Scott P. Raffone
Tomato Sauce: Plotting, Interpolating and Determining Slope
Prior lesson
We will use the marinara sauce matrix to make the "perfect marinara sauce." We will look at all the recipes and decide what we feel is essential and
Summary of Lesson:
This lesson is designed for students to see a real world application of graphing lines. They will create lines from the data that are measuring. We will use this data to show the slope of a line. The slope will either be increasing or a slope of zero. We also hope to show that even though steam is coming out that the water remains at 212
0
F or 100
0
C. Both of the samples reach a maximum temperature. The previous lesson is on plotting points and understanding what the graph looks like. We will have completed what is increasing or decreasing.
Equipment necessary:
°¤
|
Water source
|
°¤
|
Range or heating element
|
°¤
|
Thermometer for each group
|
°¤
|
Pan for each group
|
°¤
|
Agreed upon sauce ingredients (5 cups for each group)
|
Objectives: SWBAT (Students will be able to)…
°¤
|
Document the temperature over time.
|
°¤
|
Predict the graph based on their data.
|
°¤
|
Communicate that the slope of the line relates to the change of the
|
|
|
temperature over time.
|
°¤
|
Communicate that the starting time is time 0.
|
°¤
|
Compare results from the pasta sauce to the results from the water.
|
Warm-up:
The students will be asked to draw lines that increase, decrease and have no change. We will explain independent and dependent variables.
Lesson:
°¤
|
Turn on the range to a common setting and use the same range for all
|
|
|
experiments.
|
°¤
|
Students will combine ingredients to make the "perfect marinara sauce."
|
°¤
|
Students will let it cook and start second experiment.
|
°¤
|
Measure 5 cups of water into a sauce pan given to you.
|
°¤
|
Measure the temperature every minute for 10 minutes for each pan.
|
°¤
|
Make a prediction of what they think the graph will look like in colored pencil.
|
°¤
|
Continue measuring until the water boils. Put a B on the graph at the time
|
|
|
the water boils.
|
°¤
|
Make a second prediction based on what the graph looks like.
|
°¤
|
Measure again for 5 more minutes
|
°¤
|
Answer questions before continuing
|
1.
|
Explain the graph with respect to temperature over time.
|
2.
|
Were there any differences in your predictions?
|
3.
|
Do you think water will get any hotter than 212
0
F or 100
0
C?
|
4.
|
What was the temperature at time 0?
|
5.
|
Explain what happens to the graph up to 212
0
F or 100
0
C?
|
6.
|
What happened to the graph when the water boiled?
|
7.
|
Make a prediction on whether water boils at a higher temperature then tomato sauce.
|
Challenge questions:
8.
|
Why do most recipes call for water at 212
0
F or 100
0
C?
|
9.
|
Does the size of the pan or the range effect the time needed to make the water boil?
|
-
10. Do you think how we define boil will affect our answers?
-
°¤
|
Students will measure five cups of pre-made sauce into a pan.
|
°¤
|
Measure the temperature until the sauce boils. Put a B on the time it takes
|
|
|
to boil.
|
°¤
|
Continue measuring for 5 minutes.
|
°¤
|
Turn off before it burns!
|
°¤
|
Answer questions before continuing
|
-
1.
|
Was your prediction from question 7 correct?
|
2.
|
Did they both start at the same temperature?
|
3.
|
Did they both boil at the same temperature?
|
4.
|
Compare the graphs of the water and sauce with respect to time.
|
Challenge questions:
5.
|
If we started at the same temperature would it take less time, more time of the same time to boil? Explain your reasoning.
|
6.
|
Why do you think sauce boiled at a different temperature?
|
-
-
°¤
|
We will use the first sample to describe a linear equation. We will use the
|
|
|
equation y = mx + b. b would be the place where we started and m is the slope.
|
|
|
Slope is the change in y over the change in x. We increased 15 degrees in 5
|
|
|
minutes. So our slope is 3 degrees per minute.
|
-
1.
|
What is the b in our water data? Sauce data?
|
2.
|
What is the slope in our water data? Sauce data?
|
3.
|
When the water or sauce boils what is our slope?
|
°¤Clean up and hand in your lab report.
Lesson Plan Boiling Pasta
Prior Lesson
We will work on graphing lines using y = mx + b.
Summary of Lesson:
The lesson will discover the truth of an Old Italian cook that says, "We add salt to water to increase the temperature that the pasta boils." Students will boil water again using a similar approach to the sauce comparison lesson plan. They will then document the time and temperature at which time the water boils with and without salt. We will do this experiment a couple of times.
Equipment necessary:
°¤
|
Water source
|
°¤
|
Range or stove top
|
°¤
|
Thermometer for each group
|
°¤
|
Pan for each group
|
°¤
|
strainer
|
°¤
|
Salt
|
°¤
|
pasta
|
Objectives: SWBAT…
°¤
|
Plot the temperature on a graph
|
°¤
|
Predict the graph based on their data after 10 minutes.
|
°¤
|
Communicate that the slope of the line relates to the change of the
|
|
|
temperature over time.
|
°¤
|
Compare their data with the sauce boiling experiment.
|
°¤
|
Write an equation for the water over time.
|
°¤
|
Compare results from the salted water to the results from the water.
|
Warm-up:
Students will graph lines using y = mx + b
Lesson:
°¤
|
Turn on the range to a common temperature and use the same range
|
|
|
for all experiments.
|
°¤
|
Measure 4 cups of water into a sauce pan given to you.
|
°¤
|
Measure the temperature every minute until the water boils for 5 minutes.
|
°¤
|
Add 1 cup of pasta to the water for ten minutes
|
°¤
|
Measure the temperature of the water immediately after the pasta was inserted.
|
°¤
|
After 10 minutes drain the pasta.
|
°¤
|
Answer questions before continuing
|
-
11.
|
What happened to the water when we added pasta? Why
|
12.
|
Do you think water will get any hotter than 212
0
F or
|
|
|
100
0
C after we added the pasta?
|
13.
|
Make a prediction on whether water boils at a higher temperature when
|
|
|
we add 4 teaspoons of salt?
|
14.
|
Taste the pasta and make observations using all 5 senses.
|
-
Challenge questions:
-
15.
|
What do you think would happen to the temperature of the water if we
|
|
|
added 2 cups of pasta?
|
16.
|
What do you think would happen to the temperature of the water if we
|
|
|
started with 20 cups of water?
|
17.
|
Does the ratio of pasta to water make a difference in the boiling process?
|
°¤
|
A second group will repeat the above steps of the experiment with 4
|
|
|
teaspoons of salt.
|
°¤
|
Measure 4 cups of water and 4 teaspoons of salt into a sauce pan given to you.
|
°¤
|
Measure the temperature every minute until the water boils for 5 minutes.
|
°¤
|
Add 1 cup of pasta to the water for 10 minutes.
|
°¤
|
Measure the temperature of the water immediately after the pasta was inserted.
|
°¤
|
Answer questions before continuing
|
7.
|
Did it boil at the same time?
|
8.
|
Did both samples start at the same temperature?
|
9.
|
Did they both boil at the same temperature?
|
-
10. Compare the graphs of the water and salt water. What are similar and
-
____
what is different?
Challenge questions:
-
11. Did both graphs have a common slope prior to boiling?
-
12. Compare the taste of the pasta with salt and without salt? Which was more
-
pleasant?
°¤
|
The third group will repeat the experiment again with 1 cup of salt.
|
°¤
|
Measure 4 cups of water and 1 cup of salt into a sauce pan given to you.
|
°¤
|
Measure the temperature every minute until the water boils for 5 minutes.
|
°¤
|
Add 1 cup of pasta to the water for 10 minutes.
|
°¤
|
Measure the temperature of the water immediately after the pasta was inserted.
|
°¤
|
After 10 minutes drain the pasta.
|
°¤
|
Answer questions before continuing
|
1.
|
Did it boil at the same time as the last two?
|
2.
|
Did they both boil at the same temperature?
|
3.
|
Compare the graphs of the water and 2 salt water experiments. What are similar and what is different?
|
4.
|
Write the equation of each line (up until the boiling point).
|
-
Challenge questions:
-
5.
|
Make some observations on the pasta with 1 cup of salt.
|
6.
|
The question we started with was an Italian woman claimed "adding salt to water increased the temperature at which pasta boils. Is this accurate? Explain.
|
°¤
|
There is truth that salt will raise the temperature that water boils but not enough to make a difference. Too much salt alters the taste of the pasta.
|
°¤
|
Let's start with water at room temperature and add ice. Repeat experiment.
|
°¤
|
Clean up and hand in your lab report.
|
The next lesson:
We will work on the temperature scales.
Lesson Plan Playing with Dough
Prior Lesson
We will discuss the background of the Fahrenheit scale and the Celsius scale. We will convert from Fahrenheit to Celsius and vice versa.
Summary of Lesson:
We will make homemade dough to investigate the formulas of volume. We will solve as many open ended problems regarding surface area and volume.
Equipment necessary
°¤
|
Water source
|
°¤
|
Salt, Flour, Cream of tartar
|
°¤
|
Measuring cups and spoons
|
°¤
|
Butter, olive oil
|
°¤
|
3 types of breads
|
Objectives: SWBAT…
°¤
|
Measure the ingredients
|
°¤
|
Manipulate the dough to find the volume and surface area by shaping it
|
|
|
into cylinders, cubes and rectangular prisms.
|
°¤
|
Compare measurements.
|
°¤
|
Make conjectures.
|
°¤
|
Test conjectures.
|
Warm-up:
We will review the formulas for volume and surface area of cylinders, cubes and rectangular prisms.
Lesson:
°¤
|
Follow the recipe to make dough to play with.
|
°¤
|
Find the surface area and volume of the dough in different shapes.
|
°¤
|
Manipulate the dough into a rectangular prism, measure the length,
|
|
|
width and height.
|
°¤
|
Find the surface area and volume of the dough.
|
°¤
|
Manipulate the dough into a cube, measure the length, width and height.
|
°¤
|
Find the surface area and volume of the dough.
|
°¤
|
Manipulate the dough into a cylinder, measure the length, width and height.
|
°¤
|
Find the surface area and volume of the dough.
|
Challenge questions:
Given a length and a width of a rectangular prism, predict the height.
Given a diameter of a cylinder, predict the height.
Predict the radius of a sphere.
The next lesson:
Students will work on volume and surface area questions in groups.
Lesson Plan Brownies
Prior lesson:
We will be on the common ratios that we use and the visual representations. We will also compare ratios.
Summary of Lesson:
We will bake brownies. We will try to cut the recipe in half and double it using scale factors. We will compare volumes along the way.
Equipment necessary:
°¤
|
Water source
|
°¤
|
Oil, eggs and brownie mix
|
°¤
|
Pans for each group to bake brownies and oil for pans.
|
°¤
|
Measuring cups, oven mitts, mixer
|
°¤
|
Knife to cut brownies, plates
|
Objective:
°¤
|
Students will measure the brownie mix
|
°¤
|
Students will solve for the volume of the brownie mix
|
°¤
|
Students will measure the mass of the brownie mix in grams.
|
°¤
|
Students will compare measurements
|
°¤
|
Students will identify ratios
|
°¤
|
Students will solve problems using ratios
|
Warm-up:
We will work on common ratios to solve basic problems. You must give ½ of your money to the owner. You received $ 100. How much does the owner get? These are simple word problems and we want the students to feel confident at the start. We will also compare ratios (greater than / less than).
Lesson:
°¤
|
Set oven to 350
0
F.
|
°¤
|
Measure the mass of the empty brownie pan on the scale.
|
°¤
|
Look at the recipe on the back and answer the questions before continuing.
|
|
|
1.
|
How much oil do we need if we double the recipe?
|
|
|
2.
|
How many eggs do we need if we double the recipe?
|
|
|
3.
|
How much oil is needed if we cut the recipe in half?
|
°¤
|
Mix the ingredients.
|
°¤
|
Place in pan.
|
°¤
|
Measure the mass of the brownie mix on the scale.
|
°¤
|
Find the volume of the brownie mix uncooked.
|
°¤
|
Bake brownies.
|
°¤
|
Let brownies cool for 15 minutes.
|
°¤
|
Find the volume of the brownie mix cooked.
|
°¤
|
Answer questions before continuing:
|
18.
|
What was the volume of the raw brownie mix?
|
19.
|
What was the volume of the cooked brownie mix?
|
20.
|
What was the ratio of the volume of the cooked brownie mix to the raw
|
|
|
brownie mix?
|
21.
|
What is the mass of the brownie mix before cooking?
|
22.
|
What is the mass of the brownie mix after cooking?
|
23.
|
Did the volume change?
|
24.
|
Did the mass change?
|
Challenge questions:
25.
|
What do you think is happening to make the bread expand?
|
26.
|
Cut out a brownie. Explain why the mass of the brownies did not change
|
|
|
but the volume changed.
|
°¤
|
Students will double the recipe and repeat the process above.
|
-
13.
|
Compare the results in chart.
|
14.
|
Does anything in the chart surprise you?
|
-
°¤
|
Cut the brownies in half.
|
°¤
|
Cut the half in half again.
|
°¤
|
Cut it in half again?
|
°¤
|
What is the ratio of that piece to the total pan of brownie?
|
°¤
|
Enjoy the brownies and share them with your classmates.
|
The next lesson:
We will multiply ratios and solve word problems by multiplying ratios.