# Gears Ratios and Speed / Problem Solving

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Teacher Mechanics Note to the teacher On this page, students will learn about the relationship between gear ratio, gear rotational speed, wheel radius, diameter, circumference, revolutions and distance. Students will determine gear ratio by dividing the number of teeth on the driven gear by the number of teeth on the driving gear. They will determine the rotational speed of the driving gear by multiplying the gear ratio by the rotational speed of the driven axle. They will determine distance by multiplying this rotational speed by the wheel circumference. They will also have to know how to determine circumference from diameter and radius. Students will have to use both fractions and decimals to make these calculations. While the worksheet is designed to help students learn how to determine gear ratio and derive rotational speed from it, and to derive distance from wheel circumference and rotational speed, and may be successfully completed by students with little background in these areas, the existing ability to multiply and simplify fractions, the ability to use decimals, and the ability to determine circumference from diameter or radius will be necessary to successfully complete the worksheet. Teachers may wish to review any or all of these skills depending on their students background. Note that this exercise is more challenging than the exercises in Gears 1-4. To successfully complete the worksheet, students must have a working understanding of most of the concepts and equations introduced in both the Gears and Wheels worksheets. Students will also have to perform more calculations than in any of the previous Gears and Wheels worksheets. Note that there are no instructions regarding rounding. The answers assume rounding to 2 digits beyond the decimal place, except for known fractions. Teachers may wish to supply additional instructions. If they do not, students answers may vary slightly according to what rounding conventions they use. The formulas are: Wheel Circumference Revolutions Distance 1 (# Teeth on driven gear) (# Teeth on driving gear) = Gear Ratio x = (Gear Ratio) X (Speed of driven gear) = (Speed of driving gear) 4 (Speed of driving gear) (Gear Ratio) = (Speed of driven gear) The necessary formulas (above) are included with the instructions to reinforce the concepts. 5.61

2 Mechanics Teacher A. B. C. 1. Assuming the circumference of the wheel and the RPM of the motor are exactly the same for all experiments, which gear ratio would create the most speed, A, B or C? Why did you choose that answer? The gear ratio B is lowest, meaning it would create the highest speed for the driven axle. 2. If the driving gear is moving at 100 RPM, how fast will the driven gear move for pictures A, B and C? A RPM B. 300 RPM C. 100 RPM Students are expected to use the following procedure: Identify gear sizes by counting teeth Determine the gear ratio of each pair of gears Identify the information required by the question Reconstruct the equations provided as an example Enter the data provided into these equations Manipulate the equations if necessary Solve the equations Note that the first question tests comprehension of the concept of gear ratios. Some students may have more difficulty with this question than the others, which only require entering numbers in equations and solving them. Approximate classroom time: minutes depending on students background 5.62

3 Teacher Mechanics Students successfully completing the worksheet will be able to: 1. Define gear ratio 2. Understand the concept of gear ratio, in particular that low gear ratios will create more wheel speed than high gear ratios when motor speed is held constant 3. Identify gear size by counting teeth 4. Simplify fractions 5. Describe the geometry of a circle 6. Describe the relationship between radius, diameter, circumference, revolutions and distance for a wheel 7. Calculate diameter from radius 8. Calculate circumference from diameter 9. Derive driving gear RPM from driven gear RPM if given the gear ratio 10. Calculate distance from wheel circumference and revolutions 11. Multiply decimals and fractions 12. Reconstruct equations relating diameter, circumference, revolutions and distance 13. Identify data provided in word problems 14. Identify information required in the word problems 15. Manipulate these equations to solve for the required information Standards addressed: Math Standards Numbers and Operations Algebra Geometry Measurement Problem Solving Connections Technology Standards The Nature of Technology Standard 1 Design Standards 8, 9 Abilities for a Technological World Standard 12 Using Technology to Design the Future Standards 16, 18, 19 Science Standards Content Standard B Content Standard E Note: Workbook answers begin on the next page. 5.63

