MATHEMATICS 5 - download.edufile.net

MATHEMATICS 5Course Description

1

Table of Contents

Series Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

General Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Course Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Unit Breakdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Unit 1 . Numbering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Unit 2 . Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Unit 3 . Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Unit 4 . Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Unit 5 . Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Unit 6 . Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Unit 7 . More Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Unit 8 . Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Unit 9 . Operations with Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Unit 10 . Measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Unit 11 . Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Unit 12 . Area and Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2

Series Description

The objective of the EduSystem Mathematics K-6 series is to help students develop skills and mathematical concepts in accordance with the standards set forth by the Department of Education of Puerto Rico and the National Council of Teachers of Mathematics. The purpose of the series is to create awareness of why studying mathematical processes is important and how it is necessary for solving problems that relate to real-life situations.

Through its content, strategies, and techniques, the EduSystem Mathematics K-6 series instills a deep understanding of the concepts, skills, and techniques necessary for the subsequent study of higher mathematics and applications. The way in which the topics, examples, and recommended applications are presented allows students to visualize, understand, and value the usefulness of mathematics in everyday life.

The EduSystem Mathematics K-6 series covers the following areas and topics: number sense, counting, and cardinal numbers; operations and algebraic thought; numbers and operations in base ten; numbers and operations with fractions and ratios; proportional relationships; numeral systems; expressions and equations; measurement and data; statistics and probability, and geometry.

In each lesson, the objectives have been carefully aligned by taking into consideration the concepts and skills students need in order to establish connections between the different topics. The instructional focus is based upon conceptual understanding, skills development, and mathematical problems/solutions. It also focuses on the development of critical thinking skills which is the integral means of foundation for the students.

The EduSystem Mathematics K-6 series encourages the direct application of what students learn and how they visualize the importance of mathematics as a universal discipline relating to society, community, organizations and institutions. Furthermore, the incorporation of situations and real-life problems in each of the topics aims to awaken an interest in the study of mathematics for students.

Concept Development

The EduSystem Mathematics K-6 series is directed toward developing a mastery of:

b Mathematical reasoning skills and their applications.

b Application of problem solving processes and strategies.

b Use of technology as tools to access, analyze, and apply information in the solution of problems in their immediate surroundings.

3

General ObjectivesThe objectives of this Series are to:

b Help students develop an interest and appreciation for mathematics.

b Develop mathematical capability within students through experiences that stimulate their curiosity and focus it toward investigation, problem solving, and communication.

b Promote that students visualize mathematics as an integral whole and not as a group of isolated topics.

b Develop the problem solving processes in students, as a cornerstone of encouragement, furthering the development of mathematical capacity.

b Stimulate within students the need of using language and academic vocabulary to com-municate mathematical ideas.

b Develop mathematical reasoning and critical thinking skills that allow students to visuali-ze mathematics as a relevant discipline in their lives.

b Emphasize the concepts of numbers, operations, and calculations so that they are co-rrectly defined, conceived, and adequately applied.

b Promote the learning of concepts in geometry and measurement through hands-on ex-periences that incorporate experimentation and discovery of mathematical relationships using solid objects or manipulatives.

4

Course Structure

The Mathematics 5 course is composed of twelve units. Each unit is composed of lessons. Each lesson contains a presentation divided into sections that develop their individual topics. Each lesson also contains a descriptive log, activities, worksheets, and handouts related to the content and, as in most cases, website links and resources. The practice and review documents generally include word problems, as well as a section devoted solely to solving problems.

We invite you to get to know the presentation sections and the documents that are generally found in the course lessons.

The units are made up of the following:

b Lessons Each unit is composed of several lessons which are divided by topics. Furthermore, each lesson is comprised of the following:

b Presentation Each presentation is composed of the following sections:

Unit Opening Each unit begins with an image which starts off the first lesson of the unit. This section presents the unit’s theme as well as several questions in which the image or theme are explored.

IntroductionPresentation of a situation and questions to be ex-plored.

