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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Big Idea Module (BIM)

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