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Multiplying and Dividing Fractions:

Multiplying and Dividing Fractions:. A C onceptual Approach. Presented by: Ashley McCullough Russell Geisner. Why Teach Conceptually?. Mathematical Practices for CCSS #1-Perseverance in solving problems #3-Critique the reasoning of others #4-Model with mathematics

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Multiplying and Dividing Fractions:

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  1. Multiplying and Dividing Fractions: A Conceptual Approach Presented by: Ashley McCullough Russell Geisner

  2. Why Teach Conceptually? • Mathematical Practices for CCSS • #1-Perseverance in solving problems • #3-Critique the reasoning of others • #4-Model with mathematics • #5-Use tools strategically • CCSS Number and Operations-Fractions • 5.NF4- “apply previous understandings” • 5.NF5b- “explain why” • 5.NF7a- “create a story context”

  3. MULTIPLICATION • Previous Understandings • 3 x 4 = three groups of four • Visual model: • 1 x 4 = one group of four • Visual model: llll llll llll llll

  4. MULTIPLICATION • 1/2 X 4 = half of a group of four • Visual model: • 1/4 x 4 = one fourth of a group of four • Visual model: llll llll

  5. MULTIPLICATION • Story Context for 1/3 x 2/3 • There was 2/3 of a pizza left over in the fridge. For lunch, Joe ate 1/3 of the left over pizza. How much of the whole pizza did Joe eat for lunch? • Visual model:

  6. MULTIPLICATION • Story Context for 3/4 x 2/5 • Kate had 2/5 of her book left to read. On Wednesday night, she read 3/4 of that. How much of the whole book did Kate read Wednesday night? • Visual model:

  7. Multiplication • Student created word problems: • 3/4 x 2/5- Abel shaved 2/5 of his head. He got a Chewbaca tattoo on 3/4 of the shaved area. How much of Abel’s head is tattooed with Chewbaca? • 5/6 x 4/5- 4/5 of Squidward’s body is tentacles. If 5/6 of his tentacles were made into Calamari, how much of Squidward can be eaten for dinner?

  8. MULTIPLICATION • Try It: • 3/5 x 2/6 • Create a story context. • Draw a visual model.

  9. Division • Previous Understandings • Partitive Division: Group Size Unknown • 12 ÷ 3 = 4 “Twelve shared equally among three groups” • Key = What will one group get? llll llll llll

  10. Division • Story Context for 9 ÷ 3/4 - Partitive • “9 being shared into 3/4 of a group” • It took Sarah 9 hours to finish 3/4 of her homework. How long will it take Sarah to do her entire homework at this rate? • Visual model: 3 3 3 3 3 3 3  12 • 9

  11. Partitive Division • Try It: 4 ÷ 2/5 • Create a story context. • Draw a visual model.

  12. Division • Previous Understandings • Measurement Division -Number Of Groups Unknown • 12 ÷ 3 = 4 “Groups of three being made from twelve” • Key = How many groups can be made?

  13. Division • Story Context for 9 ÷ 3/4 – Measurement • “Groups of 3/4 being made from 9” • Steve had 9 candy bars. A recipe for smorescalls for 3/4 of a candy bar. How many smores can he make? • Visual model: He can make twelve smores.

  14. Measurement Division • Try It: 4 ÷ 2/5 • Create a story context. • Draw a visual model.

  15. Division • Student created word problems: • It took Emilia 7 hours to paint 2/3 of her room. How long will it take Emilia to paint her entire room? • It took Julian 6 seconds to drink 4/5 of a soda bottle. How long will it take Julian to finish the whole bottle?

  16. Multiplication and Division • Student samples show that students switched between the algorithmic procedures and visual models. • Students explained that when they were unable to identify the operation needed that the visual model helped. • Students also used the visual model to check their answers for reasonableness.

  17. Student Samples:

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