Math 7

Unit 6 Equations

Lesson 6.2  Using a Model to Solve Equations

Getting Started

There are a few things to cover BEFORE we actually get into the lesson.

All of the links below are to simulations based on a pan balance.
This is an incredibly useful idea to use as an analogy for solving equations.
I hope you will use some of these to explore the ideas of the lessons in this unit.
I’ve created a few short video clips to get you started.
Your teacher may have you do some specific explorations using these simulations.

Equality Explorer:  Basics    LINK

Video Tutorial  (Balance A)

Pan Balance Shapes   LINK

Video Tutorial     (Balance B)

Pan Balance Numbers    LINK

Video Tutorial     (Balance C)

Equality Explorer     LINK

Video Tutorial     (Balance D)

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

Solve equations by using a balance scales model and verifying the solution.

TEXT Page 226

Read/Work through the  Focus  section at the top of page 226 in  your textbook.

Explore

Explore an idea or problem.
The exploration provides the background for the ideas presented in the lesson.

TEXT Pages 226 - 227

Read/Work through the  Explore  section on Pages 226 - 227  in your textbook.

You can do this activity on your own.
Do your best to answer the questions, then watch the Video Tutorial for help or to check your answers.

If you have another student to share questions with, great!
Make up some of your own and work on them.
I just did the two examples given in the textbook.

Watch

Video Tutorial

Connect

Connect summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 227

Read/Work through the  Connect  section on Page 227 in your textbook.

Example

The Example will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example

TEXT Page 228

Work through the Example  on Page 228 in your textbook.

Watch

Video Tutorial

Fundamental Principle of Equations  (Unit Summary)

When you solve an equation, remember the balance-scales model.

To preserve equality, always perform the same operation on both sides of the equation.

Using the scale analogy:

• 	We can add the same mass to each side.
(using algebra,  add the same thing to both sides of an equation to maintain equality)

• 	We can subtract the same mass from each side.
(using algebra,  subtract the same thing from both sides of an equation to maintain equality)

•	We can divide each side into the same number of equal groups.
(using algebra,  divide both sides of an equation by the same number to maintain equality)

Later, we will show that:
• 	We can multiply each side by the same number by placing equal groups on each side that match the group already there.
(using algebra,  multiply both sides of an equation by the same number to maintain equality)

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Assessment Focus a question that gives a good example of the kind of question you would be expected to answer after completing the lesson

Take It Further questions offer enrichment and extension.

Notes

Question 6,    I solved the problem, but I didn’t “make up” my own problem.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

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