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

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

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? 7 + 3 = ______ and 70 + 15 + 15 = ________

NUMBER SENSE PRETEST (cont) 3. With the numbers below circle the largest number for each pair. 367 356 6,097 6,907 9,123 3,219

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? 500 25 3, 075 250 200 50 1,000 900

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?

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?

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 40 + 20? 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. BREAK after this slide

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

MATHEMATICAL SHIFTS Focus on coherence, application and deep understanding

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

BASE TEN NUMBER SYSTEMS & OPERATIONS PROGRESSIONS BY GRADE LEVEL

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.

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

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.

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

Counting with Bundles Video Grade 1 1.NBT.3 – Comparing numbers using symbols >, <, or = 1.NBT.4 – Add within 100 1.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.

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.

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

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 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

COUNTING & CARDINALITY OPERATIONS & ALGEBRAIC THINKING PROGRESSION BY GRADE LEVEL

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

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

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

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 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14 Decomposing is 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9 Creating Equivalent is 6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

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

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 us. Andrea Tamarazio atamarazio@e1b.org Steven Graser sgraser@e1b.org