# Let s think about how to multiply and divide fractions by fractions!

Size: px
Start display at page:

Transcription

1 Let s think about how to multiply and divide fractions by fractions! June 25, 2007 (Monday) Takehaya Attached Elementary School, Tokyo Gakugei University Grade 6, Class # 1 (21 boys, 20 girls) Instructor: Takeshi Yamada 1. Conception of the Activity (1) Origin of the activity From 1 st grade to 4 th grade, students learned the four operations of whole numbers and addition and subtraction of rational numbers. In 5 th grade, they learned how to multiply and divide decimals and the meaning and calculation of fraction x whole number and fraction whole number. After the students learned about multiplication and division of a decimal by a decimal, I asked them, What do you think that we should study next? the students replied, We want to do multiplication of fractions when the multiplier is a fraction and division of fractions when the divisor is a fraction because we haven t learned them yet. So, based on the students recommendations, we decided that they will study fraction x fraction and fraction fraction next. The students are highly motivated to learn how to calculate all types of numbers (whole numbers, decimal numbers, and fractions) using the four operations. (2) Wishes of the teacher I would like to support my students desire to want to be able to calculate all types of numbers using the four operations, and I truly hope that they master these skills. Furthermore, the students are beginning to become more aware of how their own ideas are received by their peers and whether or not their ideas are better than other ideas. This awareness will become even more evident when they begin discussing and trying to determine things such as which solution is easier to understand, or whether or not the ideas always can be applied to other numbers by looking at the many different ideas and solution methods that are presented. In addition, the students are trying to relate their own thinking and ideas to their peers thinking and ideas. I hope to develop this type of thinking in my students. In this activity, I would like to bring out the desire in my students to calculate all types of numbers using the four operations as well as develop their desire to relate to their peers thinking and ideas. In order to do this, I would like to prepare a situation where the students can feel a sense of accomplishment when they complete the calculation using the four operations and learn from their peers thinking and ideas while still valuing their own ideas. I would like my students to understand that calculation methods are supported by the characteristics of numbers and the properties of operations. I would like to provide this kind of activity to my students because this is a long-held belief of mine. 1

2 Also, at the end of this activity, I would like to summarize the number concepts (positive rational numbers and 0) that students have studied thus far. By asking the question What are we able to do by using numbers? the students will go back and read their elementary mathematics textbooks. Then, I would like to help them to once again recognize and understand that we can use numbers to express quantities and order of objects, measure quantities, and calculate. 2. Plan of the Unit Let s think about how to calculate fraction x fraction and fraction fraction! (6 lessons) Goals Goals of Grade 6: A: Have a sense of purpose and persevere in their thinking in order to search for truth B. Respect each other s strengths and behave responsibly C. Try to improve oneself by reflecting on oneself Think about how to calculate fraction x fraction and fraction fraction by using previously learned calculation methods, properties of fractions, and properties of multiplication and division. Understand the method of calculation for fraction x fraction and fraction fraction Understand that when we use numbers, we can express quantities and order of objects, measure quantities, and calculate. Activity Plan Phase 1: Let s think about how to multiply a fraction by a fraction! 1 st and 2 nd lesson: Let s think about how to calculate 2 5! 4 = 10! (A) 0.4! 0.75 = 0. 2 can be expressed with fractions as 5! 4 = 10 product of the fraction calculation, 10. So by thinking about the, students can think about how to calculate fraction x fraction. (B) Students will notice that product of two fractions can be found by multiplying both numerators and both denominators by looking at several calculation methods. In addition, they will learn the method of calculation. (C) Students can think about how to calculate by using the calculation methods, properties of fractions, and properties of multiplication and division that they learned previously. (D) Students will confirm whether this method can work for calculations involving fractions that cannot be expressed as decimals, as well as understand that it can be done. I wonder if we can change the calculation to fractions x whole number. There are several ways to calculate but all of them can be transformed to a math sentence that multiplies the both numerators and both denominators. I wonder if we can use the same method for fractions that cannot be expressed as decimals. Phase 2: Let s think about how to divide a fraction by a fraction! 1 st and 2 nd lesson: Let s think about how to calculate 20 5 = 4 Since = 0.75 can be expressed with fractions as 20 5 = 4 about how to divide fractions by thinking about the quotient, 4.! (This lesson), students can think Students can think about how to calculate by using the calculation methods, properties of 2

