All Things Beautiful: Math on the Menu

Showing posts with label Math on the Menu. Show all posts

Fiesta Time!

As the last project, and a celebration for the end of this math unit, we had a Mexican Fiesta. The boys helped to determine the quantity of food needed and the costs involved. Even though it was a bit hard to determine at times, they got an estimate of the costs.

Using the same prices from the menu we used in the activity, Combination Plates, the boys took orders from the members of our family and wrote each person up their own bills. I took all kinds of pictures, but my video card gave out and they were all lost, so you are going to have to just imagine the boys taking orders and making all those combination plates. : )

We also compared the costs of the actual meal to the menu's and also compared the prices of the menu we used to actual menus from a nearby Mexican restaurant.

source:

GEMS guide, Math on the Menu

La Fiesta Restaurate: Colorful Combinations

Now that the floor plan design has been decided on, our fictional Rosada family is having their restaurant painted before its grand opening. They have consulted with the painters and know that their budget enables them to use four colors At the initial meeting, the painters brought samples in five colors -red, green, blue, yellow and orange. The Rosadas have asked you what four-color combinations are possible with these five colors. The boys dutifully colored in blocks and figured out that there were five possible combinations.

Now add one more color, purple. How many distinct four-color combinations can be made now?

When I asked this question, James immediately said, "Well, it would by five plus five plus five; fifteen combinations." He did not need to do any paperwork to figure out the solution, but he has always been mathematically minded. By contrast, Quentin, struggled with keeping the colors straight, even using paper to work them out. I showed him that he could keep them straight by using some alternative methods for systematically arranging the colors. I told him, for the four-color combinations, to try recording the first three colors red, green, blue) and then, keeping those three colors constant, record the two possible combinations (red, green, blue, yellow and red, green, blue, orange.) Next, following the same orderly procession, link together the next combinations. He quickly found the five combinations and was able to apply

We talked about the impact of one additional color on the number of combinations.

In a math journal, students can write about what strategies they used to solve this problem, using illustrations, diagrams or charts to illustrate and support the explanations.

source:

GEMS guide, Math on the Menu

links:

Math Monday at Love2Learn2day

Combination Plates

The boys had a chance this week to pretend that they were going out to dinner at the Rosada's restaurant. For two combinations, they were given an allowance of $3.75 and for three combinations, they had an allowance of $5.50.

They were given a menu:
Burrito $2.25
Quesadilla $1.25
Enchilada $1.50
Taco $1.50
Chili Relleno $2.00
Tamale $1.75

They had to pick their items and decide how much they would cost and then how much change they would get back, if any.

source:

GEMS guide, Math on the Menu

La Fiesta Restaurante: Designing Floor Plans

La Fiesta Restaurante

The Rosada family has just purchased a new restaurant that is larger than their La Tostada Sabrosa restaurant. Since they are moving into a brand new building, they are excited about creating a floor plan. Your assignment is to assist them by coming up with a plan for them to look at.

The Floor Plan

This is the floor plan. It has windows on two sides, and a corner entrance. The doorway cannot have any objects placed in it. They need to place the kitchen, the bathroom and 11 tables (4 tables that seat up to six people, 4 tables that seat up to four people and 3 tables that seat one or two people.) We discussed determining dimensions, perimeter and area.

The City Codes

There are city building codes that the Rosadas need to follow in the design of their restaurant.

The Kitchen can:

share 2 sides with the perimeter of the restaurant, OR
share 1 side with the perimeter of the restaurant, OR
be freestanding within the restaurant

Bathroom must share one OR both sides with the perimeter of the restaurant
Tables can only have their shortest side touch the perimeter OR tables can be freestanding.
There must be one empty space (square) between any two objects in the restaurant.
Nothing may be placed on the shaded entryway squares.

The Assignments

Students need to able to show how their plans meet all the building codes. If the floor plan passes inspection, they can record their Restaurant Floor Plan. You can also have your student write a persuasive paragraph to the Rosadas explaining why they should choose his plan over any others. Alternatively, they could write in their math journals about what strategies they used to situate the kitchen, bathroom and tables. Did he have to change the strategy as he went along? They need to explain their problem-solving process in detail.

source:

GEMS guide, Math on the Menu

Combination Platters: Making Combo Plates

The Rosada family has had tremendous success selling tostadas at their restaurant and now they want to expand their menu. They want to feature combination plates with a choice from six Mexican dishes: quesadillas, enchiladas, burritos, tamales, tacos and chiles rellenos. They want their customers to be able to choose three different items on their combination plates. The Rosada family wants to know how many combination are possible. Juanita, who is one of their four children, came up with the answer of 18 different combination plates. She used a grid just like you had used. Do you agree or disagree with Juanita's answer?

