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Teaching Knowledge, Addition, Subtraction and Place Value Workshop

Teaching Knowledge, Addition, Subtraction and Place Value Workshop. Purpose of this session is to. have a clearer understanding of the strategy stages for addition and subtraction. understand the teaching model used for teaching strategy.

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Teaching Knowledge, Addition, Subtraction and Place Value Workshop

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  1. Teaching Knowledge, Addition, Subtraction and Place Value Workshop

  2. Purpose of this session is to.. • have a clearer understanding of the strategy stages for addition and subtraction. • understand the teaching model used for teaching strategy. • understand misconceptions with place value, including decimals, and gain a greater understanding of how to successfully teach knowledge. • explore equipment and activities used to teach addition & subtraction strategies including Book 5 and long term planning sheets.

  3. Overview: 9.15- 10.30-Knowledge teaching, teaching model and place value (including misconceptions) 11:00- 12.30- Observe a modelling session, explore equipment and activities used to teach addition & subtraction strategies including Book 5 and long term planning sheets. 1.15-2.45-Making sense of addition and subtraction strategies and seeing the progression of ideas.

  4. Since our last workshop reflect on... • - something you have tried. • something you are still not sure of.

  5. Framework Revision: Can you sort out the pieces linking the stages with the curriculum?

  6. Basic Facts Number knowledge Assessing Analysing data Planning Teaching Practicing / Applying

  7. Using Book 4 Using Book 4 to help teach Number Knowledge

  8. Teaching Using Book 4 Teaching Number Knowledge Book 4

  9. Number Boggle Bk4 p.33

  10. 9 - 2 = 7 5 + 3 + 8 = 16 Number Boggle Bk4 p.33

  11. Teaching Thousands Book, Book 4 p. 16 • What is the learning intention? • Which stages is it appropriate for? • What equipment is needed (any MM?) • How could you adapt / extend the activity? • Could it be used for whole class, group teaching, or adapted for independent work?

  12. Number Knowledge Planning Unit FNWS BNWS Fractions Place Value Basic Facts

  13. In groups number yourself 1 to 5 Adapt these activities to focus specifically on practising + 9 • Squeezies 2. Snakes and Chances • I have Who has 4. Rocket 5. Facts on a ring / Slidey Cards

  14. A Focus on Basic Facts Assessing Analysing data Planning Teaching Practicing / Applying

  15. NZ Curriculum and Number Framework • What to teach Effective Pedagogy • How you teach it • How you respond to students and their misconceptions

  16. Existing Knowledge & Strategies Using Imaging • Using Number Properties Using Materials New Knowledge & Strategies Developing Strategy using the teaching model Watch the DVD clips. Identify the elements of the teaching model.

  17. Discuss what you have just seen. • How do modelling books and thinking groups benefit both the teacher and the students?

  18. Using Thinking Groups • “If you teach without observing and reacting to the children, • you are teaching a programme, you are not teaching the kids.” • Peter Hughes, The University of Auckland

  19. 12 23 10 10 + 50 + 3 37 87 90 Using Materials and Imaging Hands Tens frames Abacus Place Value Material Number Lines

  20. Place ValueUnderstanding misconceptions

  21. Place Value Misconceptions Sarah can orally count up to 199 without any trouble but when writing down the numbers following 98, Sarah writes 99, 100, 1001,1002, Why has she done that? What might you do? The fundamental place value issue is that ten units must be changed for one new unit. The zero place holder idea is significant but not the main problem.

  22. Place Value Misconceptions 30 + 60 = 90 3 tens + sixty = ???? Why might a child not know this?

  23. Misconceptions with Place Value: • Jane says that 3.9 plus 4 tenths is 3.13. • Bill says that 3.9 plus 4 tenths is 7.9. • Melinda says that 3.9 plus 4 tenths is 4.3. Who is correct? What misconceptions do the other children have? How would you respond to this? Ref: Book 5, pg 48

  24. Decimal Misconceptions Summary • Decimals are two independent sets of whole numbers separated by a decimal point, e.g. 3.71 is bigger than 3.8 and 1.8 + 2.4 = 3.12 • The more decimal places a number has, the smaller the number is because the last place value digit is very small. E.g. 2.765 is smaller than 2.4 • Decimals are negative numbers. • 1/2 is 0.2 and 1/4 is 0.4, so therefore 0.4 is smaller than 0.2 • When you multiply decimals the number always gets bigger. • When you multiply a decimal number by 10, just add a zero, e.g. 1.5 x 10 = 1.50

  25. Develop Place Value UnderstandingUsing cards: make the biggest number you can • Write (numbers and words) • Make (place value equipment) • Say (two ways, 1, 10,100, …before and after) • Round (to nearest 10, 100, 1…) • Order • Dictation (numbers and words) • Match (word, number, expanded numerals/words) Add/subtract: • Mix (symbols and words, e.g. 43 + thirty) • “how many more / less ”, e.g. 35+?=40, 30+?=70 • Exchanging/bundling tens and ones, e.g. 87 + 5, Rolling Dice game How could we adapt for decimal numbers?

