# UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet

Size: px
Start display at page:

Transcription

1 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 of the Pythagorean theorem. Use the Pythagorean theorem and its converse to solve problems Applications of the Pythagorean Theorem Use the Pythagorean theorem and its converse to solve problems. Find perimeters and areas of triangles and rectangles Statistics: Measures of Center Demonstrate knowledge of three commonly used measures of center. Review math concepts from prior lessons. Demonstrate competency in finding lengths and areas for polygons graphed in the coordinate plane (highlighted review) Week 24 SP

2 FOCUS ON VOCABULARY 24 Fill in the crossword puzzle using the clues below Across 6. The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse. 7. This refers to the two sides of a right triangle that are adjacent to the right angle. 8. The middle number in the data set when the values are placed in order from least to greatest. 9. The value or values that occur most often. Down 1. A triangle that has a right angle 2. A data value that is unusually small or large compared to the overall pattern of values in the data set. 3. This refers to the side opposite the right angle in a right triangle. 4. The of a numerical data set is the difference between the greatest and least values in the data set. 5. The average of the value in the data set. Word Bank hypotenuse legs Pythagorean theorem mean median mode outlier range right triangle Week 24 SP0

3 24.1 The Pythagorean Theorem THE PYTHAGOREAN THEOREM Ready (Summary) We will explore the relationship between side lengths of right triangles and then look at a proof of the Pythagorean theorem. Then we will use this theorem to solve problems. Set (Goals) Explore the Pythagorean theorem numerically, algebraically, and geometrically. Understand a proof of the Pythagorean theorem. Use the Pythagorean theorem and its converse to solve problems. Find the area of each figure in square units. Go (Warmup) x y x y Simplify each expression. 5. a + a 6. ab + ab a+ a ab + ab 2 2 Week 24 SP1

4 24.1 The Pythagorean Theorem TWO RIGHT TRIANGLES = unit length = 1 square unit 1. Length of the shorter leg 2. Length of the longer leg 3. Area of the square on the shorter leg 4. Area of the square on the longer leg 5. Area of the square on the hypotenuse 6. Length of the hypotenuse Smaller triangle Larger triangle 7. Write a conjecture about the relationship between the area of square on the hypotenuse and the area of the squares of the legs. Week 24 SP2

5 24.1 The Pythagorean Theorem THE PYTHAGOREAN THEOREM: PART 1 Here is a right triangle with lengths a, b, and c: b c a a b a The two congruent squares on the right have been made using lengths a, b, and c. b 1. Label some right angles and some lengths. 2. Write the area of each polygonal piece inside of it. 3. Cut out both squares. Then cut them up into the polygons. Week 24 SP3

6 24.1 The Pythagorean Theorem This page is left intentionally blank. Week 24 SP4

7 24.1 The Pythagorean Theorem THE PYTHAGOREAN THEOREM: PART 2 a b a b b a = b a c c c c 1. Write the areas inside the polygonal pieces in the two square figures above. 2. Write an equation that equates the sum of the areas of the shaded polygons with the sum of the areas of the unshaded polygons. 3. Simplify your equation. 4. Use words to state the meaning of this equation as it refers to the legs and the hypotenuse of the original triangle. a c b 5. This relationship is called the Week 24 SP5

8 24.1 The Pythagorean Theorem PYTHAGOREAN THEOREM PRACTICE Pythagorean theorem: If a triangle is a right triangle, then the sum of the squares of the length of the two legs is equal to the square of the length of the hypotenuse. Converse of the Pythagorean theorem: If the sum of the squares of the lengths of the two shorter sides is equal to the square of the lengths of the hypotenuse, then the triangle is a right triangle. Use the Pythagorean theorem and its converse to answer these questions: 1. Draw the squares on the legs and the square on the hypotenuse of the right triangle below. Find the area of each square and the length of each side of the triangle. Using the correct numerical values, fill in the blanks to show the Pythagorean relationship. Area equation: ( ) + ( ) = ( ) Side length equation: ( ) 2 + ( ) 2 = ( ) 2 2. A classmate suggests that a triangle with side lengths of 4, 5, and 9 units is a right triangle. Use the Pythagorean theorem to show that this must be incorrect. Week 24 SP6

