Lesson 1 Place Value and Number Representations Unit

Lesson 1: Place Value and Number Representations Unit 3: From Powers to Circles

Lesson 1: Place Value and Number Representations • Review place value • Different Representations of Numbers

Bell Work • Complete BLM 3. 1. 1 – Label each column that represents each place value (“Value of the Place”) – Write the following numbers correctly on the chart: – 16. 8, 14. 009, 146, 400 003, 6758. 03, 0. 5 and one number of your own choice

How To Read Numbers • When reading numbers aloud it is important to remember “and” is used to express a decimal point. – Examples: • 16. 8 is sixteen and eight tenths • 14. 009 is fourteen and 9 thousandths • 1040 – one thousand forty* * “and” is not used because there is no decimal point

Number Representations • Using your whiteboard, record how you could represent the number 1025 in as many ways as you can • Be prepared to share your work

Key Terms You Should Already Know Number Representations: 1. 2. 3. 4. Standard Form Word Form Expanded Form with Powers of Ten Define the terms above and provide an example of each.

Standard Form • the form of a number that we most commonly work with • it is the number itself • Examples: 12, 234. 5, 1 000 • numbers are shown with each digit in its correct place

Word Form • the number is expressed using words • Examples: 1234 = one thousand two hundred thirty-four 13. 45 = thirteen and forty-five hundredths 0. 315 = zero decimal three one five or (more correctly) three hundred fifteen thousandths 21 405 = twenty-one thousand four hundred five

Expanded Form • when a number is written out to show the value of each digit (expanding the number from standard form) • Examples: 435 = (4 x 100) + (3 x 10) + (5 x 1) 20. 14 = (2 x 10) + (1 x 1/10) + (4 x 1/100)

Expanded Form with Powers To represent 100 as a power of 10: 100 = 10 × 10 = 102 To represent 100 000 as a power of 10: 100 000 = 10 × 10 = 105 Example: (5 × 102) + (7 × 101)+ 4 = 574 6 102 + 3 + 1 10 + 2 102) 0. 1 can also be written 1 x 10 -1; 0. 02 can also be written as 2 x 10 -2

Representing Numbers • Standard form: 574 • Word form: five hundred seventy-four • Expanded form: 500 + 70 + 4 = 5 × 100 + 7 × 10 + 4 × 1 • Expanded form with powers of 10: ?

Representing Numbers • Standard form: 603. 12 • Word form: six hundred three and twelve hundredths • Expanded form: 600 + 3 + 0. 1 + 0. 02 = 6 100 + 3 + 1 1/10 + 2 1/100 • Expanded form with powers of 10: ?

Practice • Complete Value of the Place and Representing Numbers • Make sure these notes are written in your notebook • any work not completed in class is for homework • you will write a quiz to check your understanding before moving to the next lesson