Math 7

Unit 6 Equations

Lesson 6.3  Solving Equations Involving Integers

Getting Started  (Algebra Tiles 7)

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

We will be using Algebra Tiles for a few lessons this year.

You probably don’t have any physical tiles to work with.

There are lots of websites with Algebra tiles, but many of them are more complicated than we need for this course.

Below is a link to an Algebra Tiles document I created
When you click on the link you will be asked to make a copy of the document.
I did this so you can be confident that you can do whatever you like with the document and KNOW you aren’t doing anything to the original.

LINK

Video Tutorial

Focus

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

Use algebra tiles and inspection to solve equations involving integers.

TEXT Page 231

Read/Work through the  Focus  section at the top of page 231 in  your textbook.
(view the video in the Getting Started section for information on Algebra Tiles)

Explore

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

TEXT Page 231

Read/Work through the  Explore  section on Page 231 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.

NOTE!   For an “Explore” question, this is more complicated than it needs to be!
....and...  if you can do this with tiles,  then you already KNOW the concepts in this lesson!
Do your best, but watch the video for help with this.

Watch

Video Tutorial

Connect

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

TEXT Pages 231 - 233

Read/Work through the  Connect  section on Pages 231 - 233  in your textbook.

Even if you KNOW you are going to watch the video, READING this section is still important.

Getting the same information in multiple ways can help with understanding.

Watch

Video Tutorial

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 Pages 233 - 234

Work through the Example on Pages 233 - 234  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 8,    In this question you are asked to make up your own problems.
If you do, GREAT!   But... if you want to check your work, you can use the examples shown below.
It’s good practice to solve using tiles, and also try to solve by inspection.
a)	x+2=10
b)	x-2=-10
c)	x+5 = -4
d)	x-2 = 4

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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