Lesson one. Proportions in the Port of Long Beach 1. Terminal Objective. Lesson 1

Save this PDF as:
Size: px
Start display at page:

Download "Lesson one. Proportions in the Port of Long Beach 1. Terminal Objective. Lesson 1"

Transcription

1 Proportions in the Port of Long Beach Lesson one Terminal Objective Content Standard Reference: Students will solve Port of Long Beach word problems by writing a proportion and using the cross product property to write an equation and solve it. Grade 6 Number Sense 6.1.3: Use proportions to solve problems. Use crossmultiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Materials 1. Proportions PowerPoint 2. Popsicle stick Time Required 1 class 1

2 Keyword 1. Proportion two equal ratios Introduction of Lesson Anticipatory Set: Students should know how to determine whether two ratios form a proportion and how to solve a proportion in two ways: using the equal fraction approach or crossproducts. Recall #1: Do these two ratios form a proportion? 2 3 Tell you neighbor yes or no Answer: Yes Recall #2: Tell your neighbor the cross product property. Explain how it can be used in the first problem. Answer: , so this must be a proportion. Recall #3: Equal fraction approach: Solve this proportion by thinking of them as two different fractions: 2 3 Answer: x 12 (multiply the denominator by 4 to get 12) Recall #4: Crossproducts: Solve this proportion using cross products to write an equation and solve it. 8 x Solution: 2 x x x 30 5 Student Objective: Students will solve word problems involving the Port of Long Beach that use proportions. Purpose: Proportions are used in measurement, cooking, and enlarging and reducing photos. They are also used in the Port of Long Beach to calculate quantity 2

3 Introduction of Lesson cont d changes, like changes in cargo container sizes. Explain any other real-life use of proportions that come to mind. Lesson A proportion is two equal ratios. Today all of the numbers in the ratios will include a unit or label, such as feet or shoes. Each proportion will have four numbers, each with a label. Students can use an equal fraction approach to determine if the ratios are equal or use cross-products. Show the four numbers, each with a label in this situation. Also show students that the ratios are equal. A twenty-foot container holds 15,000 shoes. A forty-foot container holds 30,000 shoes. 1 TEU 2 TEUs 15, 000 shoes 30, 000 shoes What is the definition of a proportion? Answer: A proportion is two equal ratios. How many numbers will be in the proportion? Answer: 4. Each of the numbers will have a. Answer: unit or label. Is this a proportion? 1 cargo hold 6 cargo holds 10, 000 tons 60, 000 tons 3

4 Lesson cont d The teacher will pull a Popsicle stick to pick a random person to answer. Answer: Yes, multiply both the holds and the tons by 6 or the cross-products are equal. Write a proportion to represent a situation. There are four steps: 1. Read the situation. Identify the four numbers and their labels. 2. Write two fraction bars and the equal sign. 3. Write the labels in the proportion so they match either vertically or horizontally. 4. Fill in the matching numbers. There must be a relationship both vertically and horizontally. Model the four steps to write a proportion for this situation: A crane operator unloads one container in two minutes. The operator can unload 10 containers in 20 minutes. 1. Step 1 is to identify the units. In this case, the units are containers and minutes. 2. Step 2 is to write one unit on top of the other: cont' r 1 10 min Step 3 is to write two fraction bars and the equal sign: cont' r min 4. Step 4 is to fill in the numbers so each ratio has a meaning: cont' r 1 10 min

5 Lesson cont d Show two new proportions for the same problem. Partners discuss if the new proportions make sense. After one minute, select a student at random to say the answer. 1. Does this proportion make sense? min 2 20 cont' r 1 10 Answer: Yes. 2. Does this proportion make sense? cont' r 1 2 min Answer: No, this proportion shows that it takes 10 minutes to unload one container Write a proportion for this situation: One shipping container is 8 feet tall, so 5 containers are 40 feet tall. Answer: cont'r ft Write a proportion to represent a word problem with one number missing. Students will follow the same steps, but a variable will need to be used to represent the missing number. Write a proportion to represent this problem: The Morton Salt Company can package pound bags of salt in a minute. How many bags can it package in an hour? Follow the four steps. Answer: bags 20 x or 20 bags 1min min 1 60 x bags 60 min 5

