Grade 8 The Pythagorean Theorem


 Jason Johnson
 4 years ago
 Views:
Transcription
1 THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 The Pythagorean Theorem 8.G.68 Student Pages
2 Grade 8  Lesson 1 Introductory Task Introductory Task Prerequisite Competencies 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 =p and x 3 =p, where p is positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the is irrational Introductory Task 1. To estimate the weight, in pounds, of a large fish, fishermen square the girth, multiply by the length, divide by 800, and then add 1/10 of that number. What is the weight of the tarpon below? Girth = 47 in. 6 ft 6 in Page 2 of 21
3 Grade 8  Lesson 1 Guided Practice Guided Practice 1) Ignoring air resistance, the distance d in feet an object falls in t seconds is. The Sears tower is 1,450 ft tall. If a window washer at the top of the tower drops his squeegee, about how much time passes before the squeegee hits the sidewalk below? Find the square roots of each number. 2) 49 3) 900 4) 5) 6) 7) Moesha has 196 pepper plants that she wants to form in square formation. How many pepper plants should she plant in each row? Determine whether each statement is sometimes, always, or never true. Explain or give a counter example to support your answer. 8) The ycoordinate of a point in quadrant II is negative 9) The xcoordinate of a point on the yaxis is zero 10) In quadrants I and III, the xcoordinate of a point is positive Page 3 of 21
4 Grade 8  Lesson 1 Collaborative Work 1) Graph and connect the points (3,2), (2,2), (2,7) (3,7) and (3,2) in order. Then graph and connect the points(3, 2), (2,2), (2,7), (3,7) and (3,2) in order. How are these two figures related? 2) Marika had to draw ABC that fit several requirements a. It must fit in the box shown b. The end points of have coordinates A(2,0) and B(2,0) c. Point C must be on the yaxis and its ycoordinate an integer Name all the points that could be point C O ) The area of a square postage stamp is. What is the side length of the stamp? 4) The formula represents the distance in miles d you can see from h feet above ground. On the London Eye Ferris Wheel, you are 450 ft above ground. To the nearest tenth of a mile, how far can you see? 5) A student evaluated the expression and got the answer 5. What error did the student make? 6) A tile is shown at the right. The area of the larger square is 49 Find the area of the smaller square. 2in 2in 2in Journal Question 2in Explain how an ordered pair locates a point in the coordinate plane. Page 4 of 21
5 Grade 8  Lesson 1 Homework PROBLEM SOLVING 1) John bought a bag of lawn fertilizer that will cover 400 square feet. What are the dimensions of the largest square plot of lawn that the bag of fertilizer will cover? 2) The time t in seconds for an object dropped from a height of h feet to hit the ground is given by the formula nearest tenth. How long will it take an object dropped from a height of 500 feet to hit the ground? Round to the 3) A cardboard envelope for a compact disc is a square with an area of square centimeters. What are the dimensions of the envelope? Skill Practice Plot the following points on the coordinate grid. 4) (4,5) 5) (3,4) 6) (5,0) 7) (0,3) O Page 5 of 21
6 Grade 8  Lesson 2 Introductory Task 8.G.6Explain a proof of the Pythagorean Theorem and its converse Introductory Task Each leg of the right triangle on the left below has a length of 1 unit. Suppose you draw squares on the hypotenuse and legs of the triangle, as shown on the right. How are the areas of the three squares related? For each row of the table: Draw a right triangle with the given leg lengths on dot paper Draw a square on each side of the triangle Find the areas of the squares and record the results in the table. Length of Leg 1 (units) Length of Leg 2 (units) Area of Square on Leg 1 (square units) Area of Square on Leg 2 (square units) Area of Square on Hypotenuse (square units) For each triangle, look for a relationship among the areas of the three squares. Make a conjecture about the areas of squares drawn on the sides of any right triangle 2. Draw a right triangle with side lengths that are different than those given in the table. Use your triangle to test your conjecture from question 1. Page 6 of 21
7 Grade 8  Lesson 2 Guided Practice Guided Practice: 1) Different students came up with different ways to show how the Pythagorean Theorem is true. Can you explain how each works? 2) Find the missing leg length. If necessary, round to the nearest tenth. a) R b) c) B 24 in S 7 in 8 cm R 4 in S T T 3) Find the missing 15 cm leg length. a and b represent D the lengths of the two legs and c represents the length of the hypotenuse. If necessary, round to the nearest tenth. 1) a= 7, b=24 b) a=11, b=14 c) a=18, b=22 6 in. L 4) A ramp is 1 ft high. The base of the ramp extends 14 ft along the side of a building. How long is the sloped part of the ramp to the nearest hundredth of a foot? 5) An architect drew the sketch of a bridge shown below. The Bridge has 12ftlong horizontal members and 24ftlong vertical members. What is the length in feet of each diagonal member? Round to the nearest foot. 24 ft 12 ft. Page 7 of 21
8 Grade 8  Lesson 2 Collaborative Work Collaborative Work 1) To the right is a student s representation of the Pythagorean Theorem, explain how it works. 2) Find the perimeter of a right triangle with legs of 6 cm and 8 cm. 3) The television is measured by the diagonal dimension of its screen. For example, a 24in. television has a diagonal measure of 24in. a. A television screen is 16 in. high and 22 in wide. What is its diagonal dimension to the nearest integer? b. Find the dimensions of a television screen with the same diagonal measure as the one in part (a) but with a different height and width 4) Two hikers start a trip from a camp walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of a kilometer, how far is the waterfall from the camp? 5) A stair case is 20 ft. high. The horizontal distance from one end of the stair case to other end is 24 ft. What is the distance from the top of the stair case to the bottom of the stair case? Round to the nearest foot 6) A book is leaning with one end at the top edge of a bookend. The bookend is 6 in. high. The distance along the shelf from the edge of the book to the bottom of the bookend is 4in. How long is the book? Round to the nearest inch 7) Sarah walks across a rectangular field as shown. What is the distance she walks? path 40 ft 60 ft 8) A circus performer walks on a tightrope 25 feet above the ground. The tightrope is supported by two beams and two support cables. If the distance between each beam and the base of its support cable is 15 ft, what is the length of the support cable? Round to the nearest foot. Journal Question: 9) Explain how you find the distance AB across the lake at the right. Then find AB to the nearest foot. 100 ft 50 ft A 200 ft B Page 8 of 21
9 Grade 8  Lesson 2 Homework 1) A baseball diamond is really a square 90 feet on a side. How far is second base from home plate? 2) Three right triangles surround a shaded triangle; together they form a rectangle measuring 12 units by 14 units. The figure below shows some of the dimensions but is not drawn to scale. Is the shaded triangle a right triangle? Explain how you found your answer. 3) Explain how the picture below represents the Pythagorean Theorem. Skill Building Find the length of the hypotenuse of each triangle; a and b represent the lengths of the two legs. If necessary, round to the nearest tenth. 4) a= 3, b= 4 5) a=9, b=12 6) a=6, b=4 7) a=11, b=14 Page 9 of 21
10 Grade 8  Lesson 3 Introductory Task 8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. Introductory Task 1) Doug is shipping a 32inch long umbrella. Will the umbrella fit in a box that is 24 inches long, 18inches wide and 16 inches tall? 16 in. 24 in. 18 in. Page 10 of 21
11 Grade 8  Lesson 3 Guided Practice Guided Practice 1) The hypotenuse of right triangle is 20.2 ft long. One leg is 12.6 ft long. Find the length of the other leg to the nearest tenth. 2) The bottom of an 18ft ladder is 5ft from the side of a house. Find the distance from to the top of the ladder to the ground. Round to the nearest tenth. 3) An artist is measuring a rectangular canvas. Its length is 30 in. The distance from one corner of the canvas to the other (along the diagonal) is 34 in. What is its width? 4) Stephen is constructing a ramp to test his model car. The ramp is a triangular prism. The wood costs $3.12 per square meter. (1 m 2 =10,000 cm 2 ). How much does the wood cost? Find the length of the hypotenuse for the right triangle Find the surface area of the ramp. Convert to square meters What is the total cost of the wood? 20 cm 24 cm 45 cm Page 11 of 21
12 Grade 8  Lesson 3 Collaborative Work Collaborative Work: 1) A diver swims 20m under the water to the anchor of buoy that is 10m below the surface of the water. On the surfaces, how far is the buoy located from the place where the diver started? Round to the nearest meter. 2) Gillian is building a portable pet ramp with the dimensions shown on the right. She wants to cover all the faces of the ramp with carpet, which costs $1.59 per square foot (1 square foot = 144 square inches). How much does the carpeting cost? 14 in 18 in 48 in 3) The top of the badminton net is 5ft high. Ropes connect the top of each pole to stakes in the ground. The ropes are 8.5 feet long. What is the distance from the stake to the base of the pole? 4) You stand at the edge of a 4m high diving platform. A beach ball is exactly 8 m from the base of the platform. To the nearest tenth of a meter, what is the distance d from the top of the platform to the beach ball? 5) Will a pen that is 14 cm long fit into a 3cm by 4cm by 12 cm box? 6) Satellites that relay television signals to Earth cruise at a distance of about 22,200 miles above Earth s surface. The radius of Earth is about 4,000 miles above Earth s surface. The radius of the Earth is about 4,000 miles. Find the distance a from the satellite to point T in the diagram below. Round to the nearest hundred miles. T a 22,200 mi 4,000 mi Earth Journal Question: 1) One leg of a right triangle is 3 cm and the hypotenuse is 4 cm. A student evaluates to find the length of the other leg. What error did the student make? Page 12 of 21
13 Grade 8  Lesson 3 Homework 1) A tree forms a right angle with the ground. If you place the base of a 12ft ladder 3 ft from the tree, how high up the tree will it reach? 2) A jogger runs around the city park shown below. Her friend cuts through the park on a diagonal. In miles far does each jogger run on a fivelap jog? Start/Finish Jogger s Path 500 ft Friend s Path Both 1,000 ft 3) The hypotenuse of a right triangle is 5 cm. The lengths of both legs are equal. Find the lengths of the legs. Round to the nearest tenth. 4) A computer screen has a diagonal length of 17 in and a height of 9 in. To the nearest tenth, what is the area of the screen? 5) A 10ftlong slide is attached to a deck that is 5 ft high. Find the distance from the bottom of the deck to the bottom of the slide to the nearest tenth. Skills Practice Find the length of the diagonal. 8 cm 12 cm 24 cm 8 cm 10 cm 10 cm 10 cm 10 cm 9 cm Page 13 of 21
14 Grade 8  Lesson 4 Introductory Task 8.G.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system Introductory Task The library is 5 miles north of your house. The post office is 6 miles east of your house. To the nearest mile, how far is the library from the post office? Hint: Use the coordinate plane below to map the location of the post office and the library Page 14 of 21