3 fractions, and properties of multiplication and division that they learned previously. By examining several calculation methods that are presented, students can think about a method that can be applied any time. Students will confirm whether this method can work for calculations involving fractions that cannot be expressed as decimals and understand that it can be done. I wonder if we can change the calculation to fraction whole number? There are several ways to calculate but all of them can be transformed to a math sentence that multiplies by the inverse fraction of the divisor. I wonder if we can use the same method for fractions that cannot be expressed as decimals. Phase : Let summarize what we can do with numbers! 1 st lesson: Let s think about how to multiply a whole number by a fraction and divide a whole number by a fraction! (E) Students will think about how to calculate whole number x fraction and whole number fraction by going over what we know about multiplication and division calculations. (F) Students will feel a sense of accomplishment for being able to calculate all of the different the kinds of numbers they learned with the four operations. We have not learned how to multiply a whole number by a fraction and divide a whole number by a fraction, so let s think about those calculations! If we change the whole numbers into fractions we can do the calculation just like we did with fraction x fraction and fraction fraction. Now we can calculations involving the four operations with whole numbers, decimals, and fractions. 2 nd lesson: By reviewing our math textbooks from 1 st to 6 th grades, let s summarize what we can do with numbers! (G) Students will understand that when we use numbers, we can express quantities of objects, express order of objects, measure quantities, and calculate. We can count the number of objects. We can measure length, weight, etc. We can express ratio. We can calculate

4 . About this lesson (1) Goal of the lesson Students will think about how to calculate by using the calculation methods, properties of fractions, and the property of division (i.e., when you multiply or divide both the dividend and the divisor by the same number, the quotients will remain the same) that they learned previously. To understand the ideas and solution methods presented by other students and think about which calculation method can be used in every case. (2) Lesson Development Students main activities and anticipated reactions Calculate Calculate by using an algorithm By using a property of division (when you multiply both the dividend and the divisor by the same number, the quotients will remain the same), change it to 45 60, then calculate. Understand the result of the calculation: = 0.75 Think about why the quotient of 20 5 Instructional support Observation points Because we can express a number using both decimals and fractions, and students have learned decimal decimal calculation, the teacher will suggest to the students: We can express fraction fraction using decimal decimal, so let s calculate by using decimal decimal since we already know how to do that! If the students do not come up with a calculation idea using the property of division (when you multiply or divide both the dividend and the divisor by the same number, the quotient will remain the same), the teacher will ask the students: Is there any way we can change the calculation to whole number whole number? Write down the property on the blackboard so students can use it to think about solving the problem on their own. Tell students: Let s express it using fractions! Ask the students to simplify the fraction. becomes 4 by expressing = 0.75 with fractions. Let s think about how to calculate 20 5! Think about how to calculate on their own: (A) When we calculate fraction x fraction, we multiply both numerators and both denominators. Since this is a division problem, we can divide both numerators and both denominators = 4 (B) Using a property of division (when you multiply both the dividend and divisor by the same number, the quotients will remain the same) change the division into a fraction x whole number to pursue the calculation. Can they think about how to do the calculation by utilizing the properties of fractions and the property of division? If the teacher finds the students doing the calculation 20 5 = 5in order 20 to change the calculation to a whole number calculation, and ending up with 20 5 = 100, ask them to think about a different method by saying It looks like the quotient is different from the quotient we got from the decimal calculation. If the teacher finds students who are having a hard time coming up with an idea, 4

