Grades 5-7 Math & Science

Operations With Fractions

A brief Content Overview

This chapter starts by showing how to compare fractions by writing them as equivalent fractions using the LCM of the denominators. You can compare fractions by changing them to decimal form. To add or subtract fractions and mixed number, first you write the fractions with a common denominator, then add or subtract the numerator. To multiply fractions, you can multiply their numerators and their denominators. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Students can use dimensional analysis, the multiplication of fractions, to convert units of measure in the customary system of measurement.

Objectives

Students will learn:

Comparing and Ordering Fractions

** Finding the Lest Common Multiple

** Comparing Fractions

Key Terms: multiple, least common multiple (LCM), least common denominator (LCD)

Fractions and Decimals

** Writing Fractions as Decimals

** Writing Decimals as Fractions

Key Term: terminating decima, repeating decimal

Adding and Subtracting Fractions

** Adding and Subtracting Fractions

** Adding and Subtracting Mixed Numbers

Multiplying and Dividing Fractions

** Multiplying Rational Numbers

** Dividing Rational Numbers

Key Terms: reciprocals

Measurement: Using Custormay Units of Measurement

** Identifying Appropriate Measures

** Converting Units

Key Terms: conversion factors, dimensional analysis

Problem Solving Strategy

** Working Backward

Solving Equations by Adding or Subtracting Fractions

** Using Subtraction to solve Equations

** Using Addition to Solve Equations

Solving Equations by Multiplying Fractions

** Using Multiplication to Solve Equations

** Solving Equations with Mixed Numbers

Powers of Products and Qotients

** Finding Powers of Products

** Finding Powers of Quotients

**** Resources, Tools to Monitor Progress, and Assessment: Problem of the Day, Student handbook: before the lesson to check prerequisite skills, During the Lesson to check understanding, and After the Lesson section to assess knowledge, Activities/Games, ppp - at times, Daily Cumulative (home assignment), Quizzes, and Pop Quizzes, Standardized Test Prep, Pre-Test Assessment, and Chapter TEST.

Factors, Fractions, and Exponents

Content Overview for this Chapter

You use divisibility tests to find factors of whole numbers. An exponent is a number or symbol that you place to the upper right of the base. Scientific notation is a way to write numbers as the product of two factors: a power of 10, and a decimal. A prime number is a positive integer greater that 1 with only two factors, 1 and itself. A positive integer greater than 1 with more than two factors is a composite number. The GCF of two or more expressions is the greatest factor the expressions have in common. A fraction is in simplest form when the numerator and the dnominator have no factors in common other than 1. A rational number is any number you can write as a quotient of two integers, a/b, where b is not zero.

Making Connections

Throughout this chapter, students are exposed to Interdiciplinary and Real-World Connections such as: Music (Arithmetic), Language (Geometry), Photography (Algebra), Health (Data Analysis), Economics (Problem Solving, Geometry). Science (Algebra), Geophysics, Seismology, Chemistry, and Zoology.

********************************

What you will learn in this chapter:

1. Divisibility and Factors

- to use divisibility tests

- to find factors

Key Terms: divisible; Divisibility Rules for 2, 5, and 10, Divisibility Rules for 3 and 9;

factors

2. Exponents

- to use exponents

- to use the order of operations with exponents

Key Terms: exponents, power

3. Prime Factorization and Greatest Common Factor

- to fing the prime factorization of a number

- to find the greatest common factor (GCF) of two or more numbers

Key Terms: prime number, composite number, prime factorization, greatest common factor (GCF)

4. Simplifying Fractions

- to find equivalent fractions

- to write fractions in simplest form

Key Terms: equivalent fractions, simplest form

5. Account for All Possibilities

- Problem Solving Strategies: Account for All Possibilities, Draw a Diagram, Look for a Patern, Make a Model, Make a Table, Simplify a Problem, Simulate a Problem, Solve by Graphing, Try, Test, Revise, Use Multiple Strategies, Work Backward, Write an Equation, and Write a proportion

6. Rational Numbers

- to identify and graph rational numbers

- to evaluate fractions containing variables

Key Terms: rational number

7. Exponents and Multiplication

- to multiply powers with the same base

- to find a power of a power

8. exponents and Division

- to divide expressons containing exponents

- to simplify expressions with integer exponents

9. Scientific Notation

- to write and evaluate numbers in scientific notation

- to calculate with scientific notation

Key Terms: scientific notation, standard notation

**** Resources, Tools to Monitor Progress and Assessment: Daily Skills Warm-up, Student handbook - before the lesson; Skills You Need section - during the lesson; Checking Understanding section, Activities/Games, ppp, after the lesson - Lesson Quiz, reinforcement/retention - Daily Cumulative (home assignment), Standardized Test Prep, Wrap Up, Pre-Test Assessment, and Chapter TEST.

Review

Four various problems of each section of each lesson as HOMEWORK or INCLASS assignment as time permits

Chapter Wrap Up

Cumulative Review

Mixed Review in every Lesson

Assessment

Try This exercises after every Example

Quizzes and Chapter Assessment

ASSESSMENT

After each lesson students are to:

** Try This exercises after every Example

** work minimum of four various problems of each section including the mixed review as homework or inclass when time permists.

** or/and work the excercises from the Cummulative Review handouts

** Quizzes and chapter test.

EXTRA CREDIT Chapter Project

Make a Balance Scale