  26. A Strategy Teaching Session • 11:00- 12.30- Observe a modelling session, explore equipment and activities used to teach addition & subtraction strategies including Book 5 and long term planning sheets.

  27. A Strategy Teaching Session • Start of Lesson (to build on students’ thinking) • Required knowledge check • Diagnostic Snapshot (Can they already do it?) • Teaching (eliciting, supporting and extending thinking) • - Teaching Model (materials, imaging, number properties) • Consider thinking groups & modelling book. • End of Lesson (assessment for learning) • Feedback: • Who’s got it? Who hasn’t? Set practice. • Consider next steps

  28. Teaching Strategy Development

  29. How does each person benefit? StudentsTeacher Modelling Book Thinking Groups Diagnostic Snapshot at start of lesson

  30. Diagnostic Snapshots Can they already do what I am about to teach? Consider their response not just if they got the question correct. 53 - 26 (Stage 6 AA) whole numbers 4.2 - 1.9 (Stage 7 AM) decimal tenths 6.03 - 5.8 (Stage 7 AM) decimal tenths/hundredths 23/4 - 1 2/3(Stage 8 AP) mixed fractions

  31. Strategy Modelling Discussion Eg.Stage 4-5: Addition in Parts, p.29 Stage 5-6: When One Number is Near a Hundred p.37 (Addition) Problems Like 73-19 p.38 (Subtraction) Get into thinking groups, plan a lesson using this guide

  32. “Effective teachers understand the big ideas”. So - what do the stages mean? Choose one stage to explore.

  33. The big picture – what do the stages mean?

  34. Long Term Planning Units

  35. Independent Practice Ideas • Similar Questions: • on board, modelling book, worksheets, computer • (Perhaps show thinking for 1 or 2 questions) • 2. Textbooks: e.g. Figure It Out, Pearson, NCM • 3. Games: Create or play specific to the strategy. • 4. Process: Diary writing / Thinkboard • 5. Word Story Problems: Write to match a number sentence, check, swap and solve • 6. Relevant knowledge practice to support the strategy being developed

  36. Addition and Subtraction Strategy Framework

  37. Strategy Framework Revision • 1 1-1 One-to-One Counting • 2 CA Counting From One on Materials • 3 CA Counting From One by Imaging • 4 AC Advanced Counting • 5 EA Early Additive Part-whole • 6 AA Advanced Additive Part-whole • 7 AM Advanced Multiplicative Part-whole • 8 AP Advanced Proportional Part-whole Level 1 Level 2 Level 3 Level 4 Level 5

  38. Some examples of strategy lessons

  39. Stage 5 EA Early Additive Part-Whole Book 5, p…… • What is the big idea - what are we trying to develop at this stage? • Subtraction in Parts, p.27 • Start of Lesson • Required Knowledge Check • Diagnostic Snapshot

  40. 14 - 4 = 10 14 - 6 = 10 - 2 = 8

  41. Existing Knowledge & Strategies Using Imaging • Using Number Properties Using Materials New Knowledge & Strategies How would you move to number properties? 53 - 9 What stage would this be? How would you extend into double digits, e.g. 53 - 29

  42. -20 -3 -6 53 24 30 33 53 - 29 using Place Value Partitioning 53 - 20 = 33 33 - 3 = 30 30 - 6 = 24

  43. Moving to Stage 6; Advanced Additive Part-Whole (AA) (NZC Level 3) Is this the most efficient way of solving 53 - 29? What are the big key ideas at this stage? • What key knowledge is required before moving to this stage? (Check in Book 5)

  44. Moving to Stage 6; Advanced Additive Part-Whole (AA) (NZC Level 3) • What knowledge should also be developed during this stage to be ready for the next stage? (Check on long term planning units)

  45. Long Term Planning Units knowledge strategy

  46. Existing Knowledge & Strategies Using Imaging • Using Number Properties Using Materials New Knowledge & Strategies Watch the DVD clips. See how imaging is “folded back” to materials.

  47. 53 - 26 Compensation with tidy numbers 53 - 30 + 4 Place Value Partitioning 53 - 20 - 6 Equal Additions (subtraction only) 57 - 30 Reversibility 26 + ? = 53 Standard Written Form (decomposition)

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