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
Number and Operation Session 8: Rational Numbers and Proportional Reasoning
 
Session 8 Part A Part B Part C Homework
 
Glossary
number Site Map
Session 8 Materials:
Notes
Solutions
 

A B C 
Homework

Video

Solutions for Session 8 Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5


Problem H1

Using the same model as in Problem B3 (d) to divide 3/4 by 2/3, we need to ask, "How many browns (2/3) are there in a blue rod (3/4)?" The answer is 1 1/8, or 9/8:

<< back to Problem H1


 

Problem H2

a. 

The unit is four small rectangles.

b. 

Three small rectangles represent 3/4.

c. 

Some other values the shaded part could represent are 3 1/2 (the unit is six small rectangles), 21 (the unit is one small rectangle), and 10 1/2 (the unit is two small rectangles). Other values are also possible.

<< back to Problem H2


 

Problem H3

The equation will be satisfied when these fractions represent part-part ratios, and we are finding the proportion of the combined group by adding the numerators and denominators.

<< back to Problem H3


 

Problem H4

Changing a 4-by-8 rectangle into a 6-by-6 square shows a greater relative change.

Here is how we know: When a 6-by-6 square becomes a 4-by-8 rectangle, its area changes from 36 square units to 32 square units -- a decrease of four square units. This decrease represents 4/36, or 1/9, of the square's original area.

When a 4-by-8 rectangle becomes a 6-by-6 square, its area changes from 32 square units to 36 square units -- an increase of four square units. This increase represents 4/32, or 1/8, of the rectangle's original area.

Since 1/8 is greater than 1/9, the rectangle showed a greater change.

However, you could also say that in an absolute sense, the change for both was equal, as the area of both the rectangle and the square changed by four square units.

<< back to Problem H4


 

Problem H5

After it decreases 50% in value, the investment would be worth $500. Then, after the 50% increase, it would be worth $750. Solving this involves multiplicative, or relative type of reasoning.

<< back to Problem H5


 

Learning Math Home | Number Home | Glossary | Map | ©

Session 8 | 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