# Grade 7 Mathematics. Unit 5. Operations with Fractions. Estimated Time: 24 Hours

Size: px
Start display at page:

Transcription

1 Grade 7 Mathematics Operations with Fractions Estimated Time: 24 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade 7 Mathematics Curriculum Outcomes 59

2 Grade 7 Mathematics Curriculum Outcomes 60

4 Specific Outcome Elaborations: Suggested Learning and Teaching Strategies It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] Achievement Indicators 7N5. Model addition of positive fractions, using concrete representations, and record symbolically. 7N5.2 Determine the sum of two given positive fractions with like denominators. 7N5.3 Determine a common denominator for a given set of positive fractions. 7N5.4 Simplify a given positive fraction by identifying the common factor between the numerator and denominator. Lesson 5. in the student text briefly models like fractions using pattern blocks, clocks and fraction circles. It primarily demonstrates like denominators, but includes some examples in which one of the denominators is a simple multiple of the other. Teachers will need to model several more examples using these manipulatives in order to ensure student understanding. Students should also have the opportunity to model using the manipulatives since they are hands-on experiences. Lesson 5.2 uses fraction strips and number lines to support the same indicators. Students should be able to use the models to understand fractional equivalents and how they can be useful when adding fractions and changing them to their simplest form. Using the fractions strips and number line masters in the ProGuide pp , students will combine both the fraction strips and number lines to model sums and to illustrate the concept of common denominators. Grade 7 Mathematics Curriculum Outcomes 62

5 Suggested Assessment Strategies Pencil and Paper Write an addition sentence to represent the total fraction of each hexagon that is shaded. Use an addition sentence to find the total value of the shaded hexagons in each case. A. B. Resources/Notes The national library of virtual manipulatives provides an interesting activity on adding using common denominators with various models at v/frames_asid_06_g_3_ t_.html?from=category_ g_3_t_.html C. Informal Observation An alternative, but similar activity would be to create cards with addition sentences and their equivalents in pattern blocks as used in the Pencil and Paper exercise above. Each student would receive a card with either the addition sentence, or the pattern block representation. They mix-up and match-up within the class to find their partner. Each group must then explain to another group, or to their class, why they belong together. Math Makes Sense 7 Lesson 5. Lesson 5.2 : Operations with Fractions TR: ProGuide, pp. 4 6 & pp. 7 Master 5.3, 5.8, 5.27 Master 5.0, 5., 5.4, 5.5, 5.6, 5.7, 5.9, 5.28 PM 28, PM 25 CD-ROM Masters ST: pp ST: pp Practice and HW Book pp pp. 09 Grade 7 Mathematics Curriculum Outcomes 63

6 Specific Outcome It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.5 Model addition of positive fractions with unlike denominators, using concrete representations, and record symbolically. Elaborations: Suggested Learning and Teaching Strategies In the previous lessons, students used models to add using like denominators. They also modelled unlike denominators when one denominator was a multiple of the other. Lesson 5.3 develops the addition algorithm for fractions. The addition of fractions with unlike denominators that are not simple multiples of each other will require students to multiply the numerator and denominator of each fraction by the same number. Example: 7N5.6 Determine the sum of two given positive fractions with unlike denominators. Ideally, students should use the Least Common Multiple (LCM) of the unlike denominators. Through the use of benchmarks (close to 0,,) developed in 2 Unit 3, students will estimate the solution and use their estimate to verify the reasonableness of the answer obtained using the algorithm. (This elaboration is continued on the next two page spread ) Grade 7 Mathematics Curriculum Outcomes 64

7 Suggested Assessment Strategies Resources/Notes Pencil and Paper. Create three addition sentences that give the same sum as You cannot use like denominators in the sentences 2 2 you create. 2. Magic square. The sum of each row, column and diagonal in this magic square must equal. Find the missing values. Magic Square Solution A tangram is a square puzzle that is divided into seven shapes. A. Suppose piece A is. What are the values of pieces B, C, 4 D, E, F and G? B. What is the sum of A and B? C. If you subtract D from the whole puzzle, what value remains? D. Which two tangram pieces add up to the value of C? E. Invent a problem on your own and solve it. Math Makes Sense 7 Lesson 5.3 : Operations with Fractions TR: ProGuide, pp. 2 5 Master 5.4, 5.5, 5.6, 5.7, 5.20, 5.29 PM 27 CD-ROM Masters ST: pp Practice and HW Book pp. 2 4 Grade 7 Mathematics Curriculum Outcomes 65

8 Specific Outcome It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.5 Model addition of positive fractions with unlike denominators, using concrete representations, and record symbolically. 7N5.6 Determine the sum of two given positive fractions with unlike denominators. Elaborations: Suggested Learning and Teaching Strategies Here is another example of adding fractions with unlike denominators. Find the sum of the fractions: Students should think 4 3 is a little bit more than a half and 6 is less than a half so the answer should be close to. Then they can use the previous algorithm to calculate: = = = 2 Finally, they should look at their answer and ask themselves if is reasonable based on their estimate of. 2 Note: When a common denominator must be found, the common denominator that is chosen should be the lowest common denominator. Simply multiplying the denominators of the fractions being adding or subtracted will not guarantee a lowest common denominator. The lowest common 3 denominator for + is 2, not Grade 7 Mathematics Curriculum Outcomes 66

10 Specific Outcome It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.7 Model subtraction of positive fractions, using concrete representations, and record symbolically. Elaborations: Suggested Learning and Teaching Strategies Lesson 5.4 of the student text begins with subtraction involving unlike denominators using pattern blocks. Students will learn that addition and subtraction of fractions with unlike denominators uses the same algorithm. Teachers may wish to model several examples using fraction circles or fraction strips. For example: In this case, students must understand that they are simply removing one part of a set of equivalent quantities. This can be demonstrated by modelling 4 5 using fraction strips or fraction circles and removing one portion representing. The answer 5 is the remaining portion of N5.8 Determine the difference of two given positive fractions with like denominators. 7N5.9 Determine the difference of two given positive fractions with unlike denominators. The subtraction of fractions with unlike denominators that are not simple multiples of each other will require students to multiply the numerator and denominator of each fraction by the same number. This is identical to the algorithm used for addition. Ideally, students should use the Least Common Multiple (LCM) of the unlike denominators. Through the use of benchmarks (close to 0,,) developed in 2 Unit 3, students will estimate the solution and use their estimate to verify the reasonableness of the answer obtained using the algorithm. (This elaboration is continued on the next two page spread ) Grade 7 Mathematics Curriculum Outcomes 68

11 Suggested Assessment Strategies Resources/Notes Observation Ask students to use concrete materials or diagrams to show why the following is an incorrect procedure = = = Informal Observation Students can play the game Tic-Tac-Toe Fractions. A really useful game for adding and subtracting fractions. See ProGuide (Page V) and Master 5.8a, 5.8b and 5.8c. Math Makes Sense 7 Lesson 5.4 Lesson 5.5 : Operations with Fractions TR: ProGuide, pp & pp Master 5.2, 5.4, 5.5, 5.6, 5.7, 5.2, 5.30 Master 5.4, 5.5, 5.6, 5.7, 5.22, 5.3 CD-ROM Masters ST: pp ST: pp Practice and HW Book pp. 5 7 pp Grade 7 Mathematics Curriculum Outcomes 69

12 Specific Outcome It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.7 Model subtraction of positive fractions, using concrete representations, and record symbolically. 7N5.8 Determine the difference of two given positive fractions with like denominators. Elaborations: Suggested Learning and Teaching Strategies Find the difference of the fractions: Students should think 9 4 is a little bit less than a half and 3 is a little less than a half. The difference between them should therefore be almost 0 or just a little bit more than = = = 9 = 9 Finally, they should look at their answer and ask themselves if is reasonable based on their estimate of something a little 9 bit more than 0. 7N5.9 Determine the difference of two given positive fractions with unlike denominators. Grade 7 Mathematics Curriculum Outcomes 70

13 Suggested Assessment Strategies Resources/Notes Math Makes Sense 7 Lesson 5.4 Lesson 5.5 Grade 7 Mathematics Curriculum Outcomes 7

14 Specific Outcome It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.0 Model addition and subtraction of mixed numbers with like denominators, using concrete representations, and record symbolically. 7N5. Determine the sum or difference of two mixed numbers with like denominators. 7N5.2 Model addition and subtraction of mixed numbers with unlike denominators, using concrete representations, and record symbolically. 7N5.3 Determine the sum and difference of two mixed numbers with unlike denominators. Elaborations: Suggested Learning and Teaching Strategies Now that the models for addition and subtraction have been studied separately by the students, the same models and skills can now be used in the study of mixed fractions. Lessons 5.6 and 5.7 explore the subtraction of mixed numbers using fraction circles, number lines and fraction strips. Lesson 5.7 also introduces Cuisenaire rods as a model for subtracting mixed fractions. Teachers may consult the link for use of this model in the resource section of this guide. When adding and subtracting mixed fractions students may approach the problem in different ways. They may choose to keep the mixed fraction form or, they may change the mixed fractions to improper fractions. For addition: Mixed Fraction Form = = = 2 8 = 2 and 8 = 3 8 Improper Fraction Form = = = = 8,36, = 3 8 (This elaboration is continued on the next two page spread ) Grade 7 Mathematics Curriculum Outcomes 72

15 Suggested Assessment Strategies Interview Consider the following two problems: 3 and Without calculating, explain how you could determine which answer would be greater. Journal Describe at least two ways you can calculate Resources/Notes An introduction to Cuisenaire rods and their use in the study of fractions can be found at u/participants/silha/lesso ns/cuisen2.html Math Makes Sense 7 Lesson 5.6 Lesson 5.7 : Operations with Fractions TR: ProGuide, pp & pp Master 5.3, 5.4, 5.5, 5.6, 5.7, 5.23, 5.32 Master 5.3, 5.4, 5.5, 5.6, 5.7, 5.24, 5.33 PM 28 CD-ROM Masters ST: pp ST: pp Practice and HW Book pp pp Grade 7 Mathematics Curriculum Outcomes 73

16 Specific Outcome Elaborations: Suggested Learning and Teaching Strategies It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.0 Model addition and subtraction of mixed numbers with like denominators, using concrete representations, and record symbolically. 7N5. Determine the sum or difference of two mixed numbers with like denominators. 7N5.2 Model addition and subtraction of mixed numbers with unlike denominators, using concrete representations, and record symbolically. 7N5.3 Determine the sum and difference of two mixed numbers with unlike denominators. For subtraction: Mixed Fraction Form = = Students will be challenged by 2 4 and therefore must think about regrouping. Students should think: and and which will allow them to calculate: = 2 Improper Fraction Form = = = = 2 (All Cont d) Grade 7 Mathematics Curriculum Outcomes 74

17 Suggested Assessment Strategies Resources/Notes An introduction to Cuisenaire rods and their use in the study of fractions can be found at u/participants/silha/lesso ns/cuisen2.html Math Makes Sense 7 Lesson 5.6 Lesson 5.7 Grade 7 Mathematics Curriculum Outcomes 75

19 Suggested Assessment Strategies Resources/Notes Journal Is it possible to find two mixed numbers which add together to form a whole number? Explain your answer and, if possible, give an example to support your explanation. Pencil and Paper. Andrew plays guitar in a rock band. For a song that is 36 measures long he plays for 4 measures, rests for measures, plays for another 6 measures, rests for 2 4 measures and plays for the last section. How many measures are in the last section? 2. This week, Mark practised piano for 6 4 h, and talked on the phone for 3 2 h, played soccer for 4 3 h. A. How many hours did Mark spend practising piano and playing soccer? B. Hour many more hours did Mark spend playing soccer than talking on the phone? Math Makes Sense 7 Lesson 5.6 Lesson 5.7 Grade 7 Mathematics Curriculum Outcomes 77

20 Specific Outcome It is expected that students will: 7N5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences). [C, CN, ME, PS, R, V] (Cont d) Achievement Indicators 7N5.4 Simplify the solution to a given problem involving the sum or difference of two positive fractions or mixed numbers. 7N5.5 Solve a given problem involving the addition or subtraction of positive fractions or mixed numbers, and determine if the solution is reasonable. Elaborations: Suggested Learning and Teaching Strategies For part b) students should think 2 4 bags is a little more than two bags and is almost one full bag, but not quite. 2 Therefore Kyra uses a little more than 3 bags of chips in total. Then they calculate: = = = = = 2 6 = 2 and 6 = 3 6 Kyra used in total. 3 6 bags of chips Note that the final answer must be simplified. Students must reflect upon their answer to determine if it is reasonable. In this case, the answer is very close to the estimate. Grade 7 Mathematics Curriculum Outcomes 78

