars & One-Eyed

Jacks Games• The Game of Skunk• Fact Family Triangles• Ten-Frame Bingo• 100 Chart

• Ask: • Show me. • Find the frame. • Write the matching

numeral. • How many? One more?

One less? Two more? Two less? The double? The double plus one more? How many more does it take to make ten?

• Matching piles.

Resources

• http://www.poweroften.ca/ (Trevor Calkins Website)

• (Carole Fullerton’s Blog)• http://

mindfull.wordpress.com/?s=ten+frames

• http://mindfull.wordpress.com/?s=basic+facts

• http://mindfull.wordpress.com/?s=doubles

• http://yukon-education-mathematics.wikispaces.com/ Check out the Visualization section and the Number outcome pages in the grade-specific wikis

• http://www.resourceservices.gov.yk.ca/?lang=en&module=ourcollection Do a keyword search using addition (372.7s)

Resources (cont’d)

• Book - It Makes Sense! Using 10-Frames to Build Number Sense• http://www.amazon.ca/M

akes-Sense-Ten-Frames-Number-Grades/dp/1935099108

• From the Catalogue of Curriculum Materials• Teaching Student-

Centered Mathematics

• NCTM Illuminations 5 Frames & 10-Frames (Online Games)• http://illuminations.

nctm.org/activitydetail.aspx?id=74

• http://illuminations.nctm.org/activitydetail.aspx?id=75

Follow-up Subtraction Session

• I am offering a follow-up subtraction session via Elluminate Live! online on Wednesday, April 13, 2011 from 4:30 PM - 6:00 PM

Questions & Evaluation

• Questions? • Please take a moment to complete an evaluation form.