15 Grade 8  Lesson 4 Guided Practice Guided Practice 1) On the coordinate grid plot and label the points below: A (2,4), B (2,1), and C (3, 1). Find the length of the hypotenuse to the nearest tenth ) On a graph, the points (4, 2), (7,2), (9, 5), and (2, 5) are connected in order to form a trapezoid. To the nearest tenth, what is its perimeter 3) A softball diamond has a shape of a square. The distance from home plate to second base is about 85 ft. Find the distance a player would run going from first base to second base. 4) Your school is 3 miles south of your house. The general store is 5 miles east of your school. To the nearest mile, how far is your house from the general store? Page 15 of 21
16 Grade 8  Lesson 4 Collaborative Work 1) Scott, a freshman at Michigan State University, needs to walk from his dorm room in Wilson Hall to his math class in Wells Hall. Normally, he walks 500 meters east and 600 meters north along the sidewalks, but today he is running late, so he decides to take the shortest possible route through the Tundra. a. How many meters long is Scott s shortcut? b. How much shorter is the shortcut than Scott s usual route? 2) Mrs. Kidd likes to invite the neighbors for a cookout and then hid the food in various places around the backyard. Guests start at the center of the yard and the follow her clues to find their food. Here is one set of clues: Meat at (3,3). Vegetables at (5,12). Beverages at (5,12). All Measurements are in yards. What is the distance in yards from the meat to the vegetables? 3) Tom is looking at a map of Great Adventures. The map is laid out in a coordinate system. Tom is at (2,3). The roller coaster is at (7,8) and the water ride is at (9,1). Is Tom closer to the roller coaster or the water ride? 4) Jade has crashlanded in the desert. There is village nearby, but Jade does not know the direction. Jade comes up with a cunning plan. She decides to fill up a water bottle from the plane, and to take a compass. Jade decides to walk east, south, west, north. in a pattern. Jade s plan is mapped below on the coordinate grid: N W E S = 1 square mile Jade knows he will find the village no matter what direction it is in, and can (hopefully) find his way back to the plane for fresh water and shade when he needs it. But he needs to know, at the end of each stage: How far he walked altogether. How far (in a straight line) back to the plane. Page 16 of 21
17 Journal Question List 3 coordinate pairs that are 5 units away from the origin in the first quadrant. Describe how to find the points and justify your reasoning (Note: Points on the axes are not in the quadrant) Page 17 of 21
18 Grade 8  Lesson 4 Homework PROBLEM SOLVING 1) Town A is 90 miles due South of Town B, and 18 miles due East of Town C. Smith Road goes directly from Town B to Town C. Sketch the route and find the length of Smith Road. 2) Using the Pythagorean Theorem, find the distance between (4,2) and (7,10) 3) April is an avid chess player. She sets up a coordinate system on her chess board so she can record the position of the pieces during a game. In a recent game, April noted that her king was at (4,2) at the same time that her opponent s king was at (7,8). How far apart were the two kings? Round to the nearest tenth of a unit if necessary. 4) The coordinates of points A,B, and C are (5,4), (2,1) and (4,4), respectively. Which point, B or C, is closer to point A 5) Corey makes a map of his favorite park, using a coordinate system with the units of yards. The old oak tree is at position (4,8) and the granite boulder is at position (3,7). How far apart are the old oak tree and the granite boulder? Round to the nearest tenth if necessary. SKILL BUILDING Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth if necessary. 6) (3,0), (3,2) 7) (4,3), (2,1) 8) (0,2), (5,2) O O O Page 18 of 21
19 Grade 8  Lesson 5 Golden Problem Golden Problem A juice box has a base of 6 cm by 8 cm and a height of 12 cm. A straw is inserted into a hole in the center of the top. The straw must stick out 2 cm so you can drink from it. If the straw must be long enough to touch each bottom corner of the box, what is the minimum length the straw must be? (Assume the diameter of the straw is 0 for the mathematical model.) You must show all your work and state a clear explanation. Include a sketch of the juice box labeling the dimensions. Page 19 of 21
20 Golden Problem Rubric: 3Point Response The student uses the Pythagorean Theorem to successfully find the minimum length the straw must be AND The student sketch is 100% accurate. 2Point Response The student shows correct work but does not provide the correct answer. OR The student commits a significant error but provides a correct response based on their incorrect work with clear explanations. OR The student provides the correct response and shows correct work but fails to provide clear explanations for each part. 1Point Response The student only begins to provide a solution 0Point Response The response demonstrates insufficient understanding of the problem s essential mathematical concepts. The procedures, if any, contain major errors. There may be no explanation of the required solutions, or the explanation may not be understandable. How decisions were made may not be readily understandable. OR The student shows no work or justification. Page 20 of 21
21 New Vocabulary Coordinate plane A coordinate plane is formed by the intersection of a horizontal number line called the xaxis and a vertical number line called the yaxis Irrational Number An irrational number is a number that cannot be written as the ratio of two integers. Ordered Pair An ordered pair identifies the locations of a point. The xcoordinate shows a point s position left or right from the origin. The y coordinate shows a points position up or down from the origin Perfect Square A perfect square is a number that is the square of an integer Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs (a and b) is square to the square of the length of the hypotenuse. Quadrants The x and y axes divide the coordinate plane into four regions called quadrants Square roots The square root of a number is a number that when multiplied by itself is equal to the original number. Page 21 of 21
Grade 8. The Pythagorean Theorem 8.G COMMON CORE STATE STANDARDS ALIGNED MODULES
