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

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

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

NUMBER SENSE PRETEST (cont) 2. How would you compare the answers to these two problems? = ______ and = ________

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

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?

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? , ,

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?

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?

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

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

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.

COMMON CORE FOCUS

MATHEMATICAL SHIFTS

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

EXAMPLE OF PROGRESSIONS

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

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

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

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

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

Grade 1 Place Value Mats Number Bonds

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

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

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

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 NBT.4 – Compare 3 digit numbers to NBT.5 – Fluently add and subtract within NBT.6 – Add up to 4 2-digit numbers 2.NBT.7 – Add and subtract up to 1000

COUNTING & CARDINALITY OPERATIONS & ALGEBRAIC THINKING PROGRESSIONS

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

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

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

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

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

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

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

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

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

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

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