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O PERATIONS AND A LGEBRAIC T HINKING - OA K-2 P UTTING IT TOGETHER : N UMBER S TRATEGIES AND S TORY P ROBLEM T YPES Math Teacher Leader Meeting January 10, 2012 Beth SchefelkerLee Ann Pruske Connie LaughlinHank Kepner

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D ECEMBER H OMEWORK How will you implement this information into your work in the next month? Be prepared to share your successes and/or challenges at the January MTL meeting. Work with a teacher or teacher team Explore textbooks for story problem formats Try problem types with a group of students

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L EARNING I NTENTIONS Understand strategies that can be used to solve various problem situations. Understand strategies that can be used to develop number fluency.

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S UCCESS C RITERIA You will be successful when you can identify and implement number strategies that students can use to develop number fluency and solve story problem situations.

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W HAT I S F LUENCY ? What does fluency mean to you? Read the last paragraph on pg. 18 and 19. What is the “gist” of fluency as outlined in the Progressions for the Common Core State Standards in Mathematics?

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B UILDING F LUENCY AND I NSTRUCTIONAL I MPLICATIONS “So the important press toward fluency should also allow students to fall back on earlier strategies when needed. By the end of the K-2 grade span, students have sufficient experience with addition and subtraction to know single-digit sums from memory… p. 19 0A Progressions document

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B UILDING F LUENCY AND I NSTRUCTIONAL I MPLICATIONS “So the important press toward fluency should also allow students to fall back on earlier strategies when needed. By the end of the K-2 grade span, students have sufficient experience with addition and subtraction to know single-digit sums from memory… this is not a matter of instilling facts divorced from their meanings, but rather as an outcome of a multi-year process that heavily involves the interplay of practice and reasoning.” p. 19 0A Progressions document

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M OVING FROM CONCRETE TO ABSTRACT REPRESENTATIONS Direct modeling, Counting on and Numeric Reasoning Use the chart on pg. 36 and your problem type chart to make sense of the summary reading on pg How are the problem types related to student strategies?

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K5Grade 1Grade 2 Responsible for 4 problem types Responsible for 8 problem types Responsible for 12 problem types Work within 5, then 10 Work within 20Work within 100 Physically act out problems Count on Make 10 Decompose through 10 Doubles/Near doubles Concrete models to show all parts Semi-concrete models Matching with objects Tape diagrams Abstract model Drawings show quantities H OW D OES OA G ROW ? O PERATIONS AND A LGEBRAIC T HINKING K-2

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K5Grade 1Grade 2 Responsible for 4 problem types Responsible for 8 problem types Responsible for 12 problem types Work within 5, then 10 Work within 20Work within 100 Physically act out problems Count on Make 10 Decompose through 10 Doubles/Near doubles Concrete models to show all parts Semi-concrete models Matching with objects Tape diagrams Abstract model Drawings show quantities H OW D OES OA G ROW ? O PERATIONS AND A LGEBRAIC T HINKING K-2

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L EARNING I NTENTIONS Understand strategies that can be used to solve various problem situations. Understand strategies that can be used to develop number fluency.

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G RADE 1 : C ONTENT S TANDARD 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on making ten decomposing a number leading to a ten using the relationship between addition & subtraction creating equivalent but easier or known sums

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S TRATEGIES T HAT B UILD S INGLE D IGIT A DDITION F LUENCY Counting on. Make a ten. Use an easier “equivalent” problem. Transform the problem in some way Use fives Use a helping fact Use doubles

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8 + 6 Strategies: Make a ten. Use a double. Use fives. Use some other equivalent problem. Put 8 counters on your first frame & 6 counters on your second frame.

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Write an equation. C OUNT O N : =14.

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M AKE A TEN : How could you make a ten? Move 2 counters to the top frame. Write an equation = = = 14 Then you have 10 and 4 more counters.

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U SE A DOUBLE : What doubles might you use?

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U SE A DOUBLE : What doubles might you use? Write an equation = = = 14 Reason = 12; then add 2 more.

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U SE FIVES : Can you see some fives? Where?

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U SE FIVES : Can you see some fives? Where? Reason: is 10; need to add 3 more and 1 more. Write an equation = = = 14

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S TANDARDS FOR M ATH P RACTICE Which Standard for Math Practice were you using as you worked through these activities? 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 6. Attend to precision.

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Select a problem. Tell an addition story. Draw a strategy card for the group. Everyone uses ten frames and counters to reason through the strategy and writes an equation(s) that shows the reasoning. Share, compare, and discuss as a group. Repeat with another strategy card for the same problem or a new problem. Reflect: Which strategies seem to work best for each problem?

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S TANDARDS FOR M ATH P RACTICE Which Standard for Math Practice were you using as you worked through these activities? 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 6. Attend to precision.

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W HY A 10 F RAME ? How does modeling each strategy with the same manipulative model help develop student understanding? Develops number fluency and flexibility Anchors to 5 and 10 Place value fluency

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A S YOU T HINK OF YOUR WORK … How does this information impact your work with teachers of all grades? … with Special Education, ELL, and older students who don’t have these skill sets.

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P ROFESSIONAL P RACTICE E XPLORING S TRATEGIES Number Strategies using Tens Frames: Work with a teacher or teacher team using tens frames strategies Model problem types with a group of students using tens frames Explore textbooks for number strategies using tens frames Video tape your work with teachers and or students working with ten frames and story problem types.

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L EARNING I NTENTIONS Understand strategies that can be used to solve various problem situations. Understand strategies that can be used to develop number fluency.

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S UCCESS C RITERIA You will be successful when you can identify and implement number strategies that students can use to develop number fluency and solve story problem situations.

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F EEDBACK Q UESTION : (1) Story problem types; (2) number strategies; (3) developmental learning progressions (from concrete to abstract); and (4) instructional models (like ten frames) are interrelated parts that must be cohesively connected for students to develop both fluency and number sense in the K-2 grades and the OA K-2 CCSS. Considering the 4 areas above, which areas do you need more practice to develop your skill in applying them with teachers and students?

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