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Welcome Who am I? Robyn Holder X3447 rholder@aes.ac.in Parent Workshops this Year September 22, 2011 Erma Anderson parent workshop video available for check out in library 10/12/2011 October 12 and 17, 2011 Workshop with

  1. Welcome • Who am I? Robyn Holder X3447 rholder@aes.ac.in

  2. Parent Workshops this Year • September 22, 2011 – Erma Anderson parent workshop – video available for check out in library 10/12/2011 • October 12 and 17, 2011 – Workshop with Robyn Holder • November 4 th , 2011 – morning coffee ‐ Math / Tech Home 3 ‐ 5 Number Sense Learning • February 2 nd , 2012 – Erma parent workshop (focus TBD by December) • March ? – Workshop with Robyn Holder • April 12, 2012 – morning coffee ‐ Math / Tech workshop on summer learning 2

  3. Resources • A Maths dictionary for kids (and parents) • http://www.amathsdictionaryforkids.com/dictionary.html 10/12/2011 • National Library of Virtual Manipulatives 3 ‐ 5 Number Sense • Games and manipulatives like the ones we will use today • AES Glossary of terms • I am working on that for you • In the mean time take a look at: http://www.australiancurriculum.edu.au/Mathematics/Additiona l ‐ glossary ‐ information 3

  4. Let’s Think… • Who loves reading? • Who loves math? 10/12/2011 • Who really understands and can make 3 ‐ 5 Number Sense sense of what they read? • Who really understands and can make sense of math? 4

  5. I can read this… Once upon a time a tawndy rapsig named Gub found a tix of pertollic asquees. So chortlich was 10/12/2011 he with his discovery that he murtled a handful to show Kon, a cagwitzpat. “Pagoo!” cried Kon. 3 ‐ 5 Number Sense “With these you could treeple a frange!”. “No,” smiled Gub, “I think I’ll just paible a catwicine.” 5 York Adult Assessment

  6. But do I understand? • NO! 10/12/2011 • Reading is decoding and comprehension. 3 ‐ 5 Number Sense 6

  7. I can do this algorithm… 10/12/2011 2 1 5 1 365 3 ‐ 5 Number Sense ‐ 187 178 7

  8. But do I understand? • Not necessarily… 10/12/2011 3 ‐ 5 Number Sense Many students appear to know more than they actually do because they are able to give the correct response or perform a calculation correctly by relying 8 on rules they do not understand (Thomas, 1996; Steinle & Stacey, 1998). A project funded under the Australian Government’s Numeracy Research and Development Initiative and conducted by the Association of Independent Schools of South Australia

  9. We must teach children to understand math! In the ES we believe: • all students can learn math and strive to make sense of 10/12/2011 math. • students are active learners who construct their own 3 ‐ 5 Number Sense understanding . • math is most meaningful when it is authentic and connected to the real world and everyday life. • math understanding progresses from concrete, to representational, to abstract . • number sense is the foundation of math learning. 9

  10. Our Standards 10 3 ‐ 5 Number Sense 10/12/2011

  11. Guiding Question How does number sense develop? • 10/12/2011 3 ‐ 5 Number Sense 11

  12. What is Number Sense? • "[Number sense] is an awareness and understanding about what numbers are, 10/12/2011 their relationships, their magnitude, the relative effect of operating on numbers, 3 ‐ 5 Number Sense including the use of mental mathematics and estimation“ 12 Fennell and Landis’ (1994) cited Parrish,2010

  13. What do we know? Number Sense develops gradually • Children must spend time: 10/12/2011 • exploring numbers • visualizing numbers in a variety of contexts 3 ‐ 5 Number Sense • Finding relationships between numbers (not limited by traditional algorithms) 13 Howden, 1989 cited, Erma Anderson

  14. How does Number Sense Develop? Step 15 Fact Families Multiplication and Division Step 14 Develop better multiplication strategies Step 13 Early fraction ideas with models 10/12/2011 Step 12 Early division ideas Step 11 Renaming three digit whole numbers Step 10 Skip Counting 3 ‐ 5 Number Sense Step 9 Fact Families Step 8 Patterns in the Hundreds Charts Step 7 Compensation Step 6 Conservation of numbers Step 5 Counting on Step 4 Complements of Ten Step 3 Subitising Step 2 One to One Correspondence Step 1 Rote Counting 14

  15. At School We keep moving students up the number sense ladder: • One to one correspondence 10/12/2011 1 2 3 3 ‐ 5 Number Sense • Subitising • Your turn to try • Complements of ten 15

  16. At School • Counting on 10/12/2011 3 4 5 3 ‐ 5 Number Sense • Conservation of Number • video 16

  17. At School • Compensation • When working with numbers you can take an amount from one set and add it to another set and the TOTAL will not change. 10/12/2011 3 ‐ 5 Number Sense 17

  18. To help children… • Ask children to estimate* • Always ask – is your answer reasonable? Does 10/12/2011 it make sense? • Discuss which number is biggest* • Play games like guess my number using an 3 ‐ 5 Number Sense empty number line. ? 0 100 18

  19. What is Place Value? Understanding that: • Sets of ten can be perceived as a single unit (unitizing: research shows this develops toward the end of G1) 10/12/2011 • The position of digits in numbers determine what they represent 3 ‐ 5 Number Sense Hundreds Tens ones 3 2 5 19 (Van de Walle, 2006) This is a place value chart.

  20. What do we Know? The ability to understand and to use place value is crucial to understanding 10/12/2011 mathematics. • Children must spend time: 3 ‐ 5 Number Sense • Counting objects and placing them in groups of tens • Connecting what has been done with concrete manipulatives to visual representations and then to numbers • putting numbers together and taking them apart in a wide variety of ways 20 Australian Government’s Numeracy Research and Development Initiative and US Common Core Clarification documents

  21. At School • Helping children understand how objects can be grouped by tens and counted 10/12/2011 • Helping children understand that ten can be thought of as one group of ten or ten individual 3 ‐ 5 Number Sense items • Emphasize how numbers can be broken apart • Model for children how breaking numbers apart can help them to compute 21

  22. How can you break apart… 47 • 4 ten and 7 ones (40+7 = 47) * 10/12/2011 • 3 tens and 17 ones (30+17 = 47) 3 ‐ 5 Number Sense • 2 tens and 27 ones (20+27 = 47) • 1 ten and 37 ones (10+37 = 47) • 47 ones (47 = 47) • * We refer to this as expanded notation 22

  23. In KG children work on 11‐19 18 10/12/2011 3 ‐ 5 Number Sense 23

  24. In KG children work on 11‐19 18 10/12/2011 3 ‐ 5 Number Sense 18 = 10 + 8 18 is one group of ten and 8 “ones”. 24

  25. In G1 children work on 11‐99 18 10/12/2011 3 ‐ 5 Number Sense 25

  26. In G1 children work on 11‐99 18 10/12/2011 18 = 10 + 8 3 ‐ 5 Number Sense 18 is one “ten” and 8 “ones”. 26

  27. In G2 children work on 100‐1000 325 325 = 300 + 20 + 5 325 is 3 “hundreds”, 10/12/2011 2 “tens” and 5 “ones”. 3 ‐ 5 Number Sense 27

  28. To help children Always refer to the digits in a number by what they represent 10/12/2011 • 395 3 ‐ 5 Number Sense • The digit 3 represents 300 or 3 groups of a hundred • The digit 9 represents 90 or 9 groups of ten • The digit 5 represents 5 or 5 ones 28

  29. Guiding Question How does conceptual • understanding of calculation 10/12/2011 develop? 3 ‐ 5 Number Sense 29

  30. What is Conceptual Understanding? • Literacy is the ability to apply and use mathematical knowledge, skills and 10/12/2011 practices, in flexible and adaptive ways. (Willoughby, 2000) 3 ‐ 5 Number Sense • Understanding is the key to remembering what is learned and being able to use it flexibly. (Hiebert, in Lester & Charles, 2004) 30

  31. The Bridge to Understanding Repr presentation esentation “SEEING” Stage 10/17/2011 Parent Session AISCH Concrete Abstract “DOING” Stage “SYMBOLIC” Stage 31

  32. Building Mathematical Concepts Concrete Manipulatives 10/12/2011 I I I I I I I I 3 ‐ 5 Number Sense Pictorial Representation 4 + 4 = 8 2 x 4 = 8 Abstract Symbols Significant time must be spent working with concrete materials and 32 constructing pictorial representations in order for abstract symbol and operational understanding to occur.

  33. Let’s represent 24 Expanded notation pictorial 20 + 4 = 24 10/12/2011 II . . . . 10 + 14 = 24 3 ‐ 5 Number Sense 2(10) + 4(1) = 24 24 Place value chart written Tens Ones Twenty ‐ four 2 4 33

  34. To help children with computation Ask your child questions • How did you know that? 10/12/2011 • Explain to me what you are doing. • What were you thinking about when you did 3 ‐ 5 Number Sense that? • Does that make sense? • Can you teach me what you are doing? • I’m confused… (and point out where – but don’t say that is wrong – but see if your child can find his or her own mistakes) 34

  35. Thank you • You are invited to stay and ask questions. 10/12/2011 • Feel free to write questions on a post ‐ it and stick it to the charts in the back of the 3 ‐ 5 Number Sense room • I will read all of these and they will help us as we plan forward for future parent workshops 35

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