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Transitioning to the Common Core State Standards – Mathematics

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## Transitioning to the Common Core State Standards – Mathematics

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**Transitioning to the Common Core State Standards –**Mathematics Pam Hutchison pam.ucdmp@gmail.com**Please fill in the lines:**• First Name ________Last Name__________ • Primary Email______Alternate Email_______ • . • . • . • . • School____________District______________**AGENDA**• Fractions • Fractions on a Number Line • Naming and Locating • Fractions, Whole Numbers and Mixed Numbers • Comparing • Equivalent • Assessing Fractions • Stoplighting the Standards**Spending Spree**• David spent of his money on a game. Then he spent of his remaining money on a book. If he has $20 left, how much money did he have at first?**Fraction Concepts**• Four children share six brownies so that each child receives a fair share. How many brownies (or parts of brownies) will each child receive?**Fraction Concepts**• Six children share four brownies so that each child receives a fair share. What portion of each brownie will each child receive?**Fractions**• NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.**Illustrative Mathematics**• The importance of the unit or whole • Naming the whole for the fraction • Implication for instruction**Definition of Fraction:**• Start with a unit, 1, and split it into ___ equal pieces. • Each piece represent 1/___ of the unit. • When we name the fraction__/__, we are talking about ___ of those 1/___ size pieces .**Fractions Task - NC**Mr. Rogers started building a deck on the back of his house. So far, he finished ¼ of the deck. The fraction of the completed deck is below. • Draw 2 pictures of what the completed deck might look like. Use numbers and words to explain how you created your picture.**Fraction Task - NC**Martha is making a scarf for her sister. Each day she knits 1/6 of a scarf. • What fraction of the scarf will be complete after three days? • What fraction of the scarf will be complete after six days? • How can you use a number line to prove that your answers are correct?**Fraction Concepts**• What fraction of the rectangle is shaded? How might you draw the rectangle in another way but with the same fraction shaded?**Fractions**on the Number Line**Fractions**NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. • a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.**How many pieces are in the unit?**• Are all the pieces equal? • So each piece represents ● 1 0**How far (how many pieces) is the point from 0?**• We name that point……. ● 1 0 1 5**How many pieces are in the unit?**• Are all the pieces equal? • So the denominator is • And each piece represents . ● 0 1 7**How far is the point from 0?**• So the numerator is • And the name of the point is …… ● 0 1**Fractions**NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. • b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.**How many pieces are in the unit?**• Are all the pieces equal? • So each piece represents ● 0 1**How far is the point from 0?**• How many pieces from 0? • So the name of the point is …. ● 0 1**Definition of Fraction:**• When we name the point , we’re talking about a distance from 0 of ___ of those ___ pieces. 4**●**• How many pieces are in the unit? • Are all the pieces equal? • So the denominator is and each piece represents 1 0 5**How far is the point from 0?**• So the numerator is and the fraction represented is ● 1 0 3**The denominator is**So each piece represents • The numerator is And the fraction is ● 1 0 6 5**Academic Vocabulary**• What is the meaning of denominator? • What about numerator? • Definitions should be more than a location – the denominator is the bottom number • They should be what the denominator is – the number of equal parts in one unit**Student Talk**Strategy: Rally Coach • Partner A: name the point and explain • Partner B: verify and “coach” if needed • Tip, Tip, Teach Switchroles • Partner B: name the point and explain • Partner A: verify and “coach” if needed • Tip, Tip, Teach**Explains – Key Phrases**• Here is the unit. (SHOW) • The unit is split in ___ equal pieces • Each piece represents • The distance from 0 to the point is ___ of those pieces • The name of the point is .**2**Definition of Fraction: 7 • Start with a unit, 1, • Split it into __ equal pieces. • Each piece represents of the unit • The point is __ of those pieces from 0 • So this point represents ● 1 0 7 2**6**Definition of Fraction: 8 • Start with a unit, 1, • Split it into __ equal pieces. • Each piece represents of the unit • The pointa is __ of those pieces from 0 • So this point represents ● 1 0 8 6**Partner Activity 1, cont.**Partner A 5. 6. 7. Partner B 5. 6. 7.**| | | | | | | | |**• The denominator is ……. • The numerator is ……… • Another way to name this point? 0 1 2 3 3 1**| | | | | | | | |**• The denominator is …….. • The numerator is ……… • Another way to name this point? 0 1 2 6 3 2**| | | | | | | | |**• The denominator is …… • The numerator is ……… • Another way to name this point? 0 1 2 5 3 2 1 3**| | | | | | | | |**• The denominator is ….. • The numerator is ……… • Another way to name this point? 0 1 2 7 3 1 2 3**| | | | | | | | |**• Suppose the line was shaded to 5. • How many parts would be shaded? • So the numerator would be ……… 0 1 2 15 3**| | | | | | | | |**• Suppose the line was shaded to 10. • How many parts would be shaded? • So the numerator would be ……… 0 1 2 30 3**Rally Coach**• Partner A goes first • Name the point as a fraction and as a mixed number. Explain your thinking • Partner B: coach SWITCH • Partner B goes • Name the point as a fraction and as a mixed number. Explain your thinking • Partner A: coach Page 93-94**Rally Coach Part 2**• Partner B goes first • Locate the point on the number line • Rename the point in a 2nd way (fraction or mixed number) • Explain your thinking • Partner A: coach SWITCHROLES**Rally Coach**Partner B 6. 7. 8. Partner A 6. 7. 8.**Connect to traditional**• Change to a fraction. • How could you have students develop a procedure for doing this without telling them “multiply the whole number by the denominator, then add the numerator”?**Connect to traditional**• Change to a mixed number. • Again, how could you do this without just telling students to divide?**Student Thinking**Video Clips 1 – David (5th Grade) • Two clips • First clip – 3 weeks after a conceptual lesson on mixed numbers and improper fractions • Second clip – 3.5 weeks after a procedural lesson on mixed numbers and improper fractions**Student Thinking**Video Clips 2 – Background • Exemplary teacher because of the way she normally engages her students in reasoning mathematically • Asked to teach a lesson from a state-adopted textbook in which the focus is entirely procedural. • Lesson was videotaped; then several students were interviewed and videotaped solving problems.