Multiplying and Dividing Fractions and Decimals

Size: px
Start display at page:

Download "Multiplying and Dividing Fractions and Decimals"

Transcription

1 CHAPTER Multiplying and Dividing Fractions and Decimals Lesson. Dividing Fractions Express each improper fraction as a mixed number in simplest form Express each mixed number as an improper fraction Find each product in simplest form Divide. Draw a model to help you. 0. Dividing by is the same as multiplying by. Reteach Course A

2 . 6. Solve. Draw a model to find each quotient. Joshua cuts strings into a number of equal pieces. Each piece is Into how many pieces does Joshua cut the strings? Number of halves in wholes of a string. 6 Joshua cuts the string into 6 pieces.. A jar contains 6 liters of water. It is poured equally into some bottles. Each bottle contains liter of water. How many bottles are there? Number of bottles There are bottles.. George cut tiles into pieces that were each of a tile. Into how many pieces did George cut the tiles? 6 Chapter Lesson.

3 Divide. Express the quotient in simplest form. 6 6 Dividing by is the same as multiplying by Reteach Course A

4 Solve. Draw a model to find each quotient. A faucet can fill of a container in a minute. If water flows out of the faucet at the same rate, how long will it take the faucet to fill such containers? Number of three-fifths in wholes It will take the faucet minutes to fill the containers.. A gardener uses of a pail of water to water a plot of land. How many similar plots of land can the gardener water with such pails of water? Number of five-eighths in wholes The gardener can water similar plots of land with such pails of water. Chapter Lesson.

5 . Alex is painting some sculptures. He uses of a tube of paint for each sculpture. How many similar sculptures can he paint with such tubes of paint? Divide. Express the quotient in simplest form. 6 Dividing by is the same as multiplying by. Reteach Course A

6 Solve. Show your work. A rod is meter long. William cuts the rod into shorter pieces, each Into how many pieces has William cut the rod? meter long. Number of one-ninths in five-ninths William cuts the rod into pieces. 0 Chapter Lesson.

7 . A rectangle has an area of square meter. The width of the rectangle is meter. What is its length? Number of four-fifteenths in four-fifths The length of the rectangle is meters.. Ben has of a pizza left. He cuts it into equal pieces, each of the whole pizza. 6 Into how many pieces has Ben cut the pizza? Reteach Course A

8 Find each quotient. Write your answer in simplest form. 0 Dividing by is the same as multiplying by. Divide a numerator and a denominator by the common factor,.. 6 Rewrite as a multiplication expression. Divide a numerator and a denominator by their common factor Chapter Lesson.

9 Find each quotient. Write your answer in simplest form. Write as an improper fraction. Rewrite as a multiplication expression. Divide a numerator and a denominator by the common factor,.. Write as an improper fraction. Rewrite as a multiplication expression. Divide a numerator and a denominator by their commmon factor Reteach Course A

10 Find each quotient. Write your answer in simplest form Express both mixed numbers as improper fractions. Rewrite as a multiplication expression. Divide a numerator and a denominator by the common factor,.. Express both mixed numbers as improper fractions. Rewrite as a multiplication expression. Divide a numerator and a denominator by their commmon factor... 6 Chapter Lesson.

Divide Fractions and Whole Numbers

Divide Fractions and Whole Numbers Lesson 8 Divide Fractions and Whole Numbers You can use a number line to help you divide a whole number by a fraction Divide 6 4 _ 2 Step Draw a number line from 0 to 6 Divide the number line into halves

More information

Perfect Squares that are Written as Fractions or Decimals

Perfect Squares that are Written as Fractions or Decimals Math 9: Unit 1 Lesson 2 Perfect Squares that are Written as Fractions or Decimals Part 1: Fractions There are two ways to determine the square root of a perfect square that is written as a fraction: 1.

More information

Topic 11 Fraction Equivalence and Ordering. Exam Intervention Booklet

Topic 11 Fraction Equivalence and Ordering. Exam Intervention Booklet Topic Fraction Equivalence and Ordering Exam Intervention Booklet Intervention Lesson G Factoring Numbers Materials color tiles or counters, for each student The arrays below show all of the factors of..

More information

1 /4. (One-Half) (One-Quarter) (Three-Eighths)

1 /4. (One-Half) (One-Quarter) (Three-Eighths) LESSON 4: Fractions: A fraction is a part of a whole. Slice a pizza, and you will have fractions: 1 /2 1 /4 3 /8 (One-Half) (One-Quarter) (Three-Eighths) The top number tells how many slices you have and

More information

MANIPULATIVE MATHEMATICS FOR STUDENTS

MANIPULATIVE MATHEMATICS FOR STUDENTS MANIPULATIVE MATHEMATICS FOR STUDENTS Manipulative Mathematics Using Manipulatives to Promote Understanding of Elementary Algebra Concepts Lynn Marecek MaryAnne Anthony-Smith This file is copyright 07,

More information

Fractions Presentation Part 1

Fractions Presentation Part 1 New Jersey Center for Teaching and Learning Slide / Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and

More information

UNIT 5 INTRODUCTION TO FRACTIONS

UNIT 5 INTRODUCTION TO FRACTIONS UNIT INTRODUCTION TO FRACTIONS INTRODUCTION In this Unit, we will investigate fractions and their multiple meanings. We have seen fractions before in the context of division. For example, we can think

More information

Find Equivalent Fractions. Prerequisite: Identify Equivalent Fractions. Vocabulary

Find Equivalent Fractions. Prerequisite: Identify Equivalent Fractions. Vocabulary Lesson 7 Find Equivalent Fractions Name: Prerequisite: Identify Equivalent Fractions Study the example showing how to decide if two fractions are equivalent. Then solve problems 7. Example The bars are

More information

Hillhead High School. Fractions. What you need to know. S.O Grady 1

Hillhead High School. Fractions. What you need to know. S.O Grady 1 Fractions What you need to know S.O Grady What is a fraction? A fraction is a part of a whole (). Fractions consist of two numbers, a numerator and a denominator. Top number How many parts we have Bottom

More information

8/22/2013 3:30:59 PM Adapted from UbD Framework Priority Standards Supporting Standards Additional Standards Page 1

8/22/2013 3:30:59 PM Adapted from UbD Framework Priority Standards Supporting Standards Additional Standards Page 1 Approximate Time Frame: 6-8 weeks Connections to Previous Learning: Grade 2 students have partitioned circles and rectangles into two, three, or four equal shares. They have used fractional language such

More information

DIVISION BY FRACTIONS

DIVISION BY FRACTIONS DIVISION BY FRACTIONS 6.. 6.. Division by fractions introduces three methods to help students understand how dividing by fractions works. In general, think of division for a problem like 8 as, In 8, how

More information

Multiplying Two Fractions

Multiplying Two Fractions Objective Multiplying Two Fractions Students will build upon their understanding of multiplying a fraction by a whole number to now multiply a fraction by a fraction. Using concrete models to build rectangles

More information

Number and Operations Fractions

Number and Operations Fractions Number and Operations Fractions Standards Entry Points Access Skills 3 Page 59 Pages 60 61 Pages 60 62 4 Pages 63 64 Page 65 67 5 Pages 68 69 Page 70 72 MATHEMATICS 58 CONTENT AREA Mathematics DOMAIN Number

More information

Grade 6 Module 2 Lessons 1 8

Grade 6 Module 2 Lessons 1 8 Eureka Math 01 01 Grade Module Lessons 1 8 Eureka Math, Published by the non-profit Great Minds. Copyright 01 Great Minds. No part of this work may be reproduced, distributed, modified, sold, or commercialized,

More information

created by: The Curriculum Corner

created by: The Curriculum Corner created by: The Curriculum Corner I can understand fractions. I can show and understand that fractions represent equal parts of a whole, where the top number is the part and the bottom number is the total

More information

Introduction to Fractions

Introduction to Fractions Introduction to Fractions A fraction is a quantity defined by a numerator and a denominator. For example, in the fraction ½, the numerator is 1 and the denominator is 2. The denominator designates how

More information

Chapter 7 Math Guide

Chapter 7 Math Guide I can write fractions as a sum Write as unit fractions This means the fractions are broken into each individual unit/1 single piece. The fraction is /6. The model shows that pieces are shaded in. If you

More information

Adding and Subtracting Fractions Part 1: The same sized slice

Adding and Subtracting Fractions Part 1: The same sized slice Adding and Subtracting Fractions Part : The same sized slice Exercise What to do We are learning to add simple fractions Each of these fraction problems can be shown with fraction symbols. Use fraction

More information

I can use the four operations (+, -, x, ) to help me understand math.

I can use the four operations (+, -, x, ) to help me understand math. I Can Common Core! 4 th Grade Math I can use the four operations (+, -, x, ) to help me understand math. Page 1 I can understand that multiplication fact problems can be seen as comparisons of groups (e.g.,

More information

Fourth Grade. Adding Fractions with Common Denominators. Slide 1 / 111 Slide 2 / 111. Slide 4 / 111. Slide 3 / 111. Slide 6 / 111.

Fourth Grade. Adding Fractions with Common Denominators. Slide 1 / 111 Slide 2 / 111. Slide 4 / 111. Slide 3 / 111. Slide 6 / 111. Slide / Slide / Fourth Grade Fraction Computation 0-- www.njctl.org Slide / Slide / Table of Contents Click on a topic to go to that section. Adding Fractions with Common Denominators Adding Mixed Numbers

More information

1 2 full. You drink. of the water. How much of the bottle of water do you drink? 1 2? Numbers: 2 3. length, divide it into 3 equal sections.

1 2 full. You drink. of the water. How much of the bottle of water do you drink? 1 2? Numbers: 2 3. length, divide it into 3 equal sections. . Multiplying Fractions What does it mean to multiply fractions? ACTIVITY: Multiplying Fractions Work with a partner. A bottle of water is full. You drink of the water. How much of the bottle of water

More information

Grade 4. Number and Operations - Fractions 4.NF COMMON CORE STATE STANDARDS ALIGNED MODULES 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES

Grade 4. Number and Operations - Fractions 4.NF COMMON CORE STATE STANDARDS ALIGNED MODULES 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 4 Number and Operations - Fractions 4.NF.1-2 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES

More information

Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics D-H Approximately 25 days Begin around January 4 th

Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics D-H Approximately 25 days Begin around January 4 th HIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics D-H Approximately 25 days Begin around January 4 th In

More information

You Try: 1 of the free throws and Kevin. Riley and Jasper were working on their science fair project. Riley completed and

You Try: 1 of the free throws and Kevin. Riley and Jasper were working on their science fair project. Riley completed and 1 Jason made made of the free throws and Kevin of the free throws. What fraction of the free throws did they make altogether? Area Model 1 You Try: Riley and Jasper were working on their science fair project.

More information

5th Grade. Fraction Operations Part 2.

5th Grade. Fraction Operations Part 2. 1 5th Grade Fraction Operations Part 2 2015 11 13 www.njctl.org 2 Multiplying Fractions Table of Contents click on the topic to go to that section Multiplying Fractions and Whole Numbers Multiplying with

More information

You found trigonometric values using the unit circle. (Lesson 4-3)

You found trigonometric values using the unit circle. (Lesson 4-3) You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify

More information

6.5. PROBLEM SOLVING Use Multiplication. Plan. Unlock the Problem. Math Talk. Essential Question. Name. Module 6 269

6.5. PROBLEM SOLVING Use Multiplication. Plan. Unlock the Problem. Math Talk. Essential Question. Name. Module 6 269 ? Name 6.5 Essential Question PROBLEM SOLVING Use Multiplication Unlock the Problem Erica makes 6 submarine sandwiches and cuts each sandwich into thirds. How many 1_ -size sandwich pieces does she have?

More information

GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: Read (in standard form) whole numbers. whole numbers Equivalent Whole Numbers

GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: Read (in standard form) whole numbers. whole numbers Equivalent Whole Numbers CRAWFORDSVILLE COMMUNITY SCHOOL CORPORATION 1 GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: 2019 2020 GRADING PERIOD: QUARTER 1 MASTER COPY 1 20 19 NUMBER SENSE Whole Numbers 4.NS.1: Read and write whole

More information

Unit 5: Fractions Approximate Time Frame: 6-8 weeks Connections to Previous Learning: Focus of the Unit:

Unit 5: Fractions Approximate Time Frame: 6-8 weeks Connections to Previous Learning: Focus of the Unit: Approximate Time Frame: 6-8 weeks Connections to Previous Learning: Grade 2 students have partitioned circles and rectangles into two, three, or four equal shares. They have used fractional language such

More information

42 can be divided exactly by 14 and 3. can be divided exactly by and. is a product of 12 and 3. is a product of 8 and 12. and are factors of.

42 can be divided exactly by 14 and 3. can be divided exactly by and. is a product of 12 and 3. is a product of 8 and 12. and are factors of. Worksheet 2 Factors Write the missing numbers. 14 3 42 42 can be divided exactly by 14 and 3. 1. 21 5 can be divided exactly by 21 and. 2. 35 3 can be divided exactly by and. Write the missing numbers.

More information

NAME DATE CLASS NOTES

NAME DATE CLASS NOTES NAME DATE CLASS NOTES How do painters design murals so large that you can only see them from a distance? In most cases, designs for large projects like murals are first created as small pieces of art.

More information

1 x 12 = 12 2 x 6 = 12 4 x 3 = 12 3 x 4 = 12 2 x 6 = 12

1 x 12 = 12 2 x 6 = 12 4 x 3 = 12 3 x 4 = 12 2 x 6 = 12 Juice Problem You will need a ten shape and 2 shape, s, s, 6 s, fraction cards A shop sells packs of juices. orange, mango, pineapple. These are equal proportions. Show the fraction that is orange. Find

More information

Math 205 Test 2 Key. 1. Do NOT write your answers on these sheets. Nothing written on the test papers will be graded

Math 205 Test 2 Key. 1. Do NOT write your answers on these sheets. Nothing written on the test papers will be graded Math 20 Test 2 Key Instructions. Do NOT write your answers on these sheets. Nothing written on the test papers will be graded. 2. Please begin each section of questions on a new sheet of paper. 3. Please

More information

Course 1 Unit 1 Practice

Course 1 Unit 1 Practice Course 1 Unit 1 Practice Lesson 1-1 1. The table shows the price of some fruit at Mari s grocery store. Plot each decimal on the number line below. Write the first letter of the name of the fruit above

More information

Adding Fractions with Different Denominators. Subtracting Fractions with Different Denominators

Adding Fractions with Different Denominators. Subtracting Fractions with Different Denominators Adding Fractions with Different Denominators How to Add Fractions with different denominators: Find the Least Common Denominator (LCD) of the fractions Rename the fractions to have the LCD Add the numerators

More information

Name: # Date: 2. The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter of the pool?

Name: # Date: 2. The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter of the pool? Name: # Date: Lesson 13.1 Perimeter Ms. Mastromarco 1. Find the perimeter of the rectangle. 2. The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter

More information

Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million b) 6 billion c)

Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million b) 6 billion c) Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. 3 a) 3.6 million b) 6 billion c) 1 million 4 2 1 d) 2 billion e) 4.25 million f) 1.4 billion 10 2. Use

More information

Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million

Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. a) 3.6 million 3 b) 6 billion 4 c) 1 million 2 1 d) 2 billion 10 e) 4.25 million f) 1.4 billion 2. Use

More information

Triangles, Rectangles, Squares, and Circles

Triangles, Rectangles, Squares, and Circles Triangles, Rectangles, Squares, and Circles Triangle sides Rectangle 4 sides Lesson 21 21 Square length a rectangle with 4 equal sides width Measures of a circle: Radius = 1 diameter Diameter = 2 radius

More information

Lesson 0.1 The Same yet Smaller

Lesson 0.1 The Same yet Smaller Lesson 0.1 The Same yet Smaller 1. Write an expression and find the total shaded area in each square. In each case, assume that the area of the largest square is 1. a. b. c. d. 2. Write an expression and

More information

CHAPTER 3 DECIMALS. EXERCISE 8 Page Convert 0.65 to a proper fraction may be written as: 100. i.e = =

CHAPTER 3 DECIMALS. EXERCISE 8 Page Convert 0.65 to a proper fraction may be written as: 100. i.e = = CHAPTER 3 DECIMALS EXERCISE 8 Page 21 1. Convert 0.65 to a proper fraction. 0.65 may be written as: 0.65 100 100 i.e. 0.65 65 100 Dividing both numerator and denominator by 5 gives: 65 13 100 20 Hence,

More information

numerator - how many parts count b) What fraction of the bar is shaded? d) What fraction of the rectangle is shaded?

numerator - how many parts count b) What fraction of the bar is shaded? d) What fraction of the rectangle is shaded? . [Fractions] Skill. Illustrating proper fractions. numerator - how many parts count denominator - how many equal parts in one whole Q. What fraction of the circle is shaded? The circle is divided into

More information

Square Roots of Perfect Squares. How to change a decimal to a fraction (review)

Square Roots of Perfect Squares. How to change a decimal to a fraction (review) Section 1.1 Square Roots of Perfect Squares How to change a decimal to a fraction (review) A) 0.6 The 6 is in the first decimal position called the tenths place. Therefore, B) 0.08 The 8 is in the second

More information

G R AD E 4 UNIT 3: FRACTIONS - LESSONS 1-3

G R AD E 4 UNIT 3: FRACTIONS - LESSONS 1-3 G R AD E UNIT : FRACTIONS - LESSONS - KEY CONCEPT OVERVIEW In these lessons, students explore fraction equivalence. They show how fractions can be expressed as the sum of smaller fractions by using different

More information

Modeling Addition of Fractions (12 1)

Modeling Addition of Fractions (12 1) Modeling Addition of Fractions ( ) Eight friends want to see a movie. Four of them want to see a comedy. Two want to see an action movie and two want to see a science-fiction movie. What fraction of the

More information

3rd Grade. Fractions

3rd Grade. Fractions Slide 1 / 215 Slide 2 / 215 3rd Grade Fractions 2015-03-31 www.njctl.org Equal Parts Fractions of a Group Slide 3 / 215 Table of Contents Click title to go to that section Exploring Fractions with Pattern

More information

Grade 6 Module 2 Lessons 1-19

Grade 6 Module 2 Lessons 1-19 Eureka Math Homework Helper 2015 201 Grade Module 2 Lessons 1-19 Eureka Math, A Story of R a t i o s Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced,

More information

Objectives: Students will learn to divide decimals with both paper and pencil as well as with the use of a calculator.

Objectives: Students will learn to divide decimals with both paper and pencil as well as with the use of a calculator. Unit 3.5: Fractions, Decimals and Percent Lesson: Dividing Decimals Objectives: Students will learn to divide decimals with both paper and pencil as well as with the use of a calculator. Procedure: Dividing

More information

Grade 3: Step Up to Grade 4 Teacher s Guide

Grade 3: Step Up to Grade 4 Teacher s Guide Glenview, Illinois Boston, Massachusetts Chandler, Arizona Shoreview, Minnesota Upper Saddle River, New Jersey Copyright by Pearson Education, Inc., or its affiliates. All rights reserved. Printed in the

More information

Sample: Do Not Reproduce RAT3 STUDENT PAGES. RATIONAL NUMBERS Student Pages for Packet 3: Ordering and Equivalence.

Sample: Do Not Reproduce RAT3 STUDENT PAGES. RATIONAL NUMBERS Student Pages for Packet 3: Ordering and Equivalence. Name Period Date RATIONAL NUMBERS Student Pages for Packet : Ordering and Equivalence RAT. RAT.2 Ordering Fractions on a Number Line Use sense-making strategies to compare and order fractions. Identify

More information

Singapore Math 4-U.S. Edition Class Description: Singapore math says that Singapore Primary Mathematics U.S. Edition "is a series of rigorous

Singapore Math 4-U.S. Edition Class Description: Singapore math says that Singapore Primary Mathematics U.S. Edition is a series of rigorous Singapore Math 4-U.S. Edition Class Description: Singapore math says that Singapore Primary Mathematics U.S. Edition "is a series of rigorous elementary math textbooks and workbooks meant to be part of

More information

Model Factors. Use tiles to find all the factors of the product. Record the. arrays and write the factors shown. Name

Model Factors. Use tiles to find all the factors of the product. Record the. arrays and write the factors shown. Name Lesson 5.1 Reteach Model Factors Use tiles to find all the factors of 25. Record the arrays and write the factors shown. Step 1 Record the array and list the factors. Think: Every whole number greater

More information

Diocese of Erie Mathematics Curriculum Third Grade August 2012

Diocese of Erie Mathematics Curriculum Third Grade August 2012 Operations and Algebraic Thinking 3.OA Represent and solve problems involving multiplication and division 1 1. Interpret products of whole numbers. Interpret 5x7 as the total number of objects in 5 groups

More information

3rd Grade. Fractions. Equal Parts. Slide 1 / 215 Slide 2 / 215. Slide 4 / 215. Slide 3 / 215. Slide 5 / 215. Slide 6 / 215.

3rd Grade. Fractions. Equal Parts. Slide 1 / 215 Slide 2 / 215. Slide 4 / 215. Slide 3 / 215. Slide 5 / 215. Slide 6 / 215. Slide 1 / 215 Slide 2 / 215 3rd Grade Fractions 2015-03-31 www.njctl.org Equal Parts Fractions of a Group Whole Number Fractions Slide 3 / 215 Comparing Fractions with Same D enominators or Numerators

More information

GRADE 4. M : Solve division problems without remainders. M : Recall basic addition, subtraction, and multiplication facts.

GRADE 4. M : Solve division problems without remainders. M : Recall basic addition, subtraction, and multiplication facts. GRADE 4 Students will: Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as

More information

3rd Grade. Fractions. Slide 1 / 215. Slide 2 / 215. Slide 3 / 215. Table of Contents Click title to go to that section

3rd Grade. Fractions. Slide 1 / 215. Slide 2 / 215. Slide 3 / 215. Table of Contents Click title to go to that section Slide 1 / 215 3rd Grade Slide 2 / 215 Fractions 2015-03-31 www.njctl.org Table of Contents Equal Parts Fractions of a Group Exploring Fractions with Pattern Blocks Fractions on a Number Line Click title

More information

A C E. Answers Investigation 3. Applications = 0.42 = = = = ,440 = = 42

A C E. Answers Investigation 3. Applications = 0.42 = = = = ,440 = = 42 Answers Investigation Applications 1. a. 0. 1.4 b. 1.2.54 1.04 0.6 14 42 0.42 0 12 54 4248 4.248 0 1,000 4 6 624 0.624 0 1,000 22 45,440 d. 2.2 0.45 0 1,000.440.44 e. 0.54 1.2 54 12 648 0.648 0 1,000 2,52

More information

(Progressions for the CCSSM, Number and Operation Fractions, CCSS Writing Team, August 2011, page 3)

(Progressions for the CCSSM, Number and Operation Fractions, CCSS Writing Team, August 2011, page 3) o ¾ means that there are 3 one-fourths. o Students can count one fourth, two fourths, three fourths. Students express fractions as fair sharing or, parts of a whole. They use various contexts (candy bars,

More information

Model Perimeter. So, the perimeter of the figure is 16 units. centimeters. centimeters. centimeters. centimeters

Model Perimeter. So, the perimeter of the figure is 16 units. centimeters. centimeters. centimeters. centimeters Lesson 11.1 Reteach Model Perimeter Perimeter is the distance around a figure. Find the perimeter of the figure. Step 1 Choose a unit to begin counting and label it 1. 1 1 unit Step 2 Count each unit around

More information

1 of Lesson Alignment Guide Mathematics Cranston Public Schools

1 of Lesson Alignment Guide Mathematics Cranston Public Schools Multiplyig Fractions 2.2 (Note: There have been changes to the scope and sequence of units 2.2 and 2.3) 1 of 4 1-4 5.NF.4a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts;

More information

Estimation and Number Theory

Estimation and Number Theory 2 CHAPTER Estimation and Number Theory Worksheet 1 Estimation Find each sum or difference. Then use rounding to check that your answer is reasonable. Round each number to the nearest 100. 475 1 382 5?

More information

Third Grade Mathematics Scope and Sequence

Third Grade Mathematics Scope and Sequence Third Grade Mathematics Scope and Sequence Quarter 1 Domain Operations & Algebraic Thinking Numbers & Operation in Base Ten Standard 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as

More information

a) 1/2 b) 3/7 c) 5/8 d) 4/10 e) 5/15 f) 2/4 a) two-fifths b) three-eighths c) one-tenth d) two-thirds a) 6/7 b) 7/10 c) 5/50 d) ½ e) 8/15 f) 3/4

a) 1/2 b) 3/7 c) 5/8 d) 4/10 e) 5/15 f) 2/4 a) two-fifths b) three-eighths c) one-tenth d) two-thirds a) 6/7 b) 7/10 c) 5/50 d) ½ e) 8/15 f) 3/4 MATH M010 Unit 2, Answers Section 2.1 Page 72 Practice 1 a) 1/2 b) 3/7 c) 5/8 d) 4/10 e) 5/15 f) 2/4 Page 73 Practice 2 a) two-fifths b) three-eighths c) one-tenth d) two-thirds e) four-ninths f) one quarter

More information

BREATHITT COUNTY SCHOOLS 3 rd Grade Math Curriculum Map Week Standard Key Vocabulary Learning Target Resources Assessment

BREATHITT COUNTY SCHOOLS 3 rd Grade Math Curriculum Map Week Standard Key Vocabulary Learning Target Resources Assessment Number Operations/Fractions/Algebraic Expressions Week 1 Week 2 3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.2: Fluently add and subtract within 1000 using

More information

model, compare, and order fractions and mixed numbers explore and model tenths and hundredths as decimals compare and order decimals add and subtract

model, compare, and order fractions and mixed numbers explore and model tenths and hundredths as decimals compare and order decimals add and subtract - model, compare, and order fractions and mixed numbers explore and model tenths and hundredths as decimals compare and order decimals add and subtract decimals add and subtract money 270 The Grade 4 students

More information

Grade 5 Module 3 Addition and Subtraction of Fractions

Grade 5 Module 3 Addition and Subtraction of Fractions Grade 5 Module 3 Addition and Subtraction of Fractions OVERVIEW In Module 3, students understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals.

More information

Compare fractions. Introduction. Additional materials Numeracy Level 1

Compare fractions. Introduction. Additional materials Numeracy Level 1 Additional materials Numeracy Level Introduction You may see fractions in newspapers, on adverts and sale signs, or used with weights and measures. You need to be able to read and understand them, and

More information

Real Numbers and the Number Line. Unit 1 Lesson 3

Real Numbers and the Number Line. Unit 1 Lesson 3 Real Numbers and the Number Line Unit 1 Lesson 3 Students will be able to: graph and compare real numbers using the number line. Key Vocabulary: Real Number Rational Number Irrational number Non-Integers

More information

Fractions & Decimals Student Clinical Interview

Fractions & Decimals Student Clinical Interview Fractions & Decimals Student Clinical Interview Fractions Learning Pathway Curricular Connection QUESTION/PROMPT/VISUAL Anticipated Response Notes Unit Fractions Unit A Use proportional reasoning to make

More information

We are looking for the rate of rabbits to deer. So everything should be in the form rabbits:deer

We are looking for the rate of rabbits to deer. So everything should be in the form rabbits:deer Name Ratio and Rates Word Problems - Step-by-Step Lesson Comparison Ratios Word Problems: Daniel and Paul went hunting. On the first day Daniel caught 3 rabbits and Paul caught 8 deer. On the second day

More information

Alex Benn. Math 7 - Outline First Semester ( ) (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days

Alex Benn. Math 7 - Outline First Semester ( ) (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days Math 7 - Outline First Semester (2016-2017) Alex Benn (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days 0.1 Classroom Rules Multiplication Table Unit 1 Measuring

More information

The bottom number in the fraction is called the denominator. The top number is called the numerator.

The bottom number in the fraction is called the denominator. The top number is called the numerator. For Topics 8 and 9, the students should know: Fractions are a part of a whole. The bottom number in the fraction is called the denominator. The top number is called the numerator. Equivalent fractions

More information

4th Grade Mathematics Mathematics CC

4th Grade Mathematics Mathematics CC Course Description In Grade 4, instructional time should focus on five critical areas: (1) attaining fluency with multi-digit multiplication, and developing understanding of dividing to find quotients

More information

AIMS Common Core Math Standards Alignment

AIMS Common Core Math Standards Alignment AIMS Common Core Math Standards Alignment Third Grade Operations and Algebraic Thinking (3.OA) 1. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of

More information

End-of-Year Assessment

End-of-Year Assessment End-of-Year Assessment 1 Darlene solved a multiplication problem using U.S. traditional multiplication. Her work is shown at the right. a. Make an estimate for Darlene s problem. Does her answer make sense?

More information

Problem Solving Compare Fractions

Problem Solving Compare Fractions Lesson 9. Reteach Problem Solving Compare Fractions Nick walked mile to the gym. Then he walked mile to the store. Which distance is shorter? Read the Problem What do I need to find? I need to find which

More information

Concept: The Meaning of Fractions Name:

Concept: The Meaning of Fractions Name: Fractions Section : The Meaning of Fractions ANSWERS Concept: The Meaning of Fractions Name: Warm Up:. Can You Share Your Brownies? How many different ways can you divide the grids in half so that you

More information

3.NBT NBT.2

3.NBT NBT.2 Saxon Math 3 Class Description: Saxon mathematics is based on the principle of developing math skills incrementally and reviewing past skills daily. It also incorporates regular and cumulative assessments.

More information

Number Line: Comparing and Ordering Integers (page 6)

Number Line: Comparing and Ordering Integers (page 6) LESSON Name 1 Number Line: Comparing and Ordering Integers (page 6) A number line shows numbers in order from least to greatest. The number line has zero at the center. Numbers to the right of zero are

More information

RIDGEVIEW MATH 6 SUMMER PACKET

RIDGEVIEW MATH 6 SUMMER PACKET Welcome to Ridgeview Middle School! Please complete this summer packet to the best of your ability. This packet is to provide you with an opportunity to review objectives that were taught in the previous

More information

5-6 Study Guide. Radical Expressions and Rational Exponents. Attendance Problems. Simplify each expression. (No decimal answers!

5-6 Study Guide. Radical Expressions and Rational Exponents. Attendance Problems. Simplify each expression. (No decimal answers! Page 1 of 12 Radical Expressions and Rational Exponents Attendance Problems. Simplify each expression. (No decimal answers) 11 8 7 7 2 2.. 2. 11 6. I can rewrite radical expressions by using rational exponents.

More information

Enrichment yes yes no

Enrichment yes yes no 5-1 Leap Years You probably know that a leap year has days, with the extra day being February 2. Did you know that divisibility can help you recognize a leap year That is because the number of a leap year

More information

Problem Solving Compare Fractions

Problem Solving Compare Fractions Lesson 9. Problem Solving Compare Fractions Nick walked mile to the gym. Then he walked mile to the store. Which distance is shorter? Read the Problem What do I need to find? I need to find which distance

More information

1. Find the least common multiple (LCM) of the numbers 8, 6. A) 48 B) 2 C) 24 D) 1 E) 8

1. Find the least common multiple (LCM) of the numbers 8, 6. A) 48 B) 2 C) 24 D) 1 E) 8 . Find the least common multiple (LCM) of the numbers 8, 6. A) 48 B) C) 4 D) E) 8. Find the least common multiple (LCM) of the numbers 0, 6. A) 0 B) C) 60 D) E) 80. Find the least common multiple (LCM)

More information

1. Find the least common multiple (LCM) of the numbers 8, 10. A) 80 B) 2 C) 40 D) 1 E) 8

1. Find the least common multiple (LCM) of the numbers 8, 10. A) 80 B) 2 C) 40 D) 1 E) 8 . Find the least common multiple (LCM) of the numbers 8, 0. A) 80 B) 2 C) 40 D) E) 8 2. Find the least common multiple (LCM) of the numbers 6, 4. A) 6 B) 2 C) 84 D) E) 42. Find the least common multiple

More information

Grade 3 MODULE 5 Fractions as Numbers on the Number Line

Grade 3 MODULE 5 Fractions as Numbers on the Number Line Grade MODULE 5 Fractions as Numbers on the Number Line Mathematics Curriculum GRADE GRADE MODULE 5 Table of Contents GRADE MODULE 5 Fractions as Numbers on the Number Line Module Overview... Topic A: Partitioning

More information

Word. Problems. Focused Practice to Master Word Problems. Download the free Carson-Dellosa PEEK app and bring this product to life!

Word. Problems. Focused Practice to Master Word Problems. Download the free Carson-Dellosa PEEK app and bring this product to life! Word GRADE 8 Problems Focused Practice to Master Word Problems Real world applications Multi-step word problems Whole numbers, decimals, and fractions Ratio and proportion Percents and interest Metric

More information

Description Reflect and Review Teasers Answers

Description Reflect and Review Teasers Answers 1 Revision Recall basics of fractions A fraction is a part of a whole like one half (1/ one third (1/3) two thirds (2/3) one quarter (1/4) etc Write the fraction represented by the shaded part in the following

More information

Multiplying and Dividing Fractions and Mixed Numbers

Multiplying and Dividing Fractions and Mixed Numbers 4 CHAPTER Lesson 4.1 Multiplying and Dividing Fractions and Mixed Numbers Product of Proper Fractions Look at the diagram. Then complete. 1. 3 5? 1_ 2 of 3_ 5 Complete. 2. 3_ 4 of 5_ 7 Extra Practice 5A

More information

These are skills that we have covered within our math outcomes this year

These are skills that we have covered within our math outcomes this year Patterns & Relationships Whole Number Multiplication & Division Fractions, Decimals, and Percents Measurement, Data, and Geometry Word Problem Analysis These are skills that we have covered within our

More information

2.1.1 Introduction to Fractions and Mixed Numbers

2.1.1 Introduction to Fractions and Mixed Numbers 2.1.1 Introduction to Fractions and Mixed Numbers Learning Objective(s) 1 Identify the numerator and denominator of a fraction. 2 Represent a fraction as part of a whole or part of a set. Introduction

More information

Multiplying and Dividing Fractions and Mixed Numbers

Multiplying and Dividing Fractions and Mixed Numbers 4 CHAPTER Lesson 4.1 Multiplying and Dividing Fractions and Mixed Numbers Product of Proper Fractions Look at the diagram. Then complete. 1. 3 5? 1_ 2 of 3_ 5 Complete. 2. 3_ 4 of 5_ 7 Extra Practice 5A

More information

3rd Grade Math Pacing Guide Unit 1 Board Approved: December 12, 2016

3rd Grade Math Pacing Guide Unit 1 Board Approved: December 12, 2016 Unit 1 Board Approved: December 12, 2016 # CCSS Unit 1: Represent and solve problems involving multiplication and division September/October 31 Days Go Math Chapters Covered: Completed Student Learning

More information

Pearson Education, Inc. 3 Problem of the Day 2- Look at the spinner carefully. What two fractions could you use to name how much of the spinner red Topic 2 is red? red Problem of the Day 2- Problem of

More information

Content Area: Mathematics- 3 rd Grade

Content Area: Mathematics- 3 rd Grade Unit: Operations and Algebraic Thinking Topic: Multiplication and Division Strategies Multiplication is grouping objects into sets which is a repeated form of addition. What are the different meanings

More information

Connected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6)

Connected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6) Core Standards of the Course Standard I Students will acquire number sense and perform operations with rational numbers. Objective 1 Represent whole numbers and decimals in a variety of ways. A. Change

More information

Fair Game Review. Chapter 2. Name Date. Write the decimal as a fraction Write the fraction as a decimal. 7.

Fair Game Review. Chapter 2. Name Date. Write the decimal as a fraction Write the fraction as a decimal. 7. Name Date Chapter Fair Game Review Write the decimal as a fraction.. 0.6. 0.79. 0.7. 0.86 Write the fraction as a decimal.. 8 6. 7. 6 8. 7 0 9. A quarterback completed 0.6 of his passes during a game.

More information

Dividing with fractions 12 1 = 24 2 The way to THINK about this is how many halves ( 1 ) are in 12?

Dividing with fractions 12 1 = 24 2 The way to THINK about this is how many halves ( 1 ) are in 12? Dividing with fractions 12 1 = 24 2 The way to THINK about this is how many halves ( 1 ) are in 12? 2 How can you use multiplication to divide a number by a fraction? Steps Change any whole numbers or

More information

Subtract 2-digit numbers mentally with or without regrouping. Use front-end estimation to estimate sums and differences

Subtract 2-digit numbers mentally with or without regrouping. Use front-end estimation to estimate sums and differences 3 rd Grade Math in Focus Chapter 1-Numbers to 10,000 Counting Place Value Comparing Ordering Numbers Use base-ten blocks to count, read, write numbers to 10,000 Count on by 1s, 10s, 100s, 1,000s to 10,000

More information

Answers Investigation 3

Answers Investigation 3 Applications. 7 and 2 are equivalent. It takes thirds to make whole, so 7 thirds is equivalent to 2 wholes and one third. 2. B. (See Figure.). Answers will vary. (See Figure 2.) Pay attention to whether

More information