big idea module (bim)
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BIM:
Understanding
Fractions
ELD 375
Sarah Jacobs
Kelly Collova
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Alicia Govannicci
Focus Problem
Grandma Sally loves baking breakfast muffins.She just recently found a new recipe for blue
berry muffins. Grandma Sally is so excited to
bake the muffins for her grandchildren! She took
out all the ingredients but realized she was
missing some of the measuring cups. She only has
measuring cups.
Grandma Sally realizes this is a huge problem
because she needs:
o cups of flour.
o cup of granulated sugar
o
cups of blue berries
What measuring cups does Grandma Sally have to
use in order to get the exact measurements she
needs to make the recipe?
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What is the least number of scopes that she can
use in order to get
cup of sugar?
Show your work and explain your process. Be
prepared to justify your answer. You may use any
manipulatives or drawings to help you. Make sure
to have your explanation in written form as
well:
Explain the reason why you decided to use the
method that you did:
Knowing all you have learned previously about
fractions, are there other methods you could
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have used to figure out the problem? Describe
your answer and show an example of the other
method(s).
Materials Needed For BIM
Materials:
Muffin problemSandwich worksheetPencilEraserDot paperPattern Blocks
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PencilScrap paper
UnderstandingFractions:
Halves and Quarters
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Early Elementary School Activity
Grades K-1
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Lucys favorite meal of the day is lunch. She
takes the same sandwich to lunch everyday. Her
mother likes to cut her sandwich into two equalpieces.
How many ways can Lucys mother cut her sandwich
into equal pieces? Or is there only one way for
her mother to cut her sandwich into equal
pieces? Explain your answers.
Materials:
Sandwich square worksheet Pencil Eraser Dot paper
Using the dot paper, draw each equal cut that
Lucys mother can make in the sandwich.
How many different ways can Lucys mother cut
the sandwich?
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Does each way represent equal pieces?
The next day Lucy was wondering if she can cut
her sandwich into four equal pieces calledquarters. Can a square be broken up into four
equal pieces? If so how many ways can she share
her sandwich with four friends, so they have
equal pieces?
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Draw the lines on the squares below to represent
the different ways Lucy can make four equal
pieces.
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Understanding
Fractions:Multiplying Fractions to Find
Equivalence
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Middle Elementary
School Activity
Grades 2-3
Harry had some friends over for a day full of
sled riding and snowball fighting! At different
times throughout the day, his friends had to
take a break and go inside to warm up. Harrys
mom had cocoa mix and warm water to make hot
chocolate with so that they can warm up. For
each cup of hot chocolate, the kids needed to
add 1 cup of warm water to the cocoa mix, but
they got tired of waiting their turn to use the
1 cup measuring cup. Instead, some kids decided
to use these measuring cups:
. Using
any combination of those measuring cups, how
many different ways can you find to make 1 cup?
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How did you organize your ideas to make sure
that you thought of all the combinations?
Did you seem to use one measuring cup most
often? Why?
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What other measuring cups would be useful?
What if you needed 2 cups of warm water? Now,
how many different kinds of measurements can
you use?
Understanding
Fractions:
Finding Equivalent
Fractions
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Upper Elementary
School Activity
Grades 4-5
Julie built the following
picture of a flower using
pattern blocks. She made the
flower for her schools pattern building
competition. The winner of the competition will
get to go on a math class field trip.
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Materials: Pattern Blocks Pencil
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How many green blocks can you fit into the
yellow block?
How many green blocks can you fit into the red
block?
How many green blocks would Julie need if she
wanted the make the whole flower out of green?
What fraction part of the flower are made out of
green blocks?
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If Julie were to make the flower out of all blue
blocks how many would she need?
Common Core
State Standards
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Big Idea Module: Understanding Fractions
The activities presented in our groups BIM are all related to the concept of fractions.
The objective of the focus problem is to be able to multiply fractions and recognize equivalent
fractions. The focus problem is geared towards students in sixth grade. The problem deals with
having the students help Grandma Sally figure out what measuring cups she can use to make the
blueberry muffins. Grandma Sally does not have the exact measuring cups that the recipe
ingredients, the students will have to know how to multiply fractions to find the equivalent
measurement of each ingredient needed to make the blueberry muffin recipe.
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The objective for the kindergarten and first grade problem is to understand that a whole
can be divided into equal parts in different ways. The problem focuses on dividing a whole into
halves, fourths, and quarters. The problem introduces the concept of fractions and fraction
terminology to students. The students will be able to find out by doing their own exploration,
how different equal halves and quarters are represented. The problem will stimulate some higher
order thinking about whether or not they can make halves or quarters using different types of
lines other than a straight line.
The objective for the second and third grade problem is the same objective as the focus
problem objective. In contrast to the focus problem, this problem has the students multiplying
fractions using more friendly fractions. In this problem, the students are given four different
measuring cups that are less than one cup. They need to figure out different ways they can use
the smaller measuring cups to equal one cup. The students should multiply the fractions to
figure out how many different ways they can make hot chocolate using the smaller measuring
cups.
In the fourth and fifth grade upper elementary school problem the objective is for the
students to find the equivalent shape using different size pattern blocks. The students will be
given a picture of a flower that is made out of the three different size blocks and will be asked to
use the pattern blocks as manipultives to answer the questions. For example, the students should
recognize that six small green triangle blocks are equal to one large yellow hexagon block. The
problem mostly builds off the kindergarten and first grade problem because the students are
using smaller equal parts to make a whole. In this problem the students are also expanding their
fraction terminology.
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Through the BIM, we have the students exploring different methods in order to solve the
focus problem. The objective for each problem connects and leads up to the objective in the
focus problem, which is multiplying fractions and finding equivalent fractions. Within all of
these problems, the students are explaining their thinking and justifying their answer with
concrete evidenceeither with pictures, using pattern blocks, or any other concept that works
best for them.
Common Core State Standards:
Early Elementary:
Grade 1: Geometry: Reason with shapes and their attributeso CCSS.Math.Content.1.G.A.3 Partition circles and rectangles into two and four
equal shares, describe the shares using the words, halves, fourths, and quarters,
and use the phrases half of, fourth of, and quarter of. Describe the whole as two of,
or four of the shares. Understand for these examples that decomposing into the
more equal shares creates small shares.
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o This standard supports our kindergarten and first grade problem. The problem hasthe students divide the square (the sandwich) into equal halves and fourths. The
problem also introduces students to the fraction terminology halves, fourths, and
quarters. The problem encourages students to state their answers using this
terminology and therefore supports this standard. In the problem the students are
investigating how to cut Lucys sandwich in order to have equal shares and figure
out how many equal cuts can be made in the sandwich.
Middle Elementary:
Grade 3: Numbers and Operations
Fractions: Develop understanding of fractions
as numbers
o CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in specialcases, and compare fractions by reasoning about their size.
o This standard develops an understanding of fractions as numbers and requires anunderstanding of how fractions are equivalent. The problem in our BIM relates to
this standard because it asks for students to compare fractions to find equivalent
fractions by using small measuring cups. The problem also asks for students to
come up with different combinations to make equal measurements.
Upper Elementary:
Grade 4: Numbers and Operations-Fractions: Extend understanding of fractionequivalence and ordering.
o CCSS.Math.Content.4.NF.2 Compare two fractions with different numeratorsand different denominators, e.g., by creating common denominators or
numerators, or by comparing to a benchmark fraction such as
. Recognize that
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comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with symbols >,=,or
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