NF5-21 Multiplying Unit Fractions Pages 13 14

Transcription

1 NF- Multiplying Unit Fractions Pages STANDARDS.NF.B. Goals Students will develop and apply the formula for multiplying unit fractions by unit fractions. Vocabulary denominator numerator of (to mean multiply ) unit fraction PRIOR KNOWLEDGE REQUIRED Can multiply fractions by whole numbers Understands that of can mean multiply Review half of a number. Remind students that they can find half of a number by finding half of a set. For example, to find half of six, make a set with six objects and take half of it. ASK: How many are in half of the set of six? To illustrate, draw this diagram on the board: Ask a volunteer to circle half of the dots. SAY: So half of is. Exercises: Find half. of of 8 of 0 of Answers:,,, Review that of can mean multiply. Remind students that of can mean multiply. SAY: means groups of things and / means / of a group of things. Exercises: Multiply. 8 0 Bonus: 00 Answers:,,, Bonus: 00 Half of a unit fraction. Explain to students that, just as we can talk about half of a whole number, we can also talk about half of a unit fraction. Demonstrate finding half of / by dividing an area model of the fraction / into a top half and a bottom half: of SAY: Let s extend the horizontal lines to find out what fraction of the whole rectangle is shaded. Draw the dotted line as shown in the margin and ASK: How many parts are there in total? (0) How many are shaded parts? () Write on the board: of = 0 COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION M- Teacher s Guide for AP Book.

2 Exercises: Draw a dotted line to find out how much of the whole rectangle is shaded. Answers: of =, of = Exercises: Find half of the fraction. Answers: /, /, /8, /8, /, f) / 9 f) Finding a unit fraction of a unit fraction. Tell students you want to find / of /. Draw the picture in the margin on the board and SAY: Here is half of a rectangle. Divide the shaded part into three equal pieces as shown in the margin. SAY: I would like to find / of /, so I have to take one piece. Draw a bold box around the first shaded piece and remove the shading from the two other pieces (see example in margin). of Then extend the horizontal lines to find out what fraction of the whole rectangle is shaded, as shown in the margin. SAY: Here is one third of half the rectangle. ASK: What fraction of the rectangle is one third of half of it? (one sixth) Write on the board: of = Exercises: Extend the horizontal lines in the picture. Then write what fraction of the rectangle is shaded. COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Sample solution Answers: 8,,, Selected solution: Exercises: Draw a picture to find the fraction of the fraction. of of of Answers: /8, /, /8, /0, / of of Number and Operations Fractions - M-

3 Have volunteers show their pictures, and point out that the total number of pieces in the rectangle is the product of the denominators. That is because one of the denominators tells you the number of rows, and the other denominator tells you the number of columns. Also point out that the answer is a unit fraction that is, it is one piece and is the numerator. So the answer is always the unit fraction with a denominator equal to the product of the denominators. Exercises: Find the fraction of the fraction without using a picture. of 8 of of Answers: /, /, /0, Bonus: /,8 Bonus: of, Multiplying unit fractions. Remind students that of can mean multiply. SAY: To multiply / times /, you can find / of /. / of / is equal to /, so / / is equal to / (see example below). ASK: When you think of a rectangle, how can you get the total number of pieces in the whole rectangle from the two fractions? (multiply the denominators) Write on the board: = SAY: Multiply the denominators to get the answer s denominator. Exercises: Multiply without using a picture. of of 8 of Bonus: 000, of Answers: /, /, /0, Bonus: /,000 Practice word problems. Have students solve several word problems. Check the solutions as a class. Kim drinks of a bottle of orange juice each week. What fraction of orange juice does she drink in a day? (/ / = /) To make a big muffin, a recipe calls for of a cup of blueberries. Farah is making a small muffin that is the size of a big muffin. What fraction of a cup of blueberries does Farah need? (/ / = /0 of a cup) COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION M-8 Teacher s Guide for AP Book.

4 Extensions. Here is another way of dividing the fraction / in half. Instead of dividing a model into a top half and bottom half, divide into a left half and right half of = of = No matter how you find half of /, the answer should always be the same. Draw two pictures to find the fraction of the fraction. of of. Find the missing number. = = 0 = 0 =. Multiply three unit fractions. Answers: /, /0, /00. Find as many answers as you can = 0 Answers:, ;, ;, ;, COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION Number and Operations Fractions - M-9

5 NF- Multiplying Fractions Pages STANDARDS.NF.B. Goals Students will develop and apply the formula for multiplying fractions. Vocabulary denominator improper fraction lowest term numerator unit fraction PRIOR KNOWLEDGE REQUIRED Can multiply unit fractions Understands that of can mean multiply Multiplying fractions by unit fractions. Demonstrate finding half of / by dividing an area model of the fraction into a top half and a bottom half, as shown below: Exercises: Find half of the fraction. 9 of = 0 Answers: /8 = /9, /, /, /0 = /, /, f) / = / f) Explain to students that to find half of /, you divided the area model showing / into two parts. So, to find a quarter of /, you can divide the area model into four parts. Draw on the board: Exercises: Find the unit fraction of a fraction. of of of Answers: /, /0, / = /, / = / of = 0 of Multiplying fractions in general. Tell students you want to find / of /. Draw the picture in the margin on the board. SAY: The shaded portion is two-thirds of a rectangle. Then change the picture to show / of /, as shown below: of SAY: Now the shaded portion is four fifths of two thirds of the rectangle. ASK: What fraction of the rectangle is four fifths of two thirds? (8/) COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION M-0 Teacher s Guide for AP Book.

6 PROMPT: How many parts are within the thick outline? (8) How many parts are in the whole rectangle? () Write on the board: = of = 8 Exercises: Draw pictures to find the fraction of the fraction. Answers: / or /, / or /, /8, /0 or /0, / ASK: How can you get the total number of pieces in the whole rectangle from the two fractions? (multiply the denominators) Point to the shaded, outlined portion of the rectangle and ASK: How can you get the number of pieces in this shaded rectangle from the two fractions? (multiply the numerators) Write on the board: = 8 SAY: Multiply the numerators to get the answer s numerator and multiply the denominators to get the answer s denominator. Exercises: Multiply without using a picture. Answers: 9/0, /, 8/, 8/, / 8 8 Multiplying improper fractions. SAY: You can also multiply fractions greater than. Draw on the board: = Tell students that you want to know what / of / is. Draw this new diagram on the board: COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION of ASK: How many pieces are in one whole? (0) So then how many pieces are in one half? () Now how many pieces are in four-fifths of three-halves? () Write on the board: = 0 Exercises: Multiply. Answers: /0, 0/ or /, / 8 Number and Operations Fractions - M-

7 Practice word problems. Have students solve several word problems. Check the solutions as a class. Tina drinks of a bottle of water each day. How many bottles of water does she drink in seven days? (/ = / = / bottles) i) One lane of a swimming pool is the length of an Olympic 8 swimming pool. How many lengths of an Olympic swimming pool does Orlando swim when he swims the lane five times? (/8 = /8 = /8 of an Olympic swimming pool) ii) An Olympic swimming pool for a long course is 0 m long. How many meters did Orlando swim? (0 m /8 = 0/8 = 9 /8 = 9 / m) Extensions (MP.). Multiply. Reduce your answer to lowest terms. What do you notice? Why does this make sense? Answer: The answer in lowest terms is always /, because / is always being multiplied by a fraction equivalent to.. Jan bought cups of sugar. She used of the sugar to bake a cake. Each person eats of the cake. How much sugar does each person eat? Is that more or less than cup of sugar? Answer: Each person eats / cups of sugar, which is less than / cup. (MP.). Multiply 9 and 9, and then compare your answer to 9 to check your answer. Answer / /9 = / = /8 = / < /9, because /8 < /8 = /9; / /9 = 8/ > /9, because 8/ > / = /9 NOTE: Multiplying /9 by a number greater than should produce an answer greater than /9 because you have more than one /9. If you are multiplying /9 by a number less than, the answer should be less than /9 because you have less than one /9. COPYRIGHT 0 JUMP MATH: NOT TO BE COPIED. CC EDITION M- Teacher s Guide for AP Book.