Big Idea Module Project (BIM)

7/30/2019 Big Idea Module Project (BIM)

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BIM:

Understanding Fractions

ELD 375

Sarah Jacobs

Kelly Collova

Alicia Govannicci


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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


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What measuring cups does Grandma Sally have to use in order

to get the exact measurements she needs to make the recipe?

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:


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Knowing all you have learned previously about fractions, are

there other methods you could have used to figure out the

problem? Describe your answer and show an example of the

other method(s).


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Materials Needed For BIM

Materials:

Muffin problemSandwich worksheetPencilEraserDot paperPattern BlocksPencilScrap paper


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Understanding Fractions:

Halves and Quarters

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 equal pieces.

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.


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How many different ways can Lucys mother cut the sandwich?

Does each way represent equal pieces?

The next day Lucy was wondering if she can cut her sandwich

into four equal pieces called quarters. 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

Middle Elementary School Activity

Grades 2-3


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Harry had some friends over for a day full of sled riding andsnowball 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?

What other measuring cups would be useful?


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What if you needed 2 cups of warm water? Now, how manydifferent kinds of measurements can you use?


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Understanding

Fractions:

Finding Equivalent Fractions

Upper Elementary School Activity

Grades 4-5


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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.

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 StateStandards


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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.

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


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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.

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.


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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.

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 OperationsFractions: Develop understanding of fractionsas numbers

o CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in specialcases, and compare fractions by reasoning about their size.


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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.

oCCSS.Math.Content.4.NF.2

Compare two fractions with different numerators

and different denominators, e.g., by creating common denominators or

numerators, or by comparing to a benchmark fraction such as

. Recognize that

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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o CCSS.Math.Content.6. NS.1Interpret and compute quotients of fractions, andsolve word problems involving division of fractions by fractions, e.g., by using

visual fractions models and equations to represent the problem.

o The focus problem is supported by this sixth grade standard. Students will applyand extend previous understanding of multiplication and division of fractions to

this problem. The problem starts off with Grandma Sally baking breakfast

muffins for her grandchildren. She realizes that she is missing some of the

measuring cups and only has a select few. She needs

cups of flour,

cup of

granulated sugar, and cups of blue berries. Students should recognize that

they will need to multiply or divide the measurements of the given measuring

cups in order to add the correct amount of the ingredients to the recipe.

Documents

Big Idea Module Project (BIM)