1. Lucy West Education Consultant email: lucy@lucywestpd.com http://lucywestpd.comlucy@lucywestpd.comlucywestpd.com phone: 212-233-0419 cell: 917-494-1606

2. Lucy West: lucy@lucywestpd.comlucy@lucywestpd.com Power Point Will Be Posted on Web Site www.lucywestpd.com

3. Agenda Setting our goals Number lines and fractions Video Example Array models of fractions/assessment Fractions as Divisions

4. Welcome Begin to think about your goals for today. What do you want to learn about fractions? What do you want to learn about teaching fractions?

5. Themes Vertical alignment of background knowledge children need to understand fractions, starting in K. Students articulating their mathematical reasoning and putting it in writing Models for fractions – what models are appropriate? When? How to make models more accurate? How do we reach children who do not have the prerequisite knowledge? Equivalence with fractions, comparing fractions Understanding meaning of parts of fractions Conceptual understanding of fractions Models – move away from circular models to rectangular Best practices to deepen understanding instead of teaching procedures Focus more on reasoning, less on answer Relationship between decimals and fractions Real world problems with fractions Understanding the operations – with whole numbers AND with fractions Fractions of a whole vs. fractions of a group (division, ratio,…) Dependent on context

6. Unpacking the CCSS-Fractions Understanding 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. This is Grade 3—Develop understanding of fractions as numbers. What does this mean?

7. Grade 3 CCSS Fractions (cont.) Understand a fraction as a number on the number line; represent fractions on a number line diagram.

8. Big Ideas about Number lines: Each counting number can be associated with a unique point on the number line, but there are many points on the number line that cannot be named by the counting numbers (e.g. fractions). The distance between any two consecutive counting numbers on a given number line is the same. Each fraction can be associated with a unique point on the number line, but not all of the points between integers can be named by fractions. There is no least or greatest fraction on the number line There are an infinite number of fractions between any two fractions on the number line Randall Charles

9. Working with Number Lines 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. 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.

10. Consider where to put each of the following on our number line.27 1/4.666666… 6/7 4/9 3/3.098 14% 1/6 1/2.5.478.875 12-1/2% 1/9 2/11.675 2/1 3/16 1/12 4/5 109% 75% 4/6 3/8 2-3/16 2/3 8/13

11. Developing Flexible Mental Math Strategies for Fractions, Decimals & Percents One is five of what number? 0 1

12. Developing Flexible Mental Math Strategies for Fractions, Decimals & Percents 125 is 5 of what number? 0 125

13. Developing Flexible Mental Math Strategies for Fractions, Decimals & Percents 12.5 is.5 of what number?.5 1 0 12.5 ?

14. Common Core Standards: Rational Number Watermelons cost $1.80 per kilogram. What is the cost of a watermelon that weights 1 3/4 kilograms? $1.80 $3.60 $5.40 1 kg 2 kg 3 kg.

15. Video Fractions—double number line Subtracting unlike fractions 5 th grade ELL and Sp.Ed.

16. Developing Flexible Mental Math Strategies for Fractions, Decimals & Percents Critical models for multiplication and division: The array (and open array) The open number line The double number line The ratio table

19. End of Year Celebration 4 Teachers are throwing parties for their colleagues They are all buying foot long sandwiches One teacher is having 3 friends join her; another teacher is having 4 friends join her; a third teacher is having 7 friends join her; and a fourth teacher is having 4 friends join her. Each teacher estimates how many sandwiches to buy for their party and each teacher buys a different number of sandwiches to divide among her friends. The next day the teachers wondered if each of their friends got the same amount of sandwich.

20. How much does each person get?