#### Transcript In Word Problems Back of WS #2 – Problem #8

th 8 Grade Math 1st Period Nov. 5, 2012 You have 7 min. to complete your Do Now! Quiz • • • • You MUST show your work You may use a calculator You may use your notes You may NOT talk HW Review on 11-7 PowerPoint Warm-Up At Emmit’s Evergreen Farm, the taller trees are braced by wires. A wire extends from 2 feet below the top of a tree to a stake in the ground. What is the tallest tree that can be braced with a 25-foot wire staked 15 feet from the base of the tree? Warm-Up: Answer At Emmit’s Evergreen Farm, the taller trees are braced by wires. A wire extends from 2 feet below the top of a tree to a stake in the ground. What is the tallest tree that can be braced with a 25-foot wire staked 15 feet from the base of the tree? 18 ft Using The Pythagorean Theorem In Word Problems Back of WS #2 – Problem #8: What is the length of the diagonal of a 10 cm by 15 cm rectangle? Draw a picture: Using the Pythagorean Theorem Looking for length of the hypotenuse a2 + b2 = c2 102 + 152 = x2 100 + 225 = x2 325 = x2 325 = 𝑥 2 18.028 ≈ 𝑥 The diagonal of a 10 cm by 15 cm rectangle is approx. 18.028 cm. Using The Pythagorean Theorem In Word Problems Back of WS #2 – Problem #9: The diagonal of a rectangle is 25 in. The width is 15 in. What is the length? Draw a picture: Using the Pythagorean Theorem Looking for length of a leg a2 + b2 = c2 x2 + 152 = 252 x2 + 225 = 625 -225 -225 x2 = 400 𝑥 2 = 400 x = 20 The length of the rectangle is 20 in. You Try! Back of WS #2 – Problems #10-15 • For Problem #15, fill in the following picture: HW • Back of WS #2 – Problems #10-15 • Front of WS #2 – Problems #1-7 (if you haven’t completed it already) • Tomorrow’s Do Now! Quiz will have: – Four Pythagorean Theorem word problems th 8 Grade Math 2nd Period Only Nov. 5, 2012 You have 7 min. to complete your Do Now! Quiz • • • • You MUST show your work You may use a calculator You may use your notes You may NOT talk HW Review on 11-7 PowerPoint No Warm-Up Using The Pythagorean Theorem In Word Problems Back of WS #2 – Problem #8: What is the length of the diagonal of a 10 cm by 15 cm rectangle? Draw a picture: Using the Pythagorean Theorem Looking for length of the hypotenuse a2 + b2 = c2 102 + 152 = x2 100 + 225 = x2 325 = x2 325 = 𝑥 2 18.028 ≈ 𝑥 The diagonal of a 10 cm by 15 cm rectangle is approx. 18.028 cm. Using The Pythagorean Theorem In Word Problems Back of WS #2 – Problem #9: The diagonal of a rectangle is 25 in. The width is 15 in. What is the length? Draw a picture: Using the Pythagorean Theorem Looking for length of a leg a2 + b2 = c2 x2 + 152 = 252 x2 + 225 = 625 -225 -225 x2 = 400 𝑥 2 = 400 x = 20 The length of the rectangle is 20 in. You Try! Back of WS #2 – Problems #10-15 • For Problem #15, fill in the following picture: Remediation: Using Square Roots & Cube Roots to Solve Equations Solve 𝑥 2 = 64. • Option 1: Think, “What squared gives me 64?” – Remember: Squaring is multiplying something by itself 2 times. For example, 52 = 5 ∙ 5. • Option 2: Think, “x is being squared; how do I undo squaring?” • Either way, the answer is 8 = 64. Remediation: Using Square Roots & Cube Roots to Solve Equations Solve 𝑥 2 = 35. • Option 1: Think, “What squared gives me 35?” – However, you can’t square a whole number or a fraction to give you 35. – Use Option 2 instead. • Option 2: Think, “x is being squared; how do I undo squaring?” • The answer is 35. FYI Unless the problems says otherwise: • You may leave irrational answers as square roots in traditional Pythagorean Theorem problems (not word problems). • You should give numerical approximations of irrational answers in Pythagorean Theorem word problems; round to the number of decimal places specified in the directions. Remediation: Using Square Roots & Cube Roots to Solve Equations Solve 𝑥 3 = 64. • Option 1: Think, “What cubed gives me 64?” – Remember: Cubing is multiplying something by itself 3 times. For example, 53 = 5 ∙ 5 ∙ 5. • Option 2: Think, “x is being cubed; how do I undo cubing?” • Either way, the answer is 4 = 3 64. Remediation: Using Square Roots & Cube Roots to Solve Equations Solve 𝑥 3 = 20. • Option 1: Think, “What cubed gives me 20?” – However, you can’t cube a whole number or a fraction to give you 20. – Use Option 2 instead. • Option 2: Think, “x is being cubed; how do I undo cubing?” 3 • The answer is 20. HW • Back of WS #2 – Problems #10-15 • Front of WS #2 – Problems #1-7 (if you haven’t completed it already) • Tomorrow’s Do Now! Quiz will have: – Two equations you need to solve by square rooting or cube rooting – Two Pythagorean Theorem word problems th 8 Grade Math 4th Period Nov. 5, 2012 You have 7 min. to complete your Do Now! Quiz • • • • You MUST show your work You may use a calculator You may use your notes You may NOT talk HW Review on 11-7 PowerPoint Warm-Up At Emmit’s Evergreen Farm, the taller trees are braced by wires. A wire extends from 2 feet below the top of a tree to a stake in the ground. What is the tallest tree that can be braced with a 25-foot wire staked 15 feet from the base of the tree? Warm-Up: Answer At Emmit’s Evergreen Farm, the taller trees are braced by wires. A wire extends from 2 feet below the top of a tree to a stake in the ground. What is the tallest tree that can be braced with a 25-foot wire staked 15 feet from the base of the tree? 18 ft Using The Pythagorean Theorem In Word Problems Back of WS #2 – Problem #8: What is the length of the diagonal of a 10 cm by 15 cm rectangle? Draw a picture: Using the Pythagorean Theorem Looking for length of the hypotenuse a2 + b2 = c2 102 + 152 = x2 100 + 225 = x2 325 = x2 325 = 𝑥 2 18.028 ≈ 𝑥 The diagonal of a 10 cm by 15 cm rectangle is approx. 18.028 cm. Using The Pythagorean Theorem In Word Problems Back of WS #2 – Problem #9: The diagonal of a rectangle is 25 in. The width is 15 in. What is the length? Draw a picture: Using the Pythagorean Theorem Looking for length of a leg a2 + b2 = c2 x2 + 152 = 252 x2 + 225 = 625 -225 -225 x2 = 400 𝑥 2 = 400 x = 20 The length of the rectangle is 20 in. You Try! Back of WS #2 – Problems #10-15 • For Problem #15, fill in the following picture: HW • Back of WS #2 – Problems #10-15 • Front of WS #2 – Problems #1-7 (if you haven’t completed it already) • Tomorrow’s Do Now! Quiz will have: – Four Pythagorean Theorem word problems Common Core Math I 5th Period Nov. 5, 2012 HW Review: How to Estimate a Line of Best Fit • Sketch a straight line that runs as close to as many data points as possible. • Estimate the coordinates of two points on your line, and use them to write your line’s rule (y = mx + b form). – (0, 0) and (6, 2) – 𝑚= ∆𝑦 2−0 = ∆𝑥 6−0 1 𝑥+b 3 – 𝑦= – (0, 0) b = 0 1 3 – 𝑦= 𝑥 2 6 = = 1 3 HW Review: Practice • Sketch a straight line that runs as close to as many data points as possible. • Estimate the coordinates of two points on your line, and use them to write your line’s rule (y = mx + b form). – (0, 50) and (800, 150) – 𝑚= ∆𝑦 150−50 = ∆𝑥 800−0 1 𝑥+b 8 – 𝑦= – (0, 50) b = 50 1 8 – 𝑦 = 𝑥 + 50 = 100 800 = 1 8 No Warm-Up Notes: Using Linear Models to Predict Given that your best fit 1 line is 𝑦 = 𝑥: 3 • What shadow location would you predict when the flag height is 12 feet? 25 feet? – Graphical answers (see right) – Algebraic answers: 𝑦 = 1 12 = 4 3 1 25 1 𝑦 = 25 = =8 3 3 3 Notes: Using Linear Models to Predict Given that your best fit line is 1 𝑦 = 𝑥: 3 • What flag height would locate the flag shadow 6.5 feet from the base of the pole? 10 feet from the base of the pole? – Graphical answers (see right) – Algebraic answers: 6.5 = 1 𝑥 3 6.5 = 3 1 3( 𝑥) 19.5 = x 3 1 3 10 = 𝑥 1 3 10 = 3( 𝑥) 3 30 = x Practice: Using Linear Models to Predict Given that your best fit 1 line is 𝑦 = 𝑥 + 50: 8 • Predict the flight time for westbound flights 1200 miles in distance. • Predict the distance for westbound flights with 12 hours of flight time. Practice: Using Linear Models to Predict Given that your best fit line is 1 𝑦 = 𝑥 + 50: 8 • Use your rule to predict the flight time for westbound flights 1200 miles in distance. – 𝑦= 200 1 8 1200 + 50 = • Use your rule to predict the distance for westbound flights with 12 hours of flight time. – 720 = 5360 1 𝑥 8 + 50 x = CW/HW • CW: "CW/HW: Using Linear Models to Predict"