6 Lesson cont d 1. How do you know which numbers go with each label? Answer: The proportion has to match the situation you were given, both horizontally and vertically. 2. Does it matter if I put bags on the top or bottom? Answer: No. Write a proportion only for this word problem. Do not answer the how many bags? question: One bag sells for $5. How many bags would you get for $75? Answer: bag $ 1 5 x 75 or x 1 bag bags $5 $75 Solve a proportion by using an equal fractions approach. There are four steps: 1. Write the proportion for the problem. 2. Determine the factor you need to multiply by. 3. Multiply to find the missing number. 4. Rewrite the answer so it answers the question. Use the Morton Salt Company example: The Morton Salt Company can package pound bags of salt in a minute. How many bags can it package in an hour? bags x bags 1 min 60 min 6

7 Lesson cont d 2. 1 min x min bags x bags bags are packaged in an hour. When is the equal fraction approach appropriate? Answer: One of the numerators or denominators must be a factor of the other. Here, 1 goes into 60: 20 bags x bags 1 min 60 min Solve the Morton Salt proportion you wrote earlier: 1 bag sells for $5. How many bags would you get for $75? 1. 1 bag x bags $5 $75 2. $5 x 15 $ bag x bags 4. I would get 15 bags for $75. Solve a proportion by using cross-products to write the equation and solving it. 1. Write the proportion for the problem. 2. Use cross-products property to write equation. 3. Divide both sides by the coefficient. 4. Rewrite answer so it answers the question. 7

8 Lesson cont d The Morton Salt Company receives two shipments each year totaling 120,000 tons of salt. How much salt would it receive in a year if it receives three shipments? 1. 2 shipments 3 shipments 120, 000 tons x tons 2. 2x 120, x 120, x 180, It would receive 180,000 tons of salt. Why was cross-multiplying a better way to solve the last proportion? Answer: Because 2 does not go into 3, or 2 is not a factor of 3. Write and solve a proportion to solve this problem: A crane operator unloads 30 containers in 60 minutes. How many containers are unloaded in 90 minutes? cont' r x 60 min x x x 45 cont' r 90 min containers are unloaded in 90 minutes. 8

9 Closure Have students exchange notes with their partner and look for any differences. Students should add to their notes if they see something they would like to include. Lastly, they should write the summary on the bottom of their notes. 9

Dimensional Analysis

Dimensional Analysis Dimensional Analysis Today you ll learn about Dimensional Analysis You will be able to use unit analysis to help convert units you are not used to using. By the end of the lesson, you will: Use dimensional

More information

Using Proportions to Solve Percent Problems I

Using Proportions to Solve Percent Problems I RP7-1 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving

More information

Ratio and Proportion Study Guide 12

Ratio and Proportion Study Guide 12 Ratio and Proportion Study Guide 12 Ratio: A ratio is a comparison of the relationship between two quantities or categories of things. For example, a ratio might be used to compare the number of girls

More information

Pre-Algebra Lecture 6

Pre-Algebra Lecture 6 Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals

More information

x x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m =

x x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m = Slope and Lines The slope of a line is a ratio that measures the incline of the line. As a result, the smaller the incline, the closer the slope is to zero and the steeper the incline, the farther the

More information

Lesson 13: The Formulas for Volume

Lesson 13: The Formulas for Volume Student Outcomes Students develop, understand, and apply formulas for finding the volume of right rectangular prisms and cubes. Lesson Notes This lesson is a continuation of Lessons 11, 12, and Module

More information

Five Ways to Solve Proportion Problems

Five Ways to Solve Proportion Problems Five Ways to Solve Proportion Problems Understanding ratios and using proportional thinking is the most important set of math concepts we teach in middle school. Ratios grow out of fractions and lead into

More information

Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving

Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words

More information

Rational Expressions - Proportions

Rational Expressions - Proportions .6 Rational Expressions - Proportions Objective: Solve proportions using the cross product and use proportions to solve application problems When two fractions are equal, they are called a proportion.

