Monday, October 29th
2.1 Reading and Writing Large Numbers
Getting Started – 5 min
Mental Math and Reflexes – Smartboard Notebook file using Responders.
Write the number that is 10 times as great
9,010
90,100
150,100
1,501,000
30,010,000
300,100,00
701,010,100
7,010,101,00
Math Message – 2 min
Complete the Math Message on journal page 45
Math Message Follow Up – 5 min
Student Math Journal, page 45
Ask students to share the methods they used to record the number 9,500,000,000,000 in
the place-value chart. Some students may have entered digits from right to left, moving
from ones to trillions. Others may have used the commas to organize their digit entries.
The number 9,500,000,000,000 is written in standard notation – the most familiar way of
representing whole numbers and decimal numbers. In standard notation, digits are
written in specified places. Most students should be able to read and write large numbers
in standard notation.
Have pairs of students look for patterns in the place-value chart and share the pattern they
find. Patterns include:
-Each place is 10 times the place to its right.
-Each period or group is divided into three places – ones, tens and hundreds.
-Each period or group is separated by a comma.
Ask students to write on their slates or on the board the number that is:
- 10 times as great as 9,500,000,000,000
95,000,000,000,000
- 1/10 times as great as 9,500,000,000,000
950,000,000,000
Interpreting Expanded Notation for Large Numbers – 10 min
Math Masters, page 409
Display the transparency of Math Masters, page 409 and give one copy of the same page
to each student. Ask students to write the number 235 in the place value chart at the top
half of the page. They will convert this number from standard notation into expanded
notation. In expanded notation, a number is written as the sum of the values of its digits.
For example, in the number 234, the pace of the digit 2 is hundreds, so its value is
2 * 100. The alue of the digit 3 is 3 * 10. The value of the digit 5 is 5 * 1. So, in
expanded notation, 235 is written as:
(2 * 100) + (3 * 10) + (5 * 1)
Help students see how they can apply their extended multiplication facts to write
numbers in expanded notation.
The diameter of the Sun is about 863,706 miles. Ask students to record this number in
their place-alue charts. Suggest they use the place-value chart to convert this number
from standard notation to expanded notation. When students have finished, ask a
volunteer to share this or her work.
863,706 = (8 * 100,00) + (6 * 10,000) + (3 * 1,000) + (7 * 100) + (6 * 1)
Pose additional problems such as the following:
-Write 68,250,000 in expanded notation
-Write 2,703,109 in expanded notation
Have students work independently to complete journal page 45. When most students are
finished, go over the answers.
Interpreting Number-and-Word Notation for Large Numbers – 10 min
Math Journal, page 46
On the board, draw and label five sets of three dashed lines, separated by commas, or use
an overhead and show the transparency Math Masters, page 409.
Number-and-word notation consists of the significant digits of a large number followed
by a word for the place value. Examples include 27 million and 8.5 billion. Use the
template to practice converting between standard and number-and-word notations.
1.
Convert standard notation to number-and-word notation.
Write 27,000,000 on the place-value template.
Number-and-word notation depends on the largest period. Because the digits 2 and 6 are
in the millions period, the number-and-word notation of 27,000,000 is 27 million.
Now write 8,500,000,000 on the place-value template.
The digit 8 is in the billions period and the 5 is in the millions period. Billions is the
largest period, so the number-and-word notation should be in terms of billions. Since
5000,000,000 is 0.5 billion, 8 billion + 0.5 billion = 8.5 billion
Pose additional problems such as the following:
-Convert 46,750,000 to number-and-word notation 46.75 million
-Convert 203,600,000,000 to number-and-word notation 203.6 billion
-Convert 900,000 to number-and-word notation
900 thousand or 0.9 million
2.
Convert number-and-word notation to standard notation.
Write 32.65 million on the board. Point out that the decimal point represents the
comma named by the word. So, in 32.65 million, the decimal point represents the
millions comma. Show students how to use the comma to position the nonzero digits.
Then insert zeros to complete the conversion to standard notation.
Pose additional problems such as the following:
-Convert 125 million to standard notation 125,000,000
-Convert 27.5 thousand to standard notation 27,500
-Convert 140 billion to standard notation
140,000,000,000
Have students complete journal page 46.