March 12 After the Test

March 12 After the Test

Answer the question in the chat:

Would you rather be the smartest person in the world or the funniest person in the world?

Open Ended

One thing I did good on the test yesterday is:

One thing I can improve is:

Una cosa que hice bien en la prueba ayer es:

Una cosa que puedo mejorar es:

Danielle walked from her house to several locations in town

X represents "Time" in hours

Y represents "Distance" in miles.

Multiple Choice

Danielle started at (0,0). The next point is (1,2). In the context of this problem, what does that mean?

Danielle empezó en (0,0). El siguiente punto es (1,2). En el contexto de este problema, ¿qué significa eso?

• Danielle started at her house. In 1 hour, she walked 2 miles away from her house.

  
  

  Danielle empezó en su casa. En 1 hora, caminó 2 millas lejos de su casa.

• Danielle started at her house. In 2 hours, she walked 1 mile away from her house.

  
  

  Danielle empezó en su casa. En 2 horas, caminó 1 milla desde su casa.

Multiple Select

Look at the graph between 0<x<1 (when x is between 0 and 1). Which of these correctly describes the graph during that interval?

Mira la gráfica entre 0 <x <1 (cuando x está entre 0 y 1). ¿Cuál de estos describe correctamente la gráfica durante ese intervalo?

• Continuous

• Discrete

• Linear

• Non-linear

• Proportional

The interval between 0<X<1, or between 0 and 1 hour

• It is continuous. This means there is a line connecting points (0,0) and (1,2)

• It is not discrete. That would mean the points (0,0) and (1,2) would just be 2 random unconnected points.

The interval between 0<X<1, or between 0 and 1 hour

• It is linear. That means the line connecting (0,0) and (1,2) is a straight line. It also means that her rate (or speed) was constant, that she did not speed up or slow down.

• It is also proportional. This means that it is linear but also passes through (0,0).

• 
  

The interval between 0<X<1, or between 0 and 1 hour

• When a linear equation is proportional, you can find any y-value by multiplying every x-value by a constant of proportionality. You learned this in 7th grade as Y=kX.

• 
  

Open Ended

In your own words, why is this interval of the graph "linear" and "continuous"?

Fill in the Blank

Danielle went from (0,0) to (1,2).

During this interval, how many miles did Danielle walk in one hour? (Put the number only, no units).

Multiple Choice

Danielle walked 2 miles in 1 hour. How many miles did Danielle walk in 1/2 hour?

• 1/2 mile

• 1 mile

• 2 miles

• 0 miles

Poll

Do you understand why Danielle's speed was 2 miles per hour and why she walked 1 mile every 1/2 hour?

• Yes, and I would like to explain it to the class

• Yes

• Kind of, can you go over it again?

• I'm confused

This is where it gets a little tricky.

in the interval 1<x<2, the line is flat and horizontal.

REMEMBER: Y measures the distance Danielle was from her house. In between 1 hour and 2 hour, that distance stayed the same.

Multiple Choice

Make an inference: In 1 hour, Danielle was 2 miles from her house.

In 2 hours, Danielle was still 2 hours from her house. The line was flat and horizontal the entire time. What does that mean?

• Danielle walked 2 miles during that hour

• Danielle did not move at all during that hour

• Danielle got abducted by aliens during that hour

• Danielle went home during that hour

The flat horizontal line means her DISTANCE from HOME was constant.

Since her distance from home did not change, this means she did not move during that hour; she stayed in the same place!

Multiple Choice

What was Danielle's SPEED between 1 hour and 2 hours?

• 2 miles per hour

• 1 mile per hour

• 1/2 mile per hour

• 0 miles per hour

Another way we could answer that question is finding the slope.

Our coordinates are (1,2) and (2,2).
 $\frac{y2\ -\ y1}{x2\ -\ x1}\ =\ \frac{2-2}{2-1}=\frac{0}{1}=0$  

The slope of this interval is 0. As you learned in science, SLOPE (or rate of change) is another word for speed (distance/time).

A function is a situation where every input has exactly one output.

In a map (see diagram), there should be ONE ARROW coming from each input (number in the left bubble).

As long as each input has exactly one output, it is a function.

Multiple Choice

This map diagram shows a function because

• Every output has exactly one input

• Every input has exactly one output.

Multiple Choice

{(0,-1), (2,5),(-3,-10),(-1,-4),(1,2)}

Does the table in the picture equal the ordered pairs above?

• Yes

• No

Multiple Choice

{(0,-1), (2,5),(-3,-10),(-1,-4),(1,2)}

Does the map in the picture equal the ordered pairs above?

• Yes

• No

Multiple Choice

{(0,-1), (2,5),(-3,-10),(-1,-4),(1,2)}

Does the graph in the picture equal the ordered pairs above?

• Yes

• No

Multiple Choice

{(0,-1), (2,5),(-3,-10),(-1,-4),(1,2)}

Does the equation Y=3X-1 correspond to the ordered pairs above?

• Yes

• No

{(0,-1), (2,5),(-3,-10),(-1,-4),(1,2)}

• Let's examine the equation Y=3X-1.

• (0,-1). 3(0)-1=-1. True

• (2,5). 3(2)-1=5. True

• (-3,-10) . 3(-3)-1=-10. True

• (-1,-4). 3(-1)-1=4. True

• (1,2). 3(1)-1=2. True

Multiple Choice

Cheryl is driving to her grandmother’s house for the weekend. She drives at a constant speed of 60 miles per hour on the freeway

Which of these statements is true?

• After 1 hour, her distance was 60 miles. After 2 hours, her distance was still 60 miles. This is because her speed was "constant".

• After 1 hour, her distance was 60 miles. After 2 hours her distance was 120 miles. This is because her "constant speed" of 60 miles/hour means that every hour, her distance increases by 60 miles.

In science, you learned that rate = distance/time

You also learned that distance = rate x time.

Her rate is 60mph. When we say that rate is "constant", that means she doesn't speed up or slow down.

In science, you learned that distance = rate x times

So if her rate is 60 mph, then her distance will be 60 x (time).

Therefore, in 1 hour, her distance was 60 miles

In 2 hours, her distance was 120 miles

In 3 hours, her distance was 180 miles. And so on.

Multiple Choice

The table shows how many miles Cheryl drove every hour.

Does the table represent a function?

• Yes, because every input (hours) has exactly one output (miles).

• No, because the rate does not change. Every hour, she travels the same number of miles.

This is a function.

Every input (time) has exactly one output (distance)

In 1 hour, the distance was 60 miles. That's all. Nothing else.

In 2 hours, the distance was 120 miles. Nothing else.

Each input times 60 gives you only one answer. Therefore, this is a function.

Multiple Choice

Which of these equations is linear, but also proportional?

• $y=\frac{1}{3}x$

• $y=x^2$

• $y=\left|x\right|$

• $y=2x+11$

Proportional means LINEAR but also passes through (0,0)

• In 7th grade, you learned that every input (x), multiplied by a constant of proportionality (k) = output (y)

• This is written as Y=kX

• For example, Y=3X means every X times 3 = Y.

• So (0,0), (1,3), (2,6), (3,9), (4,12), (-2,-6), (-10,-30) are all part of the proportional relationship Y=3X because every X times 3 = Y.

Proportional means linear but also passes through (0,0)

•  $y=x^2$  is not a linear equation.  (1,1), (2,4), (3,9), (4,16).  The slope will be different between every two ordered pairs.

•  $y=\left|x\right|$  does pass through (0,0) because the absolute value of 0 is 0.  but it is not linear.  If you look  at the pairs, (-2,2), (-1,1), (0,0), (1,1), (2,2).  The y values go down, stop at 0, then go back up.  This is not constant.

•  $y=2x+11$  is linear but not proportional.  The "+11" means that the line passes through (0,11) and not (0,0).

•  $y=\frac{1}{3}x$  is the only choice that follows the format Y=kX, where k is 1/3.

Multiple Choice

Just for fun: Which of these is the nickname for New York State?

• The Garbage State

• The Big Apple

• The Empire State

• The Golden State

Multiple Choice

Just for fun: Also the catchphrase of Stan Lee, this motto of New York State means "keep going higher" in Latin.

• With great power comes great responsibility

• Excelsior

• Hulk Smash

• I'm Batman

Multiple Choice

What is the capital of NY State?

• New York City

• Syracuse

• Albany

• Buffalo Soldier