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Lesson Plans
The Fourth Quadrant of Proportiona
OverviewProcedure for teachersStudent Resources and Materials
Prep for Teachers
Cue episode 124 of Cyberchase, "Size Me Up," to the appropriate starting point, which is the scene right after the kids fly through a mirror and land in an area surrounded by large rocks, approximately 2 minutes into the episode. Digit says, "Welcome to the 4th Quadrant of Proportiona." Tape a large sheet of butcher paper or drawing paper across a wall of your classroom. Duplicate the image of Digit onto transparency. Use image included or find it at http://pbskids.org/cyberchase/meet_digit.html
Introductory Activity

Explain to your students that the Cyberchase kids have been trapped by Hacker in the Fourth Quadrant of Proportiona, and must find a way out in order to save Motherboard from a virus. The kids must work with the scale and size of things around them in order to escape.

Step 1

Tell your students that they will be watching a video clip from a Cyberchase episode. The characters will be in a world where things appear to be very different from what they are accustomed to seeing.

Step 2

Provide your students with a FOCUS FOR MEDIA INTERACTION, asking your students to identify where the Cyberkids are, what they notice about the place, and how they describe it? PLAY the tape from the scene right after the kids fly through a mirror and land in an area surrounded by large rocks, approximately 2 minutes into the episode. Digit says, "Welcome to the 4th Quadrant of Proportiona." PAUSE the tape when you see Hacker saying, "And tonight, when motherboard opens an email that is addressed from you kids, it will be the last file she ever opens." Check your students' comprehension. Where are the kids? (Answer:4th Quadrant of Proportiona) What do the kids notice about this place? (Answer: The rocks and creatures around them are huge. A bee is compared to an airplane, "something you can fly…") How do the kids describe it? (Answer: "It's like everything has been multiplied in size." Everything is 'so many' times larger. Emphasize the concept of something being so many times larger as relating to multiplication

Step 3

To further illustrate this idea, take a picture of your class, or a picture from the newspaper. Ask your students how the class picture looks. (They will say it looks normal.) Point to a student and ask if the picture is exactly the same as the student in every way? Ask what is different? (Size!) It looks normal because everything in the picture is smaller. Everything in the picture is of the same relative size.

Step 4

Ask students if they can provide examples of things that are different sizes but still look normal to us. (Possible answers: photographs, drawings of real objects or people, billboards, dolls, TV images. postcards)

Step 5

Explain to the students that in order for the Cyberchase kids to defeat Hacker, they have to understand scale, and the relationship that different objects have to one another in terms of size.


Learning Activities

Step 1

Tell the students that the Cyberkids are trying to understand the size of things around them. Matt doesn't have a ruler handy, but he does have a way to measure size and figure out the scale of what's around him. What is his strategy? CUE the video to where Digit is flying ahead of the kids as they run under rocks and past huge plants. Matt says, "Whoa, that is one humongous frog." Divide your students into two groups. Provide students with a FOCUS FOR MEDIA INTERACTION, asking the groups to determine:

Group 1: Digit falls into what he thinks is a muddy hole. What does that turn out to be, and how does he find that out?

Group 2: How does Matt figure out how big the creature might be? What does he use as his measuring tool?

PLAY the video. STOP the video after the giant dog chases them into the house and the kids see the boy at the table with his mom standing next to him. Digit says, "He's the smallest in his class?" Check for comprehension. Ask Group 1 what the hole was that Digit fell into (Answer: It's a giant footprint. Digit only realizes this after he is pulled out of the mud and he flies above it. He can then see the entire footprint from above and understand what it is). Ask Group 2 how Matt figure out how big the creature might be (Answer: Matt walks along the footprint to measure it. It takes 10 of Matt's steps to reach the end of the footprint. The length of the Giant's footprint is measured in terms of Matt's shoe size.) Ask the class where the kids are? (Answer: They are in the Land of the Giants according to Jackie, as the Cyberkids run from the giant dog.)

Step 2

REWIND the tape to the beginning of the clip if necessary. Check the students' answers with the video clip for accuracy.

