Activity 15.8Slicing SquaresGive students a worksheet with four squares in a row, each approximately 3 cm on a side. Have them shade in the same fraction in each square using vertical dividing line. You can use the context of a garden or farm. For example, slice each square in fourths and shade three-fourths as in Figure 15.20. Next, tell students to slice each square into equal-sized horizontal slices. Each square must be partitioned differently, using from one to eight slices. For each sliced square, they record an equations showing the equivalent fractions. Have them examine their equations and drawings to look for any patterns. You can repeat this with four more squares and different fractions.What product tells how many parts are shaded?What product tells how many parts in the whole?Notice that the same factor is used for both part and whole
Give students an equation expressing an equivalence between two fraction but with one of the numbers missing and ask them to draw a picture to solve. Here are four different examples:5/3 = _/62/3 = 6/_8/12 = _/39/12 = 3/_The missing number can be either a numerator or a denominator. Furthermore, the missing number can either be larger or smaller that the corresponding part of the equivalent fraction. (All four possibilities are represented in the examples.) The examples shown involve simple whole-number multiples between equivalent fractions. Next, consider pairs such as 6/8 = _/12 or 9/12 = 6/_. In these equivalences, one denominator or numerator is not a whole number multiple of the other.
1. 5th Grade Fractions &Word Problems Laura Chambless RESA Consultantwww.protopage.com/lchambless
2. CCSS and Gaps What are your gaps in curriculum?1. Review CCSS for Fractions2. Think about your resources3. Think about your teaching – Highlight anything your resources covers well in YELLOW. – Highlight any part of the standard you would like more clarification on in BLUE.
3. Learning TargetUse equivalent fractions as a strategy to add and subtract fractions. 5.NF.1, 5.NF.2Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.3, 5.NF.4, 5.NF.5, 5.NF.6, 5.NF.7
4. Fraction Word Problem40 students joined the soccer club. 5/8 of the students were boys. How many girls joined the soccer club? Draw a picture and solve it.1. 2 min. working problem on own2. 5 min. sharing with group3. Class discussionFound at: http://www.mathplayground.com/wpdatabase/Fractions1_3.htm
5. Problem Solving with Bar Diagrams1. Understand: Identify what is known and what is unknown. Draw the bar diagram to promote comprehension and demonstrates understanding. (Situation vs. Solution Equation)2. Plan: Decide how you will solve the problem (find the unknown). Analyze the bar diagram to find a solution plan.3. Solve: Execute the plan. Use the bar diagram to solve.4. Evaluate: Assess reasonableness using estimation or substitution. Substitute the solution for the unknown in the bar diagram.
6. Bar DiagramsWatch Introduction Videohttp://www.mhschool.com/math/com mon/pd_video/mathconnects_bardi agram_p1/index.htmlhttp://www.mhschool.com/math/com mon/pd_video/mathconnects_bardi agram_p2/index.html
7. Practice Bar DiagramsTo: Rani earned $128 mowing lawns and $73 babysitting. How much money did Rani earn?With: Jin had $67 in his pocket after he bought a radio controlled car. He went to the store with $142. How Much did Jin spend on the car?By: There are 9 puffy stickers. There are 3 times as many plain stickers as puffy stickers. How many plain stickers are there?You pick 2 more to do by yourself. Share with partnerDraw Your Way to Problem Solving Success Handout, Robyn Silbey
8. Thinking Blockshttp://www.mathplayground.com/think ingblocks.html Explore the site  When done exploring go to my Protopage and look at your grade level math tab.
9. Fractions Stand and ShareMake a list of what you know and any connections you have about the fraction ¼.
10. Representations (Part 2 video, 5:16)Set Purpose of video: List why representations are important in the classroom. •Representations are mathematics content representing mathematical ideas is a practice that students need to learn. •Representations provide tools for working on mathematics and contribute to the development of new mathematical knowledge. •Representations support communication about mathematics. •Using multiple representations can help develop understanding and support the diverse needs of students. From: Dev-TE@M session 2
11. Benefit of Representations (Part 4 video, 2:17)Set Purpose of video: Did you benefit from our discussions, and how will your students benefit from class discussions?1. As you listen , list benefits for students2. Compare list with partner From: Dev-TE@M session 3
13. Fractions Fraction ActivityPaper Strips Fraction Kit: 1, ½, 1/4 , 1/8, 1/16Add to Fraction Kit: 1/3, 1/6, 1/12Add to Fraction Kit: 1/5, 1/10 Compare/Add/Subtract/Multi./Divide with StripsREAD and DO: 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.5, 5.NF.6, 5.NF.7Smaller Answer Wins (need dice)• Prove with Fraction Strips
15. Definition of Fractions1. Make a list of what you would like to have in a definition of a fraction2. Partner up and compare lists3. Group discussion
16. Definition of a Fraction (Part 5 and 6 videos, 11:48/4:27)Set Purpose of video: What are some key parts in creating a definition of a fraction that you will use in your room?– Give handout of working definitionArticle: Definitions and Defining in Mathematics and Mathematics Teaching by: Bass and Ball From: Dev-TE@M session 3
17. Definition Of Fractions• Identify the whole• Make d equal parts• Write 1/d to show one of the equal parts• If you have d of 1/d, then you have the whole• If you have n of 1/d, then you have n/d• n and d are whole numbers• d does not equal 0Dev-TE@M • School of Education • University of Michigan • (734)408-4461 • email@example.com For review only - Please do notcirculate or cite without permission