5 20 5 = 4 = 4 (C) Using a property of division (when you multiply both the dividend and the divisor by the same number, the quotients will remain the same) change the division into whole number x whole number to pursue the calculation = 12 = 12 = 4 Present ideas about how to calculate and understand each others ideas. (B) and (C) above use the same property of division (A) might not work with different fractions. For example: Check to see if ideas from (A) to (C). Method (B) works well = = 15 8 can be solved using the Method (B) works well. If I write the calculation process clearly: 4 2 (! 5) (! 5) = 2 = 5 4 (4! 2) Method (C) works well = 15 8 = 15 8 Method (C) works well if I write the calculation process clearly: = (! 5) (2! 4) = (! 5) (2! 4) Method (A) works well, too. If we can find a multiple of the numerator and the 2 denominator 4 and 5 can do: 4 = 6 8 = (0 2) = 5 (40 5) it works. First we Then, do the We can write the calculation process of (A) more clearly: (! 2! 5) (4! 2! 5) 2 5 = (! 5) (4! 2) encourage them by saying What did we do when we did the calculation of fraction x fraction? By helping students recall this, you are helping them to think and come up with at least one idea that uses the property of division. Can students understand the solution methods presented by their peers? Can they see the similarities and differences in the ideas by comparing them to their own ideas? If the students never come up with an idea for exploring other fractions besides 20 5, ask them Do you think the methods we looked at today always work for any fraction fraction problem? Are they actively investigating whether the methods they find during this lesson can be used for other fraction fraction calculations? When a student presents method (B), if the student did not clearly explain the process of calculation by using a non-described number such as 15 of When we write the calculation process of (B), (C), and (A) clearly, all of the math 15 8, the teacher should ask a question such as Where does this 15 come from? and clarify that the 15 is x 5. Also, make sure to record it on the blackboard. Are students actively looking for a common calculation procedure by looking at mathematical expressions (A) to (C)? If students are having difficulty finding the common calculation procedure, the teacher will ask Are there similarities in the calculation procedures when we rewrote them more clearly? If students can t see the part about inverting the denominator and the numerator of the divisor and then multiplying the dividend, ask Where can you find the in the first math expression? to help them notice the idea. If the fractions involved in the second problem, such as 4 2 5, can be expressed as decimals ask the students, Can we divide fractions without changing them into decimals? 5

6 sentences involve multiplication by the inverse of 2 5. Journals writing I understand that if we can change the problem into a calculation that we learned before, we can solve it. I think that the properties of division are very important. I was surprised that we can do the problem using method (A). I felt happy that we found the calculation method for fraction fraction 6

### Algebra 1 Summer Packet

Algebra 1 Summer Packet Name: Solve each problem and place the answer on the line to the left of the problem. Adding Integers A. Steps if both numbers are positive. Example: 3 + 4 Step 1: Add the two numbers.

### FractionWorks Correlation to Georgia Performance Standards

Cheryl Keck Educational Sales Consultant Phone: 800-445-5985 ext. 3231 ckeck@etacuisenaire.com www.etacuisenaire.com FractionWorks Correlation to Georgia Performance s Correlated to Georgia Performance

### Focus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multi-digit whole numbers.

Approximate Time Frame: 3-4 weeks Connections to Previous Learning: In fourth grade, students fluently multiply (4-digit by 1-digit, 2-digit by 2-digit) and divide (4-digit by 1-digit) using strategies

### Using Proportions to Solve Percentage Problems I

RP7-1 Using Proportions to Solve Percentage 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

### Grade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology

### Pre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value

Syllabus Pre-Algebra A Course Overview Pre-Algebra is a course designed to prepare you for future work in algebra. In Pre-Algebra, you will strengthen your knowledge of numbers as you look to transition

### Common Core Standards Alignment Chart Grade 5

Common Core Standards Alignment Chart Grade 5 Units 5.OA.1 5.OA.2 5.OA.3 5.NBT.1 5.NBT.2 5.NBT.3 5.NBT.4 5.NBT.5 5.NBT.6 5.NBT.7 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.5 5.NF.6 5.NF.7 5.MD.1 5.MD.2 5.MD.3 5.MD.4

### This scope and sequence assumes 160 days for instruction, divided among 15 units.

In previous grades, students learned strategies for multiplication and division, developed understanding of structure of the place value system, and applied understanding of fractions to addition and subtraction

### Fourth Grade. Reporting Student Progress. Libertyville School District 70. Fourth Grade

Fourth Grade Libertyville School District 70 Reporting Student Progress Fourth Grade A Message to Parents/Guardians: Libertyville Elementary District 70 teachers of students in kindergarten-5 utilize a

### Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified

Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community

### South Carolina College- and Career-Ready Standards for Mathematics. Standards Unpacking Documents Grade 5

South Carolina College- and Career-Ready Standards for Mathematics Standards Unpacking Documents Grade 5 South Carolina College- and Career-Ready Standards for Mathematics Standards Unpacking Documents

### AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic

### Grade 6: Correlated to AGS Basic Math Skills

Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and

### Remainder Rules. 3. Ask students: How many carnations can you order and what size bunches do you make to take five carnations home?

Math Concepts whole numbers multiplication division subtraction addition Materials TI-10, TI-15 Explorer recording sheets cubes, sticks, etc. pencils Overview Students will use calculators, whole-number

### Rendezvous with Comet Halley Next Generation of Science Standards

Next Generation of Science Standards 5th Grade 6 th Grade 7 th Grade 8 th Grade 5-PS1-3 Make observations and measurements to identify materials based on their properties. MS-PS1-4 Develop a model that

### Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best

### Multiplication of 2 and 3 digit numbers Multiply and SHOW WORK. EXAMPLE. Now try these on your own! Remember to show all work neatly!

Multiplication of 2 and digit numbers Multiply and SHOW WORK. EXAMPLE 205 12 10 2050 2,60 Now try these on your own! Remember to show all work neatly! 1. 6 2 2. 28 8. 95 7. 82 26 5. 905 15 6. 260 59 7.

### Extending Place Value with Whole Numbers to 1,000,000

Grade 4 Mathematics, Quarter 1, Unit 1.1 Extending Place Value with Whole Numbers to 1,000,000 Overview Number of Instructional Days: 10 (1 day = 45 minutes) Content to Be Learned Recognize that a digit

### Mathematics subject curriculum

Mathematics subject curriculum Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research on 24 June

### The Indices Investigations Teacher s Notes

The Indices Investigations Teacher s Notes These activities are for students to use independently of the teacher to practise and develop number and algebra properties.. Number Framework domain and stage:

### Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade The third grade standards primarily address multiplication and division, which are covered in Math-U-See

### Written by Wendy Osterman

Pre-Algebra Written by Wendy Osterman Editor: Alaska Hults Illustrator: Corbin Hillam Designer/Production: Moonhee Pak/Cari Helstrom Cover Designer: Barbara Peterson Art Director: Tom Cochrane Project

### Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C

Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C Using and applying mathematics objectives (Problem solving, Communicating and Reasoning) Select the maths to use in some classroom

### Foothill College Summer 2016

Foothill College Summer 2016 Intermediate Algebra Math 105.04W CRN# 10135 5.0 units Instructor: Yvette Butterworth Text: None; Beoga.net material used Hours: Online Except Final Thurs, 8/4 3:30pm Phone:

### Montana Content Standards for Mathematics Grade 3. Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011

Montana Content Standards for Mathematics Grade 3 Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011 Contents Standards for Mathematical Practice: Grade

I. Content Standard: Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems and reasonable estimates using paper and pencil, technology-supported

### Are You Ready? Simplify Fractions

SKILL 10 Simplify Fractions Teaching Skill 10 Objective Write a fraction in simplest form. Review the definition of simplest form with students. Ask: Is 3 written in simplest form? Why 7 or why not? (Yes,

### BENCHMARK MA.8.A.6.1. Reporting Category

Grade MA..A.. Reporting Category BENCHMARK MA..A.. Number and Operations Standard Supporting Idea Number and Operations Benchmark MA..A.. Use exponents and scientific notation to write large and small

### Backwards Numbers: A Study of Place Value. Catherine Perez

Backwards Numbers: A Study of Place Value Catherine Perez Introduction I was reaching for my daily math sheet that my school has elected to use and in big bold letters in a box it said: TO ADD NUMBERS

### Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: Addison-Wesley.

Course Syllabus Course Description Explores the basic fundamentals of college-level mathematics. (Note: This course is for institutional credit only and will not be used in meeting degree requirements.

### RIGHTSTART MATHEMATICS

Activities for Learning, Inc. RIGHTSTART MATHEMATICS by Joan A. Cotter, Ph.D. LEVEL B LESSONS FOR HOME EDUCATORS FIRST EDITION Copyright 2001 Special thanks to Sharalyn Colvin, who converted RightStart

### Name: Class: Date: ID: A

Name: Class: _ Date: _ Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Members of a high school club sold hamburgers at a baseball game to

### Conversions among Fractions, Decimals, and Percents

Conversions among Fractions, Decimals, and Percents Objectives To reinforce the use of a data table; and to reinforce renaming fractions as percents using a calculator and renaming decimals as percents.

### Division Strategies: Partial Quotients. Fold-Up & Practice Resource for. Students, Parents. and Teachers

t s e B s B. s Mr Division Strategies: Partial Quotients Fold-Up & Practice Resource for Students, Parents and Teachers c 213 Mrs. B s Best. All rights reserved. Purchase of this product entitles the purchaser

### South Carolina English Language Arts

South Carolina English Language Arts A S O F J U N E 2 0, 2 0 1 0, T H I S S TAT E H A D A D O P T E D T H E CO M M O N CO R E S TAT E S TA N DA R D S. DOCUMENTS REVIEWED South Carolina Academic Content

T894 Mathematics Success Grade 7 [OBJECTIVE] The student will find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. [PREREQUISITE SKILLS] Simple probability,

### Learning Disability Functional Capacity Evaluation. Dear Doctor,

Dear Doctor, I have been asked to formulate a vocational opinion regarding NAME s employability in light of his/her learning disability. To assist me with this evaluation I would appreciate if you can

### TIMSS Highlights from the Primary Grades

TIMSS International Study Center June 1997 BOSTON COLLEGE TIMSS Highlights from the Primary Grades THIRD INTERNATIONAL MATHEMATICS AND SCIENCE STUDY Most Recent Publications International comparative results

### Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple

Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple Unit Plan Components Big Goal Standards Big Ideas Unpacked Standards Scaffolded Learning Resources

### The New York City Department of Education. Grade 5 Mathematics Benchmark Assessment. Teacher Guide Spring 2013

The New York City Department of Education Grade 5 Mathematics Benchmark Assessment Teacher Guide Spring 2013 February 11 March 19, 2013 2704324 Table of Contents Test Design and Instructional Purpose...

### Math 121 Fundamentals of Mathematics I

I. Course Description: Math 121 Fundamentals of Mathematics I Math 121 is a general course in the fundamentals of mathematics. It includes a study of concepts of numbers and fundamental operations with

### Alignment of Australian Curriculum Year Levels to the Scope and Sequence of Math-U-See Program

Alignment of s to the Scope and Sequence of Math-U-See Program This table provides guidance to educators when aligning levels/resources to the Australian Curriculum (AC). The Math-U-See levels do not address

### About the Mathematics in This Unit

(PAGE OF 2) About the Mathematics in This Unit Dear Family, Our class is starting a new unit called Puzzles, Clusters, and Towers. In this unit, students focus on gaining fluency with multiplication strategies.

### Math 098 Intermediate Algebra Spring 2018

Math 098 Intermediate Algebra Spring 2018 Dept. of Mathematics Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: MyMathLab Course ID: Course Description This course expands on the

### The Algebra in the Arithmetic Finding analogous tasks and structures in arithmetic that can be used throughout algebra

Why Didn t My Teacher Show Me How to Do it that Way? Rich Rehberger Math Instructor Gallatin College Montana State University The Algebra in the Arithmetic Finding analogous tasks and structures in arithmetic

### Chapter 4 - Fractions

. Fractions Chapter - Fractions 0 Michelle Manes, University of Hawaii Department of Mathematics These materials are intended for use with the University of Hawaii Department of Mathematics Math course

### MODULE FRAMEWORK AND ASSESSMENT SHEET

MODULE FRAMEWORK AND ASSESSMENT SHEET LEARNING OUTCOMES (LOS) ASSESSMENT STANDARDS (ASS) FORMATIVE ASSESSMENT ASs Pages and (mark out of ) LOs (ave. out of ) SUMMATIVE ASSESSMENT Tasks or tests Ave for

### Honors Mathematics. Introduction and Definition of Honors Mathematics

Honors Mathematics Introduction and Definition of Honors Mathematics Honors Mathematics courses are intended to be more challenging than standard courses and provide multiple opportunities for students

### Activity 2 Multiplying Fractions Math 33. Is it important to have common denominators when we multiply fraction? Why or why not?

Activity Multiplying Fractions Math Your Name: Partners Names:.. (.) Essential Question: Think about the question, but don t answer it. You will have an opportunity to answer this question at the end of

### LLD MATH. Student Eligibility: Grades 6-8. Credit Value: Date Approved: 8/24/15

PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION LLD MATH Length of Course: Elective/Required: School: Full Year Required Middle Schools Student Eligibility: Grades 6-8 Credit Value:

### Sample Problems for MATH 5001, University of Georgia

Sample Problems for MATH 5001, University of Georgia 1 Give three different decimals that the bundled toothpicks in Figure 1 could represent In each case, explain why the bundled toothpicks can represent

### GRADE 5 MATHEMATICS Pre Assessment Directions, Answer Key, and Scoring Rubrics

ORANGE PUBLIC SCHOOLS OFFICE OF CURRICULUM AND INSTRUCTION OFFICE OF MATHEMATICS GRADE 5 MATHEMATICS Pre Assessment Directions, Answer Key, and Scoring Rubrics School Year 03-04 Grade 5 Pre Assessment

### EDU 614: Advanced Educational Psychology Online Course Dr. Jim McDonald

EDU 614: Advanced Educational Psychology Online Course Dr. Jim McDonald Course Objectives: The primary goal of EDU 614 is to help practicing teachers gain a more in-depth understanding of important ideas

### SMARTboard: The SMART Way To Engage Students

SMARTboard: The SMART Way To Engage Students Emily Goettler 2nd Grade Gray s Woods Elementary School State College Area School District esg5016@psu.edu Penn State Professional Development School Intern

### Introducing the New Iowa Assessments Mathematics Levels 12 14

Introducing the New Iowa Assessments Mathematics Levels 12 14 ITP Assessment Tools Math Interim Assessments: Grades 3 8 Administered online Constructed Response Supplements Reading, Language Arts, Mathematics

A Correlation of to the Grades K - 6 G/M-223 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley Mathematics in meeting the

### Synthesis Essay: The 7 Habits of a Highly Effective Teacher: What Graduate School Has Taught Me By: Kamille Samborski

Synthesis Essay: The 7 Habits of a Highly Effective Teacher: What Graduate School Has Taught Me By: Kamille Samborski When I accepted a position at my current school in August of 2012, I was introduced

### First and Last Name School District School Name School City, State

Unit Plan - Fractions Unit Author First and Last Name School District School Name School City, State Allison Cooper (King) Putnam County Rock Branch Elementary School Rock Branch, WV Unit Overview Unit

### PSYCHOLOGY 353: SOCIAL AND PERSONALITY DEVELOPMENT IN CHILDREN SPRING 2006

PSYCHOLOGY 353: SOCIAL AND PERSONALITY DEVELOPMENT IN CHILDREN SPRING 2006 INSTRUCTOR: OFFICE: Dr. Elaine Blakemore Neff 388A TELEPHONE: 481-6400 E-MAIL: OFFICE HOURS: TEXTBOOK: READINGS: WEB PAGE: blakemor@ipfw.edu

### Statewide Framework Document for:

Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance

### Mathematics process categories

Mathematics process categories All of the UK curricula define multiple categories of mathematical proficiency that require students to be able to use and apply mathematics, beyond simple recall of facts

### TABE 9&10. Revised 8/2013- with reference to College and Career Readiness Standards

TABE 9&10 Revised 8/2013- with reference to College and Career Readiness Standards LEVEL E Test 1: Reading Name Class E01- INTERPRET GRAPHIC INFORMATION Signs Maps Graphs Consumer Materials Forms Dictionary

### MERGA 20 - Aotearoa

Assessing Number Sense: Collaborative Initiatives in Australia, United States, Sweden and Taiwan AIistair McIntosh, Jack Bana & Brian FarreII Edith Cowan University Group tests of Number Sense were devised

### Pedagogical Content Knowledge for Teaching Primary Mathematics: A Case Study of Two Teachers

Pedagogical Content Knowledge for Teaching Primary Mathematics: A Case Study of Two Teachers Monica Baker University of Melbourne mbaker@huntingtower.vic.edu.au Helen Chick University of Melbourne h.chick@unimelb.edu.au

### What the National Curriculum requires in reading at Y5 and Y6

What the National Curriculum requires in reading at Y5 and Y6 Word reading apply their growing knowledge of root words, prefixes and suffixes (morphology and etymology), as listed in Appendix 1 of the

### Mental Computation Strategies for Part-Whole Numbers

Mental Computation Strategies for Part-Whole Numbers Annaliese Caney and Jane M. Watson University of Tasmania Abstract Mental strategies used by school students in solving problems involving operations

### A 1,200 B 1,300 C 1,500 D 1,700

North arolina Testing Program EOG Mathematics Grade Sample Items Goal. There are eighty-six thousand four hundred seconds in a day. How else could this number be written? 80,06. Jenny s vacation money

### DMA CLUSTER CALCULATIONS POLICY

DMA CLUSTER CALCULATIONS POLICY Watlington C P School Shouldham Windows User HEWLETT-PACKARD [Company address] Riverside Federation CONTENTS Titles Page Schools involved 2 Rationale 3 Aims and principles

### HOLMER GREEN SENIOR SCHOOL CURRICULUM INFORMATION

HOLMER GREEN SENIOR SCHOOL CURRICULUM INFORMATION Subject: Mathematics Year Group: 7 Exam Board: (For years 10, 11, 12 and 13 only) Assessment requirements: Students will take 3 large assessments during

### Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30%

COURSE SYLLABUS FALL 2010 MATH 0408 INTERMEDIATE ALGEBRA Course # 0408.06 Course Schedule/Location: TT 09:35 11:40, A-228 Instructor: Dr. Calin Agut, Office: J-202, Department of Mathematics, Brazosport

### COUNSELLING PROCESS. Definition

Definition COUNSELLING PROCESS The word process means an identifiable sequence of events taking place over time usually there is the implication of progressive stages in the process, Counselling has a

### Talk About It. More Ideas. Formative Assessment. Have students try the following problem.

5.NF. 5.NF.2 Objective Common Core State Standards Add Fractions with Unlike Denominators Students build on their knowledge of fractions as they use models to add fractions with unlike denominators. They

### May To print or download your own copies of this document visit Name Date Eurovision Numeracy Assignment

1. An estimated one hundred and twenty five million people across the world watch the Eurovision Song Contest every year. Write this number in figures. 2. Complete the table below. 2004 2005 2006 2007

### Helping Your Children Learn in the Middle School Years MATH

Helping Your Children Learn in the Middle School Years MATH Grade 7 A GUIDE TO THE MATH COMMON CORE STATE STANDARDS FOR PARENTS AND STUDENTS This brochure is a product of the Tennessee State Personnel

### Math Grade 3 Assessment Anchors and Eligible Content

Math Grade 3 Assessment Anchors and Eligible Content www.pde.state.pa.us 2007 M3.A Numbers and Operations M3.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among

Math 150 Syllabus Course title and number MATH 150 Term Fall 2017 Class time and location INSTRUCTOR INFORMATION Name Erin K. Fry Phone number Department of Mathematics: 845-3261 e-mail address erinfry@tamu.edu

### After your registration is complete and your proctor has been approved, you may take the Credit by Examination for MATH 6A.

MATH 6A Mathematics, Grade 6, First Semester #03 (v.3.0) To the Student: After your registration is complete and your proctor has been approved, you may take the Credit by Examination for MATH 6A. WHAT

### UNIT ONE Tools of Algebra

UNIT ONE Tools of Algebra Subject: Algebra 1 Grade: 9 th 10 th Standards and Benchmarks: 1 a, b,e; 3 a, b; 4 a, b; Overview My Lessons are following the first unit from Prentice Hall Algebra 1 1. Students

### PRIMARY ASSESSMENT GRIDS FOR STAFFORDSHIRE MATHEMATICS GRIDS. Inspiring Futures

PRIMARY ASSESSMENT GRIDS FOR STAFFORDSHIRE MATHEMATICS GRIDS Inspiring Futures ASSESSMENT WITHOUT LEVELS The Entrust Mathematics Assessment Without Levels documentation has been developed by a group of

### GUIDE TO THE CUNY ASSESSMENT TESTS

GUIDE TO THE CUNY ASSESSMENT TESTS IN MATHEMATICS Rev. 117.016110 Contents Welcome... 1 Contact Information...1 Programs Administered by the Office of Testing and Evaluation... 1 CUNY Skills Assessment:...1

### Designing and adapting tasks in lesson planning: a critical process of Lesson Study

ZDM Mathematics Education (2016) 48:411 423 DOI 10.1007/s11858-016-0770-3 ORIGINAL ARTICLE Designing and adapting tasks in lesson planning: a critical process of Lesson Study Toshiakira Fujii 1 Accepted:

### Math 96: Intermediate Algebra in Context

: Intermediate Algebra in Context Syllabus Spring Quarter 2016 Daily, 9:20 10:30am Instructor: Lauri Lindberg Office Hours@ tutoring: Tutoring Center (CAS-504) 8 9am & 1 2pm daily STEM (Math) Center (RAI-338)

### Strategic Practice: Career Practitioner Case Study

Strategic Practice: Career Practitioner Case Study heidi Lund 1 Interpersonal conflict has one of the most negative impacts on today s workplaces. It reduces productivity, increases gossip, and I believe

### IMPLEMENTING THE NEW MATH SOL S IN THE LIBRARY MEDIA CENTER. Adrian Stevens November 2011 VEMA Conference, Richmond, VA

IMPLEMENTING THE NEW MATH SOL S IN THE LIBRARY MEDIA CENTER Adrian Stevens November 2011 VEMA Conference, Richmond, VA Primary Points Math can be fun Language Arts role in mathematics Fiction and nonﬁction

### If a measurement is given, can we convert that measurement to different units to meet our needs?

HS Chemistry POGIL Activity Version 2 Topic: Measurement: Scientific Mathematics Why? In this activity we will see that it is possible to look at a situation from several points of view, or to take measurements

### ENGAGE. Daily Routines Common Core. Essential Question How can you use the strategy draw a diagram to solve multistep division problems?

LESSON 4.12 Problem Solving Multistep Division Problems FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative

### Sample worksheet from

Copyright 2017 Maria Miller. EDITION 1/2017 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, or by any information storage

### Draft -Unit 1. Whole Number Computation and Application 8 Weeks. 1 Joliet Public Schools District 86 DRAFT Curriculum Guide , Grade 5, Unit 1

Draft -Unit 1 Whole Number Computation and Application 8 Weeks 1 Joliet Public Schools District 86 DRAFT Curriculum Guide 2017-2018, Grade 5, Unit 1 2 Joliet Public Schools District 86 DRAFT Curriculum

### Author's response to reviews

Author's response to reviews Title: Global Health Education: a cross-sectional study among German medical students to identify needs, deficits and potential benefits(part 1 of 2: Mobility patterns & educational

### Investigate the program components

Investigate the program components ORIGO Stepping Stones is an award-winning core mathematics program developed by specialists for Australian primary schools. Stepping Stones provides every teacher with

### TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system

Curriculum Overview Mathematics 1 st term 5º grade - 2010 TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Multiplies and divides decimals by 10 or 100. Multiplies and divide

### West s Paralegal Today The Legal Team at Work Third Edition

Study Guide to accompany West s Paralegal Today The Legal Team at Work Third Edition Roger LeRoy Miller Institute for University Studies Mary Meinzinger Urisko Madonna University Prepared by Bradene L.

### Strategies for Solving Fraction Tasks and Their Link to Algebraic Thinking

Strategies for Solving Fraction Tasks and Their Link to Algebraic Thinking Catherine Pearn The University of Melbourne Max Stephens The University of Melbourne

### Functional Maths Skills Check E3/L x

Functional Maths Skills Check E3/L1 Name: Date started: The Four Rules of Number + - x May 2017. Kindly contributed by Nicola Smith, Gloucestershire College. Search for Nicola on skillsworkshop.org Page