Activating Prior Knowledge – Notes M4:LSN5 Writing and Solving Linear Equations Activating Prior Knowledge – Notes Transcribe the expression using mathematical symbols. 1. Four less than three times a number 2. Six more than half a number 3. Twelve more than three times a number 4. Twice as large as a number Tie to LO

Learning Objective Today, we will apply knowledge of geometry to writing and solving linear equations. CFU

Concept Development Review M4:LSN5 Writing and Solving Linear Equations Concept Development Review A triangle has three sides and three angles. The three angles always add up to 180˚. A right triangle has a 90˚ angle. CFU

Concept Development Review M4:LSN5 Writing and Solving Linear Equations Concept Development Review Congruent means the same size and shape. CFU

Concept Development Review M4:LSN5 Writing and Solving Linear Equations Concept Development Review Complementary and Supplementary Angles. Angles whose measures add up to 90° are complementary. Angles whose measures add up to 180° are supplementary. CFU

Concept Development Review – Whiteboard M4:LSN5 Writing and Solving Linear Equations Concept Development Review – Whiteboard Goal – get the variable on one side and the number on the other side of the equation in one move. What is the operation/move? x - 9 = 10 2.4x = 12 4.5 = -7+x 𝟏 𝟐 +𝒙=−𝟓 𝟖 𝟗 x = 16 CFU

Concept Development Review – Whiteboard M4:LSN5 Writing and Solving Linear Equations Concept Development Review – Whiteboard Write down the one operation that could be used to get all of x on one side of the equation in one step. 3x + 6 = 5x 10 - x = 2x 𝟓 𝟗 +𝟒𝒙=𝟖𝒙 𝟐 𝟑 x = 8 + 4x CFU

Skill Development/Guided Practice – Notes #1 M4:LSN4 Solving Linear Equations Skill Development/Guided Practice – Notes #1 Solve the linear equation 𝒙+𝟑+𝒙−𝟖+𝒙=𝟓𝟓 for the number x. State the property that justifies your first step and why you chose it. Check ? 𝒙+𝟑+𝒙−𝟖+𝒙=𝟓𝟓 𝒙+𝟑+𝒙−𝟖+𝒙=𝟓𝟓 𝟑𝒙−𝟓=𝟓𝟓 ? 𝟑𝒙−𝟓=𝟓𝟓 CFU

Skill Development/Guided Practice – Notes #2 M4:LSN4 Solving Linear Equations Skill Development/Guided Practice – Notes #2 Solve the linear equation 𝟏 𝟐 𝒙+𝟏𝟎= 𝟏 𝟒 𝒙+𝟓𝟒 for the number x. Check 𝟏 𝟐 𝒙+𝟏𝟎= 𝟏 𝟒 𝒙+𝟓𝟒 𝟏 𝟐 𝒙 = 𝟏 𝟒 𝒙+𝟒𝟒 ? −𝟏𝟎 −𝟏𝟎 𝟏 𝟐 𝒙 = 𝟏 𝟒 𝒙+𝟒𝟒 − 𝟏 𝟒 𝒙 − 𝟏 𝟒 𝒙 𝟏 𝟒 𝒙 =𝟒𝟒 ÷ 𝟏 𝟒 ÷ 𝟏 𝟒 𝒙 =𝟏𝟕𝟔 CFU

Skill Development/Guided Practice – Notes #3 M4:LSN5 Writing and Solving Linear Equations Skill Development/Guided Practice – Notes #3 3. The measure of one angle is ten less than four times the measure of the other angle. The sum of the measures of the two angles is 90˚. Determine the measure of each of the angles. Angle 1: 𝟒𝒙−𝟏𝟎 Angle 2: 𝒙 =𝟐𝟎 𝟒 𝟐𝟎 −𝟏𝟎 =𝟖𝟎−𝟏𝟎 =𝟕𝟎 Check: Equation: 𝟒𝒙−𝟏𝟎+𝒙=𝟗𝟎 𝟕𝟎+𝟐𝟎=𝟗𝟎 𝟓𝒙−𝟏𝟎=𝟗𝟎 +𝟏𝟎 +𝟏𝟎 𝟗𝟎=𝟗𝟎 𝟓𝒙=𝟏𝟎𝟎 ÷𝟓 ÷𝟓 𝒙=𝟐𝟎 CFU

Skill Development/Guided Practice – Notes #4 M4:LSN5 Writing and Solving Linear Equations Skill Development/Guided Practice – Notes #4 4. The angles of a triangle are described as follows: ∠𝐴 𝑖𝑠 𝑡ℎ𝑒 𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑎𝑛𝑔𝑙𝑒, 𝑖𝑡𝑠 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑖𝑠 𝑡𝑤𝑖𝑐𝑒 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐵. 𝑇ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐶 𝑖𝑠 2 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 ℎ𝑎𝑙𝑓 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐵. Find the measures of the three angles. Angle B: Angle A: 𝒙 𝟏 𝟐 𝒙−𝟐 𝟐𝒙 =𝟓𝟐 Angle C: 𝟐(𝟓𝟐) =𝟏𝟎𝟒 𝟏 𝟐 (𝟓𝟐)−𝟐 =𝟐𝟒 Equation: Check: 𝟐𝒙+𝒙+ 𝟏 𝟐 𝒙−𝟐 =𝟏𝟖𝟎 𝟓𝟐+𝟏𝟎𝟒+𝟐𝟒=𝟏𝟖𝟎 𝟑 𝟏 𝟐 𝒙−𝟐=𝟏𝟖𝟎 𝟏𝟓𝟔+𝟐𝟒=𝟏𝟖𝟎 𝟏𝟖𝟎=𝟏𝟖𝟎 𝟕 𝟐 𝒙=𝟏𝟖𝟐 CFU

What does this mean about the two angles? M4:LSN5 Writing and Solving Linear Equations Skill Development/Guided Practice – Notes #5 5. A pair of corresponding angles are described as follows: the measure of one angle is five less than seven times a number and the measure of the other angle is eight more than seven times the number. Are the angles congruent? Why or why not? What does congruent mean? Angle 2: Angle 1: 𝟕𝒙+𝟖 𝟕𝒙−𝟓 ? 𝟕𝒙−𝟓=𝟕𝒙+𝟖 −𝟕𝒙 −𝟕𝒙 −𝟓≠𝟖 What does this mean about the two angles? CFU

Independent Practice – Exit Ticket #1 M4:LSN5 Writing and Solving Linear Equations Independent Practice – Exit Ticket #1 1. Given a right triangle, find the measures of all the angles if one angle is a right angle and the measure of the second angle is six less than seven times the measure of the third angle. Angle 1: Angle 2: Angle 3: CFU

Independent Practice – Exit Ticket #2 M4:LSN5 Writing and Solving Linear Equations Independent Practice – Exit Ticket #2 2. In a right triangle, find the measures of all the angles if one angle is a right angle and the measure of the second angle is six less than seven times the measure of the third angle. Angle 1: Angle 2: Angle 3: CFU

Closure CFU 1. What did we learn today? 2. Why is this important to you? 3. How can you tell if a value of x is a solution to an equation? CFU

Independent Practice CFU Complete handout – show all work. *Use separate piece of paper – for work. CFU