Lesson 7E Cafeteria Consumption and Cost Develop Understanding

Learning Focus

Organize data into matrices and use the structure to facilitate computation.

How does your arrangement of the sticky notes facilitate the work of answering Elvira’s questions?

What arrangements of the sticky notes allow for consistency and regularity in doing arithmetic on collections of related data?

Open Up the Math: Launch, Explore, Discuss

Sometimes Elvira hosts after school events in the cafeteria as clubs and teams celebrate their accomplishments. Frequently, she orders too much food for such events—and occasionally not enough food.

Elvira has asked you to help her sort through her records for the past few years, hoping she can better plan on how much food to order for the upcoming soccer team and drama club events. Unfortunately, Elvira kept most of her records on sticky notes, and now everything is out of order. Fortunately, she used a different color sticky note each year, so you have a place to start.

1.

Here is the information you have identified from the past three years for the soccer team and drama club events. The blue sticky notes are from three years ago, the yellow are from two years ago, and the pink are from last year’s events. Organize the data for each year in such a way that it can be combined with similar data from other years.

Blue Sticky Note

Ordered packages of chips for the soccer team.

Way too much!

Yellow Sticky Note

Ordered packages of chips for the soccer team.

Definitely not enough!

Blue Sticky Note

Ordered dozen cookies for the drama club.

Should have ordered more!

Blue Sticky Note

Ordered gallons of drinks for the soccer team.

They poured some on their coach! (big mess)

Pink Sticky Note

Ordered packages of chips for the soccer team.

My neighbor is on the team!

Yellow Sticky Note

Ordered dozen cookies for the drama club.

I really like these kids!

Pink Sticky Note

Ordered packages of chips for the drama club.

They talked a lot with fake accents!

Blue Sticky Note

Ordered gallons of drinks for the drama club.

They talk a lot and seem to get thirsty!

Pink Sticky Note

Ordered dozen cookies for the drama club.

Too much drama, too little character!

Blue Sticky Note

Ordered packages of chips for the drama club.

Needed more!

Pink Sticky Note

Ordered dozen cookies for the soccer team.

Slipped a few extra to my neighbor!

Pink Sticky Note

Ordered gallons of drinks for the soccer team.

Watched the players like a hawk!

Pink Sticky Note

Ordered gallons of drinks for the drama club.

Seemed about right!

Yellow Sticky Note

Ordered gallons of drinks for the soccer team.

Warned them not to repeat last year’s prank!

Yellow Sticky Note

Ordered gallons of drinks for the drama club.

Drinks were gone long before the chips!

Yellow Sticky Note

Ordered dozen cookies for the soccer team.

Should I have ordered more?

Yellow Sticky Note

Ordered packages of chips for the drama club.

Sent extra home with kids!

Blue Sticky Note

Ordered dozen cookies for the soccer team.

Could have ordered more!

2.

You suggest to Elvira that for each event she should order the average amount of each item based on what she has ordered over the past three years. How might you represent this year’s order in a concise, organized way? Describe in detail how you calculated the amount of each item to be ordered for each event so Elvira can follow your description when planning for future events.

3.

Elvira just informed you that the soccer team won the state championship and the drama club took major awards at the Shakespearean Festival competition. Consequently, both groups have decided to allow each member of the team or club to invite three guests to accompany them to their celebration events. Elvira assumes that each of the guests will consume about the same amount of food as the team or club members they accompany. Explain to Elvira how to use your representation of the original amount of food to order from problem 2 to determine the new amount of food to order.

Ready for More?

Elvira can order food from either Main Street Market or Grandpa’s Grocery, and she has given you a list of the prices at each store for each item to be purchased. She would like you to find the total cost of purchasing the recommended amount of food from problem 2 for each event from each store. Elvira knows that for some events it might be best to purchase the food from Main Street Market and for other events it may be better to purchase the food from Grandpa’s Grocery. She also realizes that it is too time consuming to purchase some items from one store and some from another. You will need to keep track of the details of your computations for the total cost so Elvira can use your strategy for future events.

Main Street Market

Grandpa’s Grocery

Cost per package of chips

Cost per dozen cookies

Cost per gallon of drink

Takeaways

Matrices are rectangular arrays of data. Each piece of data in a matrix represents two characteristics, one by virtue of the row it is located in and one by virtue of the column it is in.

Here are my examples of two matrices that can be added:

Matrix

Matrix

Matrices can be added when

Here is a description of how to add matrices, such as matrix and matrix given above:

Matrices can be multiplied by a number when the data needs to be scaled up or down. This is called scalar multiplication.

Here is a description of scalar multiplication, such as multiplying matrix , given above, by a scalar :

Lesson Summary

In the lesson, we examined reasons for organizing data into rectangular arrays or matrices. Each element in a matrix represents two characteristics or quantities, one by virtue of the row it is located in and one by virtue of the column it is in. Consequently, each element has units associated with it that describe both the characteristics of the row and column in which it is located. Paying attention to these units guides the ways we can combine matrices by addition, subtraction, and scalar multiplication.

Retrieval

Use the given equation to create the rule that is missing. Then, fill in the missing values for the tables. Use the explicit rules and equations as a tool to find the values. If you are not given the explicit rule, you might consider creating it to help you with your work.

1.

Given the explicit equation:

Recursive equation:

2.

Given the recursive equation:

Explicit equation:

3.

Arithmetic or geometric?

Recursive:

Explicit:

4.

Arithmetic or geometric?

Recursive:

Explicit: