Unit 5

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					Unit 5

Circle graphs

Mrs. Z’s Class is the Best!
    Key Goals
•Add fractions with like denominators
•Order and compare fractions
•Convert between fractions and percents
•Draw a circle graph for a set of data
•Measure pieces of a circle graph             Click on me now
•Interpret a circle graph                     for an interactive
•Convert between fractions and mixed              tutorial on
numbers                                            fractions!
•Find equivalent fractions

                                                                   Click Me
                                Click Me to                        for Help!
                                 Float On!
 Add fractions with like denominators
• A fraction has two parts: the         Click me to
  numerator and the denominator          create a
• The numerator is the number on top,
  the denominator is the one that’s
  DOWN on the bottom.
• The numerator is the NUMBER of
  pieces you have
• The denominator is the size of the
  pieces         Click me to play a
                                       Try It Out
1/6 of the sections on the 1st ball are red.
3/6 of the sections on the second ball are
  red. What is the fraction of redtheis 4/6
                               The answer
                               because    size
                                of the pieces are
                                sixths. When you
                                add 1/6 to 3/6
                                you add the
                                numerators (1 +3)
                                and keep the
                                denominator the
                                same (6).
1/6 + 3/6 =

       4/12      7/9
                        4/6         2/12
4/9 + 3/9 =                            Try It Out


          The answer is 7/9
          because the size
          of the pieces are
          ninths. When you
          add 4/9 to 3/9
       7/18 add the            1/18
          numerators (4 +3)
          and keep the
          denominator the
          same (9).
6/8 + 7/8 =                                 Try It Out


       The answer is 13/8
       because the size of
       the pieces are
       eighths. When you
       add 6/8 to 7/8 you
       add the numerators
       13/16                       13/8
       (6 +7) and keep the
       denominator the
       same (8).
 Order and compare fractions
• The numerator is the NUMBER
  of pieces you have
• The denominator is the size of
  the pieces
• If something is cut into more
  pieces those pieces are going to
  be smaller.
Play a game
Strategies for comparing and ordering fractions…
    • One strategy for comparing fractions is to
      think about their relationship to one and zero.
      For example, 5/6 is almost all of the pieces,
      so it would be close to 1; 1/6 is close to none
      of the pieces, so it would be closer to zero.
    • Another strategy is to convert the fractions to
      a decimal and then compare the decimals.
      (numerator divided by denominator =
    • A third strategy is to find a common
      denominator among your fractions and
      compare the numerators.

              It helps to simplify the fractions!

         If you need a set of fraction bars, click here
Try It Out….
       4/9 _____ 6/9
         The correct answer is 4/9 < 6/9 because in these two
         fractions, the denominators are the same.
         Therefore, the pieces are the same size.
         Four of these pieces are less than six.
   <                 >                                =

                1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9

                1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
Try It Out….
                       8/9 is > 7/8
           8/9 _____ 7/8
In each of these two fractions, there is all but one piece.
    However, because 9ths are smaller than 8ths, the
    remaining 1/9 is smaller than the remaining 1/8.
      <                   >                      =
Try It Out….
                  1/3 is < 5/12
          1/3 _____ 5/12
 If you change 1/3 into an equivalent fraction, it would be
     equal to 4/12. 4 out of 12 is less than 5 out of 12.

    <                    >                    =
Convert between fractions and percents
•Fractions and percents are both ways of representing a part out
of a whole.

•An equivalent percent for a decimal or a fraction can be found
by finding an equivalent fraction out of 100 since “percent”
means “per 100”. In this case, the numerator would be the

•A fraction or decimal can be formed from a percent by
creating a fraction where the numerator is the percentage and
the denominator is 100, or by dividing the percent by 100.
Here are some examples….

