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

An Introduction to the Power of 10 - Visual Strategies For Learning Basic Addition Facts. Presented by: Ms. Paula Thompson Requested by: SETSA On: Monday, February 28, 2011 1 PM - 2 PM. Welcome & Introductions. Ms. Paula Thompson, Mathematics Consultant Yukon Education 1000 Lewes Boulevard

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

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  1. An Introduction to the Power of 10 - Visual Strategies For Learning Basic Addition Facts Presented by: Ms. Paula Thompson Requested by: SETSA On: Monday, February 28, 2011 1 PM - 2 PM

  2. Welcome & Introductions Ms. Paula Thompson, Mathematics Consultant Yukon Education 1000 Lewes Boulevard Whitehorse, Yukon Y1A 3H9 Paula.Thompson@yesnet.yk.ca www.yukon-education-mathematics.wikispaces.com/

  3. 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.

  4. 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.

  5. http://www.yesnet.yk.ca/schools/wes/projects/counting_book_K/counting_book.htmlhttp://www.yesnet.yk.ca/schools/wes/projects/counting_book_K/counting_book.html

  6. My Favourite Two Examples

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

  8. 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.

  9. 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

  10. Consider the conceptual understanding pentagon as it relates to the big ideas and the game 10-Frame Tell-About Conceptual Understanding Pentagon

  11. 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.

  12. 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.

  13. 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 Trevor Calkins’ “Aha!” Moment

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

  15. 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 Changing To A Visual Strategy

  16. 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 Is The Problem?

  17. 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. What Do I Do About It?

  18. 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

  19. 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. 10-Frame Playing Cards - 6-Frame & 4-Frame

  20. 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 Your Facts By Playing Games Pg. 8

  21. 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).

  22. “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 Teaching Addition Pg. 13Adding 10

  23. “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) Adding 9

  24. “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) Adding 8

  25. Do an “All The Facts You Need To Know” sheet (Appendix H) Graph results on the Addition Grid (E-1) 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)

  26. 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) Doubles

  27. 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) Adding 0, 1, 2 & 3

  28. 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) Friendly Facts For Addition

  29. 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) Last But Not Least . . .

  30. 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

  31. Celebrate The Mastery of Addition • Appendix I

  32. 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

  33. 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! Recap of Teaching Addition (continued)

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

  35. 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.

  36. 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!

  37. 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. Other Ideas To Consider

  38. 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

  39. Book - It Makes Sense! Using 10-Frames to Build Number Sense http://www.amazon.ca/Makes-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 Resources (cont’d)

  40. 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

  41. Questions? Please take a moment to complete an evaluation form. Questions & Evaluation

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