AREA Judo Math Inc.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "AREA Judo Math Inc."

Transcription

1 AREA 2013 Judo Math Inc.

2 7 th grade Geometry Discipline: Blue Belt Training Order of Mastery: Area 1. Square units/area overview 2. Circle Vocab (7G4) 3. What is Pi? (7G4) 4. Circumference of a circle (7G4) 5. Area of a circle 6. Area of Polygons (7G6) 7. Area of irregular shapes (7G6) Welcome to the Blue Belt Area It s very important when we measure things to sure that we are using the right units. Ever heard your teacher say that before?! That s because units will be very different depending on whether you are measuring something that s a straight line (like the distance from here to the bathroom), the area of something that is flat (like this table top), OR the volume of something 3-dimensional (like this room). For each of these measurements, having an error in units will make your solution not make any sense! The way we can determine what type of units we need to use can be done by referring to the dimension that we are measuring. Check out the table below it will give you a quick overview of dimensions and the appropriate units for each. As you can see, the dimension directly relates to the exponent that is above the unit! So anything in 2 dimensions is in 2 and anything in 3 dimensions is in 3. What about the fourth dimension, you might ask? Well, the world we live in only has 3 dimensions, but sometimes people call time the 4 th dimension time and some people suspect that our brains can perceive the 4 th dimension even though we can t see it go ahead and google it, but watch out because it might start making your mind feel like its bending! In this discipline we will be working primarily with 2 dimensional space so nothing too crazy! Standards Included: Good Luck Grasshopper. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms Judo Math Inc.

3 1. Square units/area overview Area represents 2 dimensional space and is measured in units 2. That means that if you want to find the area of something, you are essentially seeing how many little squares will fit into it Squares like this one: To make sure we have the idea of 2 dimensional space, make a list in the box below of anything that you could find the area of (make sure to not include anything where you are measuring a straight line 1D or how much fits into anything 3D) Brainstorm of objects that would be measured in 2 dimensional space: Table top floor Practice finding area by counting the number of squares in each of the shapes below. You will have to do some estimating on some of these! Area of triangle: Area of rhombus Area of circle: Now find the area of this interesting shape by counting boxes 1

4 Square Units Investigation Jan has a board in the shape of a rectangle that is 60 inches long and 48 inches wide. 1. How long is the board measured in feet? How wide is it measured in feet? 2. Find the area of the board (in square feet). 3. Jan said, To convert the inches to feet, I ought to divide by 12. The board has an area of 48x60 in =2880 inches squared. If I divide the area by 12, I can find out the area in square feet. So the area of the board is = 240 feet squared What went wrong with her problem solving?! 2

5 Based on your investigation above, answer the following questions. Draw a quick picture to prove your answer to each: 1. How many square inches are in a square foot? 2. How many square feet are in a square yard? 3. How many square feet are in a square mile? 4. How many square cm are in a square meter? 3

6 2. Circle Vocab (7G4) Before we get into some complicated circle business, it is going to be very important that we have the circle vocabulary perfectly. Inspect this circle to review your circle vocabulary before completing the following exercises: 4

7 11. Now you draw a circle that has a circumference of 4.5cm below. If you have a compass, use that to draw it, if not, try to use other tools to make this drawing as ACCURATE as possible: 5

8 3. What is Pi? (7G4) Pi is a very special and irrational number. That means that it cannot be written as a fraction because the decimals go on FOREVER AND EVER AND EVER! Here s the first 400 digits of Pi: Ask your teacher if you can have a competition to see who can memorize the most! I bet you will win Even though Pi is irrational and cannot be written as a fraction, sometimes people approximate Pi to be 22 7 Turn 22/7 into a decimal using division. How close is it to what Pi really is? 6

9 One cool thing that you might not know about Pi : anyone can find it by simply dividing a circles' circumference by its diameter. Which circle, you may ask? ANY CIRCLE!!!! Measure the circles below to discover Pi for yourself! (you will have to ask your teacher for some string to measure the circumference!) Circumference (c)= Diameter (d) = c d = How close is this to Pi?! Circumference (c)= Diameter (d) = c d = How close is this to Pi?! The picture to the right is one final look at pi as you can see, the diameter fits around the outside of the circle 3 times with just a little bit left over ( to be exact) 7

10 Now try these: 1. The earth has a circumference of 24,901.5 miles and a radius of miles. How can you use these measurements to estimate pi? 2. If Jupiter has a radius of 44,423 miles, can you estimate it s circumference? What about a circle with radius n? Check out the cartoon to the left. What do you think it means? And one final parting Pi joke for you: Question: What do you get if you divide the circumference of a jack-o-lantern by its diameter? Answer: Pumpkin Pi! 8

11 5. Circumference of a circle (7G4) As we saw above the ratio of the circumference of a circle to the diameter of a circle is always This information can actually help us to understand how to find the circumference of ANY circle. = 3.14 Since C D = π we can multiply both sides by D to get the formula: C= π D And since the diameter is twice the radius, people also write the formula like this: C= π 2 R Example: 9