9 24.1 The Pythagorean Theorem PYTHAGOREAN THEOREM PRACTICE (continued) 3. A right triangle has legs of lengths 5 and 12 units. What is the length of its hypotenuse? 4. Notice that the answer to problem #3 is a whole number. When all three sides of a right triangle have whole number side lengths, the three numbers are called a Pythagorean triple. Are the side lengths of the triangle in problem #1 a Pythagorean triple? 5. Find another Pythagorean triple in this lesson and write the three side lengths of the corresponding right triangle. 6. One triangle has sides of length 4, 6 and 8 centimeters. Another triangle has sides of length 6, 8 and 10 centimeters. Is either of these triangles a right triangle? Why? 7. Latonya said, The third side of triangle T is = 61 inches long. Is Latonya correct? Explain. 6 in. T 5 in. Week 24 SP7

10 24.2 Applications of the Pythagorean Theorem APPLICATIONS OF THE PYTHAGOREAN THEOREM Ready (Summary) We will use the Pythagorean theorem to solve problems. Set (Goals) Use the Pythagorean theorem and its converse to solve problems. Find perimeters and areas of triangles and rectangles. Go (Warmup) 1. A triangle has side lengths of 3, 5, and 6 units. Use the Pythagorean theorem to show why this cannot be a right triangle. 2. Find the length of the hypotenuse in the right triangle. 8 in x 6 in Week 24 SP8

11 24.2 Applications of the Pythagorean Theorem FIND THE MISSING PART Find the missing length in each right triangle. If needed, use fractions to write square root approximations. Example: x + 6 = 10 2 x + 36 = x = 64 x = x cm 13 ft v 5 cm w 5 ft Solve. 3. To get from home to work every day, Samos drives 7 miles east on Avenue A, and then drives north on Avenue B. He knows that the straight-line distance from his home to his place of work is about 25 miles. How many miles is his drive north on Avenue B? Picture: Symbols/Numbers: Words: Week 24 SP9

12 24.2 Applications of the Pythagorean Theorem MORE GEOMETRIC FIGURES For each problem, use fractions to write square root approximations. 1. Find the diagonal of a rectangle whose sides are 15 mm and 20 mm long. Picture: Symbols/Numbers: Words: 2. Find the diagonal of a square whose side is 10 cm long. Picture: Symbols/Numbers: Words: Week 24 SP10

13 24.2 Applications of the Pythagorean Theorem MORE GEOMETRIC FIGURES (continued) For each problem, use fractions to write square root approximations. 3. Find the height of an isosceles triangle with two congruent sides of 12 inches each and a base that is 18 inches long. Picture: Symbols/Numbers: Words: 4. Find the height of an equilateral triangle whose sides are 4 feet in length. Picture: Symbols/Numbers: Words: Week 24 SP11

14 24.3 Statistics: Measures of Center SKILL BUILDER 1 Complete each sentence with the correct word. mean median mode 1. The is/are the number(s) that appear(s) most often in a group of numbers. 2. The is the sum of a group of numbers divided by the number of addends. 3. The is the middle number in a group of numbers arranged in numerical order. 4. Ken rolled five number cubes labeled 1-6 and found that the sum was 15. What was the mean (average) of these rolls? 5. Suppose none of Ken s rolls were sixes. What could the five number cubes rolls be?,,,, 6. What is the mode(s) of your numbers from problem #5? 7. Six students recorded the number of hours they watched TV over the weekend. The minimum number of hours watched was 4 and maximum was 9. Their mean time was 7 hours. How much TV might each student have watched?,,,,, 8. Jackie played in 5 basketball games. She always scored more than 5 points. She scored in double-digits once. Her median score was 8. What might her 5 scores be so that her mean is also 8?,,,, 9. What is the range for Jackie s scores from your answer to problem #8? Week 24 SP12

15 24.3 Statistics: Measures of Center SKILL BUILDER 2A The test scores of five students in three different math classes are shown below. Find the mean, median and mode for each class. 1. Test Scores from Mrs. Adewole s class Mean: Median: Mode: 2. Test Scores from Mr. Lopez s class Mean: Median: Mode: 3. Test Scores from Ms. Tran s class Mean: Median: Mode: 4. Which class had the highest mean score? 5. Which class had the highest median score? 6. Which class had the highest mode score? Week 24 SP13

16 24.3 Statistics: Measures of Center SKILL BUILDER 2B Find the perimeter and area for each figure yd 28 yd Perimeter: Area: 8. C 16 ft A This rectangle has a vertical height of 5 ft. and a horizontal length of 16 ft. Name its coordinates. 5 ft C (, ) A (, ) T (, ) Find the perimeter and area. S (-3, -2) T Perimeter: Area: m 18.3 m Perimeter: Area: Week 24 SP14

17 24.3 Statistics: Measures of Center SKILL BUILDER 2C Find percents for each amount. Amount Find 5% Find 10% Find 15% Find 20% 10. \$ \$ \$ \$ Find the missing length of the right triangle using the Pythagorean theorem. 4 ft x Pythagorean theorem: 3 ft A bag contains 1 green, 1 purple and 1 orange colored marble. Without looking in the bag, you choose a marble, replace it, and then choose another marble. 15. Make an outcome grid to show all the possible outcomes. 16. What is the probability of drawing at least one green marble? 17. What is the probability of drawing an orange marble twice? Week 24 SP15

18 24.3 Statistics: Measures of Center SKILL BUILDER 3A 1. Find the mean, median and mode for the heights below. Students heights (in inches) Mean: Median: Mode: 2. What is the range of the students heights? Simplify Verbal Expression Algebraic Expression less than x 7. The product of n and times x divided by more than 2 times x Week 24 SP16

19 24.3 Statistics: Measures of Center SKILL BUILDER 3B Find the perimeter and area for each figure m 6 m Perimeter: Area: cm 15 cm 16 cm Perimeter: Area: 12. A rectangle is formed by connecting the coordinates (0, -1), (0, 4.5), (-9.5, 4.5), and (9.5, -1). Perimeter: Area: Week 24 SP17

20 24.3 Statistics: Measures of Center TEST PREPARATION 24 Show your work on a separate sheet of paper and choose the best answer. 1. What is the length of the missing side of the right triangle? 15 cm 17 cm A. 8 cm B. 9 cm C. 10 cm D. 11 cm x 2. What is the diagonal of a rectangle whose sides are 6 m and 8 m? E. 8 m F. 9 m G. 10 m H. 11 m 3. Jessica had the following scores for five rounds of a board game: 78, 80, 69, 75, 73. What is the mean of the scores? A. 50 B. 71 C. 74 D What is the area of triangle XYZ? W Y 3 m X Z 4 m E. 5 m F. 6 m G. 7 m H. 8 m 5. Simplify A. 1 B. -1 C D A right triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse. E. 13 cm F. 14 cm G. 15 cm H. 16 cm Week 24 SP18

21 24.3 Statistics: Measures of Center This page is left intentionally blank for notes. Week 24 SP19

22 24.3 Statistics: Measures of Center This page is left intentionally blank for notes. Week 24 SP20

23 24.3 Statistics: Measures of Center KNOWLEDGE CHECK 24 Show your work on a separate sheet of paper and write your answers on this page The Pythagorean Theorem 1. Determine whether a triangle with side lengths 4 m, 6 m, and 7 m is a right triangle. 2. A right triangle has legs of 5 mm and 12 mm. Find the length of its hypotenuse Applications of the Pythagorean Theorem 3. A square has a perimeter of 20 cm. Find the length of its diagonal rounded to the nearest tenth. 4. Find the height of an equilateral triangle whose side is 8 ft. Round your answer to the nearest tenth Statistics: Measures of Center 5. Compute the mean, median, mode, and range of the following set of numbers: 5, 5, 5, 5, 5, 5, 5, 64, 70, 55, 60, 60, 80, 45, 5 6. There are seven whole numbers in a group. The minimum number is 5 and the maximum number is 15. The mean and the median are 11 and the mode is 15. What might be the possible numbers in the group? Highlighted Review: Finding Lengths and Areas 7. The points A (-3, 3), B (-3, -4), C (1, -4), and D (1, 3) form rectangle ABCD. Find the lengths of side AB and side BC. 8. If the area of the triangle formed by points A, B, and C is 14 square units, then what is the area of the rectangle ABCD? Week 24 SP21

24 24.3 Statistics: Measures of Center Home-School Connection 24 Here are some questions from this week s lessons to review with your young mathematician. 1. Determine whether a triangle with side lengths 3 m, 4 m, and 5 m is a right triangle. 2. Find the height of an isosceles triangle with two congruent sides of 5 m and a third side that is 6 m (use the long side as the base). 3. There are five whole numbers in a group. The minimum number is 7 and the maximum number is 14. The mode is 9 and the median is 9. The mean is 10. What might be the possible numbers in the group? Parent (or Guardian) signature Selected California Mathematics Content Standards AF Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pd - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). MG Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. MG Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. SDP Compute the range, mean, median, and mode of data sets. MR Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. Week 24 SP22

### UNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet

Name Period Date UNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet 5.1 Fractions: Parts and Wholes Identify the whole and its parts. Find and compare areas of different shapes. Identify congruent

### Lesson 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

### Catty 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

### UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet

Name Period Date UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet 20.1 Solving Proportions 1 Add, subtract, multiply, and divide rational numbers. Use rates and proportions to solve problems.

### The 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...

### Students 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

### Square 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 4-digit number with different digits. 3078 2. Find the greatest

### 1. 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

### Squares 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

AREA..1.. After measuring various angles, students look at measurement in more familiar situations, those of length and area on a flat surface. Students develop methods and formulas for calculating the

### Twenty Mathcounts Target Round Tests Test 1 MATHCOUNTS. Mock Competition One. Target Round. Name. State

MATHCOUNTS Mock Competition One Target Round Name State DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems, which will be presented in pairs. Work

### The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.

ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid

### Lesson 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

### 6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date

6.00 Trigonometry Geometry/Circles Basics for the ACT Name Period Date Perimeter and Area of Triangles and Rectangles The perimeter is the continuous line forming the boundary of a closed geometric figure.

### E G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland

MATH 1012 Section 8.1 Basic Geometric Terms Bland Point A point is a location in space. It has no length or width. A point is represented by a dot and is named by writing a capital letter next to the dot.

### Meet #5 March Intermediate Mathematics League of Eastern Massachusetts

Meet #5 March 2008 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2008 Category 1 Mystery 1. In the diagram to the right, each nonoverlapping section of the large rectangle is

### The 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

### Areas of Tropezoids, Rhombuses, and Kites

102 Areas of Tropezoids, Rhombuses, and Kites MathemaHcs Florida Standards MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MP1. MP3, MP 4,MP6 Objective

### MATH 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

### The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in

The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in Grade 7 or higher. Problem C Totally Unusual The dice

### 3.3. 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

### Problem of the Month: Between the Lines

Problem of the Month: Between the Lines Overview: In the Problem of the Month Between the Lines, students use polygons to solve problems involving area. The mathematical topics that underlie this POM are

### 6-1. Angles of Polygons. Lesson 6-1. What You ll Learn. Active Vocabulary

6-1 Angles of Polygons What You ll Learn Skim Lesson 6-1. Predict two things that you expect to learn based on the headings and figures in the lesson. 1. 2. Lesson 6-1 Active Vocabulary diagonal New Vocabulary

### Meet #2. Park Forest Math Team. Self-study Packet

Park Forest Math Team Meet #2 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : rea and perimeter of polygons 3. Number Theory:

### Name Period Date. GEOMETRY AND MEASURESUREMENT Student Pages for Packet 6: Drawings and Constructions

Name Period Date GEOMETRY AND MEASURESUREMENT Student Pages for Packet 6: Drawings and Constructions GEO6.1 Geometric Drawings Review geometric notation and vocabulary. Use a compass and a ruler to make

Mathematics Geometry Grade 6AB It s the Right Thing Subject: Mathematics: Geometry: Ratio and Proportion Level: Grade 7 Abstract: Students will learn the six types of triangles and the characteristics

### Geometry 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?

### 8 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

### Elko County School District 5 th Grade Math Learning Targets

Elko County School District 5 th Grade Math Learning Targets Nevada Content Standard 1.0 Students will accurately calculate and use estimation techniques, number relationships, operation rules, and algorithms;

### 2016 Geometry Honors Summer Packet

Name: 2016 Geometry Honors Summer Packet This packet is due the first day of school. It will be graded for completion and effort shown. There will be an assessment on these concepts the first week of school.

### Name 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

### 1. 1 Square Numbers and Area Models (pp. 6-10)

Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 6-10) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is

### Core Connections, Course 2 Checkpoint Materials

Core Connections, Course Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn exactly the same way at the same time. At

### Name Period Date LINEAR FUNCTIONS STUDENT PACKET 5: INTRODUCTION TO LINEAR FUNCTIONS

Name Period Date LF5.1 Slope-Intercept Form Graph lines. Interpret the slope of the graph of a line. Find equations of lines. Use similar triangles to explain why the slope m is the same between any two

### Park Forest Math Team. Meet #2. Geometry. Self-study Packet

Park Forest Math Team Meet #2 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:

### FSA Geometry EOC Getting ready for. Circles, Geometric Measurement, and Geometric Properties with Equations.

Getting ready for. FSA Geometry EOC Circles, Geometric Measurement, and Geometric Properties with Equations 2014-2015 Teacher Packet Shared by Miami-Dade Schools Shared by Miami-Dade Schools MAFS.912.G-C.1.1

### Sample Questions from Ga. Department of Education

Strand: Measurements & Geometry Sample Questions from Ga. Department of Education Name: Concept 1 (M18 M21): Measurements (including metric) Estimates measures in both customary and metric systems. 1.

### HPS Scope Sequence Last Revised June SUBJECT: Math GRADE: 7. Michigan Standard (GLCE) Code & Language. What this Standard means:

Number and Numeration MA.7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical

### FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true.

FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth

### MEA 501 LESSON _NOTES Period. CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all

MEA 501 LESSON _NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all attain mastery at this level side lengths are given MEA 302 Compute

### TEKSING 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 Problem-Solving Model Step Description of Step 1

### Math + 4 (Red) SEMESTER 1. { Pg. 1 } Unit 1: Whole Number Sense. Unit 2: Whole Number Operations. Unit 3: Applications of Operations

Math + 4 (Red) This research-based course focuses on computational fluency, conceptual understanding, and problem-solving. The engaging course features new graphics, learning tools, and games; adaptive

### Name: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.

### h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.

ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this

### Student 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

Prentice Hall Connected Mathematics 6th Grade Units 2004 Grade 6 C O R R E L A T E D T O Expectations Grade 6 Content Standard A: Mathematical facts, concepts, principles, and theories Numeration: Understand

### The Pythagorean Theorem

. The Pythagorean Theorem Goals Draw squares on the legs of the triangle. Deduce the Pythagorean Theorem through exploration Use the Pythagorean Theorem to find unknown side lengths of right triangles

### Geometry. 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

### 1 Version 2.0. Related Below-Grade and Above-Grade Standards for Purposes of Planning for Vertical Scaling:

Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Geometry Target E [a]: Draw, construct,

### IMLEM 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 girl-scout cookies to some of her relatives and neighbors.

### 6.1 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

### Length 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

### First 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

### Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0

Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume

### Coimisiún na Scrúduithe Stáit State Examinations Commission. Junior Certificate Examination Mathematics. Paper 2 Higher Level

2016. S35 Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination 2016 Mathematics Paper 2 Higher Level Monday 13 June Morning 9:30 to 12:00 300 marks Examination number

### The 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

### SESSION THREE AREA MEASUREMENT AND FORMULAS

SESSION THREE AREA MEASUREMENT AND FORMULAS Outcomes Understand the concept of area of a figure Be able to find the area of a rectangle and understand the formula base times height Be able to find the

### Grade 6 Middle School Mathematics Contest A parking lot holds 64 cars. The parking lot is 7/8 filled. How many spaces remain in the lot?

Grade 6 Middle School Mathematics Contest 2004 1 1. A parking lot holds 64 cars. The parking lot is 7/8 filled. How many spaces remain in the lot? a. 6 b. 8 c. 16 d. 48 e. 56 2. How many different prime

### Fair 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

### Pythagorean 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

### Geometry Final Exam Review 2012 #

1 PART 1: Multiple Choice (40 x 2 points = 80%). PART 2: Open Ended (2 x 10 = 20%) 1) Find the volume and surface area of the following rectangular prisms 2) Find the surface area of the following cylinders.

### Geometry: Measuring Two-Dimensional Figures

C H A P T E R Geometry: Measuring Two-Dimensional 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

### Saxon Math Manipulatives in Motion Primary. Correlations

Saxon Math Manipulatives in Motion Primary Correlations Saxon Math Program Page Math K 2 Math 1 8 Math 2 14 California Math K 21 California Math 1 27 California Math 2 33 1 Saxon Math Manipulatives in

### METHOD 1: METHOD 2: 4D METHOD 1: METHOD 2:

4A Strategy: Count how many times each digit appears. There are sixteen 4s, twelve 3s, eight 2s, four 1s, and one 0. The sum of the digits is (16 4) + + (8 2) + (4 1) = 64 + 36 +16+4= 120. 4B METHOD 1:

### A 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

### Meet #2. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving

Math League SSD Meet #2 Self-study Packet Problem ategories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : rea and perimeter of polygons 3. Number Theory: Divisibility

### th 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

### Problem of the Month: Between the Lines

Problem of the Month: Between the Lines The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common

### INTERMEDIATE LEVEL MEASUREMENT

INTERMEDIATE LEVEL MEASUREMENT TABLE OF CONTENTS Format & Background Information...3-6 Learning Experience 1- Getting Started...6-7 Learning Experience 2 - Cube and Rectangular Prisms...8 Learning Experience

### Year End Review. Central Tendency 1. Find the mean, median and mode for this set of numbers: 4, 5, 6, 3, 7, 4, 4, 6, 7 mean. median.

Math 8 Name: Year End Review Central Tendency 1. Find the mean, median and mode for this set of numbers: 4, 5, 6, 3, 7, 4, 4, 6, 7 mean median mode Operations with Fractions 2. Solve. Show all your work.

### Chapter Possibilities: goes to bank, gets money from parent, gets paid; buys lunch, goes shopping, pays a bill,

1.1.1: Chapter 1 1-3. Shapes (a), (c), (d), and (e) are rectangles. 1-4. a: 40 b: 6 c: 7 d: 59 1-5. a: y = x + 3 b: y =!x 2 c: y = x 2 + 3 d: y = 3x! 1 1-6. a: 22a + 28 b:!23x! 17 c: x 2 + 5x d: x 2 +

### UNIT 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

### Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6

DOE Assessment Guide Questions (2015) Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6 Question Example Item #1 Which transformation of ΔMNO results in a congruent triangle? Answer Example

### G.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

### Daily Warmup. - x 2 + x x 2 + x Questions from HW?? (7x - 39) (3x + 17) 1. BD bisects ABC. Find the m ABC.

Daily Warmup Questions from HW?? B 1. BD bisects ABC. Find the m ABC. (3x + 17) (7x - 39) C 2. The figure below is a regular polygon. Find the value of x. - x 2 + x + 43 A D 4x 2 + x - 37 3. The measure

### Investigation. Triangle, Triangle, Triangle. Work with a partner.

Investigation Triangle, Triangle, Triangle Work with a partner. Materials: centimetre ruler 1-cm grid paper scissors Part 1 On grid paper, draw a large right triangle. Make sure its base is along a grid

Name Date Incoming Advanced Grade 7 Tell whether the two fractions form a proportion. 1. 3 16, 4 20 2. 5 30, 7 42 3. 4 6, 18 27 4. Use the ratio table to find the unit rate in dollars per ounce. Order

### Find the area and perimeter of each figure. Round to the nearest tenth if necessary.

Find the area and perimeter of each figure. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite sides of a parallelogram

### Name Numeration, Patterns, and Relationships

Numeration, Patterns, and Relationships 1 In standard form 5,000,000 20,000 400 8 is equal to which number? A 5,200,408 B 5,020,408 C 520,408 D 502,408 2 What is the value of 6 in 368,5,427? A 60,000 B

### 2016 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

### The 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

### Find the value of the expressions. 3 x = 3 x = = ( ) 9 = 60 (12 + 8) 9 = = 3 9 = 27

PreAlgebra Concepts Important Concepts exponent In a power, the number of times a base number is used as a factor order of operations The rules which tell which operation to perform first when more than

### Geometry 1 FINAL REVIEW 2011

Geometry 1 FINL RVIW 2011 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram.

### 3.9. 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 co-editors-in-chief of the school yearbook. They have just finished the final

### SIXTH 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 10-1: Sixth Grade

### How 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

### 7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular)

7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular) Unit #1 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers;

### Workout 5 Solutions. Peter S. Simon. Quiz, December 8, 2004

Workout 5 Solutions Peter S. Simon Quiz, December 8, 2004 Problem 1 Marika shoots a basketball until she makes 20 shots or until she has made 60% of her shots, whichever happens first. After she has made

### Summer Solutions Problem Solving Level 4. Level 4. Problem Solving. Help Pages

Level Problem Solving 6 General Terms acute angle an angle measuring less than 90 addend a number being added angle formed by two rays that share a common endpoint area the size of a surface; always expressed

### Pythagorean 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,

### TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7

EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional

### Covering 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

### Building Concepts: Ratios Within and Between Scaled Shapes

Lesson Overview In this TI-Nspire lesson, students learn that ratios are connected to geometry in multiple ways. When one figure is an enlarged or reduced copy of another by some scale factor, the ratios

### Connected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6)

Core Standards of the Course Standard I Students will acquire number sense and perform operations with rational numbers. Objective 1 Represent whole numbers and decimals in a variety of ways. A. Change

### GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)

GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance