Wickenburg Unified School District Wickenburg High School

CTE Academic Integration

Culinary Arts/Math Fractions & Conversions

Brooke Walters / CTE Culinary Arts bwalters@wickenburg.k12.az.us Aaron McDowell / Math

amcdowell@wickenburg.k12.az.us

Grade Level Participation: 10-12 Classes: Professional Foods & Culinary Arts

Lesson Description:

During the 2009-2010 school year the WHS students worked to improve their math skills in the Culinary Arts classroom. Fractions seem to be an area of much difficulty for many students. Even though fractions should be mastered at this point for high school students, we have found that many still avoid them or have difficulty working with them. The goal this year was to improve the student’s ability to work with fractions. It was our intention that students would not only be better at understanding fractions, but in addition be better equipped to work with more advanced math concepts where fractions are only a small part of the equation.

Fractions/Rationale

Below are the CTE & Math Standards that were addressed in this project.

S4 – C4 – PO 1 Math Standards:

Use dimensional analysis to keep track of units of measure while converting. Proportional Reasoning. S4 – C4 – PO 4 Solve problems using ration & proportions.

9.8 Differentiate between the basic units of measurement: Standard & metric. Culinary Arts Standards:

Formula to convert metric to standard. Formula to calculate equivalents, quarts to gallons etc. 9.9 Explain areas, weight, volume, mass and density. Calculate area, diameter, circumference etc. 14.3 Perform calculations to increase and decrease formulas. Fraction review – adding/subtracting/multiplying/dividing fractions.

14.6 Utilize weights and measures to demonstrate proper scaling and measurement techniques. Formula to convert pounds to ounces, decimals to fractions etc. 14.20 Explain the principle of food cost and food waste. Calculate percentages, trim loss. 16.6 Apply basic math skills to recipe conversions. Fraction review – adding/subtracting/multiplying/dividing fractions.

At the beginning of the school year the Culinary students completed a unit on “Culinary Math”. During this unit we returned to the basics of adding, subtracting, multiplying and dividing fractions. Worksheet posted below.

Fractions Lesson

Name_______________________________Date_________ Hour____

Part I. Adding & Subtracting Fractions with a common denominator. To add or subtract fractions that have a common denominator, the numerators are added together or subtracted and the solution is placed over the common denominator in the result. Remember to create improper fractions to solve and also make sure you reduce

your answer to the simplest form.

1. ¼ + ¼ = _________________ 6. 7/8 - 5/8 = _______________

2. ¾ - ¼ = _________________ 7. 1 1/8 - 4/8 = _______________

3. 1/8 + 3/8 = ______________ 8. 4 ½ + 12/2 = ________________

4. ½ + 5/2 = ________________ 9. 1/3 + 2/3 = ________________

5. 1 ½ + 4 ½ + ½ = _____________ 10. 1/8 + 3/8 + 2 3/8 = ____________

Part II. Adding & Subtracting fractions with unlike denominators. First you need to create improper fractions where necessary. In order to add or subtract fractions with unlike denominators, the fractions must be rewritten so that they have a common denominator. Do this by finding the lowest common factor and multiply the denominators by this factor until they are the same. After the denominators are the same, finish working the problem..

1. ½ + ¾ = __________ 6. 2 2/3 + 1 ¼ = __________

2. 2/3 + ¾ = __________ 7. 3/8 - ¼ = __________

3. 1 ½ + 2 ¾ = __________ 8. 9/10 + 1/5 = __________

4. 2/3 + ¼ = __________ 9. 7/8 + ¾ = __________

5. 1 ½ - ¼ = __________ 10. 6/10 – 1/5 = __________

Part III. Multiplying Fractions. When multiplying fractions, the numerators and the denominators are multiplied separately. It does not matter if the denominators are common. Begin by converting any mixed numbers to improper fractions. Multiply straight across to get your answer. Remember that a whole number in fraction form is over “1”. 2 = 2/1.

1. ½ X 2/3 = __________ 6. 3 X 5/8 = __________

2. 5/8 X 1/8 = __________ 7. 2 2/3 X 1/8 = __________

3. 1 ½ X 3/8 = __________ 8. 3 ¼ X 1/8 = __________

4. 3 ½ X 2/3 = __________ 9. 4 X 3/8 = __________

5. 5/8 X 2/3 = __________ 10. 1/5 X 2/3 = __________

Part IV. Dividing Fractions When dividing fractions you do not have to create common denominators. First create improper fractions where necessary. Then use the “reciprocal” (upside down fraction) on one of the fractions and multiply as you did in part III. Remember that a whole number in fraction form is over “1”. 2 = 2/1.

