Math-in-CTE Lesson Plan
Lesson Title: Casing Formula / Lesson #2Author(s): / Phone Number(s): / E-mail Address(es):
Laura Schiers / 435-559-1344 /
Valorie Black / 435-628-5930 /
Occupational Area: Clothing I
CTE Concept(s): Using Casing Formula
Math Concepts: Using Formulas, Addition of Fractions, Finding Common Denominators, Simplify and Change Improper Fractions
Lesson Objective: / Students will be able to use formulas to calculate the width of casing. They will also be able to construct various sizes of casings.
State Standard 6.2: Construct a casing.
Supplies Needed: / Seam Gauges, Variety of Elastic, Same Sized Elastic for Guided Practice, Sample Fabric, Sergers, Sewing Machines, Thread, Worksheets/Activities
The "7 Elements" / Teacher Notes
(and answer key)
1. Introduce the CTE lesson.
Today, we are going to learn how to properly measure a casing. Then you will construct your own casing. You will need to learn and practice using the Casing Formula, which is:
Width of the Elastic Plus 1/4" Plus Seam Allowance
Question: What is a casing?
Question: Does anyone know how to measure for a casing?
Question: Why is it important to measure a casing correctly? What happens if the casing is too narrow or too wide?
Question: Is elastic always the same width?
Where in clothing would you find elastic?
Besides elastic, what else could be threaded through a casing?
We are going to quickly review how to add fractions to help you find the correct width for a casing. / Casing Formula = Elastic Width + 1/4" + Seam Allowance
3. Work through the math example embedded in the CTE lesson.
Introduce the tools needed to create a casing. (Elastic of varying widths, seam gauges, sample fabric.)
Guided Practice:
Using a seam gauge, place the end of the ruler on the top edge of the elastic. Move the sliding marker found in the middle of the seam gauge to the bottom edge of the elastic. The distance from the top edge of your ruler to the sliding marker is the WIDTH measurement of your elastic. Record this measurement in the Guided Practice section of your worksheet. / Hand out the Casing Calculation Worksheet, Seam Gauges and Elastic to each student.
Be sure to hand out the same width elastic (3/4”) to each student for the guided practice section of the activity.
2. Assess students’ math awareness as it relates to the CTE lesson.
What is the width of your elastic?
Raise your hand if you know how to add this measurement to 1/4".
Question: In order to add these fractions, what do we need to find?
Question: What is a denominator?
Question: What is a common denominator?
Question: How do we find a common denominator?
Question: What is an improper fraction?
Question: What is a mixed number?
3. Example:
· Elastic Width = 3/4"
· Seam Allowance = 1/2”
*The most common seam allowance measurements that will be used are 1/4” or 1/2”. However, the math will be the same for any size of seam allowance used. For this example, we will be using a 1/2" seam allowance.
§ Write the formula with the measurements above as follows:
Elastic Width + 1/4" + Seam Allowance = Casing Width
3 + 1 + 1 = Casing Width
4 4 2
§ The denominators are 4 and 2. They each divide into 4 evenly.
§ A method to finding a common denominator for each of these fractions, is to list the multiples of each denominator and find the first number that matches.
§ For example: The multiples of 2 are: 2, 4, 6, 8, etc.
The multiples of 4 are: 4, 8, 12, 16, etc.
§ The first multiple that matches is 4. Therefore, 4 becomes the common denominator of all three fractions.
§ Now that you have found a common denominator, rewrite all three fractions having that common denominator. Multiply the numerator (top number) by the same number that you had to multiply the denominator by to get the common denominator.
3•1 + 1•1 + 1•2 = 2 + 1 + 4 = 7 or 3
4•1 4•1 2•2 4 4 4
· Add the numerators and keep your common denominator.
· If you get a fraction that can be reduced or simplified, remember to write the simplified fraction as your answer.
· Remember to reduce or simplify the fraction, divide both the numerator and the denominator by the same number, which will be a common factor.
For Example: 2 ÷ 2 = 1
8 ÷2 4
· To change an improper fraction to a mixed number, you divide the numerator by the denominator. (Remember, an improper fraction is a fraction in which the numerator is greater than the denominator.)
For Example: 13 13 ÷ 8 = 1 with 5 left over
8
Therefore, 1 is your whole number, and 5 is the numerator and 8 is still the denominator. Your answer is 1 5/8.
We have worked through the fist problem in the Guided Practice together. Now, work through the second problem in the Guided Practice on your own. All of the fractions have a common denominator. All you have to do is add the numerators and keep 4 as your denominator. / Answer: We need to find the common denominator to add fractions together.
Answer: A denominator is the bottom number of a fraction.
Answer: Two fractions that have the same denominator or bottom number.
Answer: Look at your two fractions and find a number that both denominators divide into evenly.
Answer: The numerator of the fraction is greater than the denominator of the fraction.
Answer: A mixed number has a whole number part and a fraction part. Like 2 and 1/2, or 1 and 3/4.
Some students will say 2. However, 2 divides into both numbers evenly. We are looking for a number that both numbers divide into evenly. Therefore, the number we would use is 4, not 2.
This answer (1 3/4”) is the answer to the Guided Practice problem on the worksheet.
Because each student has the same width of elastic, they should all have the same answer at the end of the guided practice.
The answer for the second problem of the Guided Practice is 1 1/4”.
4. Work through related, contextual math-in-CTE examples.
Begin working through the problems on the Casing Calculation Worksheet. / Walk around the room while students are working and answer any questions or provide extra support and information. Stop and check for understanding periodically while the students are working.
As you check for understanding, ask specific questions of individual students, for example:
What is the common denominator of this problem?
What are the multiples of the two denominators?
What is the numerator of this problem?
What do you do with the numerators?
How do you change this improper fraction to a mixed number?
5. Work through traditional math examples.
Continue working through the problems on the Casings Calculation Worksheet.
The problems at the bottom of the page will give you more practice adding fractions. You will also get more practice working with improper fractions and mixed numbers. This is the way you will see them in your math class, but now you can see that they can also be used here as well. / Walk around the room while students are working and answer any questions or provide extra support and information. Stop and check for understanding periodically while the students are working.
6. Students demonstrate their understanding.
Now that you know how to use the formula to measure the correct width for a casing, we are going to construct a casing in your sample book.
Obtain all materials and supplies needed, (listed on the casing instructions sheet in the sample book.) Prepare your fabric sample.
Using the instructions in your sample book, prepare your sewing machine on the correct machine settings.
Remember to record and show your work when you use the formula to determine the width of your casing. / Hand out sample book instructions for the casing sample if students do not already have a sample book. Provide materials need to complete the sample: elastic, fabric squares, sergers
7. Formal assessment.
The assessment will be an evaluation of the width of each students’ casing after they are made. After the casing is sewn, it will be measured according to the formula.
Possible Assessment Questions:
Question: What is the casing formula?
Question: If I have a piece of elastic that is 5/8” wide and I want a 1/2” seam allowance, how wide does my casing need to be in order for the elastic to fit properly? / Use a seam gauge to measure and check that the buttonhole lengths are correct in relation to the size of the button.
Answer: Elastic Width + 1/4" + Seam Allowance = Casing Width
Answer: 1 3/8”
NOTES: