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Fractions and Decimals Grades 2-5

Fractions and Decimals Grades 2-5. MSP Nov. 16 and 18 KCS. Decimal Work. Opening Task. Represent each decimal grid as a: Fraction (in simplest form) Decimal Percent. Approaches- How and why…. Easiest…. Hardest… What did you need to know to be successful?.

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Fractions and Decimals Grades 2-5

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  1. Fractions and DecimalsGrades 2-5 MSP Nov. 16 and 18 KCS

  2. Decimal Work

  3. Opening Task • Represent each decimal grid as a: • Fraction (in simplest form) • Decimal • Percent

  4. Approaches- How and why… • Easiest…. • Hardest… • What did you need to know to be successful?

  5. 100 percent sharing them across 80 squares

  6. Connecting the grid to the answer • Teacher: “So what was Natalie’s answer as a percentage?” • Sam: “42.5 percent.” • Teacher: “How much percent is in one square?” • Sam: “1.25 percent.” • Teacher: “So if 34 boxes are squared what percent is shaded?” • Sam (uses overhead calculator): 34 * 1.25 = 42.5 • Sam: “42.5 percent”

  7. Examining the Teacher Moves • How has the teacher “leveraged” student responses during this discussion? • Discuss the mathematical focus in each of the three stages. • Was it on computations, representations, connecting mathematical ideas or a combination?

  8. Shading Grids • Shade 3/8 of a 12x8 grid (12 across, 8 tall) • Show it 3 different ways • What is the decimal number, fraction and percent for the shaded region?

  9. Student work- Devon • Here is Devon’s progression of shading 3/8. • What did he do? • What concepts does he understand based on his representations?

  10. Student work- Devon • “I broke the rectangle into four parts. There would be six columns in each half and then three columns in each fourth. “ • “Then, I split the fourths into eighths. There are 1 ½ columns in each eighth. Then I shaded in 3 of the 8ths.”

  11. “For the percent it’s either 25 or 50 percent. I’m not sure.” • T: “Why are you not sure? What do you know about how you shaded the rectangle?” • D: “I broke it into eighths. Fourths are 25% and eighths are half of that (uses calculator to divide 25 by 2). Each eighth is 12.5% so it would be 12.5+12.5+12.5 which is 37.5 percent. • T: “How would we write that as a decimal?” • D: “I know 37.5% is less than one so it’s 0.375.” • Based on Devon’s comments above what mathematics does he know? • How did the teacher moves help Devon connect his strategy to the mathematical concepts? • What would you do next with Devon to make sure he understood the concept? Student work- Devon

  12. Great White Shark Ratio • A great white shark is 6 meters long (average) • A great white shark’s tooth is 8 cm long • Find the proportion(ratio) of the great white shark’s body length to tooth length • Measure your height • Using the great white shark ratio above, find the “expected” length of your tooth • Compare you and your partner?

  13. Shark • 8 cm/ 600 cm = 1 cm / 75 cm • 1 cm of tooth for every 75 cm of body • 129 cm human body • 129-75 = 54, 1 r 54…. 1.4 • 129/75

  14. Share your inner “shark”

  15. How can we organize our data?

  16. Graphing our data

  17. Equivalent Fractions • Find equivalent fractions for • 1/2 • 2/3 • 3/7

  18. Equivalent Fractions • How did you do to find equivalent fractions? • How can you prove that they are equivalent? • With manipulatives? • With an area model (circle or rectangle) • With an equation? • With words?

  19. Comparing Fractions • Two pizzas are on the counter. The pepperoni pizza is cut into 5 slices. The cheese pizza is cut into 8 slices. • If you take two pieces from the pepperoni pizza and four pieces from the cheese pizza, which pizza has more left? • How do you know?

  20. Comparing Fractions • What did you to solve the task? • Can you prove your answer with: • A circular shaped pizza • A rectangular shaped pizza • Individual pieces of pizza • Cross multiplication (butterfly  ) • Finding equivalent fractions with common denominators

  21. Comparing Fractions • Let’s look at student work • What strategy does the student use? • What do they know? • What misconceptions do they have? • Ideas for interventions?

  22. Fractions on a Number Line • Let’s count around the class by 3/8 • What number do you think we will land on? • Why? • As we count, write down your number. • Where did we end up? • How close was our estimation?

  23. Fractions on a Number Line • Stand if your fraction can be simplified to a whole number • Stand if your fraction can be simplified to ½ • Stand if your fraction can be simplified to ¼ or ¾ • Stand if your fraction cannot be simplified at all

  24. Fractions on a Number Line • Mark the following fractions • 1/12, 13/12, 9/8, 15/8, 7/4, 9/6, 7/13

  25. Fractions on a Number Line • In Between • What strategies did you use as you played?

  26. Fractions on a Number Line • In Between • What mathematical concepts are embedded in the task?

  27. Fractions of a group • In a basket there are 24 apples. 1/3 of them are red. ½ of them green. The rest are yellow. How many of each color are there? • Prove your answer using both pictures and an equation

  28. True or false • 2/5 of 50 = 20% of 100 • Prove this using a picture and an equation. • Explain your answer in words.

  29. True or false • 2/5 of 50 = 20% of 100 • Approaches?

  30. True or false • 2/5 of 50 = 20% of 100 • Explanations?

  31. Comparing Fractions of a Group Tasks • Look at these two tasks • 1) 2/5 of 50 = 20% of 100 • 2) In a basket there are 24 apples. 1/3 of them are red. ½ of them green. The rest are yellow. How many of each color are there? • How are they similar? • How are they different? • What are the different issues and struggles students have?

  32. Proportional Squares • If the smallest square is 1 unit by 1 unit, what is the area of each square? The entire unit?

  33. Proportions • Make a pattern block picture that includes at least 10 shapes and is ½ blue. • How can you prove that it is ½ blue? • Make a pattern block picture that is ¾ blue. How can you prove that it is ¾ blue?

  34. What does this look like in Grades 3-5? • It takes you 45 minutes to drive 30 miles. How long will it take to travel 120 miles? • How would we expect students to solve this task? • Where would they struggle?

  35. Proportional Reasoning in 5th Grade • How much oatmeal and flour for 120 cookies?

  36. Condominium Demographics • In a condominium, 9/17 of the people are married and 3/5 of the men are single. • How many people are: • Married men? • Married women? • Single men? • Single women? • Extension: Find more possible answers (there are many)

  37. Approaches

  38. Solutions

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