CHAPTER 8EXTENDING NUMBER SENSE: PLACE VALUE

By: Amanda Roberts

Jessica Carlson

Anna Groves

MYSTERY BOX

Activity

Kids must make sense of numbers and how they are used in and out of school

HINDU-ARABIC COUNTING SYSTEM

1)Place Value2) Base of Ten3) Use of Zero4) Additive property

PLACE VALUE

Place value is one of the key building blocks for the rest of math.

Development of Place value rests on two main ideas:

1)Explicit grouping or trading rules are defined and consistently followed.

2)Position of digit determines number being represented.

http://hubpages.com/hub/place-value-games

PLACE VALUE

Hindu-Arabic system means that all numbers can be represented by using the numbers 0-9.

Because our system only uses 10 digits place value is a very important concept.

Zero is a place holder and shows the lack of a quantity.

http://www.familylearning.org.uk/place_value_games.html

MODELING

• There are two types of materials that are best used to help students develop an understanding of place value.

• Ungrouped materials are things such as cubes, beans, straws, or popsicle sticks. They are separate and can be grouped together by the student.

• Pregrouped materials are already in sets of 5, 10, or 20 before the student touches them.

MODELING

Place value is proportional or nonproportional

Proportional models are things such as base ten blocks in which the size of ten is ten times the size of one.

Nonproportional models do not have any type of size relationship.

EARLY CHILDHOOD

Counting from11-19 is hard for kids to understand, so skip and teach larger numbers.

25 vs. 52, what is difference in numbers, kids don’t see difference

What makes up the number 25, what goes into it? Groups of ones, tens, 100’s.

HOW TO TEACH

To teach start with concrete physical models, move to semi concrete, go to symbolic representations

100’s chart, used to show kids how to add/subtract, check for understanding cover #

Class Activity

EXTENDING PLACE VALUE

Kids lack understanding of relative sizes of numbers greater than one hundred.

To help them understand the size of a number we can break it down for them in multiple ways.

Ex: 123 is 1 (100) 2(10) 3(1) 12(10) 3(1) 123(1)

Children also have a hard time in seeing the difference between numbers with the same digits.

Ex: 2130 vs. 1032 To help students see the difference in

these numbers we can use the front-end or back-end approach.

2130 54121030 5489

3042342

5657 5656

2211 3311

9994 9949

1111 1100

8324 1224

4737 3747

2003 2030

COUNTING AND PATTERNS

Skip counting: counting by a number greater than one.

Calculators are helpful to show students patterns and help distinguish place value.

They are also helpful in developing their number sense and helping them understand larger numbers.

http://members.learningplanet.com/act/count/free.asp

COUNTING AND PATTERNS

Counting backwards also helps to develop place value patterns.

To count backwards with students start out by using a number line, then move on to a calculator.

Knowing patterns helps in the understanding of place value.

READING/WRITING WITH NUMBERS

Reading large numbers is hard for kids.

As a teacher you will probably see things written like this.100 64 for the actual number 164.

Put in place value chartOnes, tens, hundreds chart

Models are helpful for kids to understand how large numbers work

READING/ WRITING NUMBERS CONT.

To develop facility in reading large numbers children need careful instruction and practice in actually naming them aloud.

1,000,980

Hundreds Tens Ones

3 8 0

Reads 3 100’s, 8 10’s, and 0 1’s.Realizes there are no 1’sRereads 38 10’s which is 380

ROUNDING

Integrates understanding of approximate values with place value and naming numbers

Numbers are rounded to make them easier to use

Rounded numbers make more senseAttention is given to back end of the

digit, not the first numberBe specific in telling students what

place value to round to.

0

5

10

15

20

25

CLOSURE

Price tagsIf you would round up STANDIf you would round down, TOUCH THE GROUND

If the number stays the same, SIT DOWN

$ 9.99