12 9. A circle has a diameter of 8 meters. What is the circumference of the circle? Use 3.14 for pi. 10. A circle has a radius of 7 feet. Find the circumference of the circle. Do not approximate pi (leave it your answer as pi) 11. James states The circumference of a circle is approximately 6 times the radius of the circle. Is James statement correct? Explain your reasoning. 10

13 5. Area of Circles (7G6) This initial activity may be done as a class with your teacher OR you can follow the steps below. Start by cutting out the wedges below then follow all of the instructions on the next page. You will be DISCOVERING one way to come up with the area of a circle! 11

14 (leave page blank for cutout on the previous page.) 12

15 Discovering the Area of the Circle! We are going to find the area of a circle by relating it to a rectangle (which, as you know, has an area of A=l*w). 1. Arrange your 16 cutout wedges just like the picture here: 2. When the circle is divided into wedges and arrange like this, does it look like another shape you know? 3. What do you think would happen if we cut the circle up into 32 wedges, or 55 wedges, or 1000 wedges?! Slice each wedge in half and then arrange in an alternating fashion again. What has changed? 4. What are the dimensions of the rectangle that is formed? 5. Since the top and bottom of the rectangle make up half of the circumference and the circumference (from the last section) is 2πr and half of that is. And the height is the radius of the circle 6. Therefore the area for this Rectangle aka a circle is: A = π r 2 13

16 With your new formula, practice finding the area of the following circles. Round your answer to the nearest tenth and use 3.14 for pi. 14

17 9. Find the area of a circle with a diameter of 10 meters. 10. What is the area of a circle that has a radius of 6cm? (use 3.14 for pi) 11. Sam drew a circle with a radius of 4 inches and Sally drew a circle with a radius of 8 inches. Sally said since the radius of my circle is twice the radius of your circle, the area of my circle is twice the area of your circle. Is Sally s statement correct. If not, explain what she could say isntead. 12. A circle inside of a square as shown in the picture here. The edges of the square each tough a point on the circle. If the square has an area of 16 square meters, what is the area of the circle? 15

18 13. A circular pizza can feed 4 people if it has an area of at least 200 square inches. A pizza from Joe s Pizza has a radius of 9 inches. Is it enough to feed a family of 4? 14. Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter which he finds, to the nearest millimeter, to be 5 centimeters. a. To find the area of the circle, Juan uses the formula A=πr 2 where A is the area of the circle and r is its radius. He uses 3.14 for π. What value does Juan get for the area of the circle? b. Is there any possible error in Juan's measurement of the diameter of the circle? Explain how much it could be and how much this could affect your calculation of the area.. 16

19 15. 17

20 14. The figure to the right is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm. a. Calculate the area of the large circle. b. Calculate the area of the shaded part and explain how you arrived at your solution. 18

21 15. Circumference/Area: If you are given the circumference of a circle, can you find the area? Below are a few circles for you to try this out with. Write your conclusion as a firm yes or no statement in a complete sentence. Circumference = 43.4 yd Circumference=17 yd 16. What is the area of a circle that has a circumference of 10π? 17. The circumference of a circle is 12.56ft was used to approximate pi, what is the area of the circle. 19

22 18. The circumference of the earth is approximately 25,000 miles. If you were to dig a hole to the center of the earth, how long would the tunnel be? 19. The redwood trees in California are said to have trunks so large that a far could drive through them. Estimate the circumference of the redwood tree. Use your estimate to find the area of the trunk if the tree was cut down. Explain all of your reasoning. 20. (final circle challenge!) What percent of the area of a circle is enclosed by an isosceles triangle one of whose sides is the diameter of the circle? Draw a picture to help show your solution. 20

23 5. Area of Polygons (7G6) In previous years, you have learned the basics of area, like the area of a triangle, rectangle, square, rhombus, parallelogram, and regular polygons. Fill in the blank boxes with the formula for each (if you need to look it up on a computer you can!) Shape Formula for area Triangle Rectangle & Square Rhombus & Parallelogram Trapezoid Regular Polygon 21

24 Find the area of the following shapes using the formulas from the previous page 22

25 4. If you forgot the formula for the area of a regular polygon, how could you figure out the area of the above shapes (think triangles!) Use one of the problems above to prove your solution. 23

26 5. 6. A triangle has an area of 6 square feet. The height is four feet. What is the length of the base? 6. Area of irregular shapes (7G6) Sometimes we will find ourselves needing to find the area of irregular shapes. What can we do in these situations? Well, break the shape up into pieces we can find the area of, of course! Check ou the track below. Find the area of it by breaking it up into shapes you know the area of. Area of track: m 2 24

27 Now find the area of these shapes by breaking them into familiar shapes. Make sure to always use the correct units: 25

28 Using any tools you need, draw a shape that has the following: 2 semicircles 1 rhombus 1 parallelogram 2 triangles 1 rectangle They should all be connected by at least on side. Label and find the area of your shape! Find the area given circumference: 26

Math 8 Notes Unit 8: Area and Perimeter

Math 8 Notes Unit 8: Area and Perimeter Math 8 Notes Unit 8: Area and Perimeter Syllabus Objective: (6.) The student will compute the perimeter and area of rectangles and parallelograms. Perimeter is defined as the distance around the outside

More information

The GED math test gives you a page of math formulas that

The GED math test gives you a page of math formulas that Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

More information

EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE

EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE 1 EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE INSTRUCTIONAL ACTIVITY Lesson 1 LEARNING GOAL Students will develop an understanding of diameter, radius, circumference, and pi and the relationships among

More information

AREA. The Square Inch The Square Foot The Square Yard. 1 foot. 1 foot. The Square Mile The Square Meter The Square Centimeter. 1 meter.

