2. Solving Two Step Equations August 19,2013

3. WELCOME! Math is used in everyday life activities consciously and unconsciously. Objective: The student will solve two step equations using the addition, subtraction, multiplication, and division properties of equality. Students will identify the Commutative and Associative Property. Students will identify the Commutative and Associative Property. All students will be able to solve real-world application: There are 26 students in Ms. Bean's class. The number of boys is equal to seven fewer than twice the number of girls. How many boys and how many girls are in the class?

4. Monday, Aug. 19 Round the decimals to the underlined place value. 1)4.987 2)3.134 3)79.85 4)542.91 5)12.1052 4.99 3.1 80 540 12.105

5. Properties of Math Commutative Properties of Addition and Multiplication For any numbers a and b, a + b = b + a The order in which numbers are added does not change the sum. 9 + 2 = 2 + 9 For any numbers a and b, a * b = b * a The order in which numbers are multiplied does not change the product. 6 * 5 = 5 * 6

6. Properties of Math Associative Properties of Addition and Multiplication For any numbers a, b, and c, (a + b) + c = a + (b + c) The way in which addends are grouped does not change the sum. (5 + 3) + 1 = 5 + (3 + 1) For any numbers a, b and c, (a * b) * c = a * (b * c) The way in which numbers are grouped does not change the product. (2 * 6) * 7 = 2 * (6 * 7)

7. Instruction It takes two steps to solve an equation that has more than one operation. 1.Simplify by using the addition or subtraction property of equality. (use the inverse of addition or subtraction) 2.Simplify further by using the multiplication or division property of equality. (use the inverse of multiplication or division) Consider the problem: 2x-15=5

8. Steps 2x – 15 = 5 +15 +15 Addition Property of Equality +15 +15 Addition Property of Equality 2x = 20 Division Property of Equality 2x = 20 Division Property of Equality 2 2 2 2 x = 10 x = 10

9. Practice Problems Let’s practice these problems as a group – check answers with your table group 11n + 1 = 6711n + 1 = 6711n + 1 = 6711n + 1 = 67 -2y + 4 = 8-2y + 4 = 8-2y + 4 = 8-2y + 4 = 8 5x – 2 = 35x – 2 = 35x – 2 = 35x – 2 = 3

10. Steps 11n + 1 = 67 - 1 - 1 Subtraction Property of Equality - 1 - 1 Subtraction Property of Equality 11n = 66 Division Property of Equality 11n = 66 Division Property of Equality 11 11 11 11 n = 6 n = 6

11. Steps -2y + 4 = 8 - 4 - 4 Subtraction Property of Equality - 4 - 4 Subtraction Property of Equality -2y = 4 Division Property of Equality -2y = 4 Division Property of Equality -2 -2 -2 -2 y = -2 y = -2

12. Steps 5x – 2 = 3 +2 +2 Addition Property of Equality +2 +2 Addition Property of Equality 5x = 5 Division Property of Equality 5x = 5 Division Property of Equality 5 5 5 5 x = 1 x = 1

13. Challenging Practice Problems Practice these problems with your table group 6 – 3y = -36 – 3y = -36 – 3y = -36 – 3y = -3 7 = 4 – 2y7 = 4 – 2y7 = 4 – 2y7 = 4 – 2y 3/2 = 5/2 + 7x3/2 = 5/2 + 7x3/2 = 5/2 + 7x3/2 = 5/2 + 7x

14. Steps 6 – 3y = -3 6 – 3y = -3 -6 -6 Subtraction Property of Equality -3y = -9 Division Property of Equality -3y = -9 Division Property of Equality -3 -3 -3 -3 y = 3 y = 3

15. Steps 7 = 4 – 2y 7 = 4 – 2y -4 -4 Subtraction Property of Equality -4 -4 Subtraction Property of Equality 3 = -2y Division Property of Equality 3 = -2y Division Property of Equality -2 -2 -2 -2 -3/2 = y

16. Steps 3/2 = 5/2 + 7x 3/2 = 5/2 + 7x -5/2 -5/2 Subtraction Property of Equality -2/2 = 7x -1 = 7x Division Property of Equality -1 = 7x Division Property of Equality 7 7 7 7 -1/7 = x

17. Real World Situations There are 26 students in Ms. Bean's class. The number of boys is equal to seven fewer than twice the number of girls. How many boys and how many girls are in the class? You are ordering tulip bulbs from a flowering catalog. The cost is.75 cents per bulb. You have $14 to spend. If the shipping cost is $3 for any size order, determine the number of bulbs you can order.

18. Steps x + 2x – 7 = 26 x is # of girls; 2x-7 is # of boys 3x – 7 = 26 3x – 7 = 26 +7 +7 Addition Property of Equality +7 +7 Addition Property of Equality 3x = 33 Division Property of Equality 3x = 33 Division Property of Equality 3 3 3 3 x = 11 x = 11 So there are 11 girls and 15 boys.

19. Steps.75b + 3 = 14 - 3 - 3 Addition Property of Equality - 3 - 3 Addition Property of Equality.75b = 11 Division Property of Equality.75b = 11 Division Property of Equality.75.75.75.75 b = 14.667 b = 14.667 So you can purchase about 14 bulbs. If you purchase 15 bulbs you will go over your $14 budget.

20. What have you learned!! Math is used in everyday life activities consciously and unconsciously. Objective: The student will solve two step equations using the addition, subtraction, multiplication, and division properties of equality. All students will be able to solve: