Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
MENU
Learning Math Home
Patterns, Functions, and Algebra
 
Session 4 Part A Part B Part C Part D Homework
 
Glossary
Algebra Site Map
Session 4 Materials:
Notes
Solutions
 

A B C D
Homework

Video

Solutions for Session 4, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7 | C8 | C9
C10 | C11 | C12


Problem C1

The "after" Quadperson has the same scale to its facial features; the nose is still four times as wide as it is tall, and so forth.

<< back to Problem C1


 

Problem C2

This "after" Quadperson does not have the same shape as the original. In particular, the nose becomes a flat line, but other features are scaled differently from "before."

<< back to Problem C2


 

Problem C3

Problem C1 is the relative comparison. Think about the angles and measurements in the body; we expect, for example, the head to be a certain fraction of the size of the torso, and so forth.

<< back to Problem C3


 

Problem C4

The change in Problem C1, a relative comparison, keeps these measurements in proportion, while the change in Problem C2, an absolute comparison, does not. In Problem C2, short lengths are made way too short (the nose, for example) by giving an absolute change in length, rather than a proportional change in length.

<< back to Problem C4


 

Problem C5

y1 = x/2.

<< back to Problem C5


 

Problem C6

y2 = x - 1/2.

<< back to Problem C6


 

Problem C7

Both graphs are straight lines. The graph of y1 goes through the origin (0, 0), while the graph of y2 does not. Additionally, the graph of y2 becomes negative if x < 1/2, not a good thing when measuring lengths.

a.

b.

<< back to Problem C7


 

Problem C8

Yes, the graph of y1 is proportional, since the input is always twice the output. Or, the output is half the input. (Compare that to the formula y1 = x / 2.) The graph of y2 is not proportional; try finding the outputs for two different values of x, then determine if they are proportional. This produces the different shape of Quadperson in Problem C2.

<< back to Problem C8


 

Problem C9

Note: Not drawn to the same scale as Quadperson activity

<< back to Problem C9


 

Problem C10

The equation for this table is y3 = 2x.

 

X

 

Y3

1

 

2

2

 

4

3

 

6

4

 

8

5

 

10

6

 

12

 

<< back to Problem C10


 

Problem C11

It is a proportional relationship because every output is twice the input, and if we multiply the input by any number, we multiply the output by the same number. This graph, like the last proportional graph, passes through the origin (0, 0).

<< back to Problem C11


 

Problem C12

All proportional relationships have the equation y = kx, where k is some constant number. A line graph represents a proportional relationship only when the line goes through the origin (0, 0).

<< back to Problem C12


 

Learning Math Home | Algebra Home | Glossary | Map | ©

Session 4: Index | Notes | Solutions | Video

Home | Catalog | About Us | Search | Contact Us | Site Map

  • Follow The Annenberg Learner on Facebook

© Annenberg Foundation 2013. All rights reserved. Privacy Policy