Math Access for Teachers and Home Child Care Providers

Picture Pie Fractions

Children will identify parts of a whole and create pictures using various parts of a circle using whole, half and fourths of a circle.

Content Area Standard Target
• Algebra
• Number and Operations
• Understand numbers,ways of representing numbers, relationships among numbers, and number systems
• Represent and analyze mathematical situations and structures using algebraic symbols
• Understand meanings of operations and how they relate to one another
• Connect number words and numerals to the quantities they represent, using various physical models and representations
• Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2
• Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations
• Count with understanding and recognize “how many” in sets of objects
• Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally
Obtain the Materials

• Book: Picture Pie by Ed Emberley.
• Pre-cut, different colored circles and parts of a circle.  Whole circles, half circles, fourths of a circle and eighths of a circle.
• Glue sticks, big pieces of construction paper (12 x 18) and crayons or markers.
• Chart paper for visuals during the lesson.

Note: Small parts create a choking hazard for children. Make sure that all materials you choose to use for an activity or lesson with children meet safety requirements. Small parts are not appropriate for children who are 5 years of age or younger.

Introduce the Activity

1. Explain to the children that today they are going to look at circles and parts that make up a circle.  Explain that together they will read a book called Picture Pie and they will look at how a circle, divided like a pie, can be used to make pictures of all kinds.
• “How many pieces do you usually divide a pizza pie into?” (8)
• “How many pieces make up a pizza pie?” (8).
• “How many pieces do you usually divide a round cake into?”
3. Show the children a circle.  Say, “This is a whole circle.  If this were a pizza pie, all of the parts of the pie are still intact.  Nobody has taken a piece of pizza yet.”
4. With the children watching, cut the circle in half.  Say, “Now I am going to cut the circle in half.  I am cutting the circle into 2 equal parts.”  Place a whole circle up on the chart paper and the place the 2 halves next to or under the circle.

1. You may want to use a visual for the children similar to the visual above.  It is easier for the children to grasp the concept of parts of a whole if they can see all of the different ways a circle can be divided, and all of the parts of a circle that equal a whole.
Say, “If Billy and I were to share a pizza, we would divide it into 2 equal parts.  We would divide the pizza pie in half so that we both had the same amount of pizza.”
2. Show the children another circle.  Ask, “How can we divide this circle into 4 equal parts?”  Ask, “If this is a pizza pie and we have 4 people who want to share this pie, how can we divide this pie into 4 equal parts?”
3. Show the children the process of first, cutting the circle into half.  Say, “I have two equal parts. I have cut the circle in half.  Is this enough for 4 people?” (no) “What do I need to do to create 2 more pieces from these two halves?”  (Cut those pieces in half.)
4. Show the process of cutting each half into fourths.  Place the 4 fourths onto the chart paper next to the 2 halvesSay, “Now if Billy, Kim, Brian and I were to all share a pizza, we would need to cut it into 4 equal parts.  We would cut the pizza into fourths.”
5. Repeat steps 6-8 for eighths
6. With the chart paper containing the visual representations for a whole circle, 2 half circles, 4 fourths of a circle, and 8 eighths of a circle, start by explaining equal parts
7. Point to the halved circle, Say, “How many parts does this circle have?”  (2)  “Right, it has 2 parts.  So we can say that 2 halves equal 1 circle.  Is that right?”
8. Say, “OK." Ask,  "But what about this circle?”  Point to the circle divided into fourths.  Say, “How many parts does this circle have?”  (4)  “Wow, you are right, it has 4 parts!  So can we say that 4 fourths is equal to 2 halves and 2 halves are equal to 1 whole?”
9. Ask, “Now what about the circle cut into eighths?”  “Does this circle cut into 8 equal parts equal the circle that is cut into 4 equal parts?  Does it equal the circle that is cut into 2 equal parts?  Does it equal a whole circle?” (yes)  “How can that be?”  It is fun to act as if this discovery is something magical.  Write down responses that the children might have on the chart paper.
10. Read the book Picture Pie.  There aren’t many words and the book reinforces the concept of halves, fourths, and eighths of a whole circle.  While looking at the book, have the children point out the parts of the circle.  Say, “Look at this duck.  It looks like it is made up of the various parts of a circle that we just discussed.  Ask, Can you point out the whole circle?  Can you point out the half circle?”  Do this for all of the parts of the circle.