18. Ordering Fractions Order Fractions 8/6, 2/5, 8/10, 1/12How did you figure out what order they went in?
19. Fractions Prove with Fraction StripsNumber Line: (Benchmarks) 0, ½, 1Equivalent Fractions: Same Name FrameCompare (>/<): same numerator or same denominator
20. Strategies for Comparing Fractions• Dev-TE@M session 9
21. Fraction On A Number LineWriting about Fractions: Draw a number line. Place 3/6 and 7/12 on the number line. Compare the two fractions- why did put them where you did?
22. Key Ideas About the Number LineWhat were some intentional talk moves others used to explain their number line? (Part 5 video, 5:26)Set purpose of video: Listen to the detail that is given in explaining how to construct a number line. From: Dev-TE@M session 4
23. Conventions Of A Number LineDev-TE@M • School of Education • University of Michigan • (734) 408-4461 •firstname.lastname@example.org For review only - Please do not circulate or cite withoutpermission
24. Talking Through A Number Line1. Understand the problem.2. Think about which representation you are going to use.3. Describe your thinking process while constructing the number line.4. Sum up the solution that proved your answer.Model Example: 3/10 & 6/8
25. Fraction On A Number LineUsing a number line, compare 5/6 and 3/8 and tell which one is greater . Have a partner listen to you as you construct the fractions and find the answer.
26. FractionsWhat conceptual understanding do students need? 1. Begin with simple contextual tasks. 2. Connect the meaning of fraction computation with whole number computation. 3. Let estimation and informal methods play a big role in the development of strategies. 4. Explore each of the operations using models.Van De Walle Book: Number Sense and Fraction Algorithms Pg. 310
28. Methods for Generating andExplaining Equivalent Fractions• Dev-TE@M session 9
29. Add/Subtract Fractions with Unlike Denominators Developing Equivalent Fractions• Slicing Squares Van de Walle book: pg. 304-305 3 x = 3 x 4 = 4 3 x 3 x = = 4 4
30. Add/Subtract Fractions with Unlike Denominators Developing Equivalent Fractions• Missing-Number Equivalencies Van de Walle book: pg. 304-305 5 2 6 = = 3 6 3
31. Fraction Multiplication StrategiesTOOLKIT for Multiplication of Fractions1. Skim over TOOLKIT2. Read assigned page (2 min)3. 30 second report: What are the important part of your page?4. Questions from audience
32. FractionsMultiply a fraction by a whole number• Work as a group• Use Fraction strips to show answers 4 x 1/3 ¼ x 12• What connection can you make to multiplication? What other representations can you use? Can you use a number line?
33. Multiple a Fraction by a Whole Number 4 x 1/3 (4 groups of 1/3) = 4/3 = 1 1/3I want 4 ribbons each at 1/3 of a yard. How much ribbon will I need to purchase? 1/3 2/3 3/3 4/3 ¼ x 12 (1/4 of 12) = 3I have 12 cookies and want each of my friends to have ¼ of them. How many cookies will each friend get?
34. Scaling (resizing)• 5.NF.5 – Read learning targets and discuss – Prove greater/less than given number statements with last slide. – Making equivalent fractions
35. Multiply Fraction by FractionAIMS• Fair Squares and Cross ProductsMMPI• Worksheet 1: Show different representations 2/3 of ¾ ¾ of 2/3
36. Multiply Fractions and Mixed NumbersMMPI• Area Model Rectangular Multiplication PPThttp://www.michiganmathematics.org/
37. Fraction as Division (a/b = a ÷ b)• I can explain that fractions (a/b) can be represented as a division of the numerator by the denominator (a ÷ b) can be represented by the fraction a/b.• I can solve word problems involving the division of whole numbers and interpret the quotient- which could be a whole number, mixed number, or fraction – in the context of the problem.• I can explain or illustrate my solution strategy using visual fraction models or equations that represent the problem.
38. Divide Fraction by Whole Number½÷6=6÷¼=4 ÷ 2 = (how to connect division of whole numbers with fractions)
39. Divide Fraction by Whole Number½ ÷ 6 = If I have ½ cup of sugar and divide it among 6 people, how much sugar does each person have? 1/121 2 3 4 5 6 7 8 9 10 11 126 ÷ ¼ = If I have 6 candy bars and divide each one into fourths, how many pieces will I have? 24
40. MOPLS http://mi.learnport.org Search: MOPLS Math (navigate by using top tabs)Look at Concepts Tab– Introduction– Math Behind the Math– Misconceptions– Tasks & Strategies
41. Fractions OnlineCheck out some sites on my 5th grade math Protopage
42. Learning TargetUse equivalent fractions as a strategy to add and subtract fractions. 5.NF.1, 5.NF.2Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.3, 5.NF.4, 5.NF.5, 5.NF.6, 5.NF.7
43. Closer ActivityList something you learn about story problems and fractions today.
44. Thanks for a great day Please contact me if you have any questions or would like more information.