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 The Pythagorean Theorem 8.G.68 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES NEWARK PUBLIC SCHOOLS Office of Mathematics Math Tasks 8.G.68
More informationSquare Roots and the Pythagorean Theorem
UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4digit number with different digits. 3078 2. Find the greatest
More informationLesson 6.1 Skills Practice
Lesson 6.1 Skills Practice Name Date Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Vocabulary Match each definition to its corresponding term. 1. A mathematical statement
More informationSquares and Square Roots Algebra 11.1
Squares and Square Roots Algebra 11.1 To square a number, multiply the number by itself. Practice: Solve. 1. 1. 0.6. (9) 4. 10 11 Squares and Square Roots are Inverse Operations. If =y then is a square
More informationThe Pythagorean Theorem is used in many careers on a regular basis. Construction
Applying the Pythagorean Theorem Lesson 2.5 The Pythagorean Theorem is used in many careers on a regular basis. Construction workers and cabinet makers use the Pythagorean Theorem to determine lengths
More informationPythagorean Theorem. 2.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem... 45
Pythagorean Theorem What is the distance from the Earth to the Moon? Don't let drawings or even photos fool you. A lot of them can be misleading, making the Moon appear closer than it really is, which
More informationStudents apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.
Student Outcomes Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions. Lesson Notes It is recommended that students have access to a calculator as they work
More informationACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula
ACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula Activity 141: Simplifying Radicals In this chapter, radicals are going
More informationThe Pythagorean Theorem 8.6.C
? LESSON 8.1 The Pythagorean Theorem ESSENTIAL QUESTION Expressions, equations, and relationships 8.6.C Use models and diagrams to explain the Pythagorean Theorem. 8.7.C Use the Pythagorean Theorem...
More informationWrite an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. 1. How far up the tree is the cat?
Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. 1. How far up the tree is the cat? Notice that the distance from the bottom of the ladder
More informationUNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet
Name Period Date UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet 24.1 The Pythagorean Theorem Explore the Pythagorean theorem numerically, algebraically, and geometrically. Understand a proof
More informationRepresenting Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array.
1.1 Student book page 4 Representing Square Numbers You will need counters a calculator Use materials to represent square numbers. A. Calculate the number of counters in this square array. 5 5 25 number
More informationCatty Corner. Side Lengths in Two and. Three Dimensions
Catty Corner Side Lengths in Two and 4 Three Dimensions WARM UP A 1. Imagine that the rectangular solid is a room. An ant is on the floor situated at point A. Describe the shortest path the ant can crawl
More informationPart I Multiple Choice
Oregon Focus on Lines and Angles Block 3 Practice Test ~ The Pythagorean Theorem Name Period Date Long/Short Term Learning Targets MA.MS.08.ALT.05: I can understand and apply the Pythagorean Theorem. MA.MS.08.AST.05.1:
More information1. 1 Square Numbers and Area Models (pp. 610)
Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 610) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is
More informationLesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
More informationWhirlygigs for Sale! Rotating TwoDimensional Figures through Space. LESSON 4.1 Skills Practice. Vocabulary. Problem Set
LESSON.1 Skills Practice Name Date Whirlygigs for Sale! Rotating TwoDimensional Figures through Space Vocabulary Describe the term in your own words. 1. disc Problem Set Write the name of the solid figure
More informationPythagorean Theorem Unit
Pythagorean Theorem Unit TEKS covered: ~ Square roots and modeling square roots, 8.1(C); 7.1(C) ~ Real number system, 8.1(A), 8.1(C); 7.1(A) ~ Pythagorean Theorem and Pythagorean Theorem Applications,
More informationName Date. Chapter 15 Final Review
Name Date Chapter 15 Final Review Tell whether the events are independent or dependent. Explain. 9) You spin a spinner twice. First Spin: You spin a 2. Second Spin: You spin an odd number. 10) Your committee
More informationName Date. Chapter 15 Final Review
Name Date Chapter 15 Final Review Tell whether the events are independent or dependent. Explain. 9) You spin a spinner twice. First Spin: You spin a 2. Second Spin: You spin an odd number. 10) Your committee
More information6.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Can That Be Right? 6.3 Pythagoras to the Rescue
Pythagorean Theorem What is the distance from the Earth to the Moon? Don't let drawings or even photos fool you. A lot of them can be misleading, making the Moon appear closer than it really is, which
More informationHow can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.
Common Core Standard: 8.G.6, 8.G.7 How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.2 What Is Special
More informationLength and area Block 1 Student Activity Sheet
Block 1 Student Activity Sheet 1. Write the area and perimeter formulas for each shape. 2. What does each of the variables in these formulas represent? 3. How is the area of a square related to the area
More informationStudent Instruction Sheet: Unit 4 Lesson 1. Pythagorean Theorem
Student Instruction Sheet: Unit 4 Lesson 1 Suggested time: 75 minutes Pythagorean Theorem What s important in this lesson: In this lesson you will learn the Pythagorean Theorem and how to apply the theorem
More informationA natural number is called a perfect cube if it is the cube of some. some natural number.
A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n 2, then m is a perfect square where m and n are natural numbers. A natural number is called a perfect
More informationRead each question carefully and fill in the bubble with the letter of the correct answer or answers on your answer sheet.
Student Class Date Read each question carefully and fill in the bubble with the letter of the correct answer or answers on your answer sheet. 1.1.1 Gina is traveling to the beach 20 miles away from her
More informationHonors Geometry Summer Math Packet
Honors Geometry Summer Math Packet Dear students, The problems in this packet will give you a chance to practice geometryrelated skills from Grades 6 and 7. Do your best to complete each problem so that
More informationArea and Perimeter. Practice 1 Area of a Rectangle. Find the area of each figure. Example. oneinch squares.
Name: Date: Chapter Practice 1 Area of a Rectangle Find the area of each figure. Example There are 3 rows of oneinch squares. Each row has 4 oneinch squares. 3 3 4 5 12 There are 12 oneinch squares
More informationPage 1 part 1 PART 2
Page 1 part 1 PART 2 Page 2 Part 1 Part 2 Page 3 part 1 Part 2 Page 4 Page 5 Part 1 10. Which point on the curve y x 2 1 is closest to the point 4,1 11. The point P lies in the first quadrant on the graph
More informationGeometry. Warm Ups. Chapter 11
Geometry Warm Ups Chapter 11 Name Period Teacher 1 1.) Find h. Show all work. (Hint: Remember special right triangles.) a.) b.) c.) 2.) Triangle RST is a right triangle. Find the measure of angle R. Show
More informationSquares and Square Roots
Squares and Square Roots Focus on After this lesson, you will be able to... determine the square of a whole number determine the square root of a perfect square Literacy Link A square number is the product
More informationGeometry 2001 part 1
Geometry 2001 part 1 1. Point is the center of a circle with a radius of 20 inches. square is drawn with two vertices on the circle and a side containing. What is the area of the square in square inches?
More informationName: Class: Assessment pack Semester 2 Grade 7
Name: Class: Assessment pack Semester 2 Grade 7 Math Materials covered for Grade 7 Semester 2 exam Module 6 (Expressions and Equations) 6.1 algebraic expressions 6.2 one step equation with rational coefficient
More informationInvestigation. Triangle, Triangle, Triangle. Work with a partner.
Investigation Triangle, Triangle, Triangle Work with a partner. Materials: centimetre ruler 1cm grid paper scissors Part 1 On grid paper, draw a large right triangle. Make sure its base is along a grid
More informationGrade 7, Unit 1 Practice Problems  Open Up Resources
Grade 7, Unit 1 Practice Problems  Open Up Resources Scale Drawings Lesson 1 Here is a gure that looks like the letter A, along with several other gures. Which gures are scaled copies of the original
More informationHow can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.
Common Core Standard: 8.EE.2, 8.G.6 How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.3 How Can I Find
More informationAssignment 5 unit34radicals. Due: Friday January 13 BEFORE HOMEROOM
Assignment 5 unit34radicals Name: Due: Friday January 13 BEFORE HOMEROOM Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the prime factorization
More informationMrs. Ambre s Math Notebook
Mrs. Ambre s Math Notebook Almost everything you need to know for 7 th grade math Plus a little about 6 th grade math And a little about 8 th grade math 1 Table of Contents by Outcome Outcome Topic Page
More informationFair Game Review. Chapter 4. Name Date. Find the area of the square or rectangle Find the area of the patio.
Name Date Chapter Fair Game Review Find the area of the square or rectangle... ft cm 0 ft cm.. in. d in. d. Find the area of the patio. ft 0 ft Copright Big Ideas Learning, LLC Big Ideas Math Green Name
More informationWVDE Math 7 G Draw, Construct, and Describe Geometrical Figures and Describe the Relationsips between Them Test
WVDE Math 7 G Draw, Construct, and Describe Geometrical Figures and Describe the Relationsips between Them Test 1 General Offline Instructions: Read each question carefully and decide which answer is correct.
More informationMinute Simplify: 12( ) = 3. Circle all of the following equal to : % Cross out the threedimensional shape.
Minute 1 1. Simplify: 1( + 7 + 1) =. 7 = 10 10. Circle all of the following equal to : 0. 0% 5 100. 10 = 5 5. Cross out the threedimensional shape. 6. Each side of the regular pentagon is 5 centimeters.
More informationGA Benchmark 8th Math (2008GABench8thMathset1)
Name: Date: 1. Tess will toss a fair coin 3 times. The possible results are illustrated in the tree diagram below. Based on the information given in the tree diagram, in how many ways (outcomes) can Tess
More informationGrade 8 Math Fourth Six Weeks Three Week Test
Grade 8 Math Fourth Six Weeks Three Week Test 20162017 STUDENT NAME TEACHER NAME 1. Determine the distance between (5, 3) and (7, 6). (8.7D, 8.1C) A. 9 units B. C. D. 10 units 12 units 15 units 2.
More informationa. b. c. d. 3. Ricky jogs 5 laps around a track in 8 minutes. Which of the following would be the same number of laps per minute?
