Equivalent Fractions and Fraction Addition

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

2. Fluency Practice – Equivalent Fractions 1 • ½ or (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 • Two sixths (2/6) • 2/3 = ?/12 • Eight Twelfths (8/12) • 3/5 = ?/25 • Fifteen Twenty-fifths (15/25) 2

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

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

5. 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 1 mark is 1/20 m. ¾ m is the same as 15/20 m. 5 units 1 meter 0/4 4/4

6. 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)

7. 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 x ¼ = ¾

8. Concept Development – Problem 2 • 3/8 + 3/8 + 1/8 (3 eighths + 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. • The answer is? • 7 eighths (7/8) 3/8 6/8 7/8

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

10. Concept Development – Problem 3 • 6/2 = 2/2 + 2/2 + 2/2 = 1 + 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 line. 1 2 3 6/2 0/2 2/2 4/2

11. 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 + 2/2 = 3 x 2/2 = 3 1 2 3 Think: 6/2 = 2/2 + 2/2 + 2/2 = 3 x 2/2 = 3 x 1 = 3 6/2 0/2 2/2 4/2

12. 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. • What 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 0/5 5/5 10/5 10/5

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

14. 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 1 0 2 0/5 5/5 10/5 8/5

15. 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 • What are the values of those points? • 0/3, 3/3, 6/3, 9/3 or 0, 1, 2, 3 0/3 3/3 6/3 9/3

16. Concept Development – Problem 5 • Mark the whole numbers above the number line. • Divide each of those whole number lengths into 3 smaller lengths. Mark the number 7 thirds. • 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) + 1/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3 (7/3) 7/3 7/3 0/3 0/3 0/3 3/3 3/3 3/3 6/3 6/3 6/3 9/3 9/3 9/3 0 0 0 2 2 2 1 1 1 3 3 3

17. End of Lesson Activities • Debrief • Problem Set • Exit Ticket • Homework

18. Problem Set • 1. Show each expression on a number line. Solve. • a) 2/5 + 1/5 b) 1/3 + 1/3 + 1/3 • c) 3/10 + 3/10 + 3/10 d) 2 x ¾ + ¼ • 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) 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.

19. 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

20. Homework • 1. Show each expression on a number line. Solve. • a) 4/9 + 1/9 b) ¼ + ¼ + ¼ + ¼ • c) 2/7 + 2/7 + 2/7 d) 2 x 3/5 + 1/5 • 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) 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.

21. Fraction • Terminology and review of what a fraction is. • http://www.slideshare.net/lauracstelling/fractions-powerpoint-1 • http://www.slideshare.net/SnehalBhargava/fractions-11546923 • http://www.slideshare.net/htaylor2010/understanding-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