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Main Curriculum Tie:
Background For Teachers:
Enduring Understanding (Big
Ways to Gain/Maintain Attention (Primacy):
Lesson Segment 1: How is multiplying or dividing whole numbers similar to
multiplying or dividing fractions?
Tell them they will be showing their model to others in the class, so we can compare some of the models. Give them a few minutes to discuss and find a way and record on their. Have the pairs show their models to another pair on their team. Have some pairs show the class. Ask students to be watching for how the approaches are similar and different. Discuss.
Suggest that there are many ways to model the two operations. If they have not used the following models, show these. If they have, emphasize them. Discuss how each model shows multiplying and how it shows dividing.
3 x 2 and 6/3
Multiplication of whole numbers is like repeatedly adding a number or a group n times to find how much is the total. How many is 3 if added 2 times? How many is two of three?
Division is like repeatedly subtracting a number or a group n times to find how many of the number or groups are in a total. How many 3’s be taken out of six? How many 3’s are in 6?
Multiplying and fractions is similar to multiplying whole numbers except we are working with parts to find how much of a whole or total we have if we repeatedly add a part. When we are dividing fractions, we are repeatedly subtracting as well, but we are subtracting a part to find how many of one size part can be taken out of another size part or how many of one part is in the other part or the whole.
Segment 2: How can multiplying fractions be modeled using measurement
and a number line? How can dividing fractions be modeled using
measurement and a number line?
The students will make their own fraction bars by folding equal parts, labeling the fractional part of each and cutting the strips into those fractional parts. Each part of a strip must be the same length, so students should fold and cut carefully! Students label each part with the appropriate fraction and cut the strip as follows:
Model, fold, label and cut with the students. Give each an envelope to put their fraction bars in. Overhead Fraction Tiles or Bars make this easier. As you are folding and labeling continue to ask students how many of that part are in the whole. This will reinforce parts of a whole. When cutting ask questions such as how many fourths are in a half? Three of two sixths is how much? etc. As you do, write symbolic representations such as ½ ÷ ¼ or 3 x 2/6. Actually having students fold and cut is a very visual way to deepen concepts of fractions.
Work with the students, discussing how to visualize multiplying and dividing fractions using the attached “Using Fraction Tiles For Multiplying and Dividing Fractions” worksheet. When building each problem with the fraction tiles kit, lay the one whole piece on the desk above each problem to compare. Review the algorithms for multiplying and dividing fractions as each problem is modeled and discussed. Have the students represent the problems with their fraction tiles as well as with sketches, words and math symbols.
A ruler is also a great tool for multiplying and dividing fractions when the product or quotient will be a whole number. Ask students if they have ever seen the movie, “Honey, I Shrunk The Kids”, where everything in the world seemed very magnified to the kids. Tell them they will be pretending they have been shrunken so an inch looks larger to them. Give students a strip of paper made by cutting an 8½ x 11 in 2-inch strips lengthwise. Have them fold the strip into increments of an inch to 16ths as shown in the foldable attached. As the folding is happening, ask students questions such as how many fourths in 1 whole inch? How many 16ths are in an 8th, etc. As you ask, write the question using math symbols such as 1 ÷ ¼, 1/8 ÷ 1/16, 3 x ¼ etc. Have students record your questions and answers on the Measuring an Inch Record. After the rulers are completed, have the students make up three multiplication or division problems of their own on the record paper. Two problems should be correct, but the third should be a fib. Choose a few students to write their three problems on the overhead challenging the class to “Guess the fib.”
A number line can be used to help students multiply and divide fractions as well. Have the students work in pairs to complete the “Multiplying and Dividing Fractions on a Number Line” worksheet. Then have them use the TI-73 Num Line App as described to check their problems or to do other problems you may choose for practice.
Segment 3: How can multiplying fractions be modeled using area? How can
dividing fractions be modeled using area?
Summarize: In their journal, have students describe their favorite model for
multiplying and dividing fractions and explain why this is their favorite.
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