C HAPTER 8 E XTENDING N UMBER S ENSE : P LACE V ALUE By: Amanda Roberts Jessica Carlson Anna Groves

M YSTERY B OX Activity Kids must make sense of numbers and how they are used in and out of school

H INDU -A RABIC COUNTING SYSTEM 1)Place Value 2) Base of Ten 3) Use of Zero 4) Additive property

P LACE V ALUE 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.

P LACE V ALUE 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.

M ODELING 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.

M ODELING 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.

E ARLY C HILDHOOD 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.

H OW 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

E XTENDING P LACE V ALUE 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 To help students see the difference in these numbers we can use the front-end or back-end approach

C OUNTING AND P ATTERNS 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.

C OUNTING AND P ATTERNS 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.

R EADING /W RITING WITH NUMBERS Reading large numbers is hard for kids. As a teacher you will probably see things written like this for the actual number 164. Put in place value chart Ones, tens, hundreds chart Models are helpful for kids to understand how large numbers work

R EADING / WRITING NUMBERS CONT. To develop facility in reading large numbers children need careful instruction and practice in actually naming them aloud. 1,000,980

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

R OUNDING Integrates understanding of approximate values with place value and naming numbers Numbers are rounded to make them easier to use Rounded numbers make more sense Attention is given to back end of the digit, not the first number Be specific in telling students what place value to round to.

C LOSURE Price tags If you would round up STAND If you would round down, TOUCH THE GROUND If the number stays the same, SIT DOWN $ 9.99