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UMI - 2015 WELCOME!!!

UMI - 2015 WELCOME!!!. July 7, 2015. Content Focus – Third/Fourth Grade Pre-Test Topics. 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

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UMI - 2015 WELCOME!!!

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  1. UMI - 2015 WELCOME!!! July 7, 2015

  2. Content Focus – Third/Fourth Grade Pre-Test Topics • 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. Fractions on a Number LinePlotting basic fractions on the number line • 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. Fractions on a Number LinePlotting basic fractions on the number line • 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. Fractions on a Number LinePlotting basic fractions on the number line 1 0 3/4 2

  6. Fractions on a Number LinePlotting Basic Fractions on the Number Line • Your Turn… • Represent the fractions below on a number line • 2/3 • 4/4 • 1/7 • 5/4 0 2/3 1 2 4/4 0 1 2 0 1 2 1/7 0 1 2 5/4

  7. Ordering Fractions from Least to Greatest • 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. Ordering Fractions from Least to Greatest • 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. 0 1/4 3/4 1 2 1/4 1/4 1/4 1/4

  9. Ordering Fractions from Least to Greatest • 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. Ordering Fractions from Least to Greatest • 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 1/8 1/8 1/2

  11. Ordering Fractions from Least to Greatest • 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. Ordering Fractions from Least to Greatest • 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. Ordering Fractions from Least to Greatest • 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 1/6 = 2/12 1/3 = 4/12 2/4 = 6/12 1/6, 1/3,2/4

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

  16. Finding the Missing Number to make the Fractions Equal • Using the methods described previously, find the missing number to make each fraction pair equal. 3 ? 1 ? 6 ? 8 ? 8 16 5 20 15 5 6 3 4 3 4 20 2 5 6 16

  17. Writing a Whole Number as a Fraction • 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 7 3 Writing a whole number as a fraction – A review

  18. Finally…Which is Greater? 2 3 2 8 How do you know?

  19. Resources • 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. 10th ed. Addison-Wesley. Boston.

  20. THANK YOU!!! ENJOY THE REST OF YOUR DAY!

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