Module 3 Lesson 2 Objective Make equivalent fractions

Module 3 – Lesson 2 Objective – Make equivalent fractions with sums of fractions with like denominators.

Fluency Practice – Equivalent Fractions �½ or 1 2 (What fraction piece is this? ) ◦ 1 piece out of 2. It is half of an object. � How do you say ½ ? ◦ One half �½ equals how many fourths? (? /4) ◦ ½ = 2 fourths (2/4) �½ = ? /6 ◦ Three sixths (3/6) � 1/3 = ? /6 � 2/3 = ? /12 � 3/5 = ? /25 ◦ Two sixths (2/6) ◦ Eight Twelfths (8/12) ◦ Fifteen Twenty-fifths (15/25)

Fluency Practice – Equivalent Fractions �½ = 2/ ? ◦ Two Fourths (2/4) � 1/5 = 2/? � 2/5 = 8/? ◦ Two Tenths (2/10) ◦ Eight Twentieths (8/20) �¾ = 9/? ◦ Nine Twelfths (9/12) � 4/5 = 16/? � 3/9 = 6/? � 1/7 = 2/? ◦ Sixteen Twentieths (16/20) ◦ Six Eighteenths (6/18) ◦ Two Fourteenths (2/14)

Sprint – Find the missing numerator or denominator �½ = ? /4 � 4/10 = ? /5 � 5/6 = 45/? � 35/63 = 5/? � 1/3 = ? /9 � 8/12 = 2/? � 6/7 = ? /56 1/5 = 2/? 6/9 = ? /3 45/81 = ? /9 5/8 = ? /64 ¼ = ? /12 12/16 = 3/? 4/5 = 28/? 2/5 = ? /10 9/12 = ? /4 1/6 = ? /12 5/8 = 40/? 3/7 = ? /21 5/6 = ? /42 4/5 = ? /35

Application Problem � Mr. Hopkins has a 1 meter wire he is using to make clocks. Each fourth meter is marked off with 5 smaller equal lengths. If Mr. Hopkins bends the wire at ¾ meter, what fraction of the marks is that? 1/4 Bent after 3 units 3 x 5 units = 15 units 15/20 = 3/4 Mr. Hopkins bent the wire at ¾ m or at 15/20 of the meter. bent 5 units 1 mark is 1/20 m. ¾ m is the same as 15/20 m. 1 meter 0/4 4/4

Concept Development – Problem 1 � 1/3 + 1/3 � Using a number line, mark the end points as zero and 1. Between zero and 1 estimate to make three parts of equal length and label them with their fractional value. � Now show 1/3 plus 1/3 on your number line using arrows designating lengths. � What ◦ did you get as your answer? 2/3 (two thirds)

Concept Development – Problem 1 � Express this as a multiplication equation and as an addition sentence. ◦ 1/3 + 1/3 = 2 x 1/3 = 2/3 � Following the same pattern of adding unit fractions by joining lengths, show 3 fourths (3/4) on a number line. �¼ +¼+¼=3 x¼=¾

Concept Development – Problem 2 � 3/8 + 1/8 (3 eighths + 1 eighths) � On a number line, again mark the end points as zero and one. Between zero and one, estimate to make 8 parts of equal length. This time only label what is necessary to show 3 eights. 3/8 � The answer is? ◦ 7 eighths (7/8) 6/8 7/8

Concept Development – Problem 2 � Write 3/8 6/8 7/8 a math equation to represent the problem you just demonstrated. ◦ 2 x 3/8 + 1/8 = 7/8

Concept Development – Problem 3 � 6/2 = 2/2 + 2/2 = 1 + 1 = ? � On a number line, mark the end points as 0 halves and 6 halves below the number line. Estimate to make 6 parts of equal length. This time only label 2 halves. � Record the whole number equivalents above on your number line. � Then represent 3 x 2 halves on your number 1 2 3 line. 0/2 2/2 4/2 6/2

Concept Development – Problem 3 � What is the answer? ◦ 6 halves or 3 � What is the unit of 3? ◦ 3 ones � Express this as an addition equation and as an multiplication equation. ◦ 6/2 = 2/2 + 2/2 = 3 x 2/2 = 3 0/2 1 2 3 2/2 4/2 6/2 Think: 6/2 = 2/2 + 2/2 = 3 x 2/2 =3 x 1 =3

Concept Development – Problem 4 � 8 fifths = 5/5 + 3/5 = ? � Use a number line. Mark the end points as 0 fifths and 10 fifths below it. Estimate and five a value to the halfway point. 0/5 � What 10/5 will be the value of the halfway point? ◦ 5 fifths. � Now make 10 parts of equal length from 0 fifths to 10 fifths, with the middle being 5 fifths. 0/5 5/5 10/5

Concept Development – Problem 4 � Record the whole number equivalents above the line. 0 1 2 0/5 5/5 10/5 � Label 8 fifths (8/5) on the number line and show 0 the sum of 5/51 and 3/5 on the number 2 0/5 5/5 10/5 line. 8/5 � Express this as an addition equation in two ways: as the sum of fifths and as the sum of a

Concept Development – Problem 4 � 5/5 + 3/5 = 8/5 or 5/5 + 3/5 = 1 3/5 or 1 + 3/5 = 1 3/5 � What is another way to express 1 plus 3 fifths is? ◦ 1 and 3 fifths. � 8 fifths is between what 2 whole numbers? ◦ 1 and 2 0 1 0/5 5/5 2 8/5 10/5

Concept Development – Problem 5 � 7/3 = 6/3 + 1/3 = 2 x 3/3 + 1/3 = ? � Use a number line. Mark the end points as 0 thirds and 9 thirds below the number line. Divide the whole length into three equal smaller lengths and mark their values using thirds. (Compare with a table mate after completing your number line. ) � 3 0/3 � What 3/3 6/3 are the values of those points? ◦ 0/3, 3/3, 6/3, 9/3 or 0, 1, 2, 3 9/3

Concept Development – Problem 5 � Mark 0 the whole numbers above the number line. 0/3 1 2 3 3/3 6/3 9/3 � Divide each of those whole number lengths into 3 smaller lengths. Mark the number 7 thirds. 0 1 2 0/3 3/3 6/3 3 9/3 7/3 � Show 7 thirds as two units of 3 thirds and one more third on your number line and in an equation. (Compare with a tablemate after you have completed the step. ) ◦ (2 x 3/3)0+ 1/3 = 6/3 + 1/3 2 (7/3) 1 = 2 + 1/3 = 2 1/3 0/3 3/3 6/3 7/3 3 9/3

End of Lesson Activities � Debrief � Problem Set � Exit Ticket � Homework

Problem Set � � 1. Show each expression on a number line. Solve. ◦ a) 2/5 + 1/5 ◦ c) 3/10 + 3/10 2. Express each fraction as the sum of two or three equal fractional parts. Rewrite as a multiplication equation. Show letter a) on a number line. ◦ a) 6/7 � b) 9/2 c) 12/10 d) 27/5 Express each of the following as the sum of a whole number and a fraction. Show c) and d) on a number lines. ◦ a) 9/7 � b) 1/3 + 1/3 d) 2 x ¾ + ¼ b) 9/2 c) 32/7 d) 24/9 Marisela cut four equivalent lengths of ribbon. Each was 5 eights of a yard long. How many yards of fabric did she cut? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.

Exit Ticket � 1) Show each expression on a number line. Solve. ◦ a) 5/5 + 2/5 b) 6/3 + 2/3 � Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show letter b) on a number line. ◦ a) 6/9 b) 15/4

Homework � 1. Show each expression on a number line. Solve. ◦ a) 4/9 + 1/9 ◦ c) 2/7 + 2/7 � 2. Express each fraction as the sum of two or three equal fractional parts. Rewrite as a multiplication equation. Show letter a) on a number line. ◦ a) 6/11 � b) 9/4 c) 12/8 d) 27/10 3. Express each of the following as the sum of a whole number and a fraction. Show c) and d) on a number lines. ◦ a) 9/5 � b) ¼ + ¼ + ¼ d) 2 x 3/5 + 1/5 b) 7/2 c) 25/7 d) 21/9 Natalie sawed five boards of equal length to make a stool. Each was 9 tenths of a meter long. How many meters of board did she saw? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.

Fraction � Terminology and review of what a fraction is. ◦ http: //www. slideshare. net/lauracstelling/fractionspowerpoint-1 ◦ http: //www. slideshare. net/Snehal. Bhargava/fractions 11546923 ◦ http: //www. slideshare. net/htaylor 2010/understandin g-fractions (a little with ordering fractions) ◦ http: //www. slideshare. net/kkerr/fraction-overview (adding, subtracting, multiplying, and dividing fractions) ◦ http: //www. slideshare. net/mstfdemirdag/fractions 8693215