Fractions and Rulers

1. Fractions and Rulers Fractions on a Number Line Fraction Basics Reading a Ruler

2. Rationale • Construction trades use rules and rulers for measurement. • Standard Rulers are divided into quarters, eighths, and sixteenths. • Precision measurement is the standard for quality work.

3. Objectives • Fraction Vocabulary • Equivalent Fractions • Place Fractions on a Number Line • Read a Ruler with halves, fourths, eighths, and sixteenths

4. Agenda • Pre-test on Fractions and Reading a Ruler • Fractions Equivalents and Practice • Make a Number Line • Reading a Ruler and Practice • Ruler Internet Activities • Post-test

5. Fraction Vocabulary • Warm-up: Create a Bubble Map about fractions • Fraction is written in the middle circle • Surrounding circles write any math vocabulary associated with fractions that you know • You do not need to be able to define or give an example of vocabulary word • Discussion

6. Fractions and Whole Numbers 1 = 1/1 1= 2/2 1= 4/4 ____________________________________ 2= 2/1 3= 3/1 4= 4/1 _____________________________________ 2 = 4/2 3= 9/3 5=20/4 What patterns do you see in each row?

7. Finding Equivalent Fractions ½ multiplied by 1 = ½ ½ multiplied by 2/2 = 2/4 = ½ ½ multiplied by 4/4 = 4/8 = ½ ½ multiplied by 8/8 = 8/16 = ½

8. Equal Fractions on the White Boards • What are the equal fractions in eighths and sixteenths for: ¼ ? ½ ? ¾ ?

9. Reducing to Equivalent Fractions 2/8  2/2 = ¼ 6/16  2/2 = 3/8 4/8  2/2 = 2/4  2/2= ½

10. How do you Reduce…? (White Board!) 2/8 = ¼ 4/16= ¼ 4/8 = ½ 6/8 = ¾ 12/16 = ¾ 2/16 = 1/8 6/16 = 3/8 10/16 = 5/8 14/16=7/8

11. Write a Rule • Fractions like: 2/2, 3/3, 6/6, … • Fractions like: 2/1, 5/1, 8/1, … • Fractions like: 4/2, 15/3, 25/5, … • Finding Equal Fractions like: ½ = 2/4 = 4/8 = 8/16 • Reducing Fractions like: 4/16 = 2/8 = 1/4 On the handout sheet write a rule that explains each example. Compare it with someone else’s rules. Share with the Class.

12. Possible Rules • If the numerator and denominator are equal the fraction is equal to 1. • If the denominator is 1 the fraction is equal to the numerator. • If a denominator divides evenly into a numerator the fraction is equal to a whole number • To find equal fractions multiple the numerator and denominator by the same number • To reduce fractions divide the numerator and denominator by the same number Add to or correct your rules if you need to!

13. Converting to Equivalent Fractions Converting Improper Fractions to Mixed Numbers 3/2 = 1½ 5/4 = 1¼ 19/4 = 4 ¾ Converting Mixed Numbers to Improper Fractions 3½ = 7/2 5¼ = 21/4 2 ¾ = 11/4 Complete a Flow Map for each conversion process.

14. Partner ExplanationsYou may use your Flow Map • Partner # 1 explains to Partner #2 how to convert improper fractions to mixed numbers. • Partner # 2 explains to Partner # 1 how to convert mixed numbers to improper fractions. • Repeat the process four times, but switch partners and number each time. • Each person will explain the two different processes twice.

15. Equivalent Fractions Round About Practice • Complete any three problems on your first sheet. Network with your group to check your answers and correct any errors. • Pass your sheets on to the next group. • Choose a different color sheet to work on from the new set. Complete any three problems, network to check, and correct. • Repeat process until everyone has worked 3 different problems on every different color sheet.

16. Fractions on a Number Line Use a black marker and draw a number line and put 0 at the far left and 1 at the far right. Then place these fractions where they belong on that line. • 0/2, ½ and 2/2 • 0/4, ¼, 2/4 and ¾ • 0/8, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8 and 7/8 • 0/16, 1/16, 2/16, 3/16, 4/16, 5/16, 6/16, 7/16, 8/16, 9/16, 10/16, 11/16, 12/16, 13/16, 14/16, and 15/16 Make it large enough for you to work with and use a different color marker for each set of fractions.

17. Number Line Discussion Questions using Red/Green Cards • Do any of the fractions fall on the same place on the number line? Explain your answer? • Where would fractions like: 2/4, 2/8, 6/8, 4/16, or 6/16 fall on the number line? How do we explain this? • What happens to fractions that fall beyond 1 on the number line? Beyond 2? • How many fractions are there on the number line? • Can all the fractions fit on the number line?

18. Density of NumbersPost-it Answers Between any two numbers on the number line (including fractions) there is always another number. • How does your number line illustrate this idea? • How is this similar to a ruler? Write each of your answers on post-it and stick it on your number line.

19. Inch and Fractions

20. Tape Measure Example

21. How to Read a Ruler Internet Tutorial • Classroom or Computer Laboratory • Log-in and go to the website. • Complete Tutorial and 8-Question Practice. • Complete Practice Sheets, check with key and make corrections. http://www.manawa.k12.wi.us/LWHS/Staff/Staff/Kelly%20Koller/General%20Tutorials/How%20to%20read%20a%20ruler.htm

22. Ruler Game • Finish the Tutorial/practice and handout Practice Sheets. • Click on the Ruler Game at the bottom of the screen. • Play the game until directed to stop.

23. Closure Focus Free Write In your journal or on a piece of paper: Write for 3 minutes on the topic: “Fractions that are found on a ruler” Use all the fractions and vocabulary you can think of. If you get stalled, re-write your last sentence until time is up or inspirations strikes you.