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Session 6 Part A Part B Part C Homework
 
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Session 6, Part A:
Equality and Balance (30 minutes)

In This Part: Equality | Modeling with Balance Scales

We have been using the equal sign throughout previous sessions. In this part we are going to look at the meaning of equality, which will give us some insight on using equality and its properties to solve equations.
Note 2

Problem A1

Solution  

Examine the following equations. Each equation makes a statement about quantities. Is each statement true always, sometimes, or never? Think about your reasoning for each statement.

a. 

5 + 3 = 8

b. 

2 + 14 = 12

c. 

5 + 3 = y

d. 

x + 3 = y

e. 

3x = 2x + x

f. 

3x = 3x + 1


 

Problem A2

Solution  

If someone asked you to solve the equations in Problem A1, what would the solution sets be?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
The definition of a solution set is helpful here. Consider how many different solutions there are in each solution set.   Close Tip

 

Problem A3

Solution

A chalkboard reads: 10 + 21 = ?

a. 

Replace the "?" with something that makes the equation always true.

b. 

Replace the "?" with something that makes the equation always false.

c. 

Replace the "?" with something that makes the equation sometimes true and sometimes false.


 

Problems in Part A are based on The Partners in Change Handbook: A Professional Development Curriculum in Mathematics, developed under the direction of Principal Investigator Suzanne Chapin at Boston University in 1997. Preparation of the handbook supported by the U.S. Department of Education.

Next > Part A (Continued): Modeling with Balance Scales

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