NUMBER SENSE & PLACE VALUE

December 11, 2013Erie 1 BOCESPresenter: 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?

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. 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

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

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 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.◦Decomposition of numbers

KINDERGARTEN

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.

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 formCompare three digit numbers

Grade 2

Drawings to support 10 tens as one hundred

Singapore Addition

Expanded Form

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 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

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

KINDERGARTEN Addition and Subtraction within 5

fluently

Addition and Subtraction to 10 with pictures, objects, or drawings◦Number bond

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 Fluency with addition and

subtraction to 20Begin to see two-step word

problems Relation to MD Domain

◦Length◦Graphing

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 me.

Andrea Tamarazioatamarazio@e1b.org