AREA. The Square Inch The Square Foot The Square Yard. 1 foot. 1 foot. The Square Mile The Square Meter The Square Centimeter. 1 meter. Tallahassee Community College 48 AREA The area of a figure measures the surface of the figure. The unit of measure for area cannot be a linear unit. To measure area we use square units such as: The Square

More information

Alaska Mathematics Standards Vocabulary Word List Grade 4

Alaska Mathematics Standards Vocabulary Word List Grade 4 1 add addend additive comparison area area model common factor common multiple compatible numbers compose composite number counting number decompose difference digit divide dividend divisible divisor equal

More information

Section 5.3: Solving Problems with Circles

Section 5.3: Solving Problems with Circles Section 5.3: Solving Problems with Circles Section Overview: In this section circumference and area of a circle will be explored from the perspective of scaling. Students will start by measuring the diameter

More information

How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots

How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots . Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,

More information

( ) = 28. 2r = d 2 = = r d = r. 2 = r or 1. Free Pre-Algebra Lesson 33! page 1. Lesson 33 Formulas for Circles

( ) = 28. 2r = d 2 = = r d = r. 2 = r or 1. Free Pre-Algebra Lesson 33! page 1. Lesson 33 Formulas for Circles Free Pre-Algebra Lesson 33! page 1 Lesson 33 Formulas for Circles What is a Circle? Everyone knows what a circle looks like. A sprinkler line rotates around a center pivot, forming circles of irrigated

More information

SOL Review Items. 7.1 The student will. 7.1a 1. Which fraction and decimal are equivalent to A. and B. and C. and D. and 0.

SOL Review Items. 7.1 The student will. 7.1a 1. Which fraction and decimal are equivalent to A. and B. and C. and D. and 0. 7.1 The student will a) investigate and describe the concept of negative exponents for powers of ten; b) determine scientific notation for numbers greater than zero; c) compare and order fractions, decimals,

More information

Pre-Algebra Unit 2. Rational & Irrational Numbers. Name

Pre-Algebra Unit 2. Rational & Irrational Numbers. Name Pre-Algebra Unit 2 Rational & Irrational Numbers Name Core Table 2 Pre-Algebra Name: Unit 2 Rational & Irrational Numbers Core: Table: 2.1.1 Define Rational Numbers Vocabulary: Real Numbers the set of

More information

MCAS Review - Measurement Session 4A

MCAS Review - Measurement Session 4A lass: ate: I: MS Review - Measurement Session 4 Multiple hoice Identify the choice that best completes the statement or answers the question. 1 circle has an area of 16π square centimeters. What is the

More information

0-8 Area. Find the area of each figure. 1. SOLUTION: The area of the rectangle is 6 square centimeters. 2. SOLUTION:

0-8 Area. Find the area of each figure. 1. SOLUTION: The area of the rectangle is 6 square centimeters. 2. SOLUTION: Find the area of each figure. 1. The area of the rectangle is 6 square centimeters. 2. The area of the square is 36 square inches. 3. The area of the parallelogram is 120 square meters. esolutions Manual

More information

Grade 11 Mathematics Practice Test

Grade 11 Mathematics Practice Test Grade Mathematics Practice Test Nebraska Department of Education 204 Directions: On the following pages are multiple-choice questions for the Grade Practice Test, a practice opportunity for the Nebraska

More information

Volume vs. Diameter. Teacher Lab Discussion. Overview. Picture, Data Table, and Graph

Volume vs. Diameter. Teacher Lab Discussion. Overview. Picture, Data Table, and Graph 5 6 7 Middle olume Length/olume vs. Diameter, Investigation page 1 of olume vs. Diameter Teacher Lab Discussion Overview Figure 1 In this experiment we investigate the relationship between the diameter

More information

Wheels Radius / Distance Traveled

Wheels Radius / Distance Traveled Mechanics Teacher Note to the teacher On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions and distance. Students will use formulas relating

More information

Math Final Examination Fall 2013

Math Final Examination Fall 2013 Department of Mathematics The City College of New York Math 18000 Final Examination Fall 2013 Instructions: Please Read Carefully. You must show all your work to receive credit, and explain clearly and

More information

Pre-Algebra Chapter 9 Spatial Thinking

Pre-Algebra Chapter 9 Spatial Thinking Pre-Algebra Chapter 9 Spatial Thinking SOME NUMBERED QUESTIONS HAVE BEEN DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU SHOULD NOT USE ONE

More information

Integers include positive numbers, negative numbers, and zero. When we add two integers, the sign of the sum depends on the sign of both addends.