Step 3

Ask the students to imagine what it might be like to meet a creature whose footprint was 10 times the size of one's sneaker or shoe. Can they give any examples of comparisons?

Step 4

Ask for a student volunteer who will take off a shoe and perform an experiment. Place a large sheet of butcher paper or drawing paper on the wall of the classroom.
Ask the volunteer to mark off ten lengths of their sneaker or shoe in a straight line across the paper, drawing a line after each footprint of the sneaker or shoe is made.

Step 5

Tell your students that now you have a footprint that is ten times the length of the student volunteer's footprint.

Step 6

Take the paper down from the wall and place on the floor to demonstrate size for the students. A student can walk along the foot print to illustrate that the footprint is ten times longer.

Step 7

Explain to the students that in the first part of this episode, the kids are trying to figure out how their size compares to the Giants. Stress the reasoning portion of this rather than referring to rules. Ask, "How does the Giant's height compare to the kids height?" Student should describe this in words like: '"The height of 1 giant is 10 times the kids height."
[Teacher's Note: Students might also say, '"The kids are one-tenth the height of the Giant." Although this is true, kids can become easily confused. To keep it simple and consistent, throughout the lesson we will name the large thing first. (Ex. Giants to kids) Consistency in how the ratio is set up will allow kids to express the ratio in terms of multiples of whole numbers, and will avoid fractions. Initial experience with ratios should be in terms of whole numbers whereas "one-tenth" is confusing.]

As you say these words, write the relationship as a ratio. "So one Giant's height is 10 times the height of the kids."


Write:
Giant's Height      to    Kid's Height
       1            10

or = 1:10

OR

Write:
Giant's Height    =     1 
Kid's Height     10

So the ratio 1 to 10 or scale can be written in fraction form (1/10 or as 1:10).
Stress that this is not read as a fraction '"one-tenth" but rather "1 is to 10" or "1 compared to 10." This terminology reinforces the formal definition that students will encounter: A ratio is a comparison of two numbers. The comparison is by division.

Step 8)

Now they are going to find themselves in a world in which the kids are the giants. Tell students that they will have to determine the new scale in a world in which the kids are now the giants.

Step 9)

CUE the video to where the kids have just been dumped from a boat head first, yelling, into piles of sand. Digit spits out sand and says, "Well, that was one way to get here."
Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to determine what the scale is in this new world. How much larger are the kids than the inhabitants of the world? PLAY the video. PAUSE the video when Jackie says, "Start flying Widge. You can do it." Check for comprehension. Ask students what the scale is in the new world. How does the height of the kids compare to the inhabitants in this new world? Since it takes 10 of the little inhabitants to equal the height of the kids, [Follow the thinking process as before, naming the large thing first.]
"So one of the kid's height equals 10 times the height of the little inhabitants."

Write:
Kids' height       to     Inhabitants' height
      1                    10

or = 1:10

OR

Giant's Height    =      1 
Inhabitants' height         10

Have kids say: "The ratio or scale of the kid's height to the little inhabitants is 1 to 10." In the inhabitants' world, every thing seems normal to them because every thing is in relative size to the inhabitants, and the kids become the giants.

Step 10)

Ask students what objects were used to determine the scale of this miniature world, and to whom their size was compared? (Answer: Boxes were stacked and each box was the same size as Hank, the small character who befriends the kids in this miniature world.) Ask students if they remember how many boxes were used, and how did the scale of this world compared to the Cyberchase kids? (Answer: 9 boxes were used. Each box was Hank's size so 9 boxes plus Hank made a total of 10 boxes. This means that the ratio or scale of 1 of the kids' height is 10 boxes (Hank's height). So it is the same as we stated in

The ratio:
Kids' height   =    1
Inhabitants' world    10


OR 1:10
(said "1 to 10")
 

Step 11)

Ask students if they remember what Digit's Cyberbird miniature is called? (Answer: Widget)
What is the new scale comparing Hank to Widget? Why is there a need for Widget? What is the scale of the opening of the portal to Hank?
(Think: How does Widget's height compare to Hank's? Because it takes 2 Hank's height to equal 1 Widget's height, then Widget's height is 1, and Hank's is 2. The ratio is 1 to 2, or 1/2 . It could also be written 1:2, read, " 1 Widget's height to 2 Hank's height.")