4 Mechanics Teacher Instructions Use the formulas and pictures below to answer the following questions Note: The driving gear is always on the right. Possible gear sizes are 40, 24, 14 and 8 tooth gears. The formulas are: Wheel Circumference Revolutions Distance 1 (# Teeth on driven gear) (# Teeth on driving gear) = Gear Ratio x = (Gear Ratio) X (Speed of driven gear) = (Speed of driving gear) 4 (Speed of driving gear) (Gear Ratio) = (Speed of driven gear) A. B. C. 1. Assuming the circumference of the wheel and the RPM of the motor are exactly the same for all experiments, which gear ratio would create the most speed, A, B or C? Why did you choose that answer? We know that the lower the gear ratio, the faster the driven gear will revolve for every revolution of the driving gear. By counting teeth, we know that the lowest gear ratio is the one in picture B. 2. If the driving gear is moving at 100 RPM, how fast will the driven gear move for pictures A, B and C? To find the answer to this question, we can use Formula 4. For picture A, we can see that the gear ratio is 24/14, which simplifies to 12/7, and we know from the question that the driving gear is moving at 100 RPM. So 100 RPM/(12/7) = 100 RPM x 7/12 = 58.3 RPM. For picture B, we can see that the gear ratio is 8/24, which simplifies to 1/3, and we know from the question that the driving gear is moving at 100 RPM. So 100 RPM/(1/3) = 100 RPM x 3 = 300 RPM. For picture C, we can see that the gear ratio is 24/24, which simplifies to 1/1, and we know from the question that the driving gear is moving at 100 RPM. So 100 RPM/(1) = 100 RPM. 5.64

5 Teacher Mechanics 3. If the driving gear moves at 100 RPM and the circumference of the wheel is 4.4 cm, how far will the robot move in 2 minutes for pictures A, B and C? To find the answer to this question, we can use Formula 4 and then Formula 3. For picture A, we can see that the gear ratio is 24/14, which simplifies to 12/7, and we know from the question that the driving gear will move 100 revolutions/minute x 2 minutes = 200 revolutions. So 200 revolutions/(12/7) = 200 revolutions x 7/12 = revolutions. Now we can use formula 3, above. So x 4.4 cm = cm. For picture B, we can see that the gear ratio is 8/24, which simplifies to 1/3, and we know from the question that the driving gear will move 100 revolutions/minute x 2 minutes = 200 revolutions. So 200 revolutions/(1/3) = 200 revolutions x 3 = 600 revolutions. Now we can use formula 3, above. So 600 x 4.4 cm = 2640 cm. For picture C, we can see that the gear ratio is 1/1, and we know from the question that the driving gear will move 100 revolutions/minute x 2 minutes = 200 revolutions. So 200 revolutions/1 = 200 revolutions Now we can use formula 3, above. So 200 x 4.4 cm = 880 cm. 4. If the driving gear moves at 200 RPM and the diameter of the wheel is 1.9 cm, how far will the robot move in 3 minutes for pictures A, B and C? To find the answer to this question, we can use Formula 4 and then Formula 3. For picture A, we can see that the gear ratio is 24/14, which simplifies to 12/7, and we know from the question that the driving gear will move 200 revolutions/minute x 3 minutes = 600 revolutions. So 600 revolutions/(12/7) = 600 revolutions x 7/12 = 350 revolutions. The wheel circumference is π x diameter, or π x 1.9 = 5.97 cm. Now we can use formula 3, above. So 350 x 5.97 cm = cm. For picture B, we can see that the gear ratio is 8/24, which simplifies to 1/3, and we know from the question that the driving gear will move 200 revolutions/minute x 3 minutes = 600 revolutions. So 600 revolutions/(1/3) = 600 revolutions x 3 = 1800 revolutions. The wheel circumference is π x diameter, or π x 1.9 = 5.97 cm. Now we can use formula 3, above. So 1800 x 5.97 cm = cm. For picture C, we can see that the gear ratio is 1/1 and we know from the question that the driving gear will move 200 revolutions/minute x 3 minutes = 600 revolutions. So 600 revolutions/(1) = 600 revolutions. The wheel circumference is π x diameter, or π x 1.9 = 5.97 cm. Now we can use formula 3, above. So 600 x 5.97 cm = 3582 cm. 5.65

6 Mechanics Teacher 5. If the driving gear moves at 200 RPM and the radius of the wheel is 2.5 cm, how far will the robot move in 3 minutes for pictures A, B and C? To find the answer to this question, we can use Formula 4 and then Formula 3. For picture A, we can see that the gear ratio is 24/14, which simplifies to 12/7, and we know from the question that the driving gear will move 200 revolutions/minute x 3 minutes = 600 revolutions. So 600 revolutions/(12/7) = 600 revolutions x 7/12 = 350 revolutions. The wheel circumference is 2 x π x r = 2 x π x 2.5 cm = 15.7 cm. Now we can use formula 3, above. So 350 x 15.7 cm = 5495 cm. For picture B, we can see that the gear ratio is 8/24, which simplifies to 1/3, and we know from the question that the driving gear will move 200 revolutions/minute x 3 minutes = 600 revolutions. So 600 revolutions/(1/3) = 600 revolutions x 3 = 1800 revolutions. The wheel circumference is 2 x π x r = 2 x π x 2.5 cm = 15.7 cm. Now we can use formula 3, above. So 1800 x 15.7 cm = cm. For picture C, we can see that the gear ratio is 1/1, and we know from the question that the driving gear will move 200 revolutions/minute x 3 minutes = 600 revolutions. So 600 revolutions/(1) = 600 revolutions. The wheel circumference is 2 x π x r = 2 x π x 2.5 cm = 15.7 cm. Now we can use formula 3, above. So 600 x 15.7 cm = 9420 cm. 5.66

### Mechanical systems and control: investigation

6 Mechanical systems and control: investigation gear ratio the number of turns of one gear compared to the other is known as gear ratio speed ratio the gear ratio of a gear train, also known as its speed

### Curricular Activity Template

Curricular Activity Template NAME: Cadence Ellington University: Boston University Email: cadence@bu.edu Activity Title: Black Out Racers Grade Level (s): 8 th -12th Approx. Time: 2-3 hours Subject Areas:

Name Date Period Worksheet 5.2 Applications of Angles Show all work. All answers must be given as either simplified, exact answers. A calculator is permitted unless otherwise stated. Unless stated otherwise,

### Perimeter. Perimeter is the distance around a figure. Add to find the perimeter (P) of each figure. P

Place Value: Large Numbers... 5 Comparing Numbers...6 Rounding Numbers...7 Two-Digit Addition with Regrouping...8 Three-Digit Addition with Regrouping...9 Addition of Large Numbers... 10 Problem olving:

### Section 2C Formulas with Dividing Decimals

Section 2C Formulas with Dividing Decimals x Look at the following z-score formula again from Statistics. z. Suppose we want to calculate the z-score if x 17.6 pounds, 13.8 pounds, and 2.5 pounds. Not

### ACTIVITY: Finding a Formula Experimentally

8.1 Volumes of Cylinders How can you find the volume of a cylinder? 1 ACTIVITY: Finding a Formula Experimentally Work with a partner. a. Find the area of the face of a coin. b. Find the volume of a stack

### PART 3 MODULE 6 GEOMETRY: UNITS OF GEOMETRIC MEASURE

PART 3 MODULE 6 GEOMETRY: UNITS OF GEOMETRIC MEASURE LINEAR MEASURE In geometry, linear measure is the measure of distance. For instance, lengths, heights, and widths of geometric figures are distances,

### Pacific Charter Institute Pacing Guide Grade(s): _5 Subject Area: _Math in Focus grade 5 CP: yes _X no

Week 1 Pre-requisite skills review Chapter 1 pre-test Assessment 5 chapter pre-test pp. 1-4 or MIF Student book 5A pp. 1-4 Reteach 4A (1.1, 1.2, 2.1, 3.2, 3.4) NWEA Kids start Wed. Week 2 1.1 Writing numbers

### GEOMETRY CIRCLING THE BASES PRE-VISIT - BALLPARK FIGURES - PART 2

PRE-VISIT - BALLPARK FIGURES - PART 2 OBJECTIVE: Students will be able to: Identify the formulas for finding circumference and area of a circle. Calculate the circumference and area of given circles. TIME

### Cumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.

Name Score Math Course 1 1A 1. Use the numbers 6, 12, and 18 to make two addition facts and two subtraction facts. 12 + 12 12 + 12 12 12 12 12 2. Use the numbers 5, 15, and 75 to make two multiplication

### Sum Fun Tournament Meeting (Multiple Topics)

Sum Fun Sum Fun Tournament Meeting (Multiple Topics) Sum Fun Topic There are a wide range of topics and difficulty levels covered during this meeting. Materials Needed The first four items listed below

### Exploring Bicycle Technology August 11, Front sprockets

Exploring Bicycle Technology August 11, 1996 Step 1. Identify the following parts on your bicycle: Shifters Rear sprockets Front sprockets Chain How many front sprockets are on your bicycle? How many rear

March Madness Basketball Tournament Math Project COMMON Core Aligned Decimals, Fractions, Percents, Probability, Rates, Algebra, Word Problems, and more! To Use: -Print out all the worksheets. -Introduce

### Bishop Kelley High School Summer Math Program Course: Trigonometry and Trigonometry with Pre-Calculus

015 01 Summer Math Program Course: Trigonometr and Trigonometr with Pre-Calculus NAME: DIRECTIONS: Show all work on loose-leaf paper, which ou will turn in with the packet. (NO WORK IN PACKET!) Put final

### Rescue Rover. Robotics Unit Lesson 1. Overview

Robotics Unit Lesson 1 Overview In this challenge students will be presented with a real world rescue scenario. The students will need to design and build a prototype of an autonomous vehicle to drive

### Cumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.

Name Score Math Course 1 1B 1. Use the numbers 5, 11, and 16 to make two addition facts and two subtraction facts. 11 + 12 12 + 12 12 12 12 12 2. Use the numbers 4, 16, and 64 to make two multiplication

### Common Core State Standards

0 03 Pacing Guide for Sixth Grade Common Core State Standards Math Content Standards Ratios and Proportional Relationships RP Understand ratio concepts and use ratio reasoning to solve problems. The Number

### Mathematics (Project Maths Phase 3)

*B6* Pre-Leaving Certificate Examination, 2014 Triailscrúdú na hardteistiméireachta, 2014 Mathematics (Project Maths Phase 3) Paper 1 Ordinary Level 2½ hours 300 marks Name: School: Address: Class: Teacher:

### Gears and Levers Investigations. Level A Investigations. Level B Investigations

Gears and Levers Investigations Level A Investigations A-1 The Lever How does a lever work? This Investigation introduces the students to gears and angles. Students work with pairs of gears and determine

### Algebra I: A Fresh Approach. By Christy Walters

Algebra I: A Fresh Approach By Christy Walters 2005 A+ Education Services All rights reserved. No part of this publication may be reproduced, distributed, stored in a retrieval system, or transmitted,

### Ch. 8 Review Analyzing Data and Graphs

How to find the Median Value It's the middle number in a sorted list. To find the Median, place the numbers you are given in value order and find the middle number. Look at these numbers: 3, 13, 7, 5,

### A percent is a ratio that compares a number to 100. It represents part of a whole. Model 54% on the 10-by-10 grid. Then write the percent as a ratio.

Lesson 5.1 Reteach Model Percents A percent is a ratio that compares a number to. It represents part a whole. Model 54% on the 10-by-10 grid. Then write the percent as a ratio. Step 1 The grid represents

### A 28-inch ribbon was cut into four equal lengths. How long was each piece of ribbon?

Name Score Benchmark Test 1 Math Course 1 For use after Lesson 0 1. (5) A -inch ribbon was cut into four equal lengths. How long was each piece of ribbon? A. 7 inches B. 7 1 inches. () In a class of students

### Goal: Students will apply math and geography to a baseball investigation.

Name: Take Me Out to the Ballgame Subject: Math/Geography Grade: 6-8 Goal: Students will apply math and geography to a baseball investigation. Materials: Pictometry Online (http://pol.pictometry.com/)

### Perimeter. Name. 22 Topic 17. Reteaching Find the perimeter of the figure below.

Perimeter Reteaching 1-1 Find the perimeter of the figure below. 15 m x 4 ft 4 ft 2 ft y 2 ft 5 ft 6 m 20 ft Reteaching 1-1 By using a formula: There are two equal lengths and equal widths, so you can

### Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

### Simple Machines. Dr. John B. Beaver and Dr. Barbara R. Sandall

By Dr. John B. Beaver and Dr. Barbara R. Sandall COPYRIGHT 2002 Mark Twain Media, Inc. ISBN 978-58037-864-2 Printing No. 1558-EB Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing

### Using Darts to Simulate the Distribution of Electrons in a 1s Orbital

NAME: Using Darts to Simulate the Distribution of Electrons in a 1s Orbital Introduction: The quantum theory is based on the mathematical probability of finding an electron in a given three dimensional

The Mechanical Advantage Subject Area(s) Physical Science, Science and Technology Associated Unit Yellow highlight = required component Associated Lesson Activity Title Wide World of Gears Figure 1 ADA

### Lesson 2 Pre-Visit Batting Average Part 1: Fractions

Lesson 2 Pre-Visit Batting Average Part 1: Fractions Objective: Students will be able to: Understand that fractions represent parts of a whole. Set up fractions representing batting averages and other

### MATHCOUNTS Chapter Competition Target Round Problems 1 and 2 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.

MATHCOUNTS 2012 Chapter Competition Target Round Problems 1 and 2 Name School DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems, which will be presented

### BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL 4

BIGGAR HIGH SCHOOL HOMEWORK BOOKLET NATIONAL Rounding 1. Round these numbers to the nearest 10: a) 238 b) 719 c) 682 3 2. Round these numbers to the nearest 100: a) 6783 b) 13295 c) 199 3 3. Round these

### MATHCOUNTS 2005 State Competition Target Round Problems 1 and 2

MATHCOUNTS 2005 State Competition Target Round Problems 1 and 2 Name School Chapter DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This round of the competition consists of eight problems, which will

### Year 10 Mathematics, 2007

Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 lgebra Use straightforward algebraic methods and sketch and interpret features of linear graphs Time: 20 minutes. Check that you have entered

### BEST PRACTICES Mike Johnson / Contributing Editor

BEST PRACTICES Mike Johnson / Contributing Editor GeAR drives: Key concepts: Selecting the correct lubricant There are several different gear tooth forms or designs, each with its own strengths and weaknesses

### Special Right Triangles

GEOMETRY Special Right Triangles OBJECTIVE #: G.SRT.C.8 OBJECTIVE Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling Standard) BIG IDEA (Why is

### The Science of Golf. Test Lab Toolkit The Swing: Driving. Grades Education

The Science of Golf Test Lab Toolkit The Swing: Grades 9-12 Partners in Education Science Technology Engineering Mathematics Table of Contents Welcome to the Test Lab 02 Investigate: Centripetal Force

Adaptor Core Technology: The Inception and Adapting of Calculus Based Truths within Geometric Entities Written By: Nick Siefers (Nicks@900global.com) Director of Operations 900 Global would like to introduce

### Lesson 22: Getting the Job Done Speed, Work, and Measurement Units

Lesson 22: Getting the Job Done Speed, Work, and Measurement Units Student Outcomes Students decontextualize a given speed situation, representing symbolically the quantities involved with the formula.

### Second Generation Bicycle Charging Station. Engineering Analysis

Second Generation Bicycle Charging Station By Jonathan Jerome, Michael Klinefelter, Connor Kroneberger, Kori Molever, and Robert Rosenberg Team 22B Engineering Analysis Document Submitted towards partial

### The Science of Golf. Test Lab Toolkit The Score: Handicap. Facilitator Guide Grades 6-8

The Science of Golf Test Lab Toolkit The Score: Facilitator Guide Grades 6-8 Science Technology Engineering Mathematics Table of Contents Welcome to the Test Lab 02 How to Use the Toolkit 03 Investigate:

### RATES AND RATIOS WITH COMPLEX FRACTIONS. Complex Fractions. Fraction in the denominator

RATES AND RATIOS WITH COMPLEX FRACTIONS LESSON.6 A complex fraction is a fraction that contains a fractional expression in its numerator, denominator or both. The following are examples of complex fractions.

### 25. [Perimeter] 4 2 = Measure each side length of the shape. Add together the side lengths.

25. [Perimeter] Skill 25.1 Finding the perimeter of polygons by measuring their side lengths. Measure each side length of the shape. Q. Use a ruler to find the perimeter of the scalene triangle in millimetres.

### Chain Drives. 1. As no slip takes place during chain drive, hence perfect velocity ratio is obtained

1. Introduction Chain Drives In Belt and Rope drives slipping may occur. In order to avoid slipping, steel chains are used. The chains are made up of a number of rigid links which are hinged together by

### FUNCTIONAL SKILLS MATHEMATICS (level 1)

FUNCTIONAL SKILLS MATHEMATICS (level 1) Detailed Marking Instructions Version: May 2011 Question Marking Scheme Illustrations of evidence No Give for each for awarding a mark 1 (a) Ans: 675 represent:

### Trade of Metal Fabrication. Module 1: Basic Fabrication Unit 3: Tools and Equipment Phase 2

Trade of Metal Fabrication Module 1: Basic Fabrication Unit 3: Tools and Equipment Phase 2 Table of Contents List of Figures... 3 List of Tables... 4 Document Release History... 5 Module 1 Basic Fabrication...

### 2008 Aquatic Weed Control Math Prep

2008 Aquatic Weed Control Math Prep Workbook Vol 1 By Ken Gioeli Extension Agent III / Natural Resource The Institute of Food and Agricultural Sciences IFAS is an Equal Employment Opportunity- Affirmative

### 2018 School Competition Sprint Round Problems 1 30

Name 08 School Competition Sprint Round Problems 0 0 4 5 6 7 8 DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. 9 This section of the competition consists of 0 problems. You will have 40 minutes to complete

### 2018 Chapter Competition Countdown Round Problems 1 80

2018 Chapter Competition Countdown Round Problems 1 80 This booklet contains problems to be used in the Countdown Round. 2018 MATHCOUNTS National Competition Sponsor National Sponsors Raytheon Company

### Chain Drives. Chain Drives 759 C H A P T E R

Chain Drives 759 C H A P T E R 21 Chain Drives 1. Introduction. 2. Advantages and Disadvantages of Chain Drive over Belt or Rope Drive. 3. Terms Used in Chain Drive. 4. Relation Between Pitch and Pitch

### Chain Drives ELEMEN MESIN II

Chain Drives ELEMEN MESIN II Introduction Belt and rope drives slipping may occur To avoid slipping Chains The chains are made up of number of rigid links which are hinged together by pin joints in order

### 6.RP Speed Conversions

6.RP Speed Conversions Alignments to Content Standards: 6.RP.A.3.d Task Jessica sees the following speed limit sign while visiting Australia where the units for speed are kilometers per hour: a. A conversion

### CAR DRIVE. Kelly went for a drive in her car. During the drive, a cat ran in front of the car. Kelly slammed on the brakes and missed the cat.

CAR DRIVE Kelly went for a drive in her car. During the drive, a cat ran in front of the car. Kelly slammed on the brakes and missed the cat. Slightly shaken, Kelly decided to return home. The graph below

### A Pyramid of Crunchkins

Pictured below you will see Nestle Crunchkins stacked in a triangular pyramid. Each layer is in the shape of an equilateral triangle, and the top layer is a single Nestle Crunchkin. How many Nestle Crunchkins

### Engineering Flettner Rotors to Increase Propulsion

Engineering Flettner Rotors to Increase Propulsion Author: Chance D. Messer Mentor: Jeffery R. Wehr Date: April 11, 2016 Advanced STEM Research Laboratory, Odessa High School, 107 E 4 th Avenue, Odessa

### Name Date of Data Collection. Class Period Lab Days/Period Teacher. Measuring Lung Capacity

Measuring Lung Capacity Background: The amount of air that you move in and out of your lungs while breathing normally is referred to as TIDAL VOLUME. While it is possible to inhale and exhale more forcefully

### weight of the book divided by the area of the bottom of the plunger.

Lab: Boyle s Law Datasheet Name Data: Pressure is defined as force per unit area: P = Force/Area When a book rests on top of the plunger, the pressure it exerts equals the weight of the book divided by

39 WAYS TO USE CUISENAIRE RODS VISIT OUR NEW WEBSITE WWW.KCS4EDUCATION.CO.UK FREE NEXT DAY DELIVERY BEST VALUE FOR MONEY DEDICATED CUSTOMER SERVICE Your trusted partner CALL: 0808 281 9440 ONLINE: www.kcs4education.co.uk

### Adding Whole Numbers and Money Subtracting Whole Numbers and Money Fact Families, Part 1

Adding Whole Numbers and Money Subtracting Whole Numbers and Money Fact Families, Part 1 Reteaching 1 Math Course 1, Lesson 1 To add money, line up the decimal points. Then add each column starting on

### Rounding Whole Numbers

s e s s i o n 1. 7 A Rounding Whole Numbers Math Focus Points Using place value understanding to round whole numbers to the nearest ten or hundred Telling time to the nearest 5 minutes and measuring time

### GRADE 8 BASELINE TEST 2013 MATHEMATICS. 1 Hour 30 Minutes

GRADE 8 BASELINE TEST 2013 GRADE 8 BASELINE TEST MATHEMATICS 2013 MATHEMATICS 1 Hour 30 Minutes 1 Hour 30 Minutes SCHOOL:. LEARNER:.. CLASS: 1 Baseline Assessment Instrument Gr 8 (135 marks) Read the questions

### 1. Which geometric solid would be best to use as a model of the following objects found in the real world. A. B. c.

1. Sec 5.6 Geometric & Algebra Connections Geometric Models Name: Choosing a Model Prism Pyramid Cylinder Cone Sphere Hemisphere SA = 2(lh + hw + lw) SA = LA + B SA = 2πrh + 2πr 2 SA = πrl + πr 2 SA =

### Pneumatic Reservoir Analysis Work Sheet

Pneumatic Reservoir Analysis Work Sheet Getting Started Use a pair of dial calipers to measure the length and diameter dimensions of the: 1. End Cap 2. Threaded Boss 3. Stainless Steel Tube Record these

### 13.7 Quadratic Equations and Problem Solving

13.7 Quadratic Equations and Problem Solving Learning Objectives: A. Solve problems that can be modeled by quadratic equations. Key Vocabulary: Pythagorean Theorem, right triangle, hypotenuse, leg, sum,

### In this unit, you will cover the following sections:

UNIT D 252 In this unit, you will cover the following sections: 1.0 Machines are tools that help humans do work. 1.1 Simple Machines Meeting Human Needs 1.2 The Complex Machine A Mechanical Team 2.0 An

### The Five Magic Numbers

The Five Magic Numbers Objective: Students will review the five numbers needed to construct a box and whisker plot. Students will also answer questions using a box and whisker plot they created. Background

### WHEELING IN MARCHING, OR ON A MOVABLE PIVOT. At drill day we tried to reconcile the instructions for the maneuver for wheeling while being in motion.