Integers include positive numbers, negative numbers, and zero. When we add two integers, the sign of the sum depends on the sign of both addends. Adding Integers Reteaching 31 Math Course 3, Lesson 31 Integers include positive numbers, negative numbers, and zero. When we add two integers, the sign of the sum depends on the sign of both addends.

More information

Diagnostic Test. Month Balance Change February $ March $ $13.10 April $1, $ May $ $ June $ $163.

Diagnostic Test. Month Balance Change February $ March $ $13.10 April $1, $ May $ $ June $ $163. Diagnostic Test Select the best answer for questions 1 60. Fill in the correct bubble on your answer sheet. 1. The chart shows the balance in Neil s savings account and the change from the previous month.

More information

Summer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages

Summer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages 8 Common Core Mathematics 6 6 Vocabulary absolute value additive inverse property adjacent angles the distance between a number and zero on a number line. Example: the absolute value of negative seven

More information

2. l = 7 ft w = 4 ft h = 2.8 ft V = Find the Area of a trapezoid when the bases and height are given. Formula is A = B = 21 b = 11 h = 3 A=

2. l = 7 ft w = 4 ft h = 2.8 ft V = Find the Area of a trapezoid when the bases and height are given. Formula is A = B = 21 b = 11 h = 3 A= 95 Section.1 Exercises Part A Find the Volume of a rectangular solid when the width, height and length are given. Formula is V=lwh 1. l = 4 in w = 2.5 in h = in V = 2. l = 7 ft w = 4 ft h = 2.8 ft V =.

More information

ABSOLUTE VALUE Judo Math Inc.

ABSOLUTE VALUE Judo Math Inc. ABSOLUTE VALUE 2013 Judo Math Inc. 6 th grade Number Sense Discipline: Orange Belt Training Order of Mastery: Absolute Value (6NS7-8) 1. Inequality to show position 2. Explain statements of order in the

More information

Essentials. Week by. Week. Fraction Action. Probability Pizzazz

Essentials. Week by. Week. Fraction Action. Probability Pizzazz Week by Week MATHEMATICS Essentials 6 The Titanic is miles below the surface of the Atlantic Ocean. If you dive at the rate of miles per hour, how long would it take you to get to the ship? Put six different

More information

Trades Math Practice Assessment Test

Trades Math Practice Assessment Test Trades Math Practice Assessment Test Please leave 2 or 3 digits after the decimal point rounding is optional Calculators ARE allowed For full marks, you MUST include units in your answer e.g. 2 ft. or

More information

Write an equation for each relationship. Then make a table of input-output pairs and tell whether the function is proportional.

Write an equation for each relationship. Then make a table of input-output pairs and tell whether the function is proportional. Functions Reteaching 41 Math Course, Lesson 41 A function is a rule that identifies a relationship between a set of input numbers and a set of output numbers. A function rule can be described in words,

More information

Measurement: Length, Area and Volume Part I

Measurement: Length, Area and Volume Part I IDS 101 Name Measurement: Length, Area and Volume Part I If we ask someone the size of a common object, such as a dime or penny, most people come pretty close to the actual size. However, objects that

More information

Write your answers on notebook paper. Show your work.

Write your answers on notebook paper. Show your work. UNIT 6 Getting Ready Use some or all of these exercises for formative evaluation of students readiness for Unit 6 topics. Prerequisite Skills Finding the length of the sides of special right triangles

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MGF 1106 Exam #3 Review Sheet Chapters 8-9 Fill in the missing value. 1) 816 mm = cm 2) 54.96 m = km 3) 492 L = ml 4) 800 mg = kg 5) 25 kg = mg Arrange the quantities in order from smallest to largest.

More information

Ratio Problems Involving Name Totals (page 528)

Ratio Problems Involving Name Totals (page 528) LESSON 101 Ratio Problems Involving Name Totals (page 528) In some ratio problems a total is needed in order to solve the problem. 1. Fill in the ratio box with things you know. 2. Write a proportion.

More information

2 Introduction to Variables

2 Introduction to Variables www.ck12.org CHAPTER 2 Introduction to Variables Chapter Outline 2.1 VARIABLE EXPRESSIONS 2.2 PATTERNS AND EXPRESSIONS 2.3 COMBINING LIKE TERMS 2.4 THE DISTRIBUTIVE PROPERTY 2.5 ADDITION AND SUBTRACTION

More information

Section 5.6 from Basic Mathematics Review by Oka Kurniawan was developed by OpenStax College, licensed by Rice University, and is available on the

Section 5.6 from Basic Mathematics Review by Oka Kurniawan was developed by OpenStax College, licensed by Rice University, and is available on the Section 5.6 from Basic Mathematics Review by Oka Kurniawan was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website. It is used under a Creative Commons

More information

EQ: How do I convert between standard form and scientific notation?

EQ: How do I convert between standard form and scientific notation? EQ: How do I convert between standard form and scientific notation? HW: Practice Sheet Bellwork: Simplify each expression 1. (5x 3 ) 4 2. 5(x 3 ) 4 3. 5(x 3 ) 4 20x 8 Simplify and leave in standard form

More information

Kwan went to the store with $20 and left the store with his purchases and $7.35. How much money did Kwan spend?

