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This lesson is designed to demonstrate importance for recognizing use of fractions required by everyday activities in and beyond the classroom environment. Through incorporation of video, hands-on and teacher generated activities, students become better aware of the need to enhance skills necessary for allowing accurate demonstrations in amounts less than a whole. A basic intent of the lesson is to present an opportunity for individual students to develop a better understanding of the need for being able to skillfully use fractions.
Fractions: Multiplication With Fractions
and Mixed Numbers #107

Fractions: Adding and Subtracting
Fractions and Mixed Numbers with Like
Denominators #111

Fractions: Adding and Subtracting
Fractions and Mixed Numbers with Unlike
Denominators #120
Students will be able to:
(per class)
(per group of 4)
(per group of 2)
(per student)
Draw a large circle on the chalkboard. Add an hour hand pointing to the 9 position on a clock. Draw a minute hand pointing to the 3 position on a clock. Say, "If this were a clock, what time would it be?" Allow students to tell it would be 9:15. Ask, "How do you know this?" Elicit discussion leading to conclusion that this is a known factor because everyone is so familiar with reading time. Say, "With a show of hands, how many of you wear a watch each day?" Allow for response. Ask, "About how many times during a day do you refer to a clock or watch to find out the time of day?" Allow for response. Say, "Each time you refer to a clock, you are reading a fraction." Write fraction on chalkboard. Ask, "What is a fraction?" Allow students to define a fraction in their own terms. Ask, "Why are you reading a fraction, when you look at a clock?" Lead discussion to conclusion that a clock is divided into hours and minutes (some have a seconds hand).

Select a volunteer to write-in numbers 1-12 on the chalkboard illustration as they would appear on a clock. Say, "The numbers 1-12 on most clocks show a fractional part of an hour. What is the fractional part?" Elicit discussion leading to conclusion that the numbers 1-12 show an hour being divided into twelve equal parts or twelfths. Say, "When the minute hand points to 1, 1/12 of the hour has passed." Write 1/12 on the chalkboard. Invite another volunteer to write on chalkboard the appropriate fraction when the minute hand points to 4 (4/12); when it points to 6 (6/12); 9 (9/12); and 12 (12/12). Say, "When the top number of a fraction (numerator) is the same as the bottom number (denominator) it is equivalent to one whole. On the clock, 12/12 is equivalent to one whole...?" Allow students to complete the statement as one whole hour.

Say, "Whenever you tell the time of day by referring to a clock, you are reading fractions. In what other ways do you use fractions every day?" List on chalkboard as students give examples.

Divide the class into cooperative groups of four students each. Distribute 1 small package of M & M's and a paper towel to each group. Distribute a pencil and sheet of notebook paper to each student. Say, "Now that you recognize some of the ways you use fractions in daily life, let's see how fractions are written." Instruct groups to open the package of M & M's and pour them onto the paper towel. Say, "Count the number of M & M's, then write the number of parts (M & M's) as a fraction equivalent to the whole (package). Allow time for completion of the task. Call on groups to tell the fraction they wrote as equivalent to the whole; record each on the chalkboard. NOTE: Fractions may vary as M & M's are packaged by weight as opposed to count. Say, "Each member of your group may now select one M & M, then eat it." After students have chosen one M & M each ask, "What does your fraction now become?" Groups should reduce the numerator by 4, then state the new fraction.

Write denominator on chalkboard. Say, "The denominator of a fraction is always the bottom number." Write numerator above denominator, then say, "The numerator of a fraction is always the top number. To separate the two numbers, a straight line is drawn between them." Demonstrate as you draw a line between the two terms. Ask, "What does the denominator tell about your package of M & M's?" Allow students to share their knowledge as they tell it is the number of parts that made up the whole package. Ask, "What does the numerator tell?" Allow for response.

Display an apple in view of all groups. Ask a volunteer to assist with the demonstration. Ask the volunteer to use the chalkboard and describe the apple as a fraction. Next, use the paring knife to divide the apple into quarters. Say to the volunteer, "How would you describe the apple as a fraction now?" Confirm 4/4 as the volunteer writes on the chalkboard. Say, "You may have one piece of the apple. Show what part of the apple you took as a fraction on the chalkboard." Confirm 1/4. Engage students in discussion leading to conclusion, the numerator was changed from 4 to 3 because one part of the apple was taken. Ask, "Why didn't the denominator change?" Confirm taking one part did not affect the number of parts the whole apple had been cut into.

Refer again to the M & M's. Instruct students to separate the M & M's based on color. Allow time for completion of the task. Say, "Now that your M & M's are arranged by color, write the fractional equivalent for each color. Provide time for the task to be accomplished, then allow each group to present its findings as other groups monitor and evaluate in terms of accuracy. After all groups have made their presentation, compare results. NOTE: You may want to have groups repackage the M & M's, then give them out later as treats.
Display a chart tablet in view of students. Use a black marking pen to write the heading FRACTIONS EVERYDAY. Ask, "In what ways have we already determined you use fractions everyday?" List ways on chart as they are named by students. Say, "Throughout the lesson, we are going to look for as many practical everyday uses of fractions as we can identify. What other uses can you identify at this time?" List as students contribute uses. Say, "At intervals we will add additional uses to the list. If a use comes to mind, write it on your notebook paper, then we'll add them to the chart at the appropriate time."

Say, "You are going to see a video of some people about your age." To give students a specific responsibility while viewing say, "Watch and be prepared to explain the way they are using fractions."

Fractions: Multiplication With Fractions and Mixed Numbers #107

Begin tape with visual of two young people looking at skateboards; audio is background music and "This is definitely the one." PAUSE tape on visual of Lucy and Jennifer with John standing; audio is "Hey, I wouldn't think of doing it for less than 2/3 of the profit." Allow time for students to discuss and describe the business venture. Ask, "What would John's profit from the business venture be if he received 2/3 of twelve dollars?" Allow time for students to complete the task.

To give students a specific responsibility while viewing say, "Watch the next video to learn if you have correctly figured what John's profit will be." RESUME tape. PAUSE tape and permit students to verify correctness of their answers. Visual is Jennifer with her fist in the pizza, audio is, "Oh alright, we'll take it." Allow time for students to discuss their answers and to identify reasons for any answer that was incorrect. Ask, "What other ways might fractions be used by Jennifer, John and Lucy in the pizza business?" Allow students to interact as other ways to use fractions are identified. To give students a specific responsibility while viewing say, "Watch the next video to find out if any of your ideas were actually used." FAST FORWARD tape to visual of Lucy on the phone; audio is Lucy saying, "Thank you." PAUSE tape with visual of Jennifer looking down; audio is Lucy, "Fractions again!" Ask, "Were any of your ideas used in the video?" Allow for student response. Ask, "How was Jennifer using fractions in this segment of video?" Allow students to discuss Jennifer's use of fractions; add uses seen on the video to the chart list.

Encourage students to consider whether Jennifer's strategy for doubling the dough recipe was desirable. Say, "You are already divided into groups of four. Choose a partner from within your group; both teams in your group now have a partner." Distribute a copy of the Activity Sheet to both teams in each group; provide additional notebook paper if needed. To give students a specific responsibility while viewing say, "Before you begin the activity explained on the Activity Sheet, watch the next video to find out the method Jennifer used to double the amount of water needed for her recipe." RESUME tape. PAUSE tape on visual of Jennifer smiling with John and Lucy in the background; audio is, "By all means." Ask, "What procedure did Jennifer use to double 2 3/8?" Allow time for student response. Appoint a volunteer to write the example of Jennifer's procedure on the chalkboard.

Instruct teams to work together as they implement the same procedure used by Jennifer to double the cornbread recipe given on the Activity Sheet. Allow time for the activity to be completed by all teams. Appoint individual teams to show their computation for a single ingredient on the chalkboard as classmates check their work for accuracy. Correct amounts for the doubled recipe are: 2 1/2 cups flour; 1 1/2 cups cornmeal; 1/2 cup sugar; 4 teaspoons baking powder; 1 teaspoon salt; 2 cups milk; 1/2 cup vegetable oil; and 2 eggs.

Ask, "In what other ways are fractions used in the preparation of food?" Allow students to give other examples they know about as you list them on the chart. (e.g.) Preparing 1/2 of a recipe; the part of an hour used for cooking; etc. Say, "You would be unable to work in some professions if your fraction skills were limited." Allow an opportunity for students to tell why knowledge of fractions would be important to a carpenter, a tailor and an architect. To give students a specific responsibility while viewing say, "Watch the video to see if there are other ways fractions are used in these three professions." FAST FORWARD tape to visual of two students talking to the audience; audio is, "Cooking isn't the only place that it helps to understand how to multiply fractions." STOP tape on visual of the girl and boy looking down; audio is the carpenter, "... so each of these window openings is exactly the same." Allow students to tell other ways fractions are used by tailors, architects and carpenters. Add new information to the chart list.