21 Suggested Assessment Strategies Resources/Notes Math Makes Sense 7 Lesson 5.6 Lesson 5.7 Grade 7 Mathematics Curriculum Outcomes 79

22 Grade 7 Mathematics Curriculum Outcomes 80

### Grade 7 Mathematics. Unit 2. Integers. Estimated Time: 15 Hours

Grade 7 Mathematics Integers Estimated Time: 15 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade

### Grade 7 Mathematics. Unit 3. Fractions, Decimals, and Percents. Estimated Time: 23 Hours

Grade 7 Mathematics Fractions, Decimals, and Percents Estimated Time: 23 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology

### Planning Guide. Grade 6 Improper Fractions and Mixed Numbers. Number Specific Outcome 4

Mathematics Planning Guide Grade 6 Improper Fractions and Mixed Numbers Number Specific Outcome 4 This Planning Guide can be accessed online at: http://www.learnalberta.ca/content/mepg6/html/pg6_improperfractionsmixednumbers/index.html

### Introduction to Fractions, Equivalent and Simplifying (1-2 days)

Introduction to Fractions, Equivalent and Simplifying (1-2 days) 1. Fraction 2. Numerator 3. Denominator 4. Equivalent 5. Simplest form Real World Examples: 1. Fractions in general, why and where we use

### Multiplication and Division of Decimals. Suggested Time: 3

Multiplication and Division of Decimals Suggested Time: 3 1 2 Weeks 225 Unit Overview Focus and Context Math Connects This unit will draw upon students previous knowledge of multiplication and division

### Parts and Wholes. In a tangram. 2 small triangles (S) cover a medium triangle (M) 2 small triangles (S) cover a square (SQ)

Parts and Wholes. L P S SQ M In a tangram small triangles (S) cover a medium triangle (M) small triangles (S) cover a square (SQ) L S small triangles (S) cover a parallelogram (P) small triangles (S) cover

### My Math Chapter 8 Lesson 3. Use the two pictures below to answer the questions. Engage NY Lessons 5.4 (Appendix C)

7 Flex Day (Instruction Based on Data) Recommended Resources: Decomposing Fractions Pizza Share Give Em Chocolate 8 Use cuisinaire rods and tape diagrams to model equivalent fraction values. Determine

### CBA Fractions Student Sheet 1

Student Sheet 1 1. If 3 people share 12 cookies equally, how many cookies does each person get? 2. Four people want to share 5 cakes equally. Show how much each person gets. Student Sheet 2 1. The candy

### FIDDLIN WITH FRACTIONS

FIDDLIN WITH FRACTIONS Special Area: Connections (Fourth and Fifth Grade) Written by: (Dawn Ramos, Joan Johnson, Mindy Wilshusen, St. Mary s School) Length of Unit: (6 Lessons) I. ABSTRACT The purpose

### FRACTIONS: EASY AS PIE! Grade Level: 4th Grade Presented by: Sue Gill, Clegern Elementary School, Edmond, Oklahoma Length of Unit: 7 lessons

FRACTIONS: EASY AS PIE! Grade Level: 4th Grade Presented by: Sue Gill, Clegern Elementary School, Edmond, Oklahoma Length of Unit: 7 lessons I. ABSTRACT This unit, "Fractions: Easy as Pie! is intended

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley

### Calculator Practice: Computation with Fractions

Calculator Practice: Computation with Fractions Objectives To provide practice adding fractions with unlike denominators and using a calculator to solve fraction problems. www.everydaymathonline.com epresentations

### 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

### NF5-12 Flexibility with Equivalent Fractions and Pages 110 112

NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.

### Progressing toward the standard

Report Card Language: The student can add and subtract fluently within 20. CCSS: 2.OA.2 Fluently add and subtract within 20 using mental strategies, by end of grade, know from memory all sums of two one-digit

### 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

### 0.1 Dividing Fractions

0.. DIVIDING FRACTIONS Excerpt from: Mathematics for Elementary Teachers, First Edition, by Sybilla Beckmann. Copyright c 00, by Addison-Wesley 0. Dividing Fractions In this section, we will discuss the

### Grade 5 Math Content 1

Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.

