1. July 7, 2015

2. Plotting Fractions on a Number Line Ordering Fractions from Least to Greatest Finding the Missing Number to Make the Fraction Equal Writing a Whole Number as a Fraction Determining Which is Greater---2/3 or 2/8 Multiplying Fractions

3. Helpful Math Terms Rational Numbers – any number that can be expressed as a ratio a/b, where a and b are integers of which the latter may not be zero, for example, 7/3 or -14/35 Number Line – an infinite line on which points are taken to represent real numbers by their distance from a fixed origin Plot – to locate or mark points on a line or graph Equivalent Fractions – fractions that represent or are reducible to the same proper fractions, i.e., 2/4 and 3/6 are equivalent, since they both represent the rational number 1/2 Segment – a part of a line or curve between two of its points

4. Rational Numbers (Fractions) can be represented on a number line. Once the integers 0 and 1 are assigned to points on a line, the unit segment is defined and every other rational number is assigned to a specific point. For example, to represent 3/4 on the number line, we divide the segment 0 to 1 into 4 segments of equal length and mark the line accordingly. Then, starting from 0, count 3 of these segments and stop at the mark corresponding to the right endpoint of the third segment to obtain the point assigned to the rational number 3/4.

5. 102 3/4

6. Your Turn… Represent the fractions below on a number line 2/3 4/4 1/7 5/4 102 2/3 210 4/4 102 5/4 102 1/7

7. As discussed in Principles and Standards, (p. 392) and the Common CORE Standards (Number and Operations-Fractions), Students in lower grades should experience comparing fractions between 0 and 1 in relation to such benchmarks as 0, 1/2, 3/4 and 1. In the middle grades, the comparison of fractions becomes more difficult.

8. Let’s consider first – comparison of fractions with like denominators. Turn to your partner…Explain how you know 3/4 is greater than 1/4. 1/4 102 3/41/4

9. Sometimes the fractions to be compared have unlike denominators Compare these fractions – which is least? 1/4 or 3/8; How do you know? Draw a picture to prove your response. Fraction Bars, Fraction Strips and Cuisenaire Rods can be used to compare fractions with unlike denominators.

10. Which fraction is least - 1/2, 3/8, or 1/4 Draw a diagram to prove your response Order the fractions above from least to greatest 1/4 1/8 1/2

11. Turn to your partner, explain how to order 1/5, 1/2, and 1/10 from least to greatest You may use a number line, Cuisenaire Rods, adding machine tape or draw Fraction Bars

12. Another method used to order fractions with unlike denominators is finding the least common multiple of the denominators Let’s try this one… Order 2/4, 1/3, and 1/6 from least to greatest Multiples of 4…4, 12, 16 3…3, 6, 9, 12, 15 6…6, 12, 18 2/4 = ?/12 1/3 = ?/12 1/6 = ?/12 2/4 = 6/12 1/3 = 4/12 1/6 = 2/12

13. Let’s try this one (cont.)… Order 2/4, 1/3, and 1/6 from least to greatest 2/4 = 6/12 1/3 = 4/12 1/6 = 2/12 1/3 = 4/12 2/4 = 6/12 1/6, 1/3, 2/4

14. Equivalent fractions are fractions that name the same amount. Use your tools for fractions to identify one or more fractions equivalent to the fractions below. 3/4, 8/12, 6/10 Again, you may use a number line, Cuisenaire Rods, Fraction Squares, adding machine tape or draw Fraction Bars

15. Two other methods for finding equivalent fractions – multiplication and division Let’s find two fractions that are equivalent to 18/24. One Way Use multiplication Multiply both the numerator and the denominator by the same number 18 18 2 36 24 24 2 48 Another Way Use Division Divide both the numerator and the denominator by the same number 18 18 3 6 24 24 3 8

16. Using the methods described previously, find the missing number to make each fraction pair equal. 3 ? 1 ? 6 ?8 ? 8 16 5 20 15 56 3 6 16 4 20 2 5 4 3

17. Sometimes, there is a need to write a whole number as a fraction Talk with your partner – discuss how the following whole numbers can be written as a fraction. ? 2 3 7 Writing a whole number as a fraction – A review

18. 2 3 2 8 How do you know?

19. Plotting basic facts on the number line https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/understanding- fractions-pre-alg/v/plotting-basic-fractions-on-the-number-line Comparing and ordering fractions https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions- pre-alg/v/ordering-fractions Fractions worksheets, videos and lessons http://www.adaptedmind.com/fractions.html?gclid=CLXc7vulv8YCFRc8gQodW00IeA Fraction games – Equivalent Fractions http://www.adaptedmind.com/p.php?tagId=635&utm_expid=33853517- 86.mbzy_JuITYSck_x1Nb- geg.0&utm_referrer=http%3A%2F%2Fwww.adaptedmind.com%2Ffractions.html%3Fgclid %3DCLXc7vulv8YCFRc8gQodW00IeA Writing a Whole Number as a Fraction https://learnzillion.com/lessons/1738-express-whole-numbers-as-fractions www.Yourmathgal.com Billstein, Rick, Libeskind, Shlomo, Lott, Johnny (1988). A problem solving approach to mathematics. 10 th ed. Addison-Wesley. Boston.

20. ENJOY THE REST OF YOUR DAY!