Kwan went to the store with $20 and left the store with his purchases and $7.35. How much money did Kwan spend? Name Score Benchmark Test 1 Math Course 2 For use after Lesson 0 1. (1) At Washington School there are 2 classrooms and an average of 25 students in each classroom. Which equation shows how to find the

More information

Review of Scientific Notation and Significant Figures

Review of Scientific Notation and Significant Figures II-1 Scientific Notation Review of Scientific Notation and Significant Figures Frequently numbers that occur in physics and other sciences are either very large or very small. For example, the speed of

More information

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer.

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer. Summer Packet th into 6 th grade Name Addition Find the sum of the two numbers in each problem. Show all work.. 62 2. 20. 726 + + 2 + 26 + 6 6 Decimal Addition: Remember to line up the decimals before

More information

PSSA Released Items 16 Multiple Choice Questions, 1 Open-Ended Response

PSSA Released Items 16 Multiple Choice Questions, 1 Open-Ended Response Page 1 of 21 2016-2017 PSSA Released Items 16 Multiple Choice Questions, 1 Open-Ended Response Directions Do not use a calculator. You may refer to the formula sheet shown below. Show your work on this

More information

Area of Circles. Say Thanks to the Authors Click (No sign in required)

Area of Circles. Say Thanks to the Authors Click  (No sign in required) Area of Circles Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org

More information

Reasoning: Odd one out

Reasoning: Odd one out Reasoning: Odd one out Learning objective To use mathematical reasoning to identify the odd one out in a list of mathematical statements. Links to year 6 problem solving and reasoning pupil target sheet

More information

Parallelograms (page 368)

Parallelograms (page 368) LESSON 71 Parallelograms (page 368) Name A parallelogram has two pairs of opposite, parallel sides. The opposite angles of a parallelogram have equal measures. The adjacent angles of a parallelogram are

More information

Units and Dimensionality

Units and Dimensionality Chapter 1 Units and Dimensionality If somebody asked me how tall I am, I might respond 1.78. But what do I mean by that? 1.78 feet? 1.78 miles? In fact, my height is 1.78 meters. Most physical measurements

More information

1 The Real Number Line

1 The Real Number Line Introductory Algebra Page 1 of 13 1 The Real Number Line There are many sets of numbers, but important ones in math and life sciences are the following The integers Z = {..., 4, 3, 2, 1, 0, 1, 2, 3, 4,...}.

More information

In problems #2 through #6, round your answers to the nearest tenth if necessary.

In problems #2 through #6, round your answers to the nearest tenth if necessary. Math 254CM Name Essential Mathematics Date Study Guide #5 Exam #5 is closed book. You will be given the Geometry handout and the Measurements handout. You may use a calculator on this exam. You must show

More information

PROFESSOR: WELCOME BACK TO THE LAST LECTURE OF THE SEMESTER. PLANNING TO DO TODAY WAS FINISH THE BOOK. FINISH SECTION 6.5

PROFESSOR: WELCOME BACK TO THE LAST LECTURE OF THE SEMESTER. PLANNING TO DO TODAY WAS FINISH THE BOOK. FINISH SECTION 6.5 1 MATH 16A LECTURE. DECEMBER 9, 2008. PROFESSOR: WELCOME BACK TO THE LAST LECTURE OF THE SEMESTER. I HOPE YOU ALL WILL MISS IT AS MUCH AS I DO. SO WHAT I WAS PLANNING TO DO TODAY WAS FINISH THE BOOK. FINISH

More information

GTPS Curriculum 6 th Grade Math. Topic: Topic 1- Numeration

GTPS Curriculum 6 th Grade Math. Topic: Topic 1- Numeration 9 days / September Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm

More information

Academic Vocabulary Mathematics

Academic Vocabulary Mathematics Academic Vocabulary Mathematics Carolann DeMoss Teacher on Special Assignment - Mathematics These grade level lists of mathematical vocabulary words are the result of the compilation of a number of math

More information

GRADE 5 MATHEMATICS. Form M0119, CORE 1 VIRGINIA STANDARDS OF LEARNING. Spring 2009 Released Test. Property of the Virginia Department of Education

GRADE 5 MATHEMATICS. Form M0119, CORE 1 VIRGINIA STANDARDS OF LEARNING. Spring 2009 Released Test. Property of the Virginia Department of Education VIRGINIA STANDARDS OF LEARNING Spring 2009 Released Test GRADE 5 MATHEMATICS Form M0119, CORE 1 Property of the Virginia Department of Education 2009 by the Commonwealth of Virginia, Department of Education,

More information

PublicServicePrep Comprehensive Guide to Canadian Public Service Exams

PublicServicePrep Comprehensive Guide to Canadian Public Service Exams PublicServicePrep Comprehensive Guide to Canadian Public Service Exams Copyright 2009 Dekalam Hire Learning Incorporated Teaching Material Math Addition 7 + 5 7 + 5 = 12 12 The above two equations have