                           Click on the small
                              pails to play
                            practice games!
Click on the characters to play fraction and percent games and activities!
Draw a circle graph for a set of data.
How to Make a Pie Chart
Pie charts are an easy way to visualize percentages. They are useful for analyzing polls, statistics, and managing
time or money.
                                                                                     Click me for a
1.Organize your data. First gather your data.
2.Add it all together. Add all of the numbers to get a denominator.
3.Get the numerator. Get the numerators by taking each part of the data.
4.Convert your fractions to a decimal. By taking the numerator divided by the denominator.
5.Convert the decimal to a percent. Move the decimal two places to the right.
6.Get the angle. Multiply the percent by 360 to get an angle.
7.Use a compass to draw a circle. If you don't have a compass, try tracing something round such as a lid.
8.Draw the radius. Start in the exact center of the circle and draw a radius to the outside of it. ( Hint: Use the dot
made by the compass to find the center.
9.Place your protractor. Place your protractor on the circle so that the 90 degrees are directly above the center
of the circle.
10.Draw each section. Draw the sections by using the angles you got in step six. Each time you add a section
the radius changes to the line you just drew.

  Click me to use the              Tips
 computer to create a              • Remember that all good graphs have a title and labels.
      circle graph.                • Add the name of the sections and the percent they
                                   represent to the chart.
                                   • Color each section of the pie chart a different color to
                                   easily visualize the results.
                                   • If you do not have a very good compass, it is easier to
                                   draw the circle by holding the compass still and turning
                                   the paper.
Measure Pieces of a Circle Graph
Click the links next to each step for more information.


1. Measure the angle of the sector you are trying to measure using a protractor.

2. Turn that measurement into a fraction out of 360°

3. Change that fraction into a decimal by dividing the measurement by 360°

4. Then multiply the decimal by 100 to change it into a percent.

              A full circle will consist of 360 degrees.
              Therefore 1% on a pie chart will be
              represented by 3.6 degrees.

              Just multiply the angle measure by 3.6.
                                                    Click me to test

Interpret a circle graph                               your skills!

                     When you interpret a circle
    Click me for a   graph, there are some key
     worksheet       things to remember:

                     -Look carefully at the title and
                      key so that you can tell what
                       data is being represented.

                     -Remember that each section                        Click me to print a
                     represents a part out of the                      different worksheet.
                     whole.                                                (Answer Key
                     - The larger the section, the
                     greater the percentage.

                        Click me for an online
                       explanation and trial with
Convert between fractions and mixed numbers.

• A FRACTION is a part out of a whole. The numerator tells the number
of parts you have, the denominator tells how many parts it takes to make
one whole.

• A fraction that has more parts than it takes to make one whole is called
an improper or top-heavy fraction. In these fractions, the numerator is
greater than the denominator.

• A MIXED NUMBER is a whole number with a fraction.

                                This drawing
                                represents the
                                fraction 5/4
                                and the mixed
                                number 1 ¼.

It’s good to understand both forms of this quantity because at
times it is easier to work with mixed numbers (adding and
subtracting so that you don’t have to simplify as much), and at
others it’s easier to work with improper fractions (multiplying and
dividing so that you don’t forget to multiply all of the numbers
  Learn about and practice
converting improper fractions
and mixed numbers by clicking
  the objects on this slide.
Finding Equivalent Fractions

Two fractions are EQUIVALENT if they are equal.
This means that the relationship between the
numerator and the denominator of one fraction is
the same as the relationship between the numerator
and denominator of the other fraction.
 For example

 3/6 is equivalent to 10/20 because the relationship between the numerator
 and the denominator is the same in each case: 3 is ½ of 6, and 10 is ½ of
Another way you can look at it is if two fractions
are equivalent, they will have a scale factor between
them. The SCALE FACTOR is the number that you
multiply or divide the numerator and denominator in
one fraction by to get the numerator and
denominator of the second fraction.
                            By multiplying 3/5 by 3/3 (remember, that is the same as
                            multiplying by 1 whole), I will arrive at the answer 9/15.

                            Remember that when you are doing this you must BE FAIR
            x3              and perform the same operation to both the numerator and

    3             9
                            the denominator.

                            Don’t forget that when you multiply fractions, you multiply
                            the numerators together and you multiply the denominators


A third way to determine if two fractions are
equivalent is to CROSS MULTIPLY.

Multiply the numerator of one fraction by the denominator of the other.

Repeat this with the other numerator and denominator.

If the products are equal, then the fractions are equivalent.

     4                  2
     6                 3

     12       =       12
Find equivalent fractions
                                Click me to play half baked
          Click me to               fractions on funbrain

                                                              Click me for a visual

          Click me to print a   Click us to play
              worksheet         fraction frenzy

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