1. 7/8 ÷ 2 = ______________________________________________

2. ¾ ÷ 2 = ______________________________________________

3. 1 ½ ÷ 2 = ______________________________________________

4. 3 ¾ ÷ ½ = ______________________________________________

5. 1 1/8 ÷ 2 = ______________________________________________

6. 5 3/8 ÷ 3 = ______________________________________________

7. 6 2/3 ÷ 6 = ______________________________________________

8. 4 1/3 ÷ 1/3 =______________________________________________

9. 4 1/3 ÷ 3 = ______________________________________________

10. 5 ÷ 1/3 = ______________________________________________

For the remainder of the school year the students were required to revisit fractions on a regular basis through the use of the “Recipe Conversion Worksheet” The recipe conversion worksheet (below) was an activity that was assigned before each “lab” (about every week). The students were required to practice their knowledge of fractions during the task of increasing or decreasing the yields of the recipes they were making.

Name ______________________Date ______ Period ____

Recipe Conversion

Use the recipe conversion formula below to increase or decrease the indicated recipe.

Recipe Name: __________________________

Desired yield ÷ Original Yield = recipe conversion factor

__________ ÷ __________ = ___________

Original Yield

Amount

Ingredient Show your work Desired Yield

Amount

This conversion worksheet not only required knowledge of fractions but measurements & equivalents as well.

Future 2010-2011 School year plans/improvements 2010-2011 School Year Plans

At the beginning of the 2010-2011 school year a pre-test will be given to the students enrolled in both the beginning & advanced Culinary Arts courses. The pre-test will determine the present knowledge of each student in the following areas: Adding, Subtracting, Multiplying, Dividing Fractions Determining equivalents using “unit conversion” Increasing/Decreasing recipe yields After determining the level of each student in the Culinary Arts classes, a series of activities will be assigned throughout the school year that will give them practice in the above mentioned areas. Continue with recipe conversion activities Continue with proportional reasoning – converting units Calculate trim loss with percentages Converting decimals, fractions, percentages

While students in the Culinary Arts classes are converting recipe yields they will need to have knowledge of how to convert measurements also. Using the “Unit Conversion” table will be an activity that the students will be assigned many times throughout the year. They will be able to use this concept not only in the Culinary Classroom converting quarts to gallons, but while converting such measurements as inches to miles, degrees Fahrenheit to Celsius, etc.

Equivalents:

At the end of the school year a post-test will be given to determine the effectiveness of the Math/Culinary activities.

Post Test

A survey will be filled out by each of the students to get their opinion on how well the assigned activities helped them.

Survey

Academic Integration – Wickenburg High School – 4/2011

Culinary Arts – Brooke Walters Math – Aaron McDowell Before administering the lessons on fractions in the Professional Foods classes, the students were asked to fill out a survey. The survey asked the students to rate their ability to work with fractions at that particular time. The instruction was administered and then the survey was filled out again by the same students to determine if their comfort level and ability with fractions had increased, stayed the same, or decreased. Below are the results from that survey.

Survey Question

Before Instruction

After Instruction

Rate of Increase/Decrease

I can do fractions in my sleep

7 14 100% increase

I feel pretty good about working with

fractions

18 34 88% increase

I have a little bit of difficulty working

with fractions

34 15 56% decrease

I freak out about fractions and can’t

work with them at all!

12 5 58% decrease

The numbers from the surveys show that…

• There was a 100% increase in the number of students that felt they could do fractions in their sleep.

• There was an 88% increase in the number of students that felt pretty good about working with fractions.

• There was a 56% decrease in the number of students that had a little bit of difficulty working with fractions.

• There was a 58% decrease in the number of students the “freak out” with fractions and couldn’t work with them at all.

An additional survey was given to the same students asking them how they felt after the unit of instruction on fractions was completed. Below are the results of that survey.

I feel no different

I am still lost

I am a little bit better

This unit really helped

24 7 26 16

The numbers from this survey showed that out of the 73 students that completed the survey:

• 31 of the students still felt lost or that they didn’t improve at all.

• 42 of the students felt a little better about fractions or said the instruction really helped them.

• Overall 58% of the students felt they were doing better. Application – “Recipe Conversion” The next step in the fraction unit was to take their knowledge of fractions and apply it to “recipe conversions”. Each student was tested on their ability to increase or decrease recipes using their knowledge of working with fractions. Although a formal survey was not taken after the “recipe conversion” activity/test, the instructor felt that the students were less frustrated and confused about how to work with the fractions and therefore scored better on the final evaluation than they would have without the instruction.