What Are Equivalent Fractions? Discussion Questions
Answer the following questions based on what you already know about fractions and
equivalence.
1. What does equivalent mean? It’s ok to look it up, just write it again in your
own words.
2. Now that you know what equivalent means and what a fraction is, what do
you think the phrase “equivalent fractions” mean?
3. Using the picture below, write 2 names for the shaded portion on the left.
4. Name the fraction of the shaded portion of each rectangle:
5. Are the two fractions in question #4 equivalent? Explain your answer.
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Equivalent Fractions Story Problems
Draw a picture or use manipulatives to help you solve the following word problems.
Be prepared to prove your answers to another person.
1. Sarah Sanders is preparing a lunch for all of her friends. Sarah puts 3 ice
cubes from the green ice tray that holds 8 ice cubes total into each pitcher
of lemonade. Sarah ran out of ice cubes from the green tray and now is left
to use only the blue one that hold 16. How much of the blue trays will she
need to use to put the same amount of ice in each pitcher? What fraction of
ice from the green tray did Sarah use? What fraction of ice from the blue
tray did Sarah use? Are these two fractions equivalent?
2. Grandpa Gunderson bought pizza for his three grandkids, Calvin, Nate and
Rosie. Each grandkid likes a different type of pizza. Calvin eats pepperoni
pizza, Nate eats cheese pizza, and Rosie eats Hawaiian pizza. All 3 pizzas
are the same size but each pizza is cut into different amounts of pieces. The
pepperoni is cut into 12 pieces, the cheese into 16 pieces and the Hawaiian is
cut into 8 pieces. Grandpa gave Calvin 3 pieces of pepperoni. How many
pieces should he give to Nate and how many pieces should he give to Rosie if
he wants to give them each the same total amount of pizza? What fraction
of their pizzas did each of the 3 grandkids eat?
3. Aiden Mendlesen is out milking his cows and has misplaced his normal milk
bucket. His normal bucket can hold 7/8 of a gallon of milk. All he could find
were jars that hold only 1/24 of a gallon. How many of those jars will Aiden
need?
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4. Fiona Figglesworth loves to work in her garden. She has set up 4 rows of
holes. In each row she plans on planting a different vegetables (carrots,
peas, squash, and cucumbers. Each row is long enough for 1/2 of a bag of
seed. She puts one seed in each hole. Carrots have 24 seeds in each bag,
peas have 30, squash has 16, and cucumbers have 28 seeds in each bag. How
many seeds did Fiona plant in each row?
5. Dr. Theodore Hatcher is running an experiment to find a virus. He needs to
collect the same fraction of blood samples from each tray. If he took 10
samples from the tray of 35, how many samples does he need to take from a
tray that has 7 samples? Write both of the fractions that are represented.
6. Two-thirds of the kindergarteners at Birdsong Elementary eat chicken
nuggets for lunch. If the cafeteria staff made 18 orders of chicken nuggets
for the kindergarteners, how many kindergarteners are there? What fraction
does 18 represent?
7. Darissa Dermain is famous fashion designer. She needs 12/16 of a yard of
black silk for her next amazing dress. The black silk she wants use for the
dress is only measured in fourths of a yard, how much should she order?
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8. Ricardo Recarto is selling spaghetti at Ricardo’s Ristorante. He uses 12/8
cups of sauce for each plate. If Ricardo only has a 1/2 cup measurer, how
many full scoops with the measuring cup will he need?
9. Jaqueline Porter is making jewelry to sell to make a little extra money for
Christmas presents. Each bracelet is made using 12/9 carats of gold. When
a customer asks her how many thirds of a carat are in her bracelets, for a
price comparison, what should Jaqueline say?
10. Sarah Smilling is working really hard to put together her puzzle. She has
already put together 32 of the pieces. If 4/5 of the puzzle is completed,
how many pieces does the puzzle have?
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Equivalent Fractions Direct Operation Problems
Find at least 2 fractions that are equivalent to the fractions below. Solve them in
any way that you would like to. You can use manipulatives, pictures, logic or some
other way. Make sure that you are able to prove that your answer is correct to
another person.
1.
3.
5.
7.
!
"
$
!
*
4. 2/12
&
(
6. 3/9
!)
"
(
9. 5/15
11.
2.
#
8.
10.
&
&
$
!(
12. 2/3
")
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Equivalent Fractions Data Collection And Observations
Make a list of at least 10 sets of equivalent fractions you found in the previous
problems (story problems and/or direct operation problems).
1.
6.
2.
7.
3.
8.
4.
9.
5.
10.
Equivalent Fractions Observations
Using the list above, write down a list of patterns you notice. What is meant is, if
you were given a fraction of 3/8, you could explain exactly how to make a fraction
that is equivalent. As always, do the best you can. Try to be as clear as possible.
Start by trying to find a pattern in some of the fractions on your list and then test
that pattern on the other numbers on the list to see if it works for all of them.
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Equivalent Fractions Teaching And Hypothesis Creation
Now that you have discovered a pattern in finding fractions that are equivalent, try
teaching equivalent fractions to a sibling, parent or friend (have them pretend that
they don’t know how to find equivalent fractions!). Each problem will have some
directions as to how to teach or how not to teach the problem. Follow the rules
and do the best you can. Remember that you are teaching them, NOT doing it for
them. One important rule for each problem is that you are not allowed to touch
anything, the person you are teaching has to do all the work!
1. Find a fraction equivalent to
$
&
.
Help them solve this problem by having them use a manipulative of some sort.
2. Find a fraction equivalent to
!
'
.
Help them solve this problem by having them draw a picture.
3. Find a fraction equivalent to 12/18.
You can help them solve this problem any way you would like, but you have to
keep your hands behind your back.
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4. Find a fraction equivalent to 6/9.
For this problem you are not allowed to talk.
5. Find a fraction equivalent to
!)
!%
.
For this problem you are not allowed to say any numbers.
6. Find a fraction equivalent to
!!
!*
.
For this problem you are not allowed to say numbers and you need to keep
your hands behind your back.
Equivalent Fractions Hypothesis
Write a general rule for how to find equivalent fractions:
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Equivalent Fractions Hypothesis Test And Theorem
It’s time to see if your equivalent fraction hypothesis will work every time in order
to prove it as a true theorem. Solve each of the problems using only your
hypothesis, word for word. Remember that when testing a hypothesis, you are only
allowed to do exactly as the steps in your hypothesis direct. If you need to do
something new, then you need to add to or write a new hypothesis. Then solve each
problem in a second, different way, using a model, to see if the answer you arrived
at with your hypothesis is the correct answer.
1. Three-fifteenths of the castles of Marioville has been overrun by Bowsers.
If only two of the castles are overrun by bowsers, how many castles are
there in Marioville?
2. Neri got eighteen of the twenty problems right on his last exam. The test is
worth 100 points. If each problem is worth the same number of points, how
many total points did Neri get?
3. Ilene Rightly is campaigning to become Mayor of Sitonitville. People aren’t
really that crazy about her and her style of government. In fact, only one
fifth of the citizens of Sitonitville who can vote have decided that they might
vote for her. If 10,000 people in Sitonitville can vote, how many people have
decided that they might vote for Ilene Rightly?
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Find 3 fractions that are equivalent to the following fractions:
4.
6.
"
5. 0/34
'
*
"
7.
!"
$
Equivalent Fractions Theorem
Once you have tested your hypothesis and proven that it works for every problem,
write your final theorem of how to find equivalent fractions:
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