Making Math Magic

2. Fractions, Decimals, and Percents Are they related??? Making Math Magic

3. Presented by Making Math Magic“Four Teacher For Teachers”www.makingmathmagic.comAnn BoothRhonda Allen BurnsTami PickettVonda Stamm M3 MAKING MATH MAGIC

4. We believe…… • that all students can and should learn math! • that if children like math and feel successful at math - they will learn math! • there are 3 basic stages that children need to go • through when learning math: • –Stage 1: Using Manipulatives • –Stage 2: Developing a Mental Image • –Stage 3: Using Symbols Making Math Magic

5. In short…. Students can be more successful when they have plenty of opportunities to: • Build it! Concrete • Draw it! Mental Image • Write it! Symbolic SAY IT! throughout Making Math Magic

6. We believe…… that the HOW in math instruction is as important as the WHAT, if not more so… Making Math Magic

7. Review the Standards for Mathematical Practice: Make sense of problems and persevere in solving them Reason abstractly and quantitatively (contextualize and decontextualize) Construct viable arguments and critique the reasoning of others

8. Standards for Mathematical Practice: Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

9. If we pay particular attention to the learning stages mentioned earlier, which Standards for Math Practice would/could be naturally addressed? With your talking partner discuss: • Build it! • Draw it! • Write it! Say It! Throughout Making Math Magic

10. Big Rocks: • Understand the relationship between the names (fraction, decimal, percent) • Move freely between the “part”, the “name”, and the “whole” • Explore Benchmark numbers to understand size/location, and comparisons. Making Math Magic

11. Why do middle school and high school students still struggle with fractions, decimals, and per cents? Our goal is to help students that struggle make sense of rational numbers! Making Math Magic

12. Are there some fractions, decimals, per cents that are more prevalent in real life? How long has it been since you had to deal with 9.0768% in real life???? Making Math Magic

13. Let’s concentrate on those numbers as we revisit to develop understanding. Halves, fourths, eighths Thirds, sixths Tenths Making Math Magic

14. We are going to start with percents and we are going to start with 50%. WHY????? Pre-assessment Write down (or draw) some things that you know about 50%. Making Math Magic

16. Shade 50% of your paper strip. • Compare your 50% with your talking partner. • Did you agree? • How do you know you are correct? • If I wanted to describe what I shaded with a common fraction, what fraction did I shade? Making Math Magic

17. Use a number line and mark where 50% would belong. 0% 100% Let’s compare the strip model and the number line model. Making Math Magic

18. Linear Model vs Area Model 0% 50% 100% Making Math Magic Area model using the paper strip Linear model using the paper strip

19. Let’s look at another model. Use one of the 4” squares to shade 50% You will also need this Transparency Grid Model Making Math Magic

20. Equivalence If this entire square represents my unit (my 1), what is the name for each of my inside pieces? What is my shaded part called? Making Math Magic

21. Equivalence How do I write that as a fraction? How do I write that as a decimal? Making Math Magic

22. Equivalence If this entire square represents my unit (my 1), what is the name for each piece? What would be the name for my shaded part? Making Math Magic

23. Equivalence How do I write this as a fraction? How do I write this as a decimal? Making Math Magic

24. Let’s look at all of the ways we have represented our 50%: 50%, , , 0.5, , and 0.50 These are all equivalent and can be used interchangeably. 1 2 5 10 50 100 Making Math Magic

25. Let’s look at other area or linear models.. Fraction Circles Fraction Rectangles Cuisenaire Rods Making Math Magic

26. At your table, each person use a different model to show a 50% (etc.) model.. Fraction Circles Fraction Rectangles Cuisenaire Rods Making Math Magic

27. Introducing the discrete or set model • Use either a paper circle or a paper square to fold and shade 50%. • If you have 6 beans, how can you • place them on your model to be “fair”? • What is 50% of 6? Making Math Magic

28. Reverse the process….. • If 4 represents 50% of a number, what is the number? • 50% of what number is 4? Making Math Magic

29. Using the number line to solve problems Some people prefer one number line 0 ? 24 0% 50% 100% Some people prefer two number lines 0% 50% 100% 0 ? 24 Making Math Magic

30. Using the double number line …. Some people prefer the two number lines put together 0 ? 24 0% 50% 100% Making Math Magic

31. Practicing with the models • Choose a model to show and solve: • 50% of what number is 18? • What is 0.5 of 32? • What fraction of 30 is 15? • Twenty-one is 0.50 of what number? Making Math Magic

32. Moving on to Fourths…… • Why would we do fourths next? • Start back with folding the strips. • Have the students use an 8.5 paper strip and find half. Ask them to leave this folded and fold in half again. Have them predict how many parts they will have. • How should we label these if I want to use fractions? one-fourth one-fourth one-fourth one-fourth Making Math Magic

33. Fourths…… Use one of the 8.5” number lines to label fourths . They can used their folded strip as a reference or they can fold the number line. one-fourth one-fourth one-fourth one-fourth 0 4 1 4 2 4 3 4 4 4 Discuss the difference in the labels. Making Math Magic

34. Fourths…… Ask them to use other paper strips and number lines to label using percents. You may have to lead them to the discovery of “If the whole strip is 100%, then one section is 25%”. 25% 25% 25% 25% 0% 25% 50% 75% 100% Again, discuss the difference in the labels. Making Math Magic

35. Fourths…. Because students may struggle with finding half of 0.5, we are going to use the 4” square and the grid model before we ask them to do the decimal version of the number line. Making Math Magic

36. Let’s look at another model. Use one of the 4” squares to shade 25% or one-fourth. You will also need this Transparency Grid Model Making Math Magic

37. 1 4 ? s 10 2½ 10 = = 0.2½ Making Math Magic

38. 1 4 2½ 10 = = 0.2½ = 0.25 Making Math Magic

39. Let’s do some math….. Area model Find an area model for fourths or fold one of the circles or squares into fourths. What is ¼ of 12? What is ¾ of 12? Making Math Magic

40. Area model 25% of some number is 5, what is the number? Making Math Magic

41. Area model 75% of some number is 12, what is the number? Making Math Magic

42. Number line What is 0.75 of 40? 0 0.25 0.50 0.75 1.00 ?? 0 40 Making Math Magic

43. Number line 75% of what number is 15? 0 25% 50% 75% 100% 0 15 ?? Making Math Magic

44. Try these…….. 25% of what number is 7? What is 0.5 x 64? ¾ of what number is 21? What per cent of 40 is 30? Making Math Magic

45. We are debating on doing “eighths” here or moving to thirds and coming back to eighths later. THOUGHTS????? Making Math Magic

46. Thirds…….. Because of the fractions involved in thirds when they are written as a decimal and as a percent, we decided to approach them using the grid model first. Making Math Magic

47. 1 3 Use the paper grid models to shade How many tenths? How many hundredths? Making Math Magic

48. Tenths Making Math Magic

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