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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
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Welcome & Introductions
Ms. Paula Thompson, Mathematics ConsultantYukon Education
1000 Lewes BoulevardWhitehorse, Yukon Y1A 3H9
Paula.Thompson@yesnet.yk.cawww.yukon-education-mathematics.wikispaces.com/
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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.
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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.
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http://www.yesnet.yk.ca/schools/wes/projects/counting_book_K/
counting_book.html
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My Favourite Two Examples
QuickTime™ and aH.263 decompressor
are needed to see this picture.
QuickTime™ and aH.263 decompressor
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)
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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.
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• 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
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Conceptual Understanding Pentagon
• Consider the conceptual understanding pentagon as it relates to the big ideas and the game 10-Frame Tell-About
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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.
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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.
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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
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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
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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
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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.
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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.
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• 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
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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.
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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.
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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).
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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
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+ 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
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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)
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+ 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
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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)
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+ 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
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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)
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+ 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
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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)
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+ 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
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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)
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+ 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
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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)
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+ 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
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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)
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+ 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
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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
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Celebrate The Mastery of Addition
• Appendix I
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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
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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!
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Conceptual Understanding Pentagon
• Consider the conceptual understanding pentagon as it relates to the Power of 10 system for addition. (Think/Pair/Share)
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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.
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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!
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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.
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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)
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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
![Page 48: An Introduction to the Power of 10 - Visual Strategies For Learning Basic Addition Facts Presented by: Ms. Paula Thompson Requested by: SETSA On: Monday,](https://reader036.vdocuments.us/reader036/viewer/2022062304/56649da25503460f94a8f6e5/html5/thumbnails/48.jpg)
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
![Page 49: An Introduction to the Power of 10 - Visual Strategies For Learning Basic Addition Facts Presented by: Ms. Paula Thompson Requested by: SETSA On: Monday,](https://reader036.vdocuments.us/reader036/viewer/2022062304/56649da25503460f94a8f6e5/html5/thumbnails/49.jpg)
Questions & Evaluation
• Questions? • Please take a moment to complete an evaluation form.