## 30 Mar A New Trail Mix Snack for Hiking: A Pearson Square Mixture Activity

**Situation:** AMPED students are expanding their entrepreneur spirit into food production. They have decided to create a new cereal snack mix with a 18% protein content. Below is a listing of the possible ingredients that you can combine to create this mix.

Ingredients | Protein Content | Cost (cents per oz) |

Cheerios | 9% | 17 |

Frosted Flakes | 6% | 15 |

Peanuts | 26% | 14 |

Popcorn | 12% | 60 |

M & M’s | 4% | 22 |

Coco Puffs | 41% | 26 |

Procedure:

As a pair pick 2 of the ingredients above to create your unique snack mix. You will create a 6 ounce bag of a mix with a 18% protein content.

- Show the Pearson Square work here.

- What is ingredient #1?_____________ How many ounces?________

What is ingredient #2?_____________ How many ounces?________

- What is the cost per pound (16 oz) of your snack?

4. Have your teacher initial for shopping approval. ______. After the approval, you can go get the two ingredients and make your mix following the steps below.

- Get a cup.
- Place it on the scale and “zero it out”.
- Using the number of ounces for ingredient #1 from #2 above, add that amount to your cup.
- Pour this into your baggie.
- Repeat “c” for ingredient #2 from #2 above.
- Shake your bag to mix the ingredients.

- Rate your snack taste on the scale.

Bad Good

1 2 3 4 5 6 7 8 9 10

- Describe the texture?

- Is it palatable?

- What could you do to improve the snack taste?

Teacher notes:

Students work in pairs.

Supplies needed: The ingredients can be changed to fit your preferences regarding cost, availability, etc. You will need about 100 ounces of each item for a class of 30 students. In addition, you will want sandwich/zip lock bags & cups (1 per pair of students), scale to measure in ounces.

Percent protein is fairly accurate for Cheerios, Frosted Flakes, Peanuts, and Popcorn. It is not accurate for M & M’s and Coco Puffs. Beware of students with peanut allergies…..you may need to delete peanuts and replace with a different item.

Here is a reprint from AMPED of the Pearson Square method for doing mixture problems

Agri-Business: Solving

Systems of Equations or Pearson Square

Math Standards: A.CED.2; A.CED.3; A.REI.11

CTE Standards: FPP.03.01; FPP.04.01; FPP.04.03

CTE Situation (opener):

When making maple confections the amount of invert sugar will affect the quality of the confection. Invert sugar syrup is a mixture of glucose and fructose; it is obtained by splitting sucrose into these two components. Inverted sugar is sweeter and its products tend to retain moisture and are less prone to crystallization making it valuable to bakers. By measuring the invert sugar and blending different batches of syrup you will get the optimal invert sugar outcome for the confection.

The ideal invert sugar measurement for maple candy is 1%. If we have light syrup that has .5% invert sugars and dark syrup with 2.2% invert sugars. What mixture of light and dark syrup do you need to reach the desired invert sugar level of 1% to make maple candy?

Solution using Pearson Square Method:

The value in the middle of the square (the goal of the mixture) must be intermediate between the two values that are used on the left side of the square. The numbers on the right side of the square are obtained by subtracting diagonally smallest from largest. The denominator is the sum of the numbers on the right side of the square.

Solution using the traditional systems of equations:

Solve the following system of equations:

.5L + 2.2D= 1

L + D= 1

Solution: Answer:

.5L + 2.2D=1 29.4% Dark

__-.5L – .5D= -.5 __ 70.6% Light

1.7D=.5

D=.294

L + .294=1

L=.706