notation in both ascending and descending order. Today’s lesson . . . ascending descending What: ORDERING RATIONAL NUMBERS Why: To order groups of fractions, decimals, percentages, and #’s written in scientific notation in both ascending and descending order.

Start with the whole #’s, move onto the tenths, etc. STRATEGY: Start with the whole #’s, move onto the tenths, etc. REVIEW (ORDERING DECIMALS): When comparing decimal #’s, start with the __________________________ place value digit and compare. If there is a “tie,” move on to the next digit, etc. In other words . . . Compare the whole numbers. If there is a “tie,” move on to the ______________________________ . If there is another “tie,” move on to the _______________________________. If needed, keep moving on to the next place value digit(s). greatest tenths hundredths

Examples: Put the following decimal numbers in ascending order: 1) 1.025 1.25 0.039 0.4 Answer: 2) 0.0055 0.2 0.015 0.15 3) 0.75 0.425 0.9 0.45 0.039; 0.4; 1.025; 1.25 0.0055; 0.015; 0.15; 0.2 0.425 ; 0.45; 0.75; 0.9

STRATEGY: Convert everything into decimals first! Put the following numbers in ascending (least to great) order: # Frac. Decimal % Scientific Notation Answer (List in Original Form): 1. 1/8 0.0255 13% 1.25 x 10-2 2. 1¾ 1.755 1.7% 1.7 x 103 1.25 x 10-2 0.0255 1/8 13% Decimal Version 0.017 1 ¾ 1.755 1.7 x 103

Place the decimals from #3 (above) on the below number line: On Your own: 3. ¼ 0.3 20% 2.5 x 10-3 2.5 x 10-3 20% ¼ 0.3 Place the decimals from #3 (above) on the below number line: 0.0025 0.25 0.2 0.3 Hmmm. I wonder how this number line is divided?? Tenths of course!!

(List in Original Form): Put the following numbers in descending (greatest to least) order: # Frac. Decimal % Scientific Notation Answer (List in Original Form): 1. 2/5 0.45 40.5% 4.1 x 10 -4 2. 2/3 0.6 66% 6.6 x 10-3 0.45 40.5% 2/5 4.1 x 10-4 2/3 66% 0.6 6.6 x 10-3 Place the decimals from #1 (above) on the below number line:

Cynthia ran the least distance because Word Problems: 1. Amanda, Bill, Cynthia, and Max went running. Amanda ran 3.2 miles, Bill ran 3 2/5 miles, Cynthia ran 3.2 x 10 -2 miles, and Max ran 50% of 6 miles. Who ran the least amount of distance? Cynthia ran the least distance because She only ran 0.032 miles, which is only 3.2% of a mile!

2. At Simpson Middle School, the 6th graders are absent 1/8 of the time, the 7th graders are absent 0.1 of the time, and 8th graders are absent 13.5% of the time. Which grade is absent the most? The 8th graders are absent the most!

END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

Start with the whole #’s, move onto the tenths, etc. Math-7 NOTES DATE: ______/_______/_______ What: ORDERING RATIONAL NUMBERS Why: To order groups of fractions, decimals, %’s, and #’s written in scientific notation in both ascending and descending order. NAME: STRATEGY: Start with the whole #’s, move onto the tenths, etc. ascending descending REVIEW (ORDERING DECIMALS): When comparing decimal #’s, start with the __________________________ place value digit and compare. If there is a “tie,” move on to the next digit, etc. In other words . . . Compare the whole numbers. If there is a “tie,” move on to the ______________________________ . If there is another “tie,” move on to the ___________________________. If needed, keep moving on to the next place value digit(s). Examples: Put the following decimal numbers in ascending order: 1) 1.025 1.25 0.039 0.4 Answer: 2) 0.0055 0.2 0.015 0.15 3) 0.75 0.425 0.9 0.45

STRATEGY: Convert everything into decimals first! Put the following numbers in ascending (least to great) order: # Fraction Decimal % Scientific Notation Answer (List in Original Form): 1. 1/8 0.0255 13% 1.25 x 10-2 2. 1¾ 1.755 1.7% 1.7 x 103 3. ¼ 0.3 20% 2.5 x 10-3 Decimal Version Place the decimals from #3 (above) on the below number line:

(List in Original Form): Put the following numbers in descending (greatest to least) order: # Fraction Decimal % Scientific Notation Answer (List in Original Form): 1. 2/5 0.45 40.5% 4.1 x 10 -4 2. 2/3 0.6 66% 6.6 x 10-3 Decimal Version Place the decimals from #1 (above) on the below number line: Word Problems: Amanda, Bill, Cynthia, and Max went running. Amanda ran 3.2 miles, Bill ran 3 2/5 miles, Cynthia ran 3.2 x 10-2 miles, and Max ran 50% of 6 miles. Who ran the least amount of distance? At Simpson Middle School, the 6th graders are absent 1/8 of the time, the 7th graders are absent 0.1 of the time, and 8th graders are absent 13.5% of the time. Which grade is absent the most?

(List in Original Form): (List in Original Form): PRACTICE WORK NAME:________________________________________________________________________________DATE: _____/_____/__________ “Ordering rational numbers” Order the following from least to greatest (ascending): # Fraction Decimal % Scientific Notation Answer (List in Original Form): 1. 4/5 0.08 80.5% 8 x 10 -3 2. 1/3 0.34 33% 3.3 x 10-2 3. 41/4 4.3 42.5% 4.25 x 102 Order the following from to greatest to least (descending): # Fraction Decimal % Scientific Notation Answer (List in Original Form): 4. ¼ 0.025 2% 2.5 x 10-4 5. 5/6 0.83 8.3% 8.35 x 10-2 6. 14/16 0.0975 8.75% 8.75 x 102

“Ordering rational numbers” PRACTICE WORK NAME:________________________________________________________________________________DATE: _____/_____/__________ “Ordering rational numbers”