Say, "In the next video you will see a story involving a merchant and a pieman." To give students a specific responsibility while viewing say, "Watch and be prepared to tell why they had to understand and be able to use fractions."

Fractions: Adding and Subtracting Fractions and Mixed Numbers with Like Denominators #111

Begin tape on graphic visual, The Merchant and the Pieman; audio is background music. STOP tape on visual of the pieman with his hand over his mouth; audio is music in background. Allow students to tell how fractions were being used in the video. Add unlisted examples to the chart list.

Ask, "Why is it important for a musician to know about fractions?" Allow for student responses. If you have students studying a musical instrument, ask them to explain how fractions have been an important component of their study. To give students a specific responsibility while viewing say, "Watch the next video and be prepared to list ways it shows fractions are important to music."

MATH WORKS Fractions:
Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators #120

Begin tape on visual of three musicians performing; audio is the music they are creating. STOP tape on visual of the musicians; audio is, "To musicians a working knowledge is really essential." Encourage students to interact as they tell how a working knowledge of fractions is necessary in musical professions. Add these examples to the FRACTIONS EVERYDAY chart.

Ask students to share other uses of fractions they may have noted during the lesson. Add them to the chart. Say, "We have looked at ways various people in different professions use fractions in performing their job responsibilities. In what other ways do you use fractions or observe them being used by others." Encourage discussion as you suggest other professions for consideration as: (e.g.) bank personnel; grocers; mechanics; physicians; pharmacists; nurses; sales persons; electricians; etc. Suggest there are few professional activities humans engage in that do not require a knowledge of fractions. Ask students if they know of a job where fractions are never used; classmates might suggest ways they believe they would be used in the profession named.
Review the list of uses for EVERYDAY FRACTIONS included on the chart. Then, survey students to find out if others need to be included.

Distribute 5 strips of various colored construction paper to each student. Each should be approximately 14 in. x 2 in. in size. In addition, each student will need a pair of scissors, a ruler and a black crayon. Review the fundamentals of fractions as students tell definitions for fraction, numerator, denominator and mixed number.

Demonstrate on chalkboard as you give instructions for treatment of the five strips of construction paper. Monitor activity and provide individual assistance if needed. Say, "Choose any color strip you want for each part of the activity; color is unimportant, then instruct." Choose a strip and use the crayon to label it 1 WHOLE; set the strip aside; choose another strip, then fold it in half; draw a line down the middle, then label 1/2 ONE HALF on each side; take another strip, then fold it into thirds; label each part 1/3 ONE THIRD; choose another strip, then fold it in fourths; label each part 1/4 ONE FOURTH; and fold the last strip into eighths; label each fold 1/8 ONE EIGHTH. Allow time for students to complete this part of the task before continuing. Then say, "Use the scissors and cut each strip on the fold." Next, instruct students to place the 1 WHOLE strip in front of themselves. Use each of the other strips to prove: 2 halves make one whole; 3 thirds make one whole; 4 fourths make one whole; and 8 eighths make one whole.

Have student teams-of-two verify correctness for one another as you ask them to combine various strips to show: (e.g.) one whole made up of halves; fourths; and eighths; two wholes made up of thirds, fourths and eighths; etc.
Invite a professional musician, carpenter, etc. to visit your class and demonstrate various ways fractions are used everyday in connection with their jobs.
Have students select a non-cooked cookie or candy recipe and double or triple it as necessary to serve each student two or three cookies/pieces of candy. Provide needed ingredients and allow students to measure, then prepare the confections.

Have students solve the following problems: 2-cycle engines are often used in weed cutting type lawn equipment. The fuel requirement is a specific amount of 2-cycle engine oil mixed with a gallon of unleaded regular gasoline. If your equipment calls for a mix at a ratio of 16:1 or (8 oz. oil to 1 gallon gasoline), how much 2-cycle oil should you mix with 1 1/2 gallons of gasoline? (12 oz.) How much oil should you use for 1/2 gallon gasoline? (4 oz.) You have only 1 ounce of 2-cycle engine oil remaining in your can; how much gasoline would you add to get the correct mix? (16 ounces) What fractional part of a gallon of mix would you have? (1/8)

Have students figure how many times you would have to increase the cornbread recipe to eliminate use of fractions. (x four)

Language Arts
Have students write an essay entitled THE IMPORTANCE OF FRACTIONS TO EVERYDAY LIFE. Have them share their compositions with classmates, then display them in the hallway outside your classroom.

Encourage students to use their imaginations and write a poem or short story about a world in which there are no fractions.

Master Teachers: Sharon Braden and James Parsons

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