Culminating Activity

Step 1)

Tell students that they will now be applying their knowledge of scale to create a large drawing of Digit that will be the same scale as that used in the episode. Show your students a transparency of Digit taken from the Cyberchase Web site at http://pbskids.org/cyberchase/meet_digit.html or from the image included in this lesson. Tell your students that the picture they create will have to be 10 times the size of the Digit on the transparency.

Step 2)

Tape a large piece of butcher paper to the classroom wall.

Step 3)

Ask for a student volunteer to measure Digit's height as he appears on the transparency. Note: do not project the transparency at this time. Ask the rest of the class how they could determine the height of the new drawing of Digit using string, if he needs to be ten times as large. (Kids should discuss strategies for finding how to determine 10 times Digit's height using the string). Cut the length of string that is ten times larger than Digit's height on the transparency.

Step 4)

Ask for student volunteer to use the string to mark on the butcher paper where the top of Digit's head and the bottom of his feet should be to make the new drawing.

Step 5)

Place the transparency on the overhead projector. Turn on the overhead projector and point it toward the butcher paper. Adjust to projected image of Digit until it fits into the marks on the butcher paper.

Step 6)

Ask another student to trace Digit's outline on the wall, creating a drawing of Digit in a 1:10 scale. Ask kids to explain what this scale or ratio means. Students should make statements like, "The scale 1: 10 means that the height of the projected image is 10 times the height of Digit's image on the transparency." (Again, reinforce to students that you are comparing the large image to the small image."

Step 7)

To check the scale, ask two other students to use a ruler to measure Digit's height in inches on the transparency. Once the students have measured his height in inches on the transparency, announce their findings to the class. Then ask students how many inches the new drawing should be if it is in a 1:10 scale. (Answer will vary.) Ask another student to measure the new drawing in inches. Is the drawing in correct scale? Other Cyberchase characters can be drawn to scale in the same way by repeating the process. Smaller versions of Digit (which can serve as the Widget character) have been provided. Ask what the scale of Digit to the Widget on the upper right of the transparency is. (The scale is 1:2 because Digit is twice the size of Widget on the upper right.) What is the scale of Digit to the Widget on the lower right of the transparency? (The scale is 1:3 because Digit is three times the size of the Widget on the lower right.) Ask students to draw one of the Widget characters provided, maintaining the scale to Digit, using projection and paper.

Step 8)

Ask students to log on to the Cyberchase Web site at http://www.pbskids.org/cyberchase/games/sizeandscale/sizeandscale.html. Students will use their size and scale skills to complete a jigsaw puzzle.
This puzzle is tricky because the pieces are in different scales, and students must get them into the correct proportion by making them smaller or larger.

Step 9)

Show your students how the site works. Ask your students what the buttons at the bottom of the screen mean. (The buttons allow you to "scale up" or "scale down" the puzzle pieces to get them in correct proportion to the puzzle.) Ask your students to try and complete the activity. (Allow some time for this one. It's not as easily as it first appears, but it is fun.) After your students have completed the activity, ask them what strategies they used to complete the puzzle? How was working with the different sizes and scales difficult (Student answers will vary.)

Step 10)

Invite your students to can create new "scaled up" drawings of Cyberchase characters for math bulletin boards, or other original artwork or using transparencies, an overhead projector, and scales of 1:10.



Cross-Curricilar Extensions

Art
Research how scale is used in sculpture. Investigate how scale was used to create monuments such as Mount Rushmore or the Crazy Horse Memorial.

Architecture
Students can draw a scale drawing of their room at home, labeling the room's measurements on the diagram and providing a scale determined by the student.

Social Studies
Ask your students to research maps in different scales. What sort of variety can they find? What is the smallest scaled map they can discover? The largest?


Community Connections
  • Students examine community maps and possibly neighborhood maps to determine scale.

  • Invite a model train enthusiast into your classroom to discuss how scale informs their hobby.

  • Invite an architect into your classroom to discuss how scale informs their work.