### Maths Workshop for Parents 2. Fractions and Algebra

Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)

### Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations

Grade 4 - Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)

### Subtracting Mixed Numbers

Subtracting Mixed Numbers Objective To develop subtraction concepts related to mixed numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters

### What Is Singapore Math?

What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has

### Mathematics Instructional Cycle Guide

Mathematics Instructional Cycle Guide Fractions on the number line 3NF2a Created by Kelly Palaia, 2014 Connecticut Dream Team teacher 1 CT CORE STANDARDS This Instructional Cycle Guide relates to the following

### 1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH

1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH Calendar The following tables show the CCSS focus of The Meeting activities, which appear at the beginning of each numbered lesson and are taught daily,

### Solving Rational Equations

Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,

### Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers

### 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

### Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

### Connections Across Strands Provides a sampling of connections that can be made across strands, using the theme (fractions) as an organizer

Overview Context Connections Positions fractions in a larger context and shows connections to everyday situations, careers, and tasks Identifies relevant manipulatives, technology, and web-based resources

### 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

### Calculation Policy Fractions

Calculation Policy Fractions This policy is to be used in conjunction with the calculation policy to enable children to become fluent in fractions and ready to calculate them by Year 5. It has been devised

### 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.

### Materials: Student-paper, pencil, circle manipulatives, white boards, markers Teacher- paper, pencil, circle manipulatives, worksheet

Topic: Creating Mixed Numbers and Improper Fractions SOL: 5.7- The student will add and subtract with fractions and mixed numbers, with and without regrouping, and express answers in simplest form. Problems

### 1 BPS Math Year at a Glance (Adapted from A Story of Units Curriculum Maps in Mathematics P-5)

Grade 5 Key Areas of Focus for Grades 3-5: Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: Multi-digit multiplication Module M1: Whole

### EVERY DAY COUNTS CALENDAR MATH 2005 correlated to

EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:

### Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

### Math vocabulary can be taught with what Montessorians call the Three Period Lesson.

Full Transcript of: Montessori Mathematics Materials Presentations Introduction to Montessori Math Demonstrations ( Disclaimer) This program is intended to give the viewers a general understanding of the

### Mental Computation Activities

Show Your Thinking Mental Computation Activities Tens rods and unit cubes from sets of base-ten blocks (or use other concrete models for tenths, such as fraction strips and fraction circles) Initially,

### Simplifying Improper Fractions Poster

Simplifying Improper Fractions Poster Congratulations on your purchase of this Really Good Stuff Simplifying Improper Fractions Poster a reference tool showing students how to change improper fractions

### Sample Fraction Addition and Subtraction Concepts Activities 1 3

Sample Fraction Addition and Subtraction Concepts Activities 1 3 College- and Career-Ready Standard Addressed: Build fractions from unit fractions by applying and extending previous understandings of operations

### Problem of the Month: Perfect Pair

Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:

### Comparing Fractions Objective To provide practice ordering sets of fractions.

Comparing Fractions Objective To provide practice ordering sets of fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management

### GRADE 6 MATH: RATIOS AND PROPORTIONAL RELATIONSHIPS

GRADE 6 MATH: RATIOS AND PROPORTIONAL RELATIONSHIPS UNIT OVERVIEW This 4-5 week unit focuses on developing an understanding of ratio concepts and using ratio reasoning to solve problems. TASK DETAILS Task

### Mathematics Pacing Resource Document 5.AT.2 Standard: 5.AT.2: Teacher Background Information:

Standard: : Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations

### Rational Number Project

Rational Number Project Fraction Operations and Initial Decimal Ideas Lesson : Overview Students estimate sums and differences using mental images of the 0 x 0 grid. Students develop strategies for adding

### 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

### Numeracy and mathematics Experiences and outcomes

Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different

### Mathematics Scope and Sequence, K-8

Standard 1: Number and Operation Goal 1.1: Understands and uses numbers (number sense) Mathematics Scope and Sequence, K-8 Grade Counting Read, Write, Order, Compare Place Value Money Number Theory K Count

CONTENTS Introduction...iv. Number Systems... 2. Algebraic Expressions.... Factorising...24 4. Solving Linear Equations...8. Solving Quadratic Equations...0 6. Simultaneous Equations.... Long Division

### 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

### Comparing and Ordering Fractions

Comparing and Ordering Fractions Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. www.everydaymathonline.com epresentations etoolkit Algorithms

