• Observe students during lesson activities and classroom discussion.
• Use comparisons recorded during the Small Group Extension activity to assess student progress and to remediate concepts as needed.

“Just as we have used models to represent fractions you can also use models to represent decimals. Where have you seen or used decimals?” (Sample answers: money, measurement, miles, time, sports statistics.) “Fractions and decimals are similar in that they both show parts of a whole.”

Demonstrate the following grids and explain how they are shaded. Ask students to describe what they think each grid shows.

Use a tenths grid (M-4-3-2_Tenths and Hundredths Grids.docx). “What would we color to show seven-tenths?” (7 of the 10 squares)

Use a hundredths grid (M-4-3-2_Tenths and Hundredths Grids.docx). “What would we color to show seventy-hundredths? What do you notice about these two grids?” (The same amount of the grid is shaded.)

Demonstrate to students how to label the amount colored as both a fraction and decimal by following these steps:

• Step 1. Determine the total number of unit squares in your grid. Are you using a base of 10 or a base of 100? This number is your denominator.
• Step 2. Count the number of shaded squares. Write this number as a fraction over the total number of unit squares.
• Step 3. Write your fraction as a decimal. Do this by thinking of how to say the fraction in words. For instance,  literally means “seven-tenths.” The decimal 0.7 also means “seven-tenths,” because the digit 7 is in the tenths place. Therefore,  = 0.7.
• Step 4. Find an equivalent fraction. For example, 0.7 is the same as 0.70. The first is read as “seven-tenths” or  . The latter is read as “seventy-hundredths,” or  . This means that .

Stress that:

1. The fractions from Step 4 are all equivalent values.
2. The decimal representation of a fraction should be presented with emphasis on the language of how to read a decimal correctly. For example, 0.7 is read as “zero and seven-tenths,” not, “zero point seven.”
3. The (reduced) fraction name and decimal name are the same (e.g., 0.7 and  are both called “seven-tenths.”)

For additional practice, students can complete the Fraction Decimal Shading worksheet (M-4-3-2_Fraction Decimal Shading Worksheet and KEY.doc). Students do the following:

• Shade individual squares to represent the fraction of the grid.
• Count the number of shaded squares.
• Write a fraction of the shaded squares out of 100.
• Write the fraction as a decimal. (Remind students to make a decimal point with a zero to the left.)

“A decimal that names the same part of a whole as a fraction is the fraction’s decimal equivalent. To change a fraction to a decimal, find an equivalent fraction with a denominator of 10 or 100. Look at the following three ways to model the fraction one-half.” Draw the models on the board.

“Which decimals are used to describe the shaded part of the grid?” (0.5 and 0.50) “How are the two decimals the same?” (The ones digit and the tenths digit are the same in both numbers.) “How do the shaded models show that the expressions are all equal?” (They all shade the same amount of the whole.) “Another way to show equivalent fraction and decimal amounts is with a number line.”

For additional practice, students can complete the Fraction Decimal Number Line Worksheet (M-4-3-2_Fraction Decimal Number Line Worksheet and KEY.doc). After students complete the worksheet, bring them back together and ask them to share various ways in which they have determined equivalent fractions and decimals. Ask, “What did you learn about the relationships between fractions and decimals?” Ask true or false statements:

• = 0.60          “True or False? Explain.” (True. ;  means
   “sixty-hundredths,” which can also be written as 0.60.)
• = 0.2            “True or False? Explain.” (True. ;  means
   “twenty-hundredths,” which can also be written as 0.20; 0.20 is the same as 0.2.)
• = 0.80         “True or False? Explain.” (True. ;  means
   “eighty-hundredths,” which can also be written as 0.80.)

Calculators are suitable to determine fraction and decimal relationships. Students may explore this independently, or you may instruct them to divide the numerator by the denominator to find the decimal. Remind students that, “Fraction bars are symbols that mean division.” Note that fractions on a calculator will not include zeroes to the right of the last digit after the decimal. For example, 0.50 will be represented as 0.5.

Extension:

• Routine: Write five fractions and five equivalent decimals on the board in random order. Have students match any fractions and decimal equivalents. Allow students to use grid paper if necessary. Begin by using fractions with denominators of 10 and 100, as in the lesson. Progress to other decimal and fraction equivalents such as 0.75 and .
• Small Group: Divide the class into pairs. Have one student from each pair write a decimal and his/her partner write an equivalent fraction. For example, if Gretchen selects the decimal 0.7, her partner should write . Have students take turns naming the decimal and writing the equivalent fraction. Allow students to explore whether more than one answer is possible and explain why or why not. As tenths and hundredths are mastered, encourage students to explore other equivalencies such as 0.25 and  or 0.75 and . Have students keep the comparisons that they recorded to demonstrate what they have learned.
• Expansion: Give students fractions that are greater than 1 and have them give the decimal equivalent or vice versa. For example, would be 1.3.