The document provides lesson objectives and examples for evaluating expressions with variables, solving one-step equations, and finding solutions to equations with two variables. It gives examples of filling in tables with values for expressions and equations. Students are asked to determine solutions to equations and fill in missing values in tables.

1. Chapter 1 Lesson 3 Unknown Locations Copyright 2010 MIND Research Institute For use only by licensed users EE.10 Evaluate an expression for specific values of the variable(s). EE.11 Understand that a solution to an equation is a value or set of values of the variable(s) for which the equation is a true statement. EE.12 Determine if a specific value or set of values is a solution to an equation. EE.16 Solve one-step and multi-step linear equations in one variable. EE.18 Find solutions to equations with two variables. EE.19 Understand that a two-variable linear equation (such as x + y = 6 ) can be used as a formula for determining another number when one number is given.

5. We use letters to show unknown values. What are these letters called?

6. This means that b has an unknown location.

7. 1. Based on the way the following points are marked, which have known locations and which have unknown locations? Check for Understanding 0 is always known. By the way the points are marked, points j and m have known locations, while points k and d have unknown locations.

8. 1 + b is an expression for an unknown location.

9. If 1 + b = 4 , as shown below, what is the value of b ? If b = 2 , as shown below, what is the value of 1 + b ? ?

10. 2. What is the value of 1 + b when b is 1? What about when b is 4? Check for Understanding When b = 1, 1 + b = When b = 4, 1 + b = 5 2

11. Let’s list different possible values of b and 1 + b in a table:

12. What would happen if b is zero? 1 + b would have a value of 1.

13. Here is a table showing some of the values of t and t + 3.

14. What is the value of t ? We know that the value of t + 3 is 5. So it is easy to see that t is equal to 2.

15. Let’s add t = 2 and t + 3 = 5 to the table of values.

16. 3. Fill in the missing values in the table below for k and k + 4: Check for Understanding 5 4 6

17. In symbols, the equation is: 2 + c = d

18. These values form a solution to the equation because they make 2 + c equal to d .

19. These values form a solution to the equation because they make 2 + c equal to d .

20. What about values c = 2 and d = 5? The two expressions are not equal, so c = 2, d = 5 is NOT a solution to the equation 2 + c = d.

21. 4 . Which of the following are solutions to the equation 2 + c = d ? Check for Understanding This is a solution because 2 + 2 = 4. This is not a solution because 2 + 0 does not equal 1. This is a solution because 2 + 0 = 2.

22. When w = 2, what is the value of z that forms a solution? When w = 2, we can replace w with 1 + 1, and we can always replace 3 with 1 + 1 + 1. So, w + 3 is replaced with 1 + 1 + 1 + 1 + 1. Now we can see that when w = 2, then z = 4 is a solution to this equation.

23. 5. Fill in the missing values in the following table of solutions: Check for Understanding w + 3 = 1 + z 6 5 9

24. Multiple Choice Practice 1. When you find a solution to an equation, which of the following happens?

25. Find the Errors The first mistake is in the second row, because 1 + 3 does not equal 3. Either w must change to 0 or n must change to 4. The second mistake is in the fourth row, since 8 + 3 does not equal 12. Either w must change to 9 or n must change to 11.