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763270-133350Math Lesson: Division of FractionsGrade Level: 6Lesson Summary:Students observe and then engage in modeling division of fractions in word problems and in equations. They then use those equations to identify or create examples of each of the properties of operations. Advanced students have the opportunity to divide world currencies to find exchange rates. Struggling students engage in a game to develop understanding of the value of fractions.Lesson Objectives:Interpret and compute quotients of fractions.Solve word problems involving division of fractions by fractions using visual models and equations.The students will know…why quotients of division of fractions can be larger than the dividend or the divisor. The students will be able to…divide fractions by fractions.Learning Styles Targeted: FORMCHECKBOX Visual FORMCHECKBOX Auditory FORMCHECKBOX Kinesthetic/TactilePre-Assessment:Pose the question, how could 12÷116=8? Give students a minute to think about it.Discuss student answers and ask them to explain their reasoning, but do not correct any faulty reasoning at this point.Make a note of students who do not attempt to solve the problem.Whole-Class InstructionMaterials Needed: Pattern Blocks; Show What You Know Division of Fractions*Procedure: PresentationBegin by asking what is 20 divided by 5? How many 5s fit into 20? [4]Display or project an image of pattern blocks. Take one and ask, how many times would 14 fit into 12 of this block? Then fit two 14 blocks into half of the whole pattern block. Next have students suggest how you could express this in an equation 12÷14=2.Have students analyze the equation and determine which numbers were multiplied to arrive at the answer 2.Label the digits in algebraic terms: a, b, c, and d.Write an algebraic formula to reflect the general formula for dividing two fractions: ab÷cd=adbcContrast this formula with multiplication of fractions by asking students to multiply 12×14.Demonstrate with pattern blocks. First multiply 14×4=1. Then multiply 14×2=12. Then multiply 14×1=14. Then multiply 14×12=18.Label the digits in algebraic terms: a, b, c, and d. Write an algebraic formula to reflect the general formula for multiplying two fractions: ab×cd=acbd.Contrast this formula with the formula for dividing fractions. Guided PracticePose this question and suggest that student draw it on paper: The entry road to a park is 78 of a mile long. The park service wants to plant trees on both sides of the road. They want to space them 116 mile apart so they have room to grow over the years. How many trees will they plant?Give the class five minutes to consider this question. Then invite students to explain their reasoning. Discuss student results and record the equation: 78÷116=14;14×2=28.Independent PracticeDistribute Show What You Know Division of Fractions. Give students 10 minutes to solve the equations.Discuss their results and compare reasoning.Closing ActivityRevisit the Pre-Assessment question.Ask students to explain why 12÷116=8.Advanced LearnerWorld CurrencyMaterials Needed: Internet access or business section of a newspaperProcedure: Explain that the value of each country’s currency changes as a result of changes in the economies of different countries. For example, in 1970, the value of the British pound was $2.39 US dollars. In 1994, its value was $1.53 US dollars.Use the Internet to find today’s value of the Canadian dollar, Mexican Peso, Europe’s Euro, British pound, and Chinese Yuan.Calculate how many US dollars are equal to 100 units of each currency.Have students present their reasoning and discuss their results.Struggling LearnerFind a Fraction GameMaterials Needed: Two 0–5 cubes, two 5–10 cubes, calculator for each groupProcedure:Give groups of 2–4 students 15 minutes to play this game to develop understanding of fractional values. Explain these rules:Players pick a simple fraction between 0 and 1 as a goal (for example, 13, 35, 34).Teams take turns rolling all four cubes (roll again if you roll a 10).Make two 2-digit numbers from the numbers rolled. Use them to form a fraction as close to the goal as possible.The player with the fraction closest to the goal wins the round. If students can’t determine the winner by looking at or by reducing the fractions, they can convert the fractions to decimals and see which is closest to the goal.At the end of the game, review the results and discuss players' strategies.*see supplemental resources ................
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