1. NUMBER SENSE & PLACE VALUE
January 23, 2013
Erie 1 BOCES Presenters: Andrea Tamarazio & Steven Graser

2. NUMBER SENSE ACTIVITY
Using the chart paper on your table, write the term number sense in the middle & each member at the table will draw, write, and / or provide examples or what number sense means.
Need chart paper and markers for every table

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
= ________

5. NUMBER SENSE PRETEST (cont)
3. With the numbers below circle the largest number for each pair ,097 6,907 9,123 3,219

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? , ,

8. NUMBER SENSE PRETEST (cont)
6. If 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 = 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 ? 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.
BREAK after this slide

13. Survey A Story of Units Curriculum Map
COMMON CORE FOCUS
Survey A Story of Units Curriculum Map
Discuss amount of time spent of certain aspects of curriculum map
Ask participants how much

14. MATHEMATICAL SHIFTS
Focus on coherence, application and deep understanding

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. BASE TEN NUMBER SYSTEMS & OPERATIONS PROGRESSIONS BY GRADE LEVEL

18. 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.

19. Ten Frame Video Example
KINDERGARTEN K.NBT.1 – Compose & decompose Numbers from 11 – 19 into tens & ones and some further ones
Number Bond Diagram & Equation
Five & Ten Frames
Ten Frame Video Example
Place Value Cards (Front Numeric and Back Pictorial Representation)
Model strategies these with white boards
Need to find handouts for these strategies

20. 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.

21. Grade 1 1.NBT.2 – Understand that 2-digits of a 2 digit number represent amounts of tens and ones 1.NBT.2a – Ten can be thought of as a bundle of ten ones called a ten 1.NBT.2b – The numbers from 11 – 19 are composed of a ten and 1, 2, 3, … 9 ones 1.NBT.2c – The numbers 10, 20, 30 … 90 refer to 1, 2, 3 … 9 tens (and zero ones)
Place Value Mats

22. Counting with Bundles Video
Grade 1 1.NBT.3 – Comparing numbers using symbols >, <, or = 1.NBT.4 – Add within NBT.5 – Mentally find 10 more or 10 less 1.NBT.6 – Subtract multiples of 10
Adding tens and ones separately
Counting on or back by 10s
Counting with Bundles Video
Materials needed place value mats, bundles of tens and ones
For singapore addition with regrouping, you start with the left and move to the right counting on first by tens then by ones.

23. 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.

24. Grade 2 2.NBT.1 – Understand that the 3 digits of a three digit number represent amounts of hundreds, tens, and ones 2.NBT.1a – Hundreds can be thought of a ten tens called a hundred.
Drawings to support 10 tens as one hundred
Place Value Mat

25. Additional CCLS
2.NBT.3 – Read & Write numbers to (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
Hundreds Chart
Place Value Mat
Singapore Method in progressions
Page 9 in progressions for addition and subtraction with regprouping – model these ideas for participants
Incorporate some fluency activities around skip counting and place value activities

26. COUNTING & CARDINALITY OPERATIONS & ALGEBRAIC THINKING PROGRESSION BY GRADE LEVEL

27. KINDERGARTEN K. CC. 1 – Count to 100 by 1s and 10s K. CC
KINDERGARTEN K.CC.1 – Count to 100 by 1s and 10s K.CC.4a – Understand the relationship between numbers and quantities
1, 2, 3, 4, …
10, 20, 30, 40 …. 1 2
Counting Exercise

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

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

30. 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
Example:
Making 10 is = = = 14
Decomposing is 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9
Creating Equivalent is = = = 13

31. ADDITIONAL STRATEGIES
Tape Diagram / Bar Diagram
Part-Whole Bond (Pictorial)
Number Bond
See page 16 of progression document

32. 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

33. 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

34. QUESTIONS / CONCERNS
If you have any questions or comments, please feel free to contact us.
Andrea Tamarazio
Steven Graser