More information

6 th Grade Math Connects

6 th Grade Math Connects 6 th Grade Math Connects Chapter 1: Multiply and Divide Decimals Multi-Part Lesson 1: Multiply Decimals A: Estimate Products B: Explore Multiply Decimals by Whole Numbers C: Multiply Decimals by Whole

More information

Mapping Common Core State Standard Clusters and. Ohio Grade Level Indicator. Grade 7 Mathematics

Mapping Common Core State Standard Clusters and. Ohio Grade Level Indicator. Grade 7 Mathematics Mapping Common Core State Clusters and Ohio s Grade Level Indicators: Grade 7 Mathematics Ratios and Proportional Relationships: Analyze proportional relationships and use them to solve realworld and mathematical

More information

Chapter 2 Polynomial and Rational Functions

Chapter 2 Polynomial and Rational Functions SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear

More information

Grade K-Algebra 2. Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2

Grade K-Algebra 2. Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2 Grade K-Algebra 2 Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2 Scoring Guide Sco ide Diagnostic Chart Intervention/Remediation simplify placement decisions

More information

Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 11 EXPONENTS AND ROOTS

Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 11 EXPONENTS AND ROOTS Name Period Date 8-11 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 11 EXPONENTS AND ROOTS 11.1 Squares and Square Roots Use numbers and pictures to understand the inverse relationship between squaring

More information

Chapters 1 13 Final Mastery Test

Chapters 1 13 Final Mastery Test Page 1 Chapters 1 13 Directions Circle the letter of the best answer. 1. The figure shown is a A cone B cylinder C pyramid D sphere 2. The volume of the rectangular prism shown is A 17.5 cm 3 B 70 cm 3

More information

Kindergarten Standards Counting and Cardinality Analyze, compare, create, and compose shapes. Know number names and the count sequence.

Kindergarten Standards Counting and Cardinality Analyze, compare, create, and compose shapes. Know number names and the count sequence. Kindergarten Standards 1. Representing and comparing whole numbers, initially with sets of objects Students use numbers, including written numerals, to represent quantities and to solve quantitative problems,

More information

K-8 Math Standards by Domain

K-8 Math Standards by Domain In this document, the Louisiana Student Standards for Mathematics for Kindergarten through Grade 8 are listed by domain and then by grade. The purpose of this arrangement is to show how mathematical concepts

More information

Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition

Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 5 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may

More information

Mathematics Standards: Kindergarten

Mathematics Standards: Kindergarten Kindergarten Mathematics Kindergarten In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects;

More information

Have fun & we ll see you in August!

Have fun & we ll see you in August! Kids Information Page We re so proud of you for taking the time to work on math over the summer! Here are some helpful hints for success: Find a quiet work space where you can get organized and stay focused.

More information

Circle Theorems. Angles at the circumference are equal. The angle in a semi-circle is x The angle at the centre. Cyclic Quadrilateral

Circle Theorems. Angles at the circumference are equal. The angle in a semi-circle is x The angle at the centre. Cyclic Quadrilateral The angle in a semi-circle is 90 0 Angles at the circumference are equal. A B They must come from the same arc. Look out for a diameter. 2x Cyclic Quadrilateral Opposite angles add up to 180 0 A They must

More information

Fundamentals of Mathematics I

Fundamentals of Mathematics I Fundamentals of Mathematics I Kent State Department of Mathematical Sciences Fall 2008 Available at: http://www.math.kent.edu/ebooks/10031/book.pdf August 4, 2008 Contents 1 Arithmetic 2 1.1 Real Numbers......................................................

More information

PERIL PIZZA. But that s still a daydream. For the moment you re the assistant to the glamorous. The Challenge

PERIL PIZZA. But that s still a daydream. For the moment you re the assistant to the glamorous. The Challenge 02 Death Chances of Survival: You might make it Survival Strategies: Fractions; Equivalence by: Termination PIZZA PERIL The Challenge It s your first day of work at Catwalk magazine, a dream come true.

More information

5.3 Multiplying Decimals

5.3 Multiplying Decimals 370 CHAPTER 5. DECIMALS 5.3 Multiplying Decimals Multiplying decimal numbers involves two steps: (1) multiplying the numbers as whole numbers, ignoring the decimal point, and (2) placing the decimal point

More information

English 5 th Grade A-L Vocabulary Cards and Word Walls Revised: 11/18/14

English 5 th Grade A-L Vocabulary Cards and Word Walls Revised: 11/18/14 English 5 th Grade A-L Vocabulary Cards and Word Walls Revised: 11/18/14 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State

More information

Parallelogram Area Word Problems

Parallelogram Area Word Problems Parallelogram Area Word Free PDF ebook Download: Parallelogram Area Word Download or Read Online ebook parallelogram area word problems in PDF Format From The Best User Guide Database Basic Algebra: Solving

More information

Geometry Pre-Unit 1 Intro: Area, Perimeter, Pythagorean Theorem, Square Roots, & Quadratics. P-1 Square Roots and SRF

Geometry Pre-Unit 1 Intro: Area, Perimeter, Pythagorean Theorem, Square Roots, & Quadratics. P-1 Square Roots and SRF Geometry Pre-Unit 1 Intro: Area, Perimeter, Pythagorean Theorem, Square Roots, & Quadratics P-1 Square Roots and SRF Square number the product of a number multiplied by itself. 1 * 1 = 1 1 is a square

More information

2. Relative and Circular Motion

2. Relative and Circular Motion 2. Relative and Circular Motion A) Overview We will begin with a discussion of relative motion in one dimension. We will describe this motion in terms of displacement and velocity vectors which will allow

More information

Circumference practice worksheet

Circumference practice worksheet Putting the Fun into Teaching the Circumference of Circles This is a packet I made of hands-on learning activities, games, and worksheets to help students not just learn but understand pi, and the circumference.

More information

Virginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning

Virginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning BUI L T F O VIR R G INIA 2014 2015 Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 1 Maintaining Mathematical Proficiency Add or subtract. 1. 1 + ( 3) 2. 0 + ( 12) 3. 5 ( 2) 4. 4 7 5. Find two pairs of integers whose sum is 6. 6. In a city, the record monthly high temperature

More information

Understanding and Using Variables

Understanding and Using Variables Algebra is a powerful tool for understanding the world. You can represent ideas and relationships using symbols, tables and graphs. In this section you will learn about Understanding and Using Variables

More information

ACCUPLACER Sample Questions for Students

ACCUPLACER Sample Questions for Students ACCUPLACER Sample Questions for Students Elementary Algebra Study Guide LCC Student Success Center Sam Jack Academic Coordinator 60-80-4 samj@labette.edu Cathy Hyten SSS Program Assistant 60-80-47 cathyh@labette.edu

More information

Sixth Grade Mathematics Indicators Class Summary

Sixth Grade Mathematics Indicators Class Summary Mathematics Indicators Number, Number Sense and Operations Standard 1.1 Represent and compare number less than 0 through familiar applications and extending the number line. 1.1.1 Use simple expressions

More information

California. Performance Indicator. Form B Teacher s Guide and Answer Key. Mathematics. Continental Press

California. Performance Indicator. Form B Teacher s Guide and Answer Key. Mathematics. Continental Press California Performance Indicator Mathematics Form B Teacher s Guide and Answer Key Continental Press Contents Introduction to California Mathematics Performance Indicators........ 3 Answer Key Section

More information

Large & Small Numbers

Large & Small Numbers Large & Small Numbers Scientists frequently work with very large or small numbers. Astronomers work with galaxies that contain billions of stars at great distances from us. On the other hand, biologists

More information

The Cycloid. and the Kinematic Circumference. by Miles Mathis

The Cycloid. and the Kinematic Circumference. by Miles Mathis return to updates The Cycloid and the Kinematic Circumference First published August 31, 2016 by Miles Mathis Those of you who have read my papers on π=4 will know I have explained that problem using many

More information

Elementary School Learning Progressions

Elementary School Learning Progressions What is the purpose of this document? Elementary School Learning Progressions This document is designed to help educators as they transition into the 2012 Mathematics Course of Study. All of the standards

More information

Sect Formulas and Applications of Geometry:

Sect Formulas and Applications of Geometry: 72 Sect 2.6 - Formulas and Applications of Geometry: Concept # Solving Literal Equations for a particular variable. Now, we will examine solving formulas for a particular variable. Sometimes it is useful

More information

Remember, you may not use a calculator when you take the assessment test.

Remember, you may not use a calculator when you take the assessment test. Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

More information

Measurement Year 9. The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used.

Measurement Year 9. The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used. Measurement Year 9 The topic Measurement includes units because any size has no meaning without the units. Every answer must include the units used. Precision and Estimation In general students should

More information

Section 4.7 Scientific Notation

Section 4.7 Scientific Notation Section 4.7 Scientific Notation INTRODUCTION Scientific notation means what it says: it is the notation used in many areas of science. It is used so that scientist and mathematicians can work relatively

More information

MPM1D - Practice Mastery Test #6

MPM1D - Practice Mastery Test #6 Name: Class: Date: ID: A MPMD - Practice Mastery Test #6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Calculate 0% of 00. a. b. 0 c. 000 d. 00. Seyran's

More information

Grade 6 Mathematics Practice Test

Grade 6 Mathematics Practice Test Grade 6 Mathematics Practice Test Nebraska Department of Education 206 Directions: On the following pages are questions for the Grade 6 Practice Test, a practice opportunity for the Nebraska State Accountability

More information

General Certificate of Secondary Education Foundation Tier

General Certificate of Secondary Education Foundation Tier Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature Pages Mark General Certificate of Secondary Education Foundation Tier 3 4-5 GCSE Mathematics

More information

Grade 7/8 Math Circles November 21/22/23, The Scale of Numbers

Grade 7/8 Math Circles November 21/22/23, The Scale of Numbers Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 7/8 Math Circles November 21/22/23, 2017 The Scale of Numbers Centre for Education in Mathematics and Computing Last week we quickly