More information

Introduction to Fractions

Introduction to Fractions Section 0.6 Contents: Vocabulary of Fractions A Fraction as division Undefined Values First Rules of Fractions Equivalent Fractions Building Up Fractions VOCABULARY OF FRACTIONS Simplifying Fractions Multiplying

More information

Activity 1: Using base ten blocks to model operations on decimals

Activity 1: Using base ten blocks to model operations on decimals Rational Numbers 9: Decimal Form of Rational Numbers Objectives To use base ten blocks to model operations on decimal numbers To review the algorithms for addition, subtraction, multiplication and division

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Polynomial and Rational Functions Quadratic Functions Overview of Objectives, students should be able to: 1. Recognize the characteristics of parabolas. 2. Find the intercepts a. x intercepts by solving

More information

Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities.

Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities. 3 rd Grade Math Learning Targets Algebra: Indicator 1: Use procedures to transform algebraic expressions. 3.A.1.1. Students are able to explain the relationship between repeated addition and multiplication.

More information

PERCENTS. Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% =

PERCENTS. Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% = PERCENTS Percent means per hundred. Writing a number as a percent is a way of comparing the number with 100. For example: 42% = Percents are really fractions (or ratios) with a denominator of 100. Any

More information

From the Webisode: Math Meets Fashion

From the Webisode: Math Meets Fashion lesson CCSS CONNECTIONS Percent Markups From the Webisode: Math Meets Fashion In this lesson, s solve a multi-step problem by identifying percent markups of a whole and calculating a final sale price.

More information

Determine If An Equation Represents a Function

Determine If An Equation Represents a Function Question : What is a linear function? The term linear function consists of two parts: linear and function. To understand what these terms mean together, we must first understand what a function is. The

More information

Lesson Plan Assembly Line Grade 6 Ratios

Lesson Plan Assembly Line Grade 6 Ratios CCSSM: Grade 6 DOMAIN: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems. Standard: 6.RP. Understand the concept of a ratio and use ratio

More information

Creating Graphs. Learning Objective-To create graphs that show data.

Creating Graphs. Learning Objective-To create graphs that show data. Creating Graphs Summary- Key Words- Students will be able to identify graphs, components of graphs, interpret graphs, and construct various types of graphs. Pictograph Bar Graph Circle Graph Background

More information

Building Concepts: Dividing a Fraction by a Whole Number

Building Concepts: Dividing a Fraction by a Whole Number Lesson Overview This TI-Nspire lesson uses a unit square to explore division of a unit fraction and a fraction in general by a whole number. The concept of dividing a quantity by a whole number, n, can

More information

2.3 Solving Equations Containing Fractions and Decimals

2.3 Solving Equations Containing Fractions and Decimals 2. Solving Equations Containing Fractions and Decimals Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Solve equations containing fractions

More information

Chapter 5 Section 1 Answers: pg 222 224

Chapter 5 Section 1 Answers: pg 222 224 Chapter 5 Section 1 Answers: pg 222 224 1. Terminating decimal 2. Repeating decimal 3. Terminating decimal 4. Repeating decimal 5. Sample answer: If you can write the number as a quotient of two integers,

More information

Brain Game. 3.4 Solving and Graphing Inequalities HOW TO PLAY PRACTICE. Name Date Class Period. MATERIALS game cards

Brain Game. 3.4 Solving and Graphing Inequalities HOW TO PLAY PRACTICE. Name Date Class Period. MATERIALS game cards Name Date Class Period Brain Game 3.4 Solving and Graphing Inequalities MATERIALS game cards HOW TO PLAY Work with another student. Shuffle the cards you receive from your teacher. Then put them face down

More information

Solving Equations Involving Parallel and Perpendicular Lines Examples

Solving Equations Involving Parallel and Perpendicular Lines Examples Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines

More information

1.2 Linear Equations and Rational Equations

1.2 Linear Equations and Rational Equations Linear Equations and Rational Equations Section Notes Page In this section, you will learn how to solve various linear and rational equations A linear equation will have an variable raised to a power of

More information

1.6 The Order of Operations

1.6 The Order of Operations 1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

More information

6. Block and Tackle* Block and tackle

6. Block and Tackle* Block and tackle 6. Block and Tackle* A block and tackle is a combination of pulleys and ropes often used for lifting. Pulleys grouped together in a single frame make up what is called a pulley block. The tackle refers

More information

Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

More information

Chapter 3: Ratio, Proportion & Percent

Chapter 3: Ratio, Proportion & Percent HOSP 1107 (Business Math) Learning Centre Chapter 3: Ratio, Proportion & Percent RATIO A ratio is a comparison of the relative values of numbers or quantities. We can write a ratio for any statement containing

More information

Chapter 1: Order of Operations, Fractions & Percents

Chapter 1: Order of Operations, Fractions & Percents HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain

More information

MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

More information

MA107 Precalculus Algebra Exam 2 Review Solutions

MA107 Precalculus Algebra Exam 2 Review Solutions MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write

More information

Section 4.1 Rules of Exponents

Section 4.1 Rules of Exponents Section 4.1 Rules of Exponents THE MEANING OF THE EXPONENT The exponent is an abbreviation for repeated multiplication. The repeated number is called a factor. x n means n factors of x. The exponent tells

More information

MATH-0910 Review Concepts (Haugen)

MATH-0910 Review Concepts (Haugen) Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,

More information

Teaching Pre-Algebra in PowerPoint

Teaching Pre-Algebra in PowerPoint Key Vocabulary: Numerator, Denominator, Ratio Title Key Skills: Convert Fractions to Decimals Long Division Convert Decimals to Percents Rounding Percents Slide #1: Start the lesson in Presentation Mode

More information

How Far Away is That? Ratios, Proportions, Maps and Medicine

How Far Away is That? Ratios, Proportions, Maps and Medicine 38 How Far Away is That? Ratios, Proportions, Maps and Medicine Maps A ratio is simply a fraction; it gives us a way of comparing two quantities. A proportion is an equation that has exactly one ratio

More information

Exponents. Exponents tell us how many times to multiply a base number by itself.

Exponents. Exponents tell us how many times to multiply a base number by itself. Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,

More information

Math Circle Beginners Group October 18, 2015

Math Circle Beginners Group October 18, 2015 Math Circle Beginners Group October 18, 2015 Warm-up problem 1. Let n be a (positive) integer. Prove that if n 2 is odd, then n is also odd. (Hint: Use a proof by contradiction.) Suppose that n 2 is odd

More information

PROBABILITY AND STATISTICS

PROBABILITY AND STATISTICS PROBABILITY AND STATISTICS Grade Level: Written by: Length of Unit: Middle School, Science and Math Monica Edwins, Twin Peaks Charter Academy, Longmont, Colorado Four Lessons, plus a Culminating Activity

More information

Years after 2000. US Student to Teacher Ratio 0 16.048 1 15.893 2 15.900 3 15.900 4 15.800 5 15.657 6 15.540

Years after 2000. US Student to Teacher Ratio 0 16.048 1 15.893 2 15.900 3 15.900 4 15.800 5 15.657 6 15.540 To complete this technology assignment, you should already have created a scatter plot for your data on your calculator and/or in Excel. You could do this with any two columns of data, but for demonstration

More information

Lesson Overview: Tell students that they are going to learn, how to identify equivalent fractions.

Lesson Overview: Tell students that they are going to learn, how to identify equivalent fractions. Teacher: Miss. Domonique Ragni Lesson Plan Title: Equivalent Fractions Grade Level: 3 rd grade Time allotted: 45 minutes Lesson Overview: Tell students that they are going to learn, how to identify equivalent

More information

Test 4 Sample Problem Solutions, 27.58 = 27 47 100, 7 5, 1 6. 5 = 14 10 = 1.4. Moving the decimal two spots to the left gives

Test 4 Sample Problem Solutions, 27.58 = 27 47 100, 7 5, 1 6. 5 = 14 10 = 1.4. Moving the decimal two spots to the left gives Test 4 Sample Problem Solutions Convert from a decimal to a fraction: 0.023, 27.58, 0.777... For the first two we have 0.023 = 23 58, 27.58 = 27 1000 100. For the last, if we set x = 0.777..., then 10x

More information

Measurement. Customary Units of Measure

Measurement. Customary Units of Measure Chapter 7 Measurement There are two main systems for measuring distance, weight, and liquid capacity. The United States and parts of the former British Empire use customary, or standard, units of measure.

More information

1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.

