September 11th, 2014 Day 20 xx 7-1 Learning Target – Today I will be able to compare and order integers to determine absolute value Bellringer Lesson Exit Slip Homework – pg. 64 #s 3-15, 64-68  

September 11th, 2014 Day 20 xx 7-2 & 7-3 Learning Target – Today I will be able to compare and order integers to determine absolute value Bellringer Lesson Exit Slip Homework – pg. 64 #s 3-15  

Bellringer - Inequalities 4 ___ 5 6 ___ 6 -5 ___ 5 -1 ___ -2 -10 ___ -11

Vocabulary opposite integer absolute value

The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. Zero is its own opposite. –4 and 4 are opposites –4 4 • • –5–4–3–2–1 0 1 2 3 4 5 Negative integers Positive integers 0 is neither positive nor negative

The integers are the set of whole numbers and their opposites The integers are the set of whole numbers and their opposites. By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet. The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . . Remember!

Graph the integer -7 and its opposite on a number line. Additional Example 1: Graphing Integers and Their Opposites on a Number Line Graph the integer -7 and its opposite on a number line. 7 units 7 units 1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0 The opposite of –7 is 7.

You can compare and order integers by graphing them on a number line You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.

Additional Example 2A: Comparing Integers Using a Number Line Compare the integers. Use < or >. 4 -4 > 1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0 4 is farther to the right than -4, so 4 > -4. The symbol < means “is less than,” and the symbol > means “is greater than.” Remember!

Additional Example 2B: Comparing Integers Using a Number Line Compare the integers. Use < or >. -15 -9 > -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -9 is farther to the right than -15, so -15 < -9.

Additional Example 3: Ordering Integers Using a Number Line. Use a number line to order the integers from least to greatest. –3, 6, –5, 2, 0, –8 1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0 The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

A number’s absolute value is its distance from 0 on a number line A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero.

Additional Example 4A: Finding Absolute Value Use a number line to find each absolute value. |8| 8 units 1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0 8 is 8 units from 0, so |8| = 8.

Additional Example 4B: Finding Absolute Value Use a number line to find each absolute value. |–12| 12 units –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 –12 is 12 units from 0, so |–12| = 12.

Exit Slip SOLVE |27| ___ |-30|

September 11th, 2014 Day 20 xx 8-1 Learning Target – Today I will solve multi-step equations with integers Bellringer Lesson Exit Slip Homework – None  

Bellringer Solve. 1. 3x = 102 2. = 15 3. z – 100 = 21 x = 34 2. = 15 3. z – 100 = 21 4. 1.1 + 5w = 98.6 x = 34 y 15 y = 225 z = 121 w = 19.5

Additional Example 1A: Solving By Subtraction Solve each question. Check each answer. –6 + x = –7 –6 + x = –7 + 6 + 6 Add 6 to both sides to isolate the variable. x = –1 Check –6 + x = –7 –6 + (–1) = –7 ? Substitute –1 for x. –7 = –7 ?  True.

Additional Example 1C: Solving By Addition Solve each equation. Check each answer. y – 9 = –40 y – 9 = –40 + 9 + 9 Add 9 to both sides. y = –31 Check y – 9 = –40 –31 – 9 = –40 ? Substitute –31 for y. –40 = –40 ?  True.

Additional Example 2A: Solving By Multiplication Solve each equation. Check each answer. b –5 = 6 b –5 = 6 b –5 (–5) = (–5)6 Multiply both sides by –5. b = –30

Additional Example 2B: Solving By Division Solve each equation. Check each answer. –400 = 8y –400 = 8y –400 = 8y Divide both sides by 8. 8 8 –50 = y

To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property.

Additional Example 1A: Solving Equations That Contain Like Terms Solve. 8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms. – 4 – 4 Subtract 4 from both sides. 11x = 33 33 11 11x = x = 3

Additional Example 1A Continued Check 8x + 6 + 3x – 2 = 37 8(3) + 6 + 3(3) – 2 = 37 ? Substitute 3 for x. 24 + 6 + 9 – 2 = 37 ? 37 = 37 ? 