To answer this question, Quentin made a flip-book. Each third has all six dishes, so he could use them to make all the possible combinations. All he had to do was make sure that he didn't repeat any dishes, because all combinations must have only one serving of each dish. He wrote down the combinations, using abbreviations for each of the dishes, such as Q-T-B for Quesadilla-Tamale-Burrito. He disagreed with Juanita's solution. Do you?

source:

GEMS guide, Math on the Menu

Money Matters: Setting Tostada Prices

The Rosadas decided to sell each of their tostadas for the same price, regardless of the combination of toppings a customer selected Now that the business has been going along successfully they want to know how much each of the different tostadas actually cost to prepare so that they can analyze their profit margin and adjust the cost as necessary. Based on the cost of the ingredients they want to know how much each tostada costs to prepare The based on what the students advise them to do , the Rosadas may need to change their prices.

Last week the boys determined the prices of each tostada, given the cost of the ingredients. This week they calculated the average (or mean) cost. The Rosadas have determined that they sell almost an equal number of each combinations every day. They also let us know that in the restaurant business owners need to charge three times the cost of the ingredients in order to pay for such things as rent utilities, salaries and to make a profit They decided to triple the cost of each tostada combination, add them together and then divide that number by the number of combinations. There are other ways of coming to this average, but their way did work. They came up with the average cost of $3.32, which they wanted to suggest to the Rosadas that they should make the price $3.35 as it is a more usual price. (Rounding down to $3.30 would also be a good answer.) Next week the Rosadas will expand their menu to include combination plates, and will need more help from the boys to figure out what to charge for them.

source:

GEMS guide, Math on the Menu

Money Matters: Tostada Cost Analysis

For the next part of La Tostada Sabrosa math project, the boys learned about averages and why averaging can be useful.

I gave each of the tostada toppings from our last math session a price and had them add them up to get a price for each topping combination.

Olives 35 cents

Lettuce 15 cents

Salsa 25 cents

Cheese 65 cents

Beans 25 cents

Fried Tortilla 10 cents

Quentin learned how to use a calculator for this lesson because he has already worked on adding double digit numbers but he has never worked with a calculator to solve math problems before.

Next I gave them a lesson about averages. I had Quentin measure the hand spans (the distance between the tip of the thumb to the tip of the pinkie, across the hand) of every member of the family using yarn (as we have made non-standardized measurements before) and then measure them using Unifix cubes.

He taped the yarn pieces to a piece of paper and labeled them according to whose hand span it was and how many Unifix cubes long it was.

We then discussed averages. We took the seven numbers from the seven measurements he took and put them in order from the smallest to the largest, repeating numbers if appropriate. We then made observations about the data. I told him that the amount of difference between the smallest number and the largest number is called the range.

I told James and Quentin about the differences between median (number in the center of the data) and mode (the most frequently occurring number or numbers).

Quentin also determined the average by adding all the measurements and dividing by the amount of numbers in the data. This can be done by comparing the cube trains for each measurement, if the student needs a more visual way of doing this. They can then even out the cube trains by taking some cubes off the longer trains and adding them to the shorter trains until most trains are the same length.

James was able to determine the averages of the tostada costs for tostadas with three topping combinations. He estimated that the average was $1.15, and was pleased that his estimate was spot on.

These averages will be used in future math lessons to determine one standard price for the tostadas.

La Tostada Sabrosa

source:

GEMS guide, Math on the Menu

La Tostada Sabrosa

We had tostadas for lunch, too.

I gave my boys the task of helping the (imaginary) Rosada family who are opening a new restaurant, La Tostada Sabrosa (The Delicious Tostada) that will feature, you guessed it, tostadas. The Rosadas plan to offer a choice of five different toppings to go on the fried tortillas, beans, cheese, salsa, lettuce and olives.

I gave Quentin (age 8) the task of figuring out how many combinations could be made if they allowed two different toppings from the choice of five toppings and I gave him paper manipulatives to help him figure it out, and I showed him how to transfer that information to a chart.

I gave James (age 12) the task of figuring out how many combinations could be made if they allowed three different toppings from the choice of five toppings and I gave him just a chart to work with. I let them do it any way they wished this time so that they could make their own organizational discoveries. After they had solved their problems, we discussed any patterns they had noticed. They noticed that each ingredient was used an equal amount of times. We also discussed how it would be easier to determine all the combinations if the ingredients were chosen in a systematic way. We also talked about how it was easier for Quentin to use the paper ingredients than the chart, but how James didn't want to use them because he didn't need them and considered working with the paper manipulatives as an extra, unneeded step.