Saying, Reading, and Writing Numbers plan and worksheets

Middle level lesson plan for saying, reading, writing, and saying numbers from billions to billionths with Number facts worksheet

Concept Assessment Information
Concepts Supporting Misconceptions Assessment
Dimension:

Number value

Patterns in place value help us write and read numbers accurately.

  1. Numbers are written following a certain pattern.
  2. Three digits are grouped with commas.
  3. Decimal place is a marker not a place.
  4. There is only one units place.
  5. Pattern of thousand, million...
  6. Pattern of ___, ten, hundred,
  1. Each number has a certain way to be said and written that must be memorized .
  2. A pattern for determining how numbers are written and said orally is too complicated for most people to understand.

Diagnostic

Ask students to describe how they can use a pattern to help them say and write number words.

Formative

Quiz students over the names of the place values and their order.

Summative

Students are able to create the order of places from ones to billions and tenths to millionths.

Generative

Use place value to communicate number value. Use of place value for problem solving.
Concepts Supporting Information Misconceptions Assessment
Dimension:

Communication

Numbers are communicated in a standard way.

  1. Numbers are represented orally.
  2. Numbers are represented in writing.
  3. Number words have correct spellings.
  4. Number words have a grammar.
  1. There are many standard ways to write numbers.

Diagnostic

Tell a student to write a number on the board and ask another to read the numeral and another to write the numeral in words.

Formative

Give all possible combinations of numbers and have students say and write them until they could do so for any number in the world.

Summative

Make a list of ten - twenty numbers that students had difficulty with during the practice sessions and have them read and write them.

  • 1 302,
  • 2 005,
  • 201, 006
  • ...

Generative

Recognize other ways mathematics is communicated in standard ways.
Procedure for Concept Conceptualization and Generalization

Objective:

Discover patterns in a place value chart and use then to create a procedure for writing, reading, and saying numbers from millionths to millions.

Materials:
Exploration
  1. Put students in pairs.
  2. Pass out place value number line and have students construct the number line.
  3. Challenge students to find as many patterns as they can in five minutes.
  4. Put pairs of students into groups of four and ask them to consolidate their list.
Invention
  1. Have students consolidate all group’s lists into one class list on a board to display for everyone to see.
  2. Discuss results.
  3. Be sure all patterns outlined in the supporting information are discussed.
Exploration
  1. Tell students they will explore in groups, pairs.
  2. Give students the number facts sheets.
  3. Tell students to do two things:
    1. Use the place value number line worksheet and the information on the number fact sheet to explain how all the 14 examples are read and written.
    2. Create a rule that would explain how to read or write any number less than one million and greater than one millionth.
  4. Put two pairs together and have them share their results for both.
Invention
  1. Bring the class together, share how to say and write the numbers, and disuss each.
  2. Have each group share their rule.
  3. As each group shares, have other groups give them numerals to read and write to see if the rule works or not.
  4. Continue until all groups share their rule.
  5. Have students identify which rule(s) they will use.
  6. Have students create a problem they believe will test the limits of their rule.
  7. Have students exchange their problems with their original partner, use their preferred rule, write the word number, read it to each other, and determine if the rule works.
  8. Ask students if patterns can help them solve real world problems.
Expansion
  1. Have students create a list of nine numbers: three written in words, three in numerals, and three either way for a partner to read.
  2. Have students exchange and write or say the numbers in different ways.

 

Number Facts

Historical number facts

Numeral words word bank

zero eleven ten thousand
one twelve twenty million
two thirteen thirty billion
three fourteen forty trillion
four fifteen fifty quadrillion
five sixteen sixty quintillion
six seventeen seventy sextillion
seven eighteen eighty septillion
eight nineteen ninety octillion
nine hundred nonillion
decillion

 

Written Numerals sample worksheet

6 six
72 seventy - two
45 forty - five
107 one hundred seven
1,006 one thousand, six
1,326 one thousand, three hundred twenty - six
1,165.14 one thousand, one hundred sixty - five and fourteen hundredths
5,426,384 five million,
four hundred twenty - six hundred thousand,
three hundred eighty - four
34.81 thirty - four and eighty - one hundredths
$9.67 nine dollars and sixty - seven cents
8.19 eight and nineteen hundredths
74.11/32 seventy - four and eleven thirty - seconds
100.2 one hundred and two tents
104.005 one hundred four and five thousandths

 

Place Value Number Line

Cut out each chart and tape them together.

 

107 108 109 1010 1011 1012
ten millions hundred millions billions ten billions hundred billions trillions

10,000,000

100,000,000

1,000,000,000

10,000,000,000

100,000,000,000

1,000,000,000,000

 

 

 

 

100 101 102 103 104 105 106
ones tens hundreds thousands ten thousands hundred thousands millions
1 10 100 1,000 10,000 100,000

1,000,000

 

 

 

 

10 - 4 10 - 3 10 - 2 10 - 1
ten thousandths thousandths hundredths tenths

.0001

or

1/10,000

.001

or

1/1,000

.01

or

1/100

.1

or

1/10

 

 

10 - 9 10 - 8 10 - 7 10 - 6 10 - 5
billionths hundred millionths ten millionths millionths hundred thousandths

.000000001

or

1/1,000,000,000

.00000001

or

1/1000000,000

.0000001

or

1/10,000,000

.000001

or

1/1,000,000

.00001

or

1/100,000

 

Numbers: order from billions - billionths

 

Billions - 109

Millions
 hundred million (one, two, three, four, five, six, seven, eight, nine) - 108
  ten million (twenty, thirty, forty, fifty, sixty, seventy, eighty.,ninety) - 107
   million (one, two, three, four, five, six, seven, eight, nine) - 106

Thousands
 hundred thousand - 105
  ten thousand - 104
    thousand - 103

Hundreds
 hundred (one, two, three, four, five, six, seven, eight, nine) - 102
  ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety - 101
     one, two, three, four, five, six, seven, eight, nine - 100

Decimal

 tenths - 10 - 1
   hundredths - 10 - 2

 thousandths - 10 - 3
   ten thousandths - 10 - 4
     hundred thousandths - 10 - 5

 millionths - 10 - 6
   ten millionth - 10 - 7
     hundred millionths - 10 - 8

 billionths - 10 - 9

 

Dr. Robert Sweetland's notes
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