Engage the Children

1. Explain that now the children will make their own circle pictures or designs using various parts of a circle.  Say: “I have cut up parts of a circle for you to use to create your own circle picture.  You will be using whole circles, half circles, fourths of circles and eighths of circles.”  "You can create anything you would like and you can use crayons or markers as well.  Glue the circles and circles parts onto your paper.”
2. Encourage the children to use all parts of the circle in their collages.  Say: “I see you have used a half circle".  Ask: "Can you also use an eighth of a circle in your picture?”
3. Display the children’s work.

1. After using circles, you can use squares.  Divide the square into halves, fourths & eighths.  Compare the division of the square to that of the circle.  The children can make a collage using both the circle and the squares.
2. Write the fraction equivalent onto each shape.  1 on the whole circle.  1/2 on the half of circle, 1/4 on the fourth of the circle and 1/8 on the eighth of the circle.  Explain that the bottom number  (the denominator) tells you the number of parts the whole is divided into and the top number (the numerator) tells you the number of parts of the whole.  So 1/8 is one part out of 8 possible parts.
3. By laying parts of the circle onto of one another, you can discuss equivalent fractions.  For example, 2/8s is equal to 1/4.  Lay the two eighths on top of the fourth.  Ask: “How many fourths do we need to make a half?”  (2)  Say: “So we can say that 2 fourths are equal to 1 half.”

Encourage Vocabulary

• Divide– Group a number into equal parts
• Half – One of two equal parts of the shape
• Fourth – One of four equal parts of the shape
• Eighth – One of eight equal parts of the shape
• Equal – Exactly the same amount or value
• Whole – All of the parts or the total amount of something

Glossary of MATH vocabulary

Supporting Children at Different Levels

Toddlers   Pre-K

Toddlers may:

• Not be able to conceptualize multiple fraction sizes in one lesson.
• Not be able to manipulate the small circle pieces when creating their collages.

Pre-K Children may:

• Be able to understand the concept of fraction equivalents.
• Be able to understand the concept of equivalent fractions.

Home child care providers may:

• Just focus on halves.  Eliminate the fourths and eighths from the discussion and from the options
of shapes to use for their collages.
• Reinforce the concept of halving an object.

Home child care providers may:

• Write the fraction equivalent onto each shape.  1 on the whole circle.  1/2 on the half of circle, 1/4 on the fourth of the circle and 1/8 on the eighth of the circle.  Explain that the bottom number  (the denominator) tells you the number of parts the whole is divided into and the top number (the numerator) tells you the number of parts of the whole.  So 1/8 is one part out of 8 possible parts.
• By laying parts of the circle onto of one another, begin a discussion of equivalent fractions.  2/8s is equal to 1/4.  Lay the two eighths on top of the fourth.  “How many fourths do we need to make a half?”  (2)  “So we can say that 2 fourths are equal to 1 half.”

Books

• Picture Pie by Ed Emberley (New York: Little Brown Books for Young Readers)
• Picture Pie 2 by Ed Emberley (New york: Little Brown Books for Young Readers)

Music and Movement

Outdoor Connections

• Any cooking activity helps to reinforce the concept of fractions.  Baking cookies and using amounts such as a ½ cup of sugar, 2 cups of flour etc.  Allow children to conceptualize the fraction and amounts and they can enjoy that the final product is a yummy treat. If you are outside, you can pretend to cook by putting sand and water into the sensory tables. Add measuring cups and bowls with recepies designation how many cups (1/2, 1, 1/4 etc.) of water and sand to add to the bowl.

Web Resources

# Comment on this lesson

 To report a problem with the site, please email us. © 2011. M.A.T.H.