FAT QUARTERS MP1: MP2: Reason abstractly and quantitatively.

FAT QUARTERS

Standards for Mathematical Practices: 1 & 2

MP1: Make sense of problems and persevere in solving them.
MP2: Reason abstractly and quantitatively.

Math Content Standards: 4.NBT.B.4, 4.NBT.B.5, 4.NBT.B.6, 4.MD.A.1, 4.MD.A.3, 5.NF.A.1, (4.G.A.3, 5.MD. A.1),
ELA Standards: W.4.2

Vignette Title: Fat Quarters
Messy Problem: How many ‘fat quarters’ can I get out of this remnant of fabric?
Presenter: Annie Gajadhar, Small business owner ‘Annie’s Quilt Shoppe’

ACT 1: Creating buzz ACT 1
Teacher introduces the video. For example: “I learned about this interesting problem from
one of our local businesses.”

Teacher shows the video.

Teacher poses engagement questions, as time allows.

Teacher reshows the video.

Teacher generates connection to the proposed problem. For example: “As you think about this problem, what
is the first question that comes to mind? Think/pair/share. Teacher solicits one question, write down with
name of student, and asks “who else finds that question interesting?” and take tally. Continue as time allows.

Teacher shares, “ I love all these question and I hope that we get to answer all of them by the end of the day.
Let’s start by trying to help [name of person highlighted in the video] find an answer to his/her problem.”
Teacher repeats the question.

Teacher asks, “What is your best guess? I am really curious to find out who can guess the closest.”
Think/pair/share. Find the lowest and highest guesses from the students. Record and attach students names.

Teacher asks, “What’s a number it can’t be? Try to be braver than 1,000,0000 and 1.

NOTES:
 TEACHER remains the facilitator rather than the ‘answer-key’ or wizard.

ACT 2: Exploring ACT 2

Teacher asks, “What information Is important here? What do we need to know in
order to solve this problem?” Teacher shows the video again. Students directed to
think/pair/share. Then generate a list of needed information from the class. Again,
teacher notes students’ names beside each student response.

Teacher provides ‘given data’ in response to the list generated by the students. Note: There may be some
needed data that the students have not yet identified. Provide these data points at appropriate time. For other
data, students will be need to research.

Students are tasked to solve the given messy problems.

Teacher circulates and listens to students’ problem-solving discussions and learn more about strategies.

Teacher use can use some of these approaches to redirect students who are experiencing difficulties:
 “Some successful groups are using [name the method – eg. tables]”
 “Do you really want to keep doing this (a specific method) It’s tedious.” Then lead student to a strong
method.

Students share their ‘answers.’

NOTES:
 Teachers remind students that modeling is about taking what little you know and making bigger
conclusions out of it.
 [For some of the Messy problems], the teachers remind students that All our answers will be
different. All our answers will be wrong. Who’s going to be least wrong?

ACT 3: Closing the Loops and Extensions

In no particular order, … ACT 3
Student determine the ‘range’ on their math answers.

Students complete closure activity.

Teacher can pose an extend question or two.

Teacher goes back to list of ‘interesting questions’ students generated in ACT 1, and asks the ‘owner’ of the
question if their question was answered.

Teacher arranges for ‘vignette presenter’ to come and share their ‘solution’ with the students.

Teacher finds out whose ‘best guess’ (from Act 1) is closest to the solution calculated by the ‘expert.’

TEACHER RESOURCES:

Background information

What is a fat quarter?, Could read following books for background, launch, or extension: “Selena and the Bear
Paw Quilt,” “Keeping Quilt,” “Sam Johnson and the Blue Ribbon Quilt,” Quilt samples (real or online)

Explanation of a Fat Quarter- http://quilting.about.com/od/stepbystepquilting/ss/fat_quarters.htm

Vocabulary

Length, Width, Quilt, Fat quarter, Remnant, Bolt of fabric

Sample question to engage students (ACT 1).

 How many of you have a quilt?
 Do you know anyone that has made a quilt?
 Have you ever made a quilt?

What information do we need to solve this problem? (have students develop a list of the things that they need
to know). Sample Questions

 How big is a fat quarter?
 How much fabric did I start with?
 What is the length and width of original bolt?
 How much fabric was sold off of the bolt?
 How much fabric is left?

Sample questions to help students identify needed information
 How would you describe what you are trying to find?
 What information is needed?
 What steps are needed to solve this problem?

Information needed to solve the problem, and sources.

1. Size of a ‘Fat Quarter: Student can find out on-line 18” X 22”
http://quilting.about.com/od/stepbystepquilting/ss/fat_quarters.htm

2. All cotton quilting fabric is 44” wide
3. A new bolt of fabric contents 10 yards. 5 quilters have purchased this fabric:

2 yards,
1 ½ yards
2 yards,
1 ¾ yards
1 yard.

One suggested strategy to solve the problem, with associated standards (ACT 2)

Explore
In order to solve this task, students will need to determine the difference between the original length of fabric
and what has been sold, and then determine how many fat quarters can be cut for the remainder.

How much fabric is there?
Find the difference between the original amount of fabric on the bolt and what has been sold. (4.MD.A.1,
5.NF.A.1, 5.MD. A.1* if the students convert yards to inches)

How many fat quarters?
Find out how many fat quarters fit into the given amount of remaining fabric. (4.MD.A.3) If they multiply
(4.NBT.B.5) If they divide whole number quotients (4.NBT.B.6) If they are adding and subtracting (4.NBT.B.4

Closure activity (ACT 3)

Write a multi-paragraph paper which summarizes the steps you used to solve this problem (W.4.2)

Extensions.

Make a quilt out of paper using lines of symmetry (4.G.A.3