Exploration: Fraction Units & Mixed Numbers

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Abel Cummings
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Exploration: Fraction Units & Mixed Numbers GENERATE EQUIVALENT FORMS OF RATIONAL NUMBERS INCLUDING WHOLE NUMBERS, FRACTIONS & DECIMALS Prerequisites none Preparation Worksheet #1, #2 & #3 for each

1 Exploration: Fraction Units & Mixed Numbers GENERATE EQUIVALENT FORMS OF RATIONAL NUMBERS INCLUDING WHOLE NUMBERS, FRACTIONS & DECIMALS Prerequisites none Preparation Worksheet #1, #2 & #3 for each student Overhead #1 & #2 Exploring Unit Size Show students Overhead #1, covering the last two questions at the bottom with a sheet of paper. Record 10 days below the first question and then uncover the next question How many weeks have passed?. The answer is still referring to the same amount of time but since the unit has been changed to weeks, the answer looks very different. Discuss the answer (1 weeks) with students. Ask: Where did the 1 come from? Where did the 3 come from? Where did the 7 come from? If two more days passed, how would the answer change? Uncover the final question, How much of a month has passed? (10/28 months). As students give the answer and discuss their reasoning, do not forget to record the units along with the answer on the overhead. Once again ask: Where did the 10 come from? Where did the 28 come from? If another week passed, how would the answer change? : pg. 1 of 8

2 EXPLORATION: FRACTION UNITS & MIXED NUMBERS LESSON PAGES Show students Overhead #2, covering the last question at the bottom with a sheet of paper. By now students are getting the idea, but I still think it is worth going through a second example. Record that there are 9 cupcakes, and then uncover the second question How many packages of cupcakes are there? Discuss and record that there are 4 ½ packages of cupcakes. The most important part of these examples is that students understand that the answer depends on the unit. In this instance, when the unit is cupcakes, the answer is 9. When the unit is packages of cupcakes, the answer is 4 ½. Pass out Worksheet #1 for students to practice. Exploring Mixed Numbers and Improper Fractions Pass out a set of fraction circles to students. I d like you to think of these as mini pies. For this exercise a full circle equals 1-whole. Display 3-half slices of pie on the overhead making sure to leave a little space between each piece so students can tell the size of the pieces. How much pie to I have? Discuss that there are two correct ways to express the amount of pie, 1 ½ pies or 3/2 pies. Label one the mixed number answer and the other the improper fraction answer and move on to the next example. : pg. 2 of 8

3 Display the following on the overhead and ask students to record what they think would be the improper fraction answer and the mixed number answer to the question How much pie do I have? Discuss and record the answers (2 ⅔ and 8/3). With your fraction circles, show me what 9/6 pie would look like? Once student have displayed 9/6 on their desk, ask How would you record the mixed number answer? Some students may record the mixed answer in lowest form (1 ½), some may not (1 3/6). At this point I would casually mention that they are both the correct answers because they are equivalent. However, I would not make a bigger point of this since equivalent fractions will be a focus of a later exploration. Pass out Worksheet #2 and allow students to work through Part 1 with their fraction circles. After working with pictures and fraction circles students should begin seeing the mixed number or improper fractions in their mind s eye. This gives them a feeling for how to convert between the two, rather than simply following a rules. Questions #8 and #9 are focused on getting students to create their own rule. #8 presents numbers that are two large to make drawing a picture practical. Question #9 asks students to put into words the strategies they ve been developing in their heads. As a class discuss students strategies: EXPLORATION: FRACTION UNITS & MIXED NUMBERS LESSON PAGES How did your strategy help you to solve question #8? Is it easier for you to convert from an improper fraction to a mixed number or the other way around? What makes that easier? How would you explain to someone who is struggling how to convert from a mixed number to an improper fraction? How would you explain to someone who is struggling how to convert from an improper fraction to a mixed number? For additional practice with these concept, assign Worksheet #3 as homework. : pg. 3 of 8

4 Sunday Monday Tuesday Wednesday Thursday Friday Saturday EXPLORATION: FRACTION UNITS & MIXED NUMBERS OVERHEAD # How many days have passed? How many weeks have passed? How much of a month has passed? pg. 4 of 8

5 Aunt May s Cupcakes Aunt May s Cupcakes Aunt May s Cupcakes EXPLORATION: FRACTION UNITS & MIXED NUMBERS OVERHEAD #2 Aunt May s Cupcakes Aunt May s Cupcakes How many cupcakes? How many packages of cupcakes? pg. 5 of 8

6 Name: If then... #1 = #2 = = 1-whole Fraction Unit Practice If then... #5 = #6 = Date: = 1-whole EXPLORATION: FRACTION UNITS & MIXED NUMBERS WORKSHEET #1 #3 = #7 = #4 Draw what would ¼ look like: #8 Draw what would ⅓ look like: If = 1-whole If = 1-whole then... then... #9 = #13 = #10 = #14 = #11 = #15 = #12 Draw what would ½ look like: #16 Draw what would 2-wholes look like: pg. 6 of 8

7 Name: #1 #2 #3 How much pie? Drawing Date: Mixed Number Answer Improper Fraction Answer 7 5 EXPLORATION: FRACTION UNITS & MIXED NUMBERS WORKSHEET #2 #4 # #6 7 6 # #8. What is 6 written as an improper fraction? What is written as a mixed number? 13 4 #9. What was your strategy in #8? pg. 7 of 8

$Give the mixed number & improper fraction Fraction$ Unit Practice How many books of matches?

EXPLORATION: FRACTION UNITS & MIXED NUMBERS

$Give the mixed number & improper fraction.$

8 Name: How much is shaded? Give the mixed number & improper fraction Fraction Unit Practice How many books of matches? Date: How many jars of jam? EXPLORATION: FRACTION UNITS & MIXED NUMBERS WORKSHEET #3 How many rhinos? How many packages of light bulbs? How much is shaded? Give the mixed number & improper fraction. How many bags of money? How many dollars? How many droppers of medicine? 1 in 2 in How many feet? How much is shaded? Give the mixed number & improper fraction. How many beakers of water? pg. 8 of 8

Activity 2 Multiplying Fractions Math 33. Is it important to have common denominators when we multiply fraction? Why or why not?

$Activity 2 Multiplying Fractions Math 33. Is it important to have common denominators when we multiply fraction? Why or why not?$ Activity Multiplying Fractions Math Your Name: Partners Names:.. (.) Essential Question: Think about the question, but don t answer it. You will have an opportunity to answer this question at the end of