Grade 5 Fraction Equivalency 5.N.7 Demonstrate an understanding of fractions by using concrete and pictorial representations to create sets of equivalent fractions compare fractions with like and unlike

### PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION ELEMENTARY MATH GRADE 2 MATH IN FOCUS

PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION ELEMENTARY MATH GRADE 2 MATH IN FOCUS Length of Course: Term Elective / Required: Required Schools: Elementary Student Eligibility:

### Open-Ended Problem-Solving Projections

MATHEMATICS Open-Ended Problem-Solving Projections Organized by TEKS Categories TEKSING TOWARD STAAR 2014 GRADE 7 PROJECTION MASTERS for PROBLEM-SOLVING OVERVIEW The Projection Masters for Problem-Solving

### GRADE 6 MATH: SHARE MY CANDY

GRADE 6 MATH: SHARE MY CANDY UNIT OVERVIEW The length of this unit is approximately 2-3 weeks. Students will develop an understanding of dividing fractions by fractions by building upon the conceptual

### Grade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills

Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate

### II. 2008 Core Knowledge National Conference, 2 nd Grade, Action! Action! We Want Fractions 1

ACTION! ACTION! We Want Fractions! Grade Level or Special Area: Second Grade Written by: Monique Cavaleri, Marie Maggio, Anne Slack, P.S.108, Brooklyn New York Length of Unit: 5 Lessons I. ABSTRACT Fractions

### Decomposing Numbers (Operations and Algebraic Thinking)

Decomposing Numbers (Operations and Algebraic Thinking) Kindergarten Formative Assessment Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Field-tested by Kentucky

### Math Content by Strand 1

Math Content by Strand 1 Number and Operations with Whole Numbers Multiplication and Division Grade 3 In Grade 3, students investigate the properties of multiplication and division, including the inverse

### 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,

### A Concrete Introduction. to the Abstract Concepts. of Integers and Algebra using Algebra Tiles

A Concrete Introduction to the Abstract Concepts of Integers and Algebra using Algebra Tiles Table of Contents Introduction... 1 page Integers 1: Introduction to Integers... 3 2: Working with Algebra Tiles...

### Such As Statements, Kindergarten Grade 8

Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential

### Ratio and Percent. Suggested Time: 2

Ratio and Percent Suggested Time: 2 1 2 Weeks 171 Unit Overview Focus and Context Students can develop a deep understanding of numbers through experiences with a variety of models, such as fraction strips,

### Differentiated plans for Years 5 & 6. Fractions, decimals, percentages & ratios

Differentiated plans for Years 5 & 6 Fractions, decimals, percentages & ratios Ian Lowe, MAV Professional Officer, 2006 IF YOU USE ANY OF THIS PLEASE PROVIDE FEEDBACK TO IAN AT ilowe@mav.vic.edu.au THIS

### Contents. Sample worksheet from www.mathmammoth.com

Contents Introduction... 4 Warmup: Mental Math 1... 8 Warmup: Mental Math 2... 10 Review: Addition and Subtraction... 12 Review: Multiplication and Division... 15 Balance Problems and Equations... 19 More

### Number Relationships. Suggested Time: 4

Number Relationships Suggested Time: 4 1 2 Weeks 55 NUMBER RELATIONSHIPS Unit Overview Focus and Context This unit focuses on finding factors and multiples of whole numbers to 100, classifying numbers

### OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

### Rational Number Project

Rational Number Project Fraction Operations and Initial Decimal Ideas Lesson 1: Overview Students review how to model fractions with fraction circles by ordering unit fractions, using 1-half as a benchmark

### Number Sense and Numeration, Grades 4 to 6

Number Sense and Numeration, Grades 4 to 6 Volume 3 Multiplication A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 2006 Every effort has been made in this publication to identify

### CHICAGO PUBLIC SCHOOLS (ILLINOIS) MATH & SCIENCE INITIATIVE COURSE FRAMEWORK FOR ALGEBRA Course Framework: Algebra

Chicago Public Schools (Illinois) Math & Science Initiative Course Framework for Algebra Course Framework: Algebra Central Concepts and Habits of Mind The following concepts represent the big ideas or

### Pocantico Hills School District Grade 1 Math Curriculum Draft

Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next

### Summative Task: Demonstrate an understanding of fractional relationships. EQAO question.

Unit Plan Grade 6/7 Number Sense and Numeration Fractions, Ratios and Percents Term 3 Grade 6 OEs and SEs: OEs: read, represent, compare, and order whole numbers to 1 000 000, decimal numbers to thousandths,