Indicate the answer choice that best completes the statement or answers the question. 1. Jake goes to the grocery store and buys 3 apples, 2 cans of soup, and 1 box of cereal. The apples cost $0.89 each;
More informationMath A Regents Exam 0800 Page a, P.I. A.A.12 The product of 2 3 x and 6 5 x is [A] 10x 8
Math A Regents Exam 0800 Page 1 1. 080001a, P.I. A.A.1 The product of x and 6 5 x is [A] x 8 [B] x 15 [C] 1x 8 [D] 1x 15 5. 080005a Which table does not show an example of direct variation? [A] [B]. 08000a,
More informationYou may use a calculator. Answer the following questions. (5 pts; partial credit at teacher discretion)
PreTest Unit 7: Pythagorean Theorem KEY You may use a calculator. Answer the following questions. (5 pts; partial credit at teacher discretion) 1. What is the IFTHEN statement for the Pythagorean Theorem?
More informationG.MG.A.3: Area of Polygons
Regents Exam Questions G.MG.A.3: Area of Polygons www.jmap.org Name: G.MG.A.3: Area of Polygons If the base of a triangle is represented by x + 4 and the height is represented by x, which expression represents
More information5 th Grade MATH SUMMER PACKET ANSWERS Please attach ALL work
NAME: 5 th Grade MATH SUMMER PACKET ANSWERS Please attach ALL work DATE: 1.) 26.) 51.) 76.) 2.) 27.) 52.) 77.) 3.) 28.) 53.) 78.) 4.) 29.) 54.) 79.) 5.) 30.) 55.) 80.) 6.) 31.) 56.) 81.) 7.) 32.) 57.)
More informationIMLEM Meet #5 March/April Intermediate Mathematics League of Eastern Massachusetts
IMLEM Meet #5 March/April 2013 Intermediate Mathematics League of Eastern Massachusetts Category 1 Mystery You may use a calculator. 1. Beth sold girlscout cookies to some of her relatives and neighbors.
More informationMathematics, Grade 8
Session 1, MultipleChoice Questions 44084 C 1 13608 C 2 (0.5)(0.5)(0.5) is equal to which of the following? A. 0.000125 B. 0.00125 C. 0.125 D. 1.25 Reporting Category for Item 1: Number Sense and Operations
More informationModel Perimeter. So, the perimeter of the figure is 16 units. centimeters. centimeters. centimeters. centimeters
Lesson 11.1 Reteach Model Perimeter Perimeter is the distance around a figure. Find the perimeter of the figure. Step 1 Choose a unit to begin counting and label it 1. 1 1 unit Step 2 Count each unit around
More information1. Convert 60 mi per hour into km per sec. 2. Convert 3000 square inches into square yards.
ACT Practice Name Geo Unit 3 Review Hour Date Topics: Unit Conversions Length and Area Compound shapes Removing Area Area and Perimeter with radicals Isosceles and Equilateral triangles Pythagorean Theorem
More information1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown.
Name 1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown. Determine the horizontal distance between the technician and the base of the telephone pole to the
More information2016 Summer Break Packet for Students Entering Geometry Common Core
2016 Summer Break Packet for Students Entering Geometry Common Core Name: Note to the Student: In middle school, you worked with a variety of geometric measures, such as: length, area, volume, angle, surface
More informationSIXTH GRADE MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED:
SIXTH GRADE MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED: Perimeter of Polygons Area of Parallelograms Area of Triangles Area of a Trapezoid Area of Irregular Figures Activity 101: Sixth Grade
More informationFirst Name: Last Name: Select the one best answer for each question. DO NOT use a calculator in completing this packet.
5 Entering 5 th Grade Summer Math Packet First Name: Last Name: 5 th Grade Teacher: I have checked the work completed: Parent Signature Select the one best answer for each question. DO NOT use a calculator
More informationCovering and Surrounding Practice Answers
Investigation Additional Practice. a. units, Area 8 square units b. 8 units, Area 33 square units c. 3 units, Area 33 square units d. units, 7 Area 7 square units 8. a. Students should draw and label a
More informationRoberto Clemente Middle School. Summer Math Packet For students entering Math 7
Roberto Clemente Middle School Summer Math Packet For students entering Math 7 Name: 1. Write each expression in the correct column. Equal to 5.4 Equal to 5.42 2.36 + 3.06 2.16 + 3. 36 2.71 2 1.80 3 9.53
More informationGeometry. Practice Pack
Geometry Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Lines and Angles Practice 1.1 What Is Geometry?........................ 1 Practice 1.2 What Is Geometry?........................ 2 Practice
More informationUNIT 10 PERIMETER AND AREA
UNIT 10 PERIMETER AND AREA INTRODUCTION In this Unit, we will define basic geometric shapes and use definitions to categorize geometric figures. Then we will use the ideas of measuring length and area
More informationFoundations of Math 11: Unit 2 Proportions. The scale factor can be written as a ratio, fraction, decimal, or percentage
Lesson 2.3 Scale Name: Definitions 1) Scale: 2) Scale Factor: The scale factor can be written as a ratio, fraction, decimal, or percentage Formula: Formula: Example #1: A small electronic part measures
More information3.1 Solving Systems by Graphing. In consistent systems, Independent systems consist of. Three Cases: A. consistent and independent
3.1 Solving Systems by Graphing In consistent systems, 2. y Independent systems consist of Three Cases: x A. consistent and independent B. inconsistent and independent 3. y C. consistent and dependent
More informationMATH MEASUREMENT AND GEOMETRY
Students: 1. Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems. 1. Compare weights, capacities, geometric measures, time, and
More information8 th Grade Domain 3: Geometry (28%)
8 th Grade Domain 3: Geometry (28%) 1. XYZ was obtained from ABC by a rotation about the point P. (MGSE8.G.1) Which indicates the correspondence of the vertices? A. B. C. A X, B Y, C Z A Y, B Z, C X A
More informationWVDE Math 7 G Solve Reallife and Mathematical Problems involving Angle Measure, Area, Surface Area, and Volume Test
WVDE Math 7 G Solve Reallife and Mathematical Problems involving Angle Measure, Area, Surface Area, and Volume Test 1 General Offline Instructions: Read each question carefully and decide which answer
More informationGeometry Review 4/28/16
Geometry Review 4/28/16 Name: Date: SHOW ALL YOUR WORK!!! Finish for homework! 1. A photograph 3 inches wide and 5 inches long is to be enlarged so that the length is 15 inches. The new width will be 3.
