Thursday Homework: Equations worksheet #1 & study for quiz (on fractions, decimals, integers, & order of operations) 1st:Fill out planner 2nd: Get out homework and warm up sheet 3rd: Grab homework sheet 4th: Complete warm up below: −𝟏𝟓+𝟏𝟐 −𝟑𝟏−𝟓 −𝟕𝟐 −𝟗 𝟐𝟎(−𝟏𝟎) 𝟏𝟕.𝟏𝟏 −𝟎.𝟒 −𝟐.𝟒(5.1) −𝟎.𝟐𝟕 ÷(−𝟎.𝟑) Friday

1. Dress code check 2. Go over homework – Trade & Grade 3. Cornell Notes – One Step Equations 5. Practice & Homework

1.1 One-Step Equations Essential Question: How do you solve for a variable in an equation? Encourage participants to take notes on the steps of the CORNELL WAY.

Class Notes 1.1 One-Step Equations Essential Question: How do you solve for a variable in an equation? Class Notes

Equation: math statement that shows one side is = to the other Encourage participants to take notes on the steps of the CORNELL WAY.

7 x 3 Equation: math statement that shows one side is = to the other Variable: Letter that represents a # Coefficient: the number in front of the variable It is a number that is multiplied by a variable in an algebraic expression. 7 x Coefficient Variable A variable by itself has a coefficient of 1 y = 1y Constant: a number by itself 3 Constant

Vocabulary Inverse operations undo each other. Addition & subtraction Or Multiplication & Division If an equation contains addition, solve it by subtracting from both sides to “undo” the addition.

Ex. x + 87 = 152 Encourage participants to take notes on the steps of the CORNELL WAY.

Solve the equation. Check your answer. x + 87 = 152 x + 87 = 152 87 is added to x. – 87 – 87 Subtract 87 from both sides to undo the addition. x = 65 Check x + 87 = 152 Substitute 65 for x in the equation. 65 + 87 = 152 ? 152 = 152 ?  65 is the solution.

Solve the equation. Check your answer. 18 is added to y. –18 –18 Subtract 18 from both sides to undo the addition. 54 = y Check 72 = 18 + y Substitute 54 for y in the equation. 72 = 18 + 54 ? 72 = 72 ?  54 is the solution.

Social Studies Application Johnstown, Cooperstown, and Springfield are located in that order in a straight line along a highway. It is 12 miles from Johnstown to Cooperstown and 95 miles from Johnstown to Springfield. Find the distance d between Cooperstown and Springfield. It is _____ miles from Cooperstown to Springfield. Draw a Picture of map: distance between Johnstown and Springfield distance between Johnstown and Cooperstown distance between Cooperstown and Springfield = + 95 = 12 + d 95 = 12 + d 12 is added to d. –12 –12 Subtract 12 from both sides to undo the addition. 83 = d

Solve y – 23 = 39. Check your answer. 23 is subtracted from y. + 23 + 23 Add 23 to both sides to undo the subtraction. y = 62 Check y – 23 = 39 62 – 23 = 39 ? Substitute 62 for y in the equation. 39 = 39 ?  62 is the solution.

Solve each equation. 1. x + 15 = 72 2. 81 = x + 24 6. Susan is taller than James. The difference in their height is 4 inches. James is 62 inches tall. How tall is Susan? x = 57 x = 57 3. x – 9 = 21 4. 14 = x – 3 x = 30 66 inches x = 17 5. Kaitlin is 2 inches taller than Reba. Reba is 54 inches tall. How tall is Kaitlin? 56 inches

Solving Multiplication Equations Solve the equation. Check your answer. 5p = 75 p is multiplied by 5. 5p = 75 Divide both sides by 5 to undo the multiplication. 5 5 p = 15 Check 5p = 75 5(15)= 75 ? Substitute 15 for p in the equation. 75 = 75 ?  15 is the solution.

Check 16 = 8r Solve the equation. Check your answer. 16 = 8r r is multiplied by 8. 16 = 8r Divide both sides by 8 to undo the multiplication. 8 8 2 = r Check 16 = 8r 16 = 8(2) ? Substitute 2 for r in the equation. 16 = 16 ?  2 is the solution.

Problem Solving Application The area of an iPad is 56 square inches. Its length is 8 inches. What is its width? It’s width is _________inches. w 56 Important information or Draw a picture: 8 Make a plan

Practice Solve each equation. 1. 10y = 300 2. 2y = 82 3. 63 = 9y 4. 78 = 13x y = 30 y = 41 y = 7 x = 6 5. The area of a board game is 468 square inches. Its width is 18 inches. What is the length? 26 inches

Solving Division Equations Solve the equation. Check your answer. x 7 = 5 x is divided by 7. x 7 = 5 7  x 7 = 7  5 Multiply both sides by 7 to undo the division. x = 35 Check x 7 = 5 35 7 = 5 ? Substitute 35 for x in the equation. 5 = 5 ? 35 is the solution. 

Solve the equation. Check your answer. p 6 13 = p is divided by 6. p 6 13 = 6  p 6 6  13 = Multiply both sides by 6 to undo the division. 78 = p Check p 6 13 = ? 78 6 13 = Substitute 78 for p in the equation. 13 = 13 ? 78 is the solution. 

The pine tree is 42 feet tall. Application At Elk Meadows Park an aspen tree is one-third the height of a pine tree. height of pine height of aspen = 3 The aspen tree is 14 feet tall. How tall is the pine tree? Let h represent the height of the pine tree. Substitute 14 for height of aspen. h is divided by 3. h 3 14 = 3  h 3 3  14 = Multiply both sides by 3 to undo the division. 42 = h The pine tree is 42 feet tall.

Jamie’s father weighs 190 pounds. Jamie weighs one-half as much as her father. father’s weight Jamie’s weight = 2 Jamie weighs 95 pounds. How many pounds does her father weigh? Let w represent her father’s weight. Substitute 95 for Jamie’s weight. w is divided by 2. w 2 95 = 2  w 2 2  95 = Multiply both sides by 2 to undo the division. 190 = w Jamie’s father weighs 190 pounds.

Solve each equation. Check your answers. x 10 x = 70 1. = 7 2. 11 = x 4 x = 44 The area of Sherry’s flower garden is one- fourth the area of her vegetable garden. The area of the flower garden is 17 square feet. Let x represent the area of her vegetable garden. Find the area of her vegetable garden. 68 square feet