More information

Geometry Final Exam 2014 Study Guide. Name Date Block

Geometry Final Exam 2014 Study Guide. Name Date Block Geometry Final Exam 014 Study Guide Name Date Block The final exam for Geometry will take place on June 5. The following study guide will help you prepare for the exam. Everything we have covered is fair

More information

Part 1 - Pre-Algebra Summary Page 1 of 22 1/19/12

Part 1 - Pre-Algebra Summary Page 1 of 22 1/19/12 Part 1 - Pre-Algebra Summary Page 1 of 1/19/1 Table of Contents 1. Numbers... 1.1. NAMES FOR NUMBERS... 1.. PLACE VALUES... 3 1.3. INEQUALITIES... 4 1.4. ROUNDING... 4 1.5. DIVISIBILITY TESTS... 5 1.6.

More information

Name: Period: Unit 3 Modeling with Radical and Rational Functions

Name: Period: Unit 3 Modeling with Radical and Rational Functions Name: Period: Unit Modeling with Radical and Rational Functions 1 Equivalent Forms of Exponential Expressions Before we begin today s lesson, how much do you remember about exponents? Use expanded form

More information

Programme 6 Area of Circles and Composite Shapes Worksheet 1: Programme Questions

Programme 6 Area of Circles and Composite Shapes Worksheet 1: Programme Questions Worksheet 1: Programme Questions 1. The large pizza is a 12 inch one. What is the diameter of the smaller size pizza? 2. What formula gives the area of a circle? 3. Whose pizza was better value, Katie

More information

Geometry Final Exam REVIEW

Geometry Final Exam REVIEW Name: Class: _ Date: _ Geometry Final Exam 09-10 - REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the perimeter and area of the parallelogram.

More information

Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides.

Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. Mth101 Chapter 8 HW Name Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 1) 1) Rectangle 6 in. 12 in. 12 in.

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 7 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students understand and use scientific notation* and square roots. They convert between fractions and decimals. MA.7.1.1

More information

Ohio s State Tests PRACTICE TEST GEOMETRY. Student Name

Ohio s State Tests PRACTICE TEST GEOMETRY. Student Name Ohio s State Tests PRACTICE TEST GEOMETRY Student Name The Ohio Department of Education does not discriminate on the basis of race, color, national origin, sex, religion, age, or disability in employment

More information

algebraic expression angle exponent equation Vocabulary Flash Cards Review Review Review Review Review Review Big Ideas Math Red

algebraic expression angle exponent equation Vocabulary Flash Cards Review Review Review Review Review Review Big Ideas Math Red algebraic expression angle base (of a power) coordinate plane equation exponent expression factor A figure formed by two rays with the same endpoint An expression that contains numbers, operations, and

More information

Unit 1: Introduction Measurement and Scientific Notation. Measurements in physics are carried out in SI units, aka the.

Unit 1: Introduction Measurement and Scientific Notation. Measurements in physics are carried out in SI units, aka the. Measurement and Scientific Notation Measurements in physics are carried out in SI units, aka the. Measurement Unit Symbol Length Mass Time Speed Acceleration Force Energy Prefixes Prefix Symbol Factor

More information

Silver Spring International Middle School Algebra Summer Packet

Silver Spring International Middle School Algebra Summer Packet Name: Silver Spring International Middle School Algebra Summer Packet It is NOT mandatory to complete but, STRONGLY encouraged. MONTGOMERY COUNTY PUBLIC SCHOOLS SILVER SPRING INTERNATIONAL MIDDLE SCHOOL

More information

Relationships Between Quantities

Relationships Between Quantities Algebra 1 Relationships Between Quantities Relationships Between Quantities Everyone loves math until there are letters (known as variables) in problems!! Do students complain about reading when they come

More information

Lesson 12.1 Skills Practice

Lesson 12.1 Skills Practice Lesson 12.1 Skills Practice Name Date Introduction to Circles Circle, Radius, and Diameter Vocabulary Define each term in your own words. 1. circle 2. center of a circle 3. radius of a circle 4. diameter

More information

Fourth Grade Number Sense and Algebraic Concepts

Fourth Grade Number Sense and Algebraic Concepts Slide 1 / 308 Slide 2 / 308 Fourth Grade Number Sense and Algebraic Concepts 2015-11-23 www.njctl.org Compare numbers Round Numbers Patterns Slide 3 / 308 Table of Contents Algebraic Equations/Number Sentences

More information

The Theorem of Pythagoras

The Theorem of Pythagoras CONDENSED LESSON 9.1 The Theorem of Pythagoras In this lesson you will Learn about the Pythagorean Theorem, which states the relationship between the lengths of the legs and the length of the hypotenuse

More information

1 Modular Arithmetic Grade Level/Prerequisites: Time: Materials: Preparation: Objectives: Navajo Nation Math Circle Connection

1 Modular Arithmetic Grade Level/Prerequisites: Time: Materials: Preparation: Objectives: Navajo Nation Math Circle Connection 1 Modular Arithmetic Students will explore a type of arithmetic that results from arranging numbers in circles instead of on a number line. Students make and prove conjectures about patterns relating to

More information