More informationThe Pythagorean Theorem and Right Triangles
The Pythagorean Theorem and Right Triangles Student Probe Triangle ABC is a right triangle, with right angle C. If the length of and the length of, find the length of. Answer: the length of, since and
More information2018 TAME Middle School Practice State Mathematics Test
2018 TAME Middle School Practice State Mathematics Test (1) Noah bowled five games. He predicts the score of the next game he bowls will be 120. Which list most likely shows the scores of Kent s first
More informationGeometry: Measuring TwoDimensional Figures
C H A P T E R Geometry: Measuring TwoDimensional Figures What does landscape design have to do with math? In designing a circular path, pool, or fountain, landscape architects calculate the area of the
More informationThe Grade 6 Common Core State Standards for Geometry specify that students should
The focus for students in geometry at this level is reasoning about area, surface area, and volume. Students also learn to work with visual tools for representing shapes, such as graphs in the coordinate
More informationPerimeters of Composite Figures
8. Perimeters of Composite Figures How can you find the perimeter of a composite figure? ACTIVITY: Finding a Pattern Work with a partner. Describe the pattern of the perimeters. Use your pattern to find
More informationLooking for Pythagoras An Investigation of the Pythagorean Theorem
Looking for Pythagoras An Investigation of the Pythagorean Theorem I2t2 2006 Stephen Walczyk Grade 8 7Day Unit Plan Tools Used: Overhead Projector Overhead markers TI83 Graphing Calculator (& class set)
More informationRosa Parks Middle School Summer Math Packet Incoming C2.0 IM
Rosa Parks Middle School Summer Math Packet Incoming C2.0 IM Student Name: Teacher Name: Date: Dear Student and Parent, The purpose of this packet is to provide a review of objectives that were taught
More informationSkills Practice Skills Practice for Lesson 4.1
Skills Practice Skills Practice for Lesson.1 Name Date Squares and More Using Patterns to Generate Algebraic Functions Vocabulary Match each word with its corresponding definition. 1. linear function a.
More informationth Grade Test. A. 128 m B. 16π m C. 128π m
1. Which of the following is the greatest? A. 1 888 B. 2 777 C. 3 666 D. 4 555 E. 6 444 2. How many whole numbers between 1 and 100,000 end with the digits 123? A. 50 B. 76 C. 99 D. 100 E. 101 3. If the
More informationMeasurement and Data Core Guide Grade 4
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (Standards 4.MD.1 2) Standard 4.MD.1 Know relative sizes of measurement units within each system
More information3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage
Grasshoppers Everywhere! Area and Perimeter of Parallelograms on the Coordinate Plane. LEARNING GOALS In this lesson, you will: Determine the perimeter of parallelograms on a coordinate plane. Determine
More informationArea of Composite Figures. ESSENTIAL QUESTION do you find the area of composite figures? 7.9.C
? LESSON 9.4 Area of Composite Figures ESSENTIAL QUESTION How do you find the area of composite figures? Equations, expressions, and relationships Determine the area of composite figures containing combinations
More informationGrade Tennessee Middle/Junior High School Mathematics Competition 1 of 8
Grade 6 0 Tennessee Middle/Junior High School Mathematics Competition of 8. What is the starting number in this flowchart? Start Multiply by 6 Subtract 4 Result: 3 Divide by a..5 is the starting number.
More informationGeometry Page 1 of 54
TEST NAME: Geometry TEST ID: 115140 GRADE: 06 SUBJECT: Mathematics TEST CATEGORY: My Classroom Geometry Page 1 of 54 Student: Class: Date: 1. Lisa had two vases with dimensions as shown below. Which statement
More informationTEKSING TOWARD STAAR MATHEMATICS GRADE 6. Student Book
TEKSING TOWARD STAAR MATHEMATICS GRADE 6 Student Book TEKSING TOWARD STAAR 2014 Six Weeks 1 Lesson 1 STAAR Category 1 Grade 6 Mathematics TEKS 6.2A/6.2B ProblemSolving Model Step Description of Step 1
More informationName Date MASCOT PAINTING. Use the picture on the left and enlarge it by using the grid below. II Classroom Strategies Blackline Master
MASCOT PAINTING Use the picture on the left and enlarge it by using the grid below. Page 206 Classroom Strategies Blackline Master II  64 Draw Me in 3D Use cubes to construct the building described in
More informationSummer Math Learning Packet
Summer Math Learning Packet Sixth grade math was a blast, The year just went by so fast! Let s keep everything fresh in your mind, So you can rely on it in a bind. Just complete two problems a day, And
More information#2. Rhombus ABCD has an area of 464 square units. If DB = 18 units, find AC. #3. What is the area of the shaded sector if the measure of <ABC is 80?
1 PreAP Geometry Chapter 12 Test Review Standards/Goals: F.1.a.: I can find the perimeter and area of common plane figures, such as: triangles, quadrilaterals, regular polygons, and irregular figures,
More informationSquares Multiplication Facts: Square Numbers
LESSON 61 page 328 Squares Multiplication Facts: Square Numbers Name Teacher Notes: Introduce Hint #21 Multiplication/ Division Fact Families. Review Multiplication Table on page 5 and Quadrilaterals on
More informationPellissippi State Middle School Mathematics Competition
Grade 6 1 Pellissippi State 2009 Middle School Mathematics Competition Sponsored by: Oak Ridge Associated Universities Eighth Grade Scoring Formula: 4R W + 30 Directions: For each problem there are 5 possible
More informationEssentials. Week by. Week. Calculate!
Week by Week MATHEMATICS Essentials Grade WEEK 7 Calculate! Find two numbers whose product would be between 0 and 50. Can you find more solutions? Find two numbers whose product would be between,500 and,600.
More informationUse a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 )
Use a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 ) A telescope is supported by a tower that casts a shadow 40 meters long. The distance from the top of the tower to the
More information7. Three friends each order a large
005 MATHCOUNTS CHAPTER SPRINT ROUND. We are given the following chart: Cape Bangkok Honolulu London Town Bangkok 6300 6609 5944 Cape 6300,535 5989 Town Honolulu 6609,535 740 London 5944 5989 740 To find
More informationEssential Mathematics Practice Problems for Exam 5 Chapter 8
Math 254B Essential Mathematics Practice Problems for Eam 5 Chapter 8 Name Date This eam is closed book and closed notes, ecept for the Geometry Formula sheet that is provided by the instructor. You can
More information2009 Grade 6 Tennessee Middle/Junior High School Mathematics Competition 1
2009 Grade 6 Tennessee Middle/Junior High School Mathematics Competition 1 1. A rock group gets 30% of the money from sales of their newest compact disc. That 30% is split equally among the 5 group members.
More informationFair Game Review. Chapter 7. Name Date
Name Date Chapter 7 Fair Game Review Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. 1. 2. 3. 4. 5. 6. 141 Name Date Chapter 7 Fair Game
More informationMATH 130 FINAL REVIEW version2
MATH 130 FINAL REVIEW version2 Problems 1 3 refer to triangle ABC, with =. Find the remaining angle(s) and side(s). 1. =50, =25 a) =40,=32.6,=21.0 b) =50,=21.0,=32.6 c) =40,=21.0,=32.6 d) =50,=32.6,=21.0
More informationDO NOW 1) Solve x = 15x
Algebra I 04/20/17 DO NOW 1) Solve x 2 + 56 = 15x 2) The length of a rectangle is three more than the width, w. Express the area as a polynomial in simplest form. Area = (length)(width) 1 1) Solve x 2
More informationUnit 6, Activity 1, Measuring Scavenger Hunt
Unit 6, Activity 1, Measuring Scavenger Hunt Name: Measurement Descriptions Object 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Blackline Masters, Mathematics, Grade 7 Page 61 Unit 6, Activity 4, Break it Down Name
More information3.9. Pythagorean Theorem Stop the Presses. My Notes ACTIVITY
Pythagorean Theorem SUGGESTED LEARNING STRATEGIES: Marking the Text, Predict and Confirm, Shared Reading Jayla and Sidney are coeditorsinchief of the school yearbook. They have just finished the final
More information4. Answers will vary. Possible answers: 7. P = 4 12 ft = 48 ft, A = 12 ft 12 ft = 144 ft 2
Answers Investigation Applications. a. Possible answers: 4. Answers will vary. Possible answers: The bumpercar ride has an area of 4 m, which is the total number of square meters used to cover the floor
More informationPyle Middle School Summer Math Packet Incoming C2.0 Math 7
Pyle Middle School Summer Math Packet Incoming C2.0 Math 7 Dear Student and Parent, The purpose of this packet is to provide a review of objectives that were taught the previous school year and provide
More information6 th Grade Middle School Math Contest 2017 Page 1 of 9
1. In 2013, Mia s salary was a certain amount. In 2014, she received a 10% raise from 2013. In 2015, she received a 10% decrease in salary from 2014. How did her 2015 salary compare to her 2013 salary?
More information2 A rectangle 3 cm long and. Find the perimeter and area of each figure. Remember to include the correct units in your answers.
5 Homework Draw each rectangle on the dot paper. Find the perimeter and area. A rectangle 5 cm long and cm wide A rectangle cm long and cm wide Perimeter = Area = Perimeter = Area = Find the perimeter
More information