Additional Example 1B: Solving Equations That Contain Like Terms Solve. 4(x – 6) + 7 = 11 4(x – 6) + 7 = 11 Distributive Property 4(x) – 4(6) + 7 = 11 Simplify by multiplying: 4(x) = 4x and 4(6) = 24. 4x – 24 + 7 = 11 4x – 17 = 11 + 17 +17 Add 17 to both sides. 4x = 28 Divide both sides by 4. 4 x = 7

September 11th, 2014 Day 20 xx 8-3 Learning Target – Today I will solve one-step equations with integers Bellringer Lesson Exit Slip Homework – pg. 86 #s 18-40 ODD ONLY  

Inverse Property of Addition Words Numbers Algebra The sum of a number and its opposite, or additive inverse, is 0. 3 + (–3) = 0 a + (–a ) = 0

Warm Up Use mental math to find each solution. 1. 7 + y = 15 2. x ÷ 9 = 9 3. 6x = 24 4. x – 12 = 30 y = 8 x = 81 x = 4 x = 42

Additional Example 1A: Solving By Subtraction Solve each question. Check each answer. –6 + x = –7 –6 + x = –7 + 6 + 6 Add 6 to both sides to isolate the variable. x = –1 Check –6 + x = –7 –6 + (–1) = –7 ? Substitute –1 for x. –7 = –7 ?  True.

Additional Example 1C: Solving By Addition Solve each equation. Check each answer. y – 9 = –40 y – 9 = –40 + 9 + 9 Add 9 to both sides. y = –31 Check y – 9 = –40 –31 – 9 = –40 ? Substitute –31 for y. –40 = –40 ?  True.

Additional Example 2A: Solving By Multiplication Solve each equation. Check each answer. b –5 = 6 b –5 = 6 b –5 (–5) = (–5)6 Multiply both sides by –5. b = –30

Additional Example 2A Continued Check b –5 = 6 –30 ? = 6 Substitute –30 for b. – 5 True. 6 = 6  b –5 = 6.

Additional Example 2B: Solving By Division Solve each equation. Check each answer. –400 = 8y –400 = 8y –400 = 8y Divide both sides by 8. 8 8 –50 = y

Additional Example 2B: Solving By Division Check –400 = 8y Substitute –50 for y. ? –400 = 8(–50) True. –400 = –400 

September 11th, 2014 Day 20 xx 8-2 Learning Target – Today I will translate words into numbers, variables and operations Lesson Homework – pg. 77 #s 1-20 EVEN ONLY & 47  

Algebraic Expressions Operation Verbal Expressions Algebraic Expressions • add 3 to a number • a number plus 3 + • the sum of a number and 3 n + 3 • 3 more than a number • a number increased by 3 • subtract 12 from a number • a number minus 12 • the difference of a number and 12 - x – 12 • 12 less than a number • a number decreased by 12 • take away 12 from a number • a number less than 12

Algebraic Expressions Operation Verbal Expressions Algebraic Expressions • 2 times a number • 2 multiplied by a number 2m or 2 • m + • the product of 2 and a number • 6 divided into a number ÷ a 6 ÷ 6 or • a number divided by 6 • the quotient of a number and 6

Additional Example 1: Translating Verbal Expressions into Algebraic Expressions Write each phrase as an algebraic expression. A. the quotient of a number and 4 quotient means “divide” n 4 B. w increased by 5 increased by means “add” w + 5

Additional Example 1: Translating Verbal Expressions into Algebraic Expressions Write each phrase as an algebraic expression. C. the difference of 3 times a number and 7 the difference of 3 times a number and 7 3 • x – 7 3x – 7 D. the quotient of 4 and a number, increased by 10 the quotient of 4 and a number, increased by 10 4 n + 10

When solving real-world problems, you may need to determine the action to know which operation to use. Action Operation Put parts together Add Put equal parts together Multiply Find how much more Subtract Separate into equal parts Divide

Additional Example 2B: Translating Real-World Problems into Algebraic Expressions On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly. The total points include 2 points for each short-answer question. Multiply to put equal parts together. 2q In addition to the points for short-answer questions, the total points included 50 points on the essay. Add to put the parts together: 50 + 2q

Check It Out: Example 2A Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours. You need to put equal parts together. This involves multiplication. 8 units/h · h hours = 8h

Lesson Quiz for Student Response Systems 1. Which of the following is an algebraic expression that represents the phrase ‘15 less than a number’? A. x – 15 B. x + 15 C. 15 – x D. 15x

Lesson Quiz for Student Response Systems 2. Which of the following is an algebraic expression that represents the phrase ‘the product of a number and 36’? A. 36x C. B. D. x + 36 36 x x 36

Lesson Quiz for Student Response Systems 3. Which of the following is an algebraic expression that represents the phrase ‘5 times the sum of y and 17’? A. 5(y + 17) B. y + 17 C. 5y + 17 D. 5(y – 17)

Lesson Quiz for Student Response Systems 4. Which of the following is an algebraic expression that represents the phrase ‘9 less than the product of a number and 7’? A. 7x + 9 B. 7x – 9 C. 9x + 7 D. 9x – 7

Lesson Quiz for Student Response Systems 5. A painter charges $675 for labor and $30 per gallon of paint. Identify an algebraic expression that represents the total cost of painting, if the painter used x gallons of paint. A. 30 + 675x B. 675x C. 675 + 30x D. 30x