14 March 2012 WHEELING IN MARCHING, OR ON A MOVABLE PIVOT POC: Steve Giovannini, Don Miskey At drill day we tried to reconcile the instructions for the maneuver for wheeling while being in motion. 1. Right

### Equivalent forms: fractions, decimals, and percents Block 1 Student Activity Sheet

Block 1 Student Activity Sheet 1. List two real-life examples of fractions. 2. List two real-life examples of decimals. 3. List two real-life examples of percents. 4. Consider the table below showing Courtney

### Vocabulary: Objectives: Materials: For Each Station: (Have 2 stations for each liquid; 8 stations total, in student groups of 3-4) Students will:

Author: Ms. Adrienne Maribel López Date Created: August 2007 Subject: Properties of Matter Level: 6 th 8 th grade Standards: NYS Learning Standards for Mathematics, Science, and Technology-- Intermediate

### U.S. TSUBAKI BS/DIN ROLLER CHAIN

TSUBAKI BS/DIN ROLLER CHAIN BS/DIN Roller Chain These chains are manufactured to International Standards Organization metric dimensions (ISO 606), British Standard (BS 228), and DIN 8187. They are available

### 8.3 Trigonometric Ratios-Tangent. Geometry Mr. Peebles Spring 2013

8.3 Trigonometric Ratios-Tangent Geometry Mr. Peebles Spring 2013 Bell Ringer 3 5 Bell Ringer a. 3 5 3 5 = 3 5 5 5 Multiply the numerator and denominator by 5 so the denominator becomes a whole number.

### Algebra 3.5 day 1.notebook. September 10, Bellwork

Bellwork 1 Go over Quiz 2 Partners 3 Before we have our HW quiz, check your work and answers with last night's HW with your partner. If there is something your partner is not sure about, help them. If

### ROUND TOSS-UP: What is the square root of one million? (1000) (10 points) BONUS: How many zeros are at the end of ?

ROUND 1 1. TOSS-UP: What is 24% of 50? (12) (10 points) BONUS: A clothing store is having a 60% off sale on its dresses. Brandi has a coupon that lets her take 20% off of the sale price. If she pays \$24

### 2.6 Related Rates Worksheet Calculus AB. dy /dt!when!x=8

Two Rates That Are Related(1-7) In exercises 1-2, assume that x and y are both differentiable functions of t and find the required dy /dt and dx /dt. Equation Find Given 1. dx /dt = 10 y = x (a) dy /dt

### DECIMALS. Chapter INTRODUCTION

hut6929_ch04_a.qxd 2/8/04 2:47 PM Page 279 Chapter DECIMALS 4 INTRODUCTION When you look into the cockpit of a plane, you have to be impressed with the number of gauges that face the pilot. It is remarkable

### WAT305 Math Part 1 ABC Math

WAT305 Math Part 1 ABC Math Good to know for certification: You have used 35 150lb cylinders of Chlorine in 2011 how many pounds total did you use? How many pounds per month did you use? If demand is expected

### Math 081 Worksheet Section 8.4 v01 Spring 2011 Dressler. Name. 6) 12 dm. Find the area of the geometric figure. 1) 5 m. Rectangle. 25.

Math 081 Worksheet Section 8.4 v01 Spring 2011 Dressler Name 6) 12 dm Find the area of the geometric figure. 1) 5 dm Rectangle 5 m ) 6.8 m 12 units 25.5 units 2) 22.5 units Rectangle 3 m 8).9 m 20 yd 52

### Kungl Tekniska Högskolan

Centre for Autonomous Systems Kungl Tekniska Högskolan hic@kth.se March 22, 2006 Outline Wheel The overall system layout : those found in nature found in nature Difficult to imitate technically Technical

### BOOK BASIC. NotB oring MIDDLE GRADES MATH. The. Series Concept & Development by Imogene Forte & Marjorie Frank IP 416-7

The BASIC NotB oring SERIES IP 416-7 MIDDLE GRADES MATH BOOK Inventive Exercises to Sharpen Skills and Raise Achievement Series Concept & Development by Imogene Forte & Marjorie Frank INCENTIVE PUBLICATIONS

### Bouncing Ball A C T I V I T Y 8. Objectives. You ll Need. Name Date

. Name Date A C T I V I T Y 8 Objectives In this activity you will: Create a Height-Time plot for a bouncing ball. Explain how the ball s height changes mathematically from one bounce to the next. You

### 2:04:55. (You can check the internet to see if this time has been beat!)

Lesson: World Record Marathon Time Game Grades: 4-6 Skills: Number sense, time Time: 30 minutes As of 10/2006, the world record for the marathon is: 2:04:55 (You can check the internet to see if this time

### A Low Cost Digital Angle Gage, version 3

A Low Cost Digital Angle Gage, version 3 By R. G. Sparber Copyleft protects this document. 1 Sometimes re-inventing the wheel has advantages. What you see here is just a variation on a sine bar. The accuracy

