Exploring Fractions and Patterns

Math Explorations based on the book

The Lion’s Share By Matthew McElligott

By Bethany @

MathGeekMama.com

Teaching Tips for The Lion’s Share

• This is a wonderful book for introducing fractions and what happens to numbers as you “half” them.

• Depending on the age of your students, this can provide for wonderful discussion of how ½ is the same as dividing by two, observing patterns, and even exponential growth. I hope the activities in this download will allow you to have deep mathematical discussions and provide for further math inquiry. J

• Activity 1: This activity is meant to be a more formal look at the math in the book. First students chart the fractions as the cake continues to be cut in half, then they chart the number of cakes each animal must make. There are discussion questions to help students dissect it and compare the two. For the picture representation of fractions, encourage students to begin with a long rectangle (because of the space) and continue halving the previous “half.” Don’t worry if they’re unable to draw a picture for the very bottom fractions.

• Activity 2: Recognizing patterns. This activity is meant to help students practice recognizing other patterns with multiplication/division. If students do not recognize that multiplying by a fraction is the same as dividing, help point that out. (NOTE: Includes an answer key)

• Activity 3: “When halving isn’t halving.” This is a fun way to take what they have learned from The Lion’s Share and apply it to area and perimeter. All each student will need for the initial activity is a piece of printer paper (8.5/11), scissors and a ruler. This should allow for a lot of interesting discussion as students try to figure out what happens to the perimeter, and if it is the same every time.

o If students are interested in further exploration, let them build rectangles with base 10 blocks or (better yet) Cheese-It crackers and “half” different size rectangles to see if they can find a size that will “half” the perimeter as well.

Have Fun!!

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Finding the Lion’s Share: Fill in the chart below to determine each animal’s share of the cake, first by

drawing a picture, and then writing it as a fraction. J

Animal Picture of their share (shade how much

cake they got) Fraction of the Cake

Elephant

   

Hippo

   

Gorilla

   

Tortoise

   

Warthog

   

Macaw

   

Frog

   

Beetle

   

Ant

   

 

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Bring on the Cake!

The animals in The Lion’s Share began to try and outdo each other by offering to make more and more cakes for the King. Fill in the chart below to see how many cakes each animal had to

make, and the answer the questions on the right.

Animal Number of Cakes Ant

Beetle

Frog

Macaw

Warthog

Tortoise

Gorilla

Hippo

Elephant

 

Think About It…

1. What do you notice about the fractions of cake slices and the number of cakes the animals had to make? 2. How is the number of cakes increasing? 3. Describe in your own words what happens when you “half” a fraction.

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Recognizing Patterns Determine the missing numbers in the following patterns.

Then describe the pattern (ex. Multiply by 2, etc.)

1. 3,  9,  _______,  _______,  _______,  729  

2. 1,_______, 116 ,_______, _______,1

1,024  

3. 7,  14,  28,  _______,  _______,  _______

4. _______,  _______,  _______,  108,  324,  972

5. !!, _______, !

!", !!", _______, _______

    6.  8,  4,  2,  1,  _______,  _______,  _______

1. _______________________

2. _______________________

3._______________________ 4._______________________ 5._______________________ 6._______________

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Recognizing Patterns Determine the missing numbers in the following patterns.

Then describe the pattern (ex. Multiply by 2, etc.)

1. 3,  9,  __27__,  __81___,  __243__,  729  

2. 1, 14, 116, 164, 1256

, 11024

 

3. 7,  14,  28,  _56___,  __112__,  __224__

4. __4__,  __12__,  __36__,  108,  324,  972

5. !!, !!, !!", !!", !!"#

, !!"#

 

    6.  8,  4,  2,  1,  _1/2___,  __1/4__,  _1/8___

1. ____Multiply by 3_________

2. _Multiply by ¼ or divide by 4

3._____Multiply by 2________ 4._____Multiply by 3________ 5. Multiply by 1/3 or divide by 3 6. Mult iply by ½ or divide by 2

When Halving Isn’t Halving Using a regular piece of printer paper, measure the area and perimeter and

fill in the chart below. Then carefully cut it in half and find the measurements again. Continue until you have completed the chart.

Fraction of the Paper

Total Area (inches2)

Total Perimeter (inches)

 1    

   

 12!    

     

 

 14!    

   

 18!    

   

 116!    

   

 

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Think About It…

1. When you cut the area in half, was the perimeter cut in half too? How do you know? 2. How is the perimeter changing? Is it constant? 3. Does it make a difference which way you cut the paper in half?

 

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