1. NUMBER SENSE & PLACE VALUE December 11, 2013 Erie 1 BOCES Presenter: Andrea Tamarazio

2. NUMBER SENSE ACTIVITY Using the Frayer Model on your table, write the term number sense in the middle and then complete each section.

3. NUMBER SENSE PRETEST 1. Explain how you would group the following numbers to make them easier to add together? 12, 6, 3, 8, 5, 14, and15

4. NUMBER SENSE PRETEST (cont) 2. How would you compare the answers to these two problems? 7 + 3 = ______ and 70 + 15 + 15 = ________

5. NUMBER SENSE PRETEST (cont) 3. With the numbers below circle the largest number for each pair. 367 356 6,0976,907 9,1233,219

6. NUMBER SENSE PRETEST (cont) 4. A bicycle built for two is 10 feet long. A rectangle mountain bike is 5’8” long. Which is longer, 2 regular mountain bikes put end to end or 1 bicycle built for two? How do you know?

7. NUMBER SENSE PRETEST (cont) 5. What do you think would be the easiest way to combine the numbers below to add them to 6,000? 500 25 3, 075 250 200 50 1,000 900

8. NUMBER SENSE PRETEST (cont) 6. I bought 5 cartons of eggs so I could feed a boy scout troop breakfast, how many eggs would I have if each carton had a dozen eggs in it?

9. NUMBER SENSE PRETEST (cont) 7. If you know that 27 + 27 = 54 and also that 2 x 27 = 54 what would you do to find out what 4 x 27 equals?

10. NUMBER SENSE PRETEST (cont) 8. Make up an addition story using the numbers 3, 6, and 12 (you may use numbers more than once).

11. NUMBER SENSE PRETEST (cont) 9. Which strategy do you think would work best for solving the problem 40 + 20? Skip Counting by 2s Counting on your fingers Thinking of money Skip Counting by 20s Making a Picture Adding by Place Value

12. NUMBER SENSE NCTM: Children must understanding number meanings if they are to make sense of the way numbers are used in real life situations. YANG: The lack of number sense results in mindless application of standard written algorithms that are learned in school. HEIBERT: Students are good rule followers however they do not always understand the procedures they learn. GERSTEN & CHARD: Number sense refers to a child’s fluidity and flexibility with numbers.

13. COMMON CORE FOCUS

14. MATHEMATICAL SHIFTS

15. MATHEMATICAL PRACTICES Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

16. EXAMPLE OF PROGRESSIONS

17. K – 5 Number and Operations in Base Ten Work in base-ten system is intertwined with their work on counting and cardinality, and with the meaning and properties of addition, subtraction, multiplication, and division Only ten digits to represent every number makes the base-ten system remarkably efficient In Grades K – 3, the students are using computation strategies but once they move to Grade 4 they must move to computation algorithm

18. K – 2 NUMBER & OPERATIONS IN BASE TEN Take a couple of minutes to read your grade level progressions document Have a table discussion about important ideas Create a chart of key ideas to share out

19. KINDERGARTEN BASE TEN SYSTEM Teachers help children lay the foundation for understanding the base ten system by drawing special attention to 10. Children learn to view the whole numbers 11 – 19 as 10 ones and some more ones. ◦ Decomposition of numbers

20. KINDERGARTEN Number Bond Diagram & Equation Five & Ten Frames Ten Frame Video Example Place Value Cards (Front Numeric and Back Pictorial Representation)

21. GRADE 1 BASE TEN SYSTEM Students learn to view 10 ones as a unit called a “ten”. Students need the ability to compose and decompose this unit and to view the numbers 11 – 19 as composed of 1 ten and some ones. Compare numbers with >, <, or = Add within 100 using place value strategies

22. Grade 1 Place Value Mats Number Bonds

23. Grade 1 Adding tens and ones separately Counting on or back by 10s Counting with Bundles Video

24. GRADE 2 BASE TEN SYSTEM Students extend their base ten understanding to 100s. They add and subtract within 1000 with composing and decomposing and they understand and explain their reasoning. Fluent with addition and subtraction to 100. Read and write numbers to 1000 in all forms ◦ Base-ten numerals, number names, and expanded form Compare three digit numbers

25. Grade 2 Drawings to support 10 tens as one hundred Singapore Addition Expanded Form

26. Additional CCLS 2.NBT.3 – Read & Write numbers to 1000 (Numerals, Number Names and Expanded Form) 2.NBT.2 – Skip Count by 5s, 10s, and 100s to 1000 2.NBT.4 – Compare 3 digit numbers to 1000 2.NBT.5 – Fluently add and subtract within 100 2.NBT.6 – Add up to 4 2-digit numbers 2.NBT.7 – Add and subtract up to 1000

27. COUNTING & CARDINALITY OPERATIONS & ALGEBRAIC THINKING PROGRESSIONS

28. COUNTING & CARDINALITY Several progressions originate from knowing number names and the count sequence Usually rote counting happens before knowledge of what the number represents Counting in a variety of arrangements ◦ Students should be able to count out a given number of objects as well as counting the number of objects given Subitizing objects ◦ Perceptual & Conceptual

29. KINDERGARTEN 1, 2, 3, 4, … 10, 20, 30, 40 …. 1 2 Counting Exercise

30. KINDERGARTEN K.CC.5 – Counting items in an array or scattered formation Array Scattered Configuration

31. KINDERGARTEN K.CC.6 – Compare number of objects in groups K.CC.7 – Compare written numbers Pictures of objects Numeral Cards

32. KINDERGARTEN Addition and Subtraction within 5 fluently Addition and Subtraction to 10 with pictures, objects, or drawings ◦ Number bond

33. GRADE 1 1.OA.6 – Add and subtraction within 20 Counting on Making 10 Decomposing number leading to a 10 Creating equivalent but easier or known sums

34. ADDITIONAL STRATEGIES Tape Diagram / Bar Diagram Part-Whole Bond (Pictorial) Number Bond

35. Grade 2 Fluency with addition and subtraction to 20 Begin to see two-step word problems Relation to MD Domain ◦ Length ◦ Graphing

36. GRADE 2 2.NBT.1a 2.NBT.2 2.NBT.4 2,NBT,5 2.NBT.6 2.NBT.7 Addition Record combining of hundreds tens and ones on separate lines Recording newly composed units on the same line Subtraction Decomposing where needed first Subtraction with renaming Video Example

37. ACTIVITY SHARE OUT Take time to create activities to use in your classroom What do you have in your classroom that you would like to share? ◦ Activities ◦ Strategies

38. QUESTIONS / CONCERNS If you have any questions or comments, please feel free to contact me. Andrea Tamarazio atamarazio@e1b.org