### Models for Dividing Fractions Grade Six

Ohio Standards Connection Number, Number Sense and Operations Benchmark H Use and analyze the steps in standard and nonstandard algorithms for computing with fractions, decimals and integers. Indicator

### Numerator Denominator

Fractions A fraction is any part of a group, number or whole. Fractions are always written as Numerator Denominator A unitary fraction is one where the numerator is always 1 e.g 1 1 1 1 1...etc... 2 3

### Introduction Read aloud Pizza Fractions by Jerry Pallotta to give students a visual representation of fractions.

3rd th Grade Objective CCSS Math/Number and Operations-Fractions:.NF. Extend understanding of fraction equivalence and ordering.. Compare two fractions with different numerators and different denominators

### Working with Equivalent Fractions, Decimals & Percentages

Virtual Math Girl: Module 3 (Student) and 4 (Teacher) Working with Equivalent s, Decimals & Percentages Activities and Supplemental Materials The purpose of Virtual Math Girl Module 3 (Student) and 4 (Teacher)

Ohio Standards Connection Patterns, Functions and Algebra Benchmark E Solve open sentences and explain strategies. Indicator 4 Solve open sentences by representing an expression in more than one way using

### Rational Number Project

Rational Number Project Fraction Operations and Initial Decimal Ideas Lesson 2: Overview Students review equivalence ideas with paper folding. Students develop a symbolic rule for finding equivalent fractions.

### Baseball Multiplication Objective To practice multiplication facts.

Baseball Multiplication Objective To practice multiplication facts. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common

### Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

A W weet Copyright 203 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without

Fourth Grade Fractions http://upload.wikimedia.org/wikibooks/en/9/92/fractions_of_a_square.jpg North Carolina Department of Public Instruction www.ncdpi.wikispaces.net Overview The implementation of the

### 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

### Modeling in Geometry

Modeling in Geometry Overview Number of instruction days: 8-10 (1 day = 53 minutes) Content to Be Learned Mathematical Practices to Be Integrated Use geometric shapes and their components to represent

### Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter A. Elementary

Elementary 111.A. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter A. Elementary Statutory Authority: The provisions of this Subchapter A issued under the Texas Education Code,

### Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.

Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find

### Welcome to Harcourt Mega Math: The Number Games

Welcome to Harcourt Mega Math: The Number Games Harcourt Mega Math In The Number Games, students take on a math challenge in a lively insect stadium. Introduced by our host Penny and a number of sporting

### The Distributive Property

The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com

### Fractions In Action! Dawn Jesse

Fractions In Action! Dawn Jesse Fractions In Action Dawn Jesse Fractions In Action is an interactive activity that consists of direct instruction, cooperative learning and is inquire based. As the students

### New York State Testing Program Grade 3 Common Core Mathematics Test. Released Questions with Annotations

New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions with Annotations August 2013 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY

### Planning For Success Mathematics: Numeration Inquiry Investigations. Operations: Multiplication and Division. Number Sense and Numeration

Planning For Success Mathematics: Numeration Inquiry Investigations Operations: Multiplication and Division Number Sense and Numeration OVERALL EXPECTATIONS By the end of Grade 4, students will: solve

### FRACTIONS, DECIMALS AND PERCENTAGES

Fractions Fractions Part FRACTIONS, DECIMALS AND PERCENTAGES Fractions, decimals and percentages are all ways of expressing parts of a whole. Each one of these forms can be renamed using the other two

### Factor Trees. Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers.

Factor Trees Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### 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

### The Lattice Method of Multiplication

The Lattice Method of Multiplication Objective To review and provide practice with the lattice method for multiplication of whole numbers and decimals. www.everydaymathonline.com epresentations etoolkit

### Everyday Mathematics GOALS

Copyright Wright Group/McGraw-Hill GOALS The following tables list the Grade-Level Goals organized by Content Strand and Program Goal. Content Strand: NUMBER AND NUMERATION Program Goal: Understand the

### Unit 1: Family Letter

Name Date Time HOME LINK Unit 1: Family Letter Introduction to Third Grade Everyday Mathematics Welcome to Third Grade Everyday Mathematics. It is part of an elementary school mathematics curriculum developed