1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved. 1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points

More information

Preliminary Mathematics

Preliminary Mathematics Preliminary Mathematics The purpose of this document is to provide you with a refresher over some topics that will be essential for what we do in this class. We will begin with fractions, decimals, and

More information

Teacher Answer Key: Measured Turns Introduction to Mobile Robotics > Measured Turns Investigation

Teacher Answer Key: Measured Turns Introduction to Mobile Robotics > Measured Turns Investigation Teacher Answer Key: Measured Turns Introduction to Mobile Robotics > Measured Turns Investigation Phase 1: Swing Turn Path Evaluate the Hypothesis (1) 1. When you ran your robot, which wheel spun? The

More information

Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

More information

Graphing Rational Functions

Graphing Rational Functions Graphing Rational Functions A rational function is defined here as a function that is equal to a ratio of two polynomials p(x)/q(x) such that the degree of q(x) is at least 1. Examples: is a rational function

More information

DRAFT. New York State Testing Program Grade 7 Common Core Mathematics Test. Released Questions with Annotations

DRAFT. New York State Testing Program Grade 7 Common Core Mathematics Test. Released Questions with Annotations DRAFT New York State Testing Program Grade 7 Common Core Mathematics Test Released Questions with Annotations August 2014 Developed and published under contract with the New York State Education Department

More information

MATH 110 Landscape Horticulture Worksheet #4

MATH 110 Landscape Horticulture Worksheet #4 MATH 110 Landscape Horticulture Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As a Landscape Horticulturist,

More information

Unit 2 Number and Operations Fractions: Multiplying and Dividing Fractions

Unit 2 Number and Operations Fractions: Multiplying and Dividing Fractions Unit Number and Operations Fractions: Multiplying and Dividing Fractions Introduction In this unit, students will divide whole numbers and interpret the answer as a fraction instead of with a remainder.

More information

Oral and mental starter

Oral and mental starter Lesson Objectives Order fractions and position them on a number line (Y6) Vocabulary gauge, litre numerator, denominator order Resources OHT. individual whiteboards (optional) Using fractions Oral and

More information

Multiplication and Division with Rational Numbers

Multiplication and Division with Rational Numbers Multiplication and Division with Rational Numbers Kitty Hawk, North Carolina, is famous for being the place where the first airplane flight took place. The brothers who flew these first flights grew up

More information

Ratios (pages 288 291)

Ratios (pages 288 291) A Ratios (pages 2 29) A ratio is a comparison of two numbers by division. Ratio Arithmetic: to : Algebra: a to b a:b a b When you write a ratio as a fraction, write it in simplest form. Two ratios that

More information

EE6-5 Solving Equations with Balances Pages 77 78

EE6-5 Solving Equations with Balances Pages 77 78 EE6-5 Solving Equations with Balances Pages 77 78 STANDARDS 6.EE.B.5, 6.EE.B.6 Goals Students will use pictures to model and solve equations. Vocabulary balance equation expression sides (of an equation)

More information

Activities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median

Activities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median Activities/ Resources for Unit V: Proportions, Ratios, Probability, Mean and Median 58 What is a Ratio? A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a

More information

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman hundredths tenths ones tens Decimal Art An Introduction to Decimals Directions: Part 1: Coloring Have children

More information

Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org

Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org Number of Lessons: 7 Grades: 3-5 Number & Operations In this unit plan, students explore relationships among

More information

Fraction Problems. Figure 1: Five Rectangular Plots of Land

Fraction Problems. Figure 1: Five Rectangular Plots of Land Fraction Problems 1. Anna says that the dark blocks pictured below can t represent 1 because there are 6 dark blocks and 6 is more than 1 but 1 is supposed to be less than 1. What must Anna learn about

More information

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.

Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions. Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear

More information

Introducing Multiplication of Fractions A Lesson for Fifth and Sixth Graders

Introducing Multiplication of Fractions A Lesson for Fifth and Sixth Graders Introducing Multiplication of Fractions A Lesson for Fifth and Sixth Graders by Marilyn Burns From Online Newsletter Issue Number 12, Winter 200 2004 Teaching multiplication of fractions is, in one way,

More information

Unit 3 - Lesson 3. MM3A2 - Logarithmic Functions and Inverses of exponential functions

Unit 3 - Lesson 3. MM3A2 - Logarithmic Functions and Inverses of exponential functions Math Instructional Framework Time Frame Unit Name Learning Task/Topics/ Themes Standards and Elements Lesson Essential Questions Activator Unit 3 - Lesson 3 MM3A2 - Logarithmic Functions and Inverses of

More information

Multiplying Fractions by Whole Numbers

Multiplying Fractions by Whole Numbers Multiplying Fractions by Whole Numbers Objective To apply and extend previous understandings of multiplication to multiply a fraction by a whole number. www.everydaymathonline.com epresentations etoolkit

More information

Fractions and Linear Equations

Fractions and Linear Equations Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps

More information

Geometry Notes RIGHT TRIANGLE TRIGONOMETRY

Geometry Notes RIGHT TRIANGLE TRIGONOMETRY Right Triangle Trigonometry Page 1 of 15 RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right

More information

Objective To guide the development and use of a rule for generating equivalent fractions. Family Letters. Assessment Management

Objective To guide the development and use of a rule for generating equivalent fractions. Family Letters. Assessment Management Equivalent Fractions Objective To guide the development and use of a rule for generating equivalent fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

More information

PERCENTS - compliments of Dan Mosenkis

PERCENTS - compliments of Dan Mosenkis PERCENTS - compliments of Dan Mosenkis Percent Basics: Percents are connected to many ideas: fractions, decimals, proportions, relative amounts, and multiplicative change. You could say they are like the

More information

Solving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions.

Solving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions. Solving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

More information

Linear Equations. 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber

Linear Equations. 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Linear Equations 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI- 83

More information

Graphing Linear Equations in Two Variables

Graphing Linear Equations in Two Variables Math 123 Section 3.2 - Graphing Linear Equations Using Intercepts - Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the

More information

Partial Fractions Decomposition

Partial Fractions Decomposition Partial Fractions Decomposition Dr. Philippe B. Laval Kennesaw State University August 6, 008 Abstract This handout describes partial fractions decomposition and how it can be used when integrating rational

More information

Arc Length and Areas of Sectors

Arc Length and Areas of Sectors Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a sector.

More information

Solving Equations by the Multiplication Property

Solving Equations by the Multiplication Property 2.2 Solving Equations by the Multiplication Property 2.2 OBJECTIVES 1. Determine whether a given number is a solution for an equation 2. Use the multiplication property to solve equations. Find the mean

More information

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17 NS6-0 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE

More information

MATH 110 Automotive Worksheet #4

MATH 110 Automotive Worksheet #4 MATH 110 Automotive Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As an automotive technician, you will use ratios

More information

Student Exploration: Unit Conversions

Student Exploration: Unit Conversions Name: Date: Student Exploration: Unit Conversions Vocabulary: base unit, cancel, conversion factor, dimensional analysis, metric system, prefix, scientific notation Prior Knowledge Questions (Do these

More information

Lesson Plan -- Percent of a Number/Increase and Decrease

Lesson Plan -- Percent of a Number/Increase and Decrease Lesson Plan -- Percent of a Number/Increase and Decrease Chapter Resources - Lesson 4-11 Find a Percent of a Number - Lesson 4-11 Find a Percent of a Number Answers - Lesson 4-12 Percent of Increase and

More information

N Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

N Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Performance Assessment Task Swimming Pool Grade 9 The task challenges a student to demonstrate understanding of the concept of quantities. A student must understand the attributes of trapezoids, how to

More information

Graphic Organizers SAMPLES

Graphic Organizers SAMPLES This document is designed to assist North Carolina educators in effective instruction of the new Common Core State and/or North Carolina Essential Standards (Standard Course of Study) in order to increase

More information

Mathematics Task Arcs

Mathematics Task Arcs Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

More information

The gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.

The gas can has a capacity of 4.17 gallons and weighs 3.4 pounds. hundred million$ ten------ million$ million$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.

More information

Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

More information

Solutions to Homework Problems for Basic Cost Behavior by David Albrecht

Solutions to Homework Problems for Basic Cost Behavior by David Albrecht Solutions to Homework Problems for Basic Cost Behavior by David Albrecht Solution to Problem #11 This problem focuses on being able to work with both total cost and average per unit cost. As a brief review,

More information

Assessment For The California Mathematics Standards Grade 3

Assessment For The California Mathematics Standards Grade 3 Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

More information

Performance Assessment Task Bikes and Trikes Grade 4. Common Core State Standards Math - Content Standards

Performance Assessment Task Bikes and Trikes Grade 4. Common Core State Standards Math - Content Standards Performance Assessment Task Bikes and Trikes Grade 4 The task challenges a student to demonstrate understanding of concepts involved in multiplication. A student must make sense of equal sized groups of

More information

Ratios and Proportional Relationships: Lessons 1-6

Ratios and Proportional Relationships: Lessons 1-6 Unit 7-1 Lesson 1-6 Ratios and Proportional Relationships: Lessons 1-6 Name Date Classwork Book Math 7: Mr. Sanford Lessons 1-6: Proportional Relationship Lesson 1-1 Lesson 1: An Experience in Relationships

More information

Lesson 4: Solving and Graphing Linear Equations

Lesson 4: Solving and Graphing Linear Equations Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A-2-M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,

More information

Fractions as Numbers INTENSIVE INTERVENTION. National Center on. at American Institutes for Research

Fractions as Numbers INTENSIVE INTERVENTION. National Center on. at American Institutes for Research National Center on INTENSIVE INTERVENTION at American Institutes for Research Fractions as Numbers 000 Thomas Jefferson Street, NW Washington, DC 0007 E-mail: NCII@air.org While permission to reprint this

More information

Negative Integer Exponents

Negative Integer Exponents 7.7 Negative Integer Exponents 7.7 OBJECTIVES. Define the zero exponent 2. Use the definition of a negative exponent to simplify an expression 3. Use the properties of exponents to simplify expressions

More information

Objectives for the lesson

Objectives for the lesson Foundations of Mathematical Reasoning Student Pages 14.C, Blood alcohol content Lesson 14 Part C, Blood alcohol content Theme: Risk Assessment Blood alcohol content (BAC) is a measurement of how much alcohol

More information

Section 1.1 Linear Equations: Slope and Equations of Lines

Section 1.1 Linear Equations: Slope and Equations of Lines Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of

More information

PowerScore Test Preparation (800) 545-1750

PowerScore Test Preparation (800) 545-1750 Question 1 Test 1, Second QR Section (version 1) List A: 0, 5,, 15, 20... QA: Standard deviation of list A QB: Standard deviation of list B Statistics: Standard Deviation Answer: The two quantities are

More information

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

More information

Decimal Notations for Fractions Number and Operations Fractions /4.NF

Decimal Notations for Fractions Number and Operations Fractions /4.NF Decimal Notations for Fractions Number and Operations Fractions /4.NF Domain: Cluster: Standard: 4.NF Number and Operations Fractions Understand decimal notation for fractions, and compare decimal fractions.

More information

Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3

Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3 Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels

More information

This document contains Chapter 2: Statistics, Data Analysis, and Probability strand from the 2008 California High School Exit Examination (CAHSEE):

This document contains Chapter 2: Statistics, Data Analysis, and Probability strand from the 2008 California High School Exit Examination (CAHSEE): This document contains Chapter 2:, Data Analysis, and strand from the 28 California High School Exit Examination (CAHSEE): Mathematics Study Guide published by the California Department of Education. The

More information

1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =

1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) = Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is

More information

Assessment Anchors and Eligible Content

Assessment Anchors and Eligible Content M07.A-N The Number System M07.A-N.1 M07.A-N.1.1 DESCRIPTOR Assessment Anchors and Eligible Content Aligned to the Grade 7 Pennsylvania Core Standards Reporting Category Apply and extend previous understandings

More information

Mathematics Common Core Sample Questions

Mathematics Common Core Sample Questions New York State Testing Program Mathematics Common Core Sample Questions Grade7 The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and

More information

Lesson/Unit Plan Name: Number Lines, Fractions, and Bar Models

Lesson/Unit Plan Name: Number Lines, Fractions, and Bar Models Grade Level/Course: Grades and Lesson/Unit Plan Name: Number Lines, Fractions, and Bar Models Rationale/Lesson Abstract: Students will be able to use bar models to help them identify points on a number

More information

north seattle community college

north seattle community college INTRODUCTION TO FRACTIONS If we divide a whole number into equal parts we get a fraction: For example, this circle is divided into quarters. Three quarters, or, of the circle is shaded. DEFINITIONS: The

More information