LAUNCH THREE DAY ITINERARY



THREE DAY ITINERARY: MATH READING AND WRITING ANSWER KEY

Day 1

Watch video about Jupiter on OPT

Watch video of the launch on OPT

READ the short article and annotate the text

Decide from your reading: What question are you being asked to answer?

The question I am being asked to answer is:

I am being asked to compare time in seconds and use conversions to find the altitude in miles and kilometers of the rocket launch. I am specifically being asked to find how many minutes after the spaceship launches it will take for the spaceship to reach an orbit altitude at 200 kilometers, by finding a pattern in our data (table) and using that information to convert miles to kilometers and seconds to minutes.

Work on Problem 1.

Part A: fill out the table using the given formula and a calculator

|Elapsed Time (seconds) | Altitude (miles) | Altitude (Kilometers) |

|160 |46 ( x 1.6) = |74 |

|192 |60 ( x 1.6) = |96 |

|268 |81 ( x 1.6) = |130 |

|274 |83 ( x 1.6) = |133 |

|315 |95 ( x 1.6) = |152 |

|319 |97 ( x 1.6) = |155 |

|339 |112 ( x 1.6) = |179 |

Part B: Compare and discuss your results with your partner. If you need to correct any errors, do so. Your teacher will furnish the answers for you to check your work.

Day 2

Watch the video on OPT.

Complete Problem 2: Graph the information from the table you filled out on Day 1.

Complete Problem 3. Convert seconds to minutes using the given formula.

There is 60 seconds in one minute. Therefore the given formula:

Seconds ÷ 60 = number of minutes.

For example:

160 seconds ÷ 60 = about 2.7 minutes (3 minutes rounded)

Converting miles to kilometers:

At an orbit altitude of 200 kilometers:

200 kilometers = 1.6 multiplied by x (miles) :

200 = 1.6x

Divide both sides by 1.6 : (1.6 x ÷ 1.6) = (200 ÷ 1.6):

x = 125 miles

This means that at an altitude of 200 kilometers, this will give us an altitude of 125 miles.

Taking data from our table to find seconds at 200 kilometers:

From our earlier conversion (kilometers to miles): I know that 125 miles will give us an altitude of 200 kilometers.

In dividing time in seconds by the altitude in miles, for example 160 (time in seconds) ÷ 46 (altitude in miles) = 3.4 (rounded to about 3).

This means that the relationship between the time in seconds and the altitude in miles is that you can multiply the altitude in miles by 3 to find your time in seconds.

In order to solve for the amount of seconds needed for an altitude of 125 miles (200 kilometers), I can multiply 125 by 3 to find the amount of time in seconds:

125 x 3 = 375 seconds

This means that at around/ close to 375 seconds, the rocket will be at an orbit altitude of 200 kilometers.

Converting from minutes to seconds: 1 minute = 60 seconds

At 375 seconds, I can convert to minutes by using the following formula:

Seconds ÷ 60 = number of minutes

375 seconds (rounded) ÷ 60 seconds per minute= about 6.2, rounded to 6 minutes

It will take about 6 minutes for the spacecraft to reach an orbit altitude of 200 kilometers.

Compare and discuss your graph with your partner. What patterns do you notice on the graph?

[pic]

If I were to compare time in seconds (x) to altitude in km (y) we have a slope of about:

Slope: Change in y/ change in x:

(96 – 74)/ (192 – 160) = 22/32, which simplifies to 11/16.

This means that for every increase in about 11 kilometers, there is an increase of about 16 seconds.

Taking the data from earlier in the table, I can see that after approximating (rounding) that I can multiply the amount of miles by 3 to find the estimated total elapsed time in seconds. (112 miles x 3 = 336 seconds).

Looking at the graph, when approximating a line through our given plotted points, our line is about at 375- 380 seconds (x axis) when looking at an altitude of 200 kilometers (y axis).

Day 3

Answer the questions using the sentence frame starters. Be sure to use EVIDENCE from your TABLE and GRAPH to explain and to justify your CLAIM using your MATH REASONING.

DAY THREE WRITING

MY CLAIM:

It will take the rocket approximately_6 minutes to reach orbit altitude.

JUSTIFY and EXPLAIN my CLAIM using MATH REASONING and citing EVIDENCE from the patterns I observed on my TABLE and my GRAPH.

From my TABLE I noticed:

In comparing kilometers to miles from our table, when we increase our kilometers by about 3 (133 – 130), we increase our miles by about 2 ( 83 – 81) In comparing seconds to kilometers, as the kilometers increase by about 24 (179 – 155), the seconds increase by about 20 ( 339 – 319). I also noticed that after approximating, I can multiply the amount of miles in my table by 3 to estimate the elapsed time in seconds.

More Simple student friendly response:

From my table I noticed that the altitude I am looking for, 200 kms, is not part of my data.  I can see that it will be more than 339 seconds, which converts to 5.65 minutes. (339 ÷ 60 = 5.65). The time in minutes for the rocket to reach 200 kms will thus be more than 5.65 minutes.

From my GRAPH I noticed:

From my graph I notice that the graph is increasing.  I can look at the x axis, time in seconds, and see that the approximate altitude in kms for 200 is close to 350 seconds, maybe a little bit more, say 360 seconds and divide by 60 secs in one minute, then that would be approximately an estimate of 6 minutes.  My graph shows me that it has to be more than 5.65 minutes, so I think I am correct.

I know my CLAIM is REASONABLE because the patterns showed (from the table and the graph):

Possible Answers:

In looking at the table, I was able to see a pattern of multiplying the altitude in miles by 3 to approximate the elapsed time in seconds. (112 x 3 = 336, which is a close estimate of 339). I was also able to see a slope in my table as the change in y (change in altitude in kilometers) compared to the change in x (change in seconds):

For example: As the kilometers increase by about 24 (155 to 179), the seconds increase by about 20 (319 to 339). If I follow this pattern, I can add 24 to an altitude of 179 to be at 203, which will give me about 360 seconds (adding 20 to 339). 360 seconds represents 6 minutes, (360 ÷ 60 = 6), which is our estimated answer.

More Simple Student Friendly Answer:

From my table I noticed that the altitude I am looking for, 200 kms, is not part of my data.  I can see that it will be more than 339 seconds, which converts to 5.65 minutes. (339 ÷ 60 = 5.65). The time in minutes for the rocket to reach 200 kms will thus be more than 5.65 minutes and on my graph I noticed that when looking at the time in seconds (x axis) it must be more than or around 360 seconds, which is about 6 minutes after dividing 360 by 60 seconds for each minute.

VOCABULARY:

Converting:

Seconds to minutes

Miles to kilometers

Patterns

Estimate/ approximate

Equation

Rounding

Graph

Table

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