CHAPTER 9 : EQUATIONS & INEQUALITIES - LESSON 9.1 : EQUATIONS

For today, students are to read through pages 29 through 32 of their textbook. The first part on page 29 should feel like a continuation of what they have just learned in Chapter 8. Help them to understand that the difference between an equation and and expression is that while an expression is just a statement of terms, such as 3x + 2, an equation is a statement of equality between two expressions, such as 3x + 2 = 11. In this case, this statement of equality is only true when the variable x is equal to 3, because 3 * 3 + 2 = 11.

It will get slightly more challenging on the next 2 pages as it involves fractions, but it is all the same concept. Have them work through the examples on pages 30 and 31.

Lastly, on page 32, section B deals with balancing equations. This is an extension of what they will have just learned but is a bit more complex. Focus particularly on the second paragraph where it shows inequalities (3 x 4 does not equal 5 + 8). Now the challenge becomes helping them understand what to add or subtract to make the statements equal. Help them think of it as balancing weights on a scale. Since 12 does not equal 13, right now the weights are uneven. But if we "add more weight" to 12, by adding 1 we now have an equality. We could achieve an equality likewise by subtracting 1 from 13.

For the last 2 paragraphs dealing with multiplication and division, make sure you emphasize the importance of parentheses. The *entire* expression must be multiplied by some number on both sides for it to work. For example, (4 + 2) * 7 = (3 + 3) * 7. That is a true statement. 42 = 42. But 4 + 2 * 7 is NOT equal to 3 + 3 * 7. 18 does not equal 24.

Please let me know if you have any questions. I will be available to respond in the GroupMe, especially between the hours of 9am and 11am.