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 9/3 520/4
• 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 14/167/8

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 elses 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/General20Tutorials/How20to20read20a
  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.