Sarah JacobsKelly CollovaAlicia Govannicci Dr. BulgarELD 375May 2, 2013

Big Idea Module: Understanding Fractions

The activities presented in our group’s 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

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 evidence – either 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 attributes

o 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 has

the 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 Lucy’s 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 special

cases, and compare fractions by reasoning about their size.

o This standard develops an understanding of fractions as numbers and requires an

understanding 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 fraction

equivalence and ordering.

o CCSS.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 12 . Recognize that

comparisons are valid only when the two fractions refer to the same whole.

Record the results of comparisons with symbols >,=,or <, and justify the

conclusions, e.g., using a visual fraction model.

o This standard supports our fourth and fifth grade problem. In this problem we

have the students find equivalent shapes using different size pattern blocks. In the

problem, we encourage the students to provide their answers using greater than,

less than, and equal to symbols to represent if the shapes are equivalent to each.

Middle School (Focus Question):

Grade 6: The Number System: Apply and extend previous understandings of

multiplication and division to divide fractions by fractions.

o CCSS.Math.Content.6. NS.1 – Interpret and compute quotients of fractions, and

solve 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 apply

and 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 23 cups of flour,

12cup of

granulated sugar, and 113 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.