### SECTION 1. READING AND WRITING NUMBERS PLACE VALUE

Ten Millions Millions Hundred-thousands Ten-thousands Thousands Hundreds Tens Ones Decimal point Tenths Hundredths Thousandths Ten-thousandths Hundred-thousandths Millionths SECTION 1. READING AND WRITING

### Agood tennis player knows instinctively how hard to hit a ball and at what angle to get the ball over the. Ball Trajectories

42 Ball Trajectories Factors Influencing the Flight of the Ball Nathalie Tauziat, France By Rod Cross Introduction Agood tennis player knows instinctively how hard to hit a ball and at what angle to get

### Part 1: Decimals. The decimal point separates the whole numbers from the fractional part of a

Part 1: Decimals Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 1328. 1095 In a whole number the decimal point is all the way to the right, even

### Section 4.2 Objectives

Section 4. Objectives Determine whether the slope of a graphed line is positive, negative, 0, or undefined. Determine the slope of a line given its graph. Calculate the slope of a line given the ordered

### 1) Solve for x. Round answers to the nearest tenth. (1 mark each = 2 marks)

WorkPlace Math 20 Chapter 1 Review Name /60 1) Solve for x. Round answers to the nearest tenth. (1 mark each = 2 marks) 3 x 4.3 2 a) = b) = 0 8 x 2) Calculate the slope. Express our answers as a fraction

### Standardized GRADE 5. Test Tutor MATH. Michael Priestley. Standardized Test Tutor: Math, Grade 5 Michael Priestley, Scholastic Teaching Resources

Standardized GRADE 5 Test Tutor MATH Michael Priestley Scholastic Inc. grants teachers permission to photocopy the reproducible pages from this mini-book for classroom use. No other part of this publication

### Subject:Engineering Mechanics Ch 1. Simple Machines

Shaikh Sir's Reliance Academy, Coaching Classes for Diploma Engg. Subject:Engineering Mechanics Ch 1. Simple Machines List Of Types: Definitions and theory Questions Problems on general Machines 1) Problem

### Reliable Speed Prediction: Propulsion Analysis and a Calculation Example

Reliable Speed Prediction: Propulsion Analysis and a Calculation Example Donald M. MacPherson VP Technical Director HydroComp, Inc. ABSTRACT Speed prediction is more than just bare-hull resistance. Speed

### Multiplying Fractions or Mixed Numbers

s e s s i o n 4 A. 3 Multiplying Fractions or Mixed Numbers Math Focus Points Multiplying a fraction or mixed number and a whole number Using a representation and reasoning to multiply a whole number by

### ( ) ADVANCED HONORS CHEMISTRY - CHAPTER 14 NAME: THE BEHAVIOR OF GASES GRAHAM'S LAW WORKSHEET - ANSWERS - V8 PAGE:

ADVANCED HONORS CHEMISTRY - CHAPTER 14 NAME: THE BEHAVIOR OF GASES DATE: GRAHAM'S LAW WORKSHEET - ANSWERS - V8 PAGE: 1. How fast would a ecule of sulfur dioxide travel if an atom of krypton (aarrgghh!)

### Case 12 Multistage Centrifugal Refrigeration System Halocarbon Refrigerant

Case 12 Multistage Centrifugal Refrigeration System Halocarbon Refrigerant Copy Right By: Thomas T.S. Wan 温 ) April 15, 2011 All Rights Reserved Case Background: This case is to show how to achieve the

### Parking Lot HW? Joke of the Day: What do you call a leg that is perpendicular to a foot? Goals:

Parking Lot Joke of the Day: HW? What do you call a leg that is perpendicular to a foot? a right ankle Goals: Agenda 1 19 hw? Course Recommendations Simplify Radicals skill practice L8 2 Special Right

### A school trip. An evening of your favourite television programmes. A rehearsal plan. To cook a two course meal.

Experience & Outcome: MNU 2-10a use and interpret electronic and paper-based timetables and schedules to plan events and activities, and make time calculations as part of my planning. recognise types of

### The Cycle Shop Performance Task

The Cycle Shop Performance Task Did you enjoy this activity? Why or why not? How do you think this type of activity compares to more traditional math practice problems? Do you think this type of activity

### ENGINEERING ANALYSIS OF THOROUGHBRED RACING. Rubin Boxer. Revelation Software

ENGINEERING ANALYSIS OF THOROUGHBRED RACING by Rubin Boxer Revelation Software P.O. Box 21344 Santa Barbara, CA 93121-1344 Phone: (805) 962-9045 www.revelationprofits.com Copyright 1997-2004 Revelation

### 11-1 Solving Two-Step Equations. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Solve. 1. n + 9 = 17 2. 6x = 42 3. 71 z = 55 4. y 8 n = 8 x = 7 z = 16 = 9 y = 72 Problem of the Day Rhombus ABCD has a perimeter of