Topics to Be DevelopedSections of concept development, where mathematical ideas and concepts are explained. On some occasions, skills are developed from the situation presented in the introduction and other examples are offered.

5

b Handouts and Worksheets

b Lesson 0

This lesson is composed of a series of unit documents and of formative and cumulative evaluation that can be used before, during, or after the study of each unit.

Homework

Practice for each concept building section. Students are provided with a reasonable amount of exercises so that they can master the skills and concepts studied in the lesson.

What I Know!

A pretest of the concepts and skills to be discussed within the unit.

Think and Practice

It presents exercises and problems after every concept development section. It has activities that help practice, enrich, end reinforce the concepts learned throughout the lesson.

Practice

Lesson closure in which students apply what they learned through some exercise.

Think About It

A reasoning question, is presented and identified with a lightbulb. The goal is to develop students’ reasoning and analysis capacities.

Connection

Activity that initiates the unit. It relates Mathematics with other fields of study.

6

What I Learned

The skills and concepts learned in the unit are measured. It allows students to do a self-evaluation. The teacher may use it as a test.

Problem Solving

It explains strategies and procedures for the development of problem solving skills.

Reviewing the Units

Practice exercises that allow the student to confirm what they have learned in previous units.

Unit review

Practice exercises that allow students to confirm what they have learned in the unit.

Think

It presents activities and includes mathematical reasoning exercises. It can be found in some units.

Knowing Technology

It presents technology in its different manifestations, including the computer as well as all the gadgets present in our daily lives. It can be found in some units.

7

Breakdown of UnitsBelow is an itemization of the division of each unit in lessons, including the name of each lesson with its corresponding objectives, skills, and keywords.

Unit 1 . Numbering

At the end of this unit, the student will achieve the objectives found in the following lessons.

Unit Concepts

b comparing decimal numbers b ones

b ordering decimal numbers

b ordering whole numbers

b place value

b roman numerals

b tens

b tenths

b thousands

b thousandths

b comparing whole numbers

b decimal point

b equal to

b even and odd numbers

b greater than

b hundreds

b hundredths

b less than

b millions

Lesson 0 . Numbering

Code: C319G05U01L00

b Unit Documents: Connection, I Learned, Problem Solving, Unit Review I & II, What I Know and Knowing Technology

Lesson 1 . Numbers to the Ten Millions

Code: C319G05U01L01

Objective

b Recognize and write numbers to the ten millions.

8

Lesson 2 . Comparing and Ordering Numbers to the Ten Millions

Code: C319G05U01L02

Objective

b Compare and order numbers to the ten millions.

Lesson 3 . Decimal Numbers to the Thousandths

Code: C319G05U01L03

Objective

b Recognize decimal numbers to the thousandths.

Lesson 4 . Comparing and Ordering Decimals

Code: C319G05U01L04

Objective

b Compare and order decimal numbers.

Lesson 5 . Even and Odd Numbers

Code: C319G05U01L05

Objective

b Recognize even and odd numbers.

Lesson 6 . Roman Numerals

Code: C319G05U01L06

Objective

b Read and write roman numerals.

9

Unit 2 . Addition and Subtraction


Unit Concepts

b addition

b difference

b estimation

b properties of addition

b rounding

b strategies to add

b strategies to subtract

b subtraction

b total

Lesson 0 . Addition and Subtraction

Code: C319G05U02L00

b Unit Documents: Knowing Technology, What I Learned, Problem Solving, Reviewing the Units I & II, Think, Unit Review I & II and What I Know

Lesson 1 . Rounding Whole Numbers

Code: C319G05U02L01

Objective

b Round whole numbers.

Lesson 2 . Rounding Decimal Numbers

Code: C319G05U02L02

Objective

b Round decimal numbers.

10

Lesson 3 . Adding and Subtracting Whole Numbers

Code: C319G05U02L03

Objective

b Add and subtract whole numbers.

Lesson 4 . Estimating Totals and Differences of Whole Numbers

Code: C319G05U02L04

Objective

b Estimate totals and differences of whole numbers.

Lesson 5 . Adding and Subtracting Decimals to the Thousandths

Code: C319G05U02L05

Objective

b Add and subtract decimals to the thousandths.

Lesson 6 . Estimating Totals and Differences of Decimal Numbers

Code: C319G05U02L06

Objective

b Estimate totals and differences of decimal numbers.

11

Unit 3 . Multiplication


Unit Concepts

b addition

b Associative Property

b base

b Commutative Property

b composite number

b Distributive Property

b division

b estimation

b exponent

b exponential expression

b factor

b multilication

Lesson 0 . Multiplication

Code: C319G05U03L00


Lesson 1 . Properties of Multiplication

Code: C319G05U03L01

Objective

b Use the properties of multiplication.

b Multiplicative Identity Property

b Multiplicative Property

b Multiplicative Property of Zero

b order of operations

b prime factorization

b prime number

b product

b properties of multiplication

b strategies to multiply

b subtraction

b three-digit

b three-digit multiply

12

Lesson 2 . Estimating Products

Code: C319G05U03L02

Objective

b Estimate the product of a multiplication.

Lesson 3 . Multiplying Two-Digit Factors

Code: C319G05U03L03

Objective

b Multiply two-digit factors.

Lesson 4 . Multiplying by 10, 100, and 1,000

Code: C319G05U03L04

Objective

b Multiply by 10, 100, and 1,000.

Lesson 5 . Multiplying Three-Digit Factors

Code: C319G05U03L05

Objective

b Multiply three-digit factors.

Lesson 6 . Prime factorization

Code: C319G05U03L06

Objectives

b Define prime numbers, composite numbers, factors and prime factorization.

b Decompose composite numbers in prime factors.

b Use the factor tree and consecutive division methods to find the prime factors of composite numbers.

b Factor composite numbers.

13

Lesson 7 . Exponential Expression in Usual Form

Code: C319G05U03L07

Objectives

b Know the terms base and exponent as part of the mathematical vocabulary.

b Recognize that the base number is multiplied by itself the number of times indica-ted by the exponent.

b Calculate and write the exponential expressions in standard form.

Lesson 8 . Write an Expression in Exponential Form

Code: C319G05U03L08

Objectives

b Identify the correct base number in order to write an exponential expression.

b Write a standard expression in exponential form.

Lesson 9 . Order of Operations

Code: C319G05U03L09

Objectives

b Learn the order of operations when there are expressions with addition, subtrac-tion, multiplication and division, parenthesis, brackets, and power.

b Use the order of operations to solve exercises containing operations such as addi-tion, subtraction, multiplication and division, parenthesis, brackets, and powers.

14

Unit 4 . Geometry


Unit Concepts

b angles b parallel lines

b perpendicular lines

b points

b quadrilaterals

b radius

b rays

b round figures

b segments

b similarity

b symmetry

b vertex

b axis of symmetry

b center

b chord

b circle

b circumference

b congruence

b diameter

b geometric shape

b line

b oblique lines

Lesson 0 . Geometry

Code: C319G05U04L00

b Unit Documents: Knowing Technology, What I Learned, Problem Solving, Reviewing The Units I & II, Think, Unit Review I & II and What I Know

Lesson 1: Basic Geometric Concepts

Code: C319G05U04L01

Objective

b Recognize basic geometric concepts.

Lesson 2 . Perpendicular, Oblique, and Parallel Lines

Code: C319G05U04L02

Objective

b Recognize perpendicular, oblique, and parallel lines.

15

Lesson 3 . AngleClassification

Code: C319G05U04L03

Objective

b Classify angles according to their measures.

Lesson 4 . TriangleClassification

Code: C319G05U04L04

Objective

b Classify triangles according to the measures of its sides and angles.

Lesson 5 . QuadrilateralClassification

Code: C319G05U04L05

Objective

b Recognize and classify quadrilaterals.

Lesson 6 . Axis of Symmetry in a Figure

Code: C319G05U04L06

Objective

b Identify the axis of symmetry in a figure.

Lesson 7 . Similar and Congruent Figures

Code: C319G05U04L07

Objective

b Recognize similar and congruent figures.

Lesson 8 . Geometric Figures

Code: C319G05U04L08

Objective

b Recognize geometric figures.

16

Lesson 9 . Circles

Code: C319G05U04L09

Objective

b Recognize the circle and its parts.

17

Unit 5 . Multiplication and Division


Unit Concepts

b dividend

b division

b divisor

b estimation

b inverse operations

b multiplication

b quotient

b remainder

Lesson 0 . Multiplication and Division

Code: C319G05U05L00

b Unit Documents: Problem Solving, Unit Review I & II, What I Know and What I Learned

Lesson 1 . Fact Families

Code: C319G05U05L01

Objective

b Form fact families.

Lesson 2 . Dividing by Multiples of 10

Code: C319G05U05L02

Objective

b Divide by multiples of 10.

18

Lesson 3 . One- Digit Divisors

Code: C319G05U05L03

Objective

b Divide by one-digit divisors.

Lesson 4 . Four or Five-Digit Dividends

Code: C319G05U05L04

Objective

b Divide with four or five-digit numbers in the dividend.

Lesson 5 . Two-Digit Divisors

Code: C319G05U05L05

Objective

b Divide by two-digit divisors.

Lesson 6 . Verifying a Division through Multiplication

Code: C319G05U05L06

Objective

b Verify a division through multiplication.

Lesson 7 . Division with Zeros in the Quotient

Code: C319G05U05L07

Objective

b Divide with zeros in the quotient.

Lesson 8 . Estimating Quotients

Code: C319G05U05L08

Objective

b Esstimate quotients.

19

Lesson 9 . Numerical and Algebraic Expressions

Code: C319G05U05L09

Objectives

b Know the meaning of the terms of variable, numeric expression and variable ex-pression.

b Recognize that a variable in an algebraic expression is taking the place of a nume-rical value (number).

b Read numerical and algebraic expressions correctly.

b Know the difference between numerical expressions and algebraic expressions.

b Write a mathematical expression as an algebraic expression.

20

Unit 6 . Statistics


Unit Concepts

b sample b tally table

b frequency table

b frequency

b bar graph

b linear graph

b circle graph

b pictograph

b survey

b population

b data

b mean

b range

b median

b mode

Lesson 0 . Statistics

Code: C319G05U06L00

b Unit Documents: Connection, Knowing Technology, What I Learned, Problem Sol-ving, Reviewing the Units I & II, Unit Review I & II and What I Know

Lesson 1 . Experiments, Surveys, and Predictions

Code: C319G05U06L01

Objectives

b Define what are experiments, surveys, and predictions.

b Gather and organize data.

Lesson 2 . Mean, Median, and Range

Code: C319G05U06L02

Objective

b Find the mean, median, range and mode of a set of data.

21

Lesson 3 . Graphs & Pictographs

Code: C319G05U06L03

Objective

b Draw bar graphs, linear graphs, circle graphs, and pictographs.

Lesson 4 . Ordered Pairs

Code: C319G05U06L04

Objective

b Llocate ordered pairs in a coordinate plane.

22

Unit 7 . More Multiplication


Unit Concepts

b decimal numbers

b dividend

b division

b divisor

b factors

b multiplication

b product

b quotient

b remainder

Lesson 0 . More Multiplication

Code: C319G05U07L00


Lesson 1 . Multiplying a Decimal Number by a Whole Number

Code: C319G05U07L01

Objective

b Multiply a decimal number by a whole number.

Lesson 2 . Multiplying Two Decimal Numbers

Code: C319G05U07L02

Objective

b Multiply two decimal numbers.

23

Lesson 3 . Zeros as part of the Products of a Multiplication of Decimals

Code: C319G05U07L03

Objective

b Add zeros to the products of a multiplication of decimals.

Lesson 4 . Dividing a Decimal Number by a Whole Number

Code C319G05U07L04

Objective

b Divide a decimal number by a whole number.

24

Unit 8 . Fractions


Unit Concepts

b common factor b like fractions

b mixed numbers

b multiple

b ordering

b proper fractions

b simplify

b unlike fractions

b whole part

b comparing

b equivalence

b factors

b fractional part

b fractions

b greatest common factor (GCF)

b improper fractions

b least common multiple (LCM)

Lesson 0 . Fractions

Code: C319G05U08L00

b Unit Documents: Problem Solving, Reviewing the Units I & II, Think, Knowing Tech-nology, What I Learned, Unit Review I & II and What I Know

Lesson 1 . Equivalent Fractions

Code: C319G05U08L01

Objective

b Recognize and find equivalent fractions.

Lesson 2 . Greatest Common Factor (GCF)

Code: C319G05U08L02

Objective

b Find the greatest common factor of two or more numbers.

25

Lesson 3 . Simplifying Fractions

Code: C319G05U08L03

Objective

b Simplify fractions.

Lesson 4 . Least Common Multiple (LCM)

Code: C319G05U08L04

Objective

b Find the least common multiple of two or more numbers.

Lesson 5 . Comparing and Ordering Fractions

Code: C319G05U08L05

Objectives

b Compare fractions.

b Order fractions.

Lesson 6 . Changing a Mixed Number to an Improper Fraction

Code: C319G05U08L06

Objective

b Change from a mixed number to an improper fraction or a whole number.

Lesson 7 . Changing an Improper Fraction to a Mixed Number

Code: C319G05U08L07

Objective

b Change an improper fraction to a mixed number.

26

Unit 9 . Operations with Fractions


Unit Concepts

b addition

b area

b conversion of fractions to decimals

b decimal fraction

b decimal number

b division

b improper fractions

b like fractions

b minimum expression

Lesson 0 . Operations with Fractions

Code: C319G05U09L00

b Unit Documents: Connection, What I Learned, Problem Solving, Unit Review I & II and What I Know

Lesson 1 . Adding Like and Unlike Fractions

Code: C319G05U09L01

Objective

b Add like and unlike fractions.

Lesson 2 . Subtracting Like and Unlike Fractions

Code: C319G05U09L02

Objective

b Subtract like and unlike fractions.

b mixed number division

b mixed numbers

b multiplication

b reciprocal

b simplest form

b simplify

b subtraction

b unlike fractions

27

Lesson 3 . Adding and Subtracting Mixed Numbers

Code: C319G05U09L03

Objective

b Add and subtract mixed numbers.

Lesson 4 . Multiplying and Dividing Fractions

Code: C319G05U09L04

Objective

b Multiply and divide fractions.

Lesson 5 . Multiplying Mixed Numbers

Code: C319G05U09L05

Objectives

b Change mixed numbers to improper fractions and vice versa.

b Multiply mixed numbers converted to improper fractions.

b Recognize that the results in fractions have to be simplified.

b Simplify the results of the multiplication of mixed numbers.

Lesson 6 . Dividing Mixed Numbers

Code: C319G05U09L06

Objectives

b Divide mixed numerals.

b Change mixed numbers to improper fractions.

b Change the operation to multiplication and find the reciprocal or multiplicative inverse of the second fraction.

b Use the cross cancelling process to help in the multiplication process.

b Multiply fractions.

b Simplify results, writing them in their minimum expression.

28

Lesson 7 . Write Fractions as Decimals

Code: C319G05U09L07

Objectives

b Recognize decimal fractions.

b Represent decimal fractions as decimal numbers.

b Move the decimal point of the numerator to the left according to the number of zeros that the denominator has.

b Recognize that the decimal numbers consist of a whole part and another decimal part.

b Convert proper and improper fractions to decimals through the division of the numerator by the denominator.

29

Unit 10 . Measuring


Unit Concepts

b capacity b prefix

b temperature

b time

b units of capacity

b units of length

b units of mass

b units of time

b Celsius degrees

b English System

b equivalence

b Fahrenheit degrees

b length

b mass

b metric system

Lesson 0 . Measuring

Code: C319G05U10L00


Lesson 1 . MetricSystem:PrefixesandValues

Code: C319G05U10L01

Objective

b Recognize prefix values in the metric system.

Lesson 2 . Metric System’s Units of Length, Mass, and Capacity

Code: C319G05U10L02

Objective

b Use the units of length, mass and capacity of the metric system and its submulti-ples multiples.

30

Lesson 3 . Converting Units of Length, Mass, and Capacity from the English System

Code: C319G05U10L03

Objective

b Convert units of length, capacity and mass from the English System.

Lesson 4 . Temperature of a Thermometer in Celsius and Fahrenheit Degrees

Code: C319G05U10L04

Objective

b Measure the temperature of a thermometer in Celsius and Fahrenheit degrees.

Lesson 5 . Elapsed Time

Code: C319G05U10L05

Objective

b Find the elapsed time.

Lesson 6 . Converting Units of Time

Code: C319G05U10L06

Objective

b Convert units of time.

31

Unit 11 . Ratios and Proportions


Unit Concepts

b decimal numbers

b denominator

b equivalent ratios

b fractions

b numerator

b probability

b ratios

b simplify

Lesson 0 . Ratios and Proportions

Code: C319G05U11L00

b Unit Documents: Connection, What I Learned, Problem Solving, Unit Review I & II and What I Know

Lesson 1 . Ratios

Code: C319G05U11L01

Objectives

b Recognize ratios.

b Read and write ratios.

Lesson 2 . Equivalent Ratios

Code: C319G05U11L02

Objectives

b Recognize equivalent ratios.

b Read and write proportions.

32

Lesson 3 . Reading and Writing Percentages

Code: C319G05U11L03

Objective

b Read and write percentages.

Lesson 4 . The Percentage of a Given Number

Code: C319G05U11L04

Objective

b Find the percentage of a given number.

Lesson 5 . Changing Percentages to Fractions

Code: C319G05U11L05

Objective

b Change percentages to fractions.

Lesson 6 . Changing Decimals to Percentages

Code: C319G05U11L06

Objective

b Change decimals to percentages.

Lesson 7 . Changing Fractions to Percentages

Code: C319G05U11L07

Objective

b Change fractions to percentages.

Lesson 8 . Probability

Code: C319G05U11L08

Objective

b Find the probability of an event.

33

Unit 12 . Area and Perimeter


Unit Concepts

b area

b irregular two-dimensional figures

b parallelograms

b perimeter

b two-dimensional figures

b polyhedra

b volume

Lesson 0 . Area and Perimeter

Code: C319G05U12L00


Lesson 1 . The Perimeter of a Two-Dimensional Figure

Code: C319G05U12L01

Objective

b Estimate and find the perimeter of two-dimesnional figures

Lesson 2: The Area of a Two-Dimensional Figures

Code: C319G05U12L02

Objective

b Find the area of two-dimesnional figure

34

Lesson 3: The Volume of a Polyhedron

Code: C319G05U12L03

Objective

b Find the volume of a polyhedron.

Lesson 4 . The Area of Irregular Two-Dimesnional Figures

Code: C319G05U12L04

Objective

b Find the area of irregular two-dimesnional figures.

Lesson 5 . The Area of Parallelograms

Code: C319G05U12L05

Objective

b Find the area of a parallelogram.

MATHEMATICS 5 - download.edufile.net

Documents

Transcript of MATHEMATICS 5 - download.edufile.net