The Indices Investigations Teacher s Notes


 Asher Pope
 4 years ago
 Views:
Transcription
1 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: Two activities are designed for capable students who are beyond stage 8 Activity 2 is appropriate for students who are at stage 8, advanced proportional Curriculum reference: Number, levels 5 and 6 Numeracy Project book reference: This investigation is not related to any activity in the Numeracy Project resource books Prior knowledge. Students should be able to: Use power notation and the language of powers Work with fractions, decimals and fractions Understand algebraic notation During these activities, students will meet: Powers involving fractions, decimals, integers and algebraic expressions All sorts of things that come from understanding powers Background Each activity can be set as a project to last students a week. Answers are not provided, as students can come up with all sorts of interesting discoveries, and can even follow a single discovery into a branch of mathematics that is new for them. Periodic meetings with students may be needed to check that they have developed a plan of attack and are on track. Rather than marking these investigations, students have been asked to prepare