number sense & place value

NUMBER SENSE & PLACE VALUEJanuary 23, 2013Erie 1 BOCESPresenters: 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.

NUMBER SENSE PRETEST1. 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 3566,097 6,9079,123 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?

50025

3, 075 250200501,000900

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 2sCounting on your fingersThinking of moneySkip Counting by 20sMaking a PictureAdding 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

Survey

A Story of Units Curriculum Map

MATHEMATICAL SHIFTS

MATHEMATICAL PRACTICESMake sense of problems and persevere

in solving themReason abstractly and quantitativelyConstruct viable arguments and

critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in

repeated reasoning

EXAMPLE OF PROGRESSIONS

BASE TEN NUMBER SYSTEMS & OPERATIONS PROGRESSIONS BY GRADE LEVEL

KINDERGARTEN BASE TEN SYSTEMTeachers 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.

KINDERGARTENK.NBT.1 – Compose & decompose Numbers from 11 – 19 into tens & ones and some further ones

Number Bond Diagram & Equation

Five & Ten FramesTen Frame Video Example

Place Value Cards (Front Numeric and Back Pictorial Representation)

GRADE 1 BASE TEN SYSTEMStudents 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 ones1.NBT.2a – Ten can be thought of as a bundle of ten ones called a ten1.NBT.2b – The numbers from 11 – 19 are composed of a ten and 1, 2, 3, … 9 ones1.NBT.2c – The numbers 10, 20, 30 … 90 refer to 1, 2, 3 … 9 tens (and zero ones)

Place Value Mats

Grade 11.NBT.3 – Comparing numbers using symbols >, <, or =1.NBT.4 – Add within 1001.NBT.5 – Mentally find 10 more or 10 less1.NBT.6 – Subtract multiples of 10

Adding tens and ones separately

Counting on or back by 10s

Counting with Bundles Video

GRADE 2 BASE TEN SYSTEMStudents 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 22.NBT.1 – Understand that the 3 digits of a three digit number represent amounts of hundreds, tens, and ones2.NBT.1a – Hundreds can be thought of a ten tens called a hundred.

Drawings to support 10 tens as one hundred

Additional CCLS2.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

COUNTING & CARDINALITY OPERATIONS & ALGEBRAIC THINKING PROGRESSION BY GRADE LEVEL

KINDERGARTENK.CC.1 – Count to 100 by 1s and 10sK.CC.4a – Understand the relationship between numbers and quantities

1, 2, 3, 4, …

10, 20, 30, 40 ….

1

2

Counting Exercise

KINDERGARTENK.CC.5 – Counting items in an array or scattered formation

Array

Scattered Configuration

KINDERGARTEN K.CC.6 – Compare number of objects in groupsK.CC.7 – Compare written numbers

Pictures of objects

Numeral Cards

GRADE 11.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 2.NBT.1a2.NBT.22.NBT.42,NBT,52.NBT.62.NBT.7

AdditionRecord combining of hundreds tens

and ones on separate linesRecording newly composed units on

the same lineSubtractionDecomposing where needed firstSubtraction with renaming

Video Example

ACTIVITY SHARE OUTTake 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 / CONCERNSIf you have any questions or

comments, please feel free to contact us.

Andrea Tamarazioatamarazio@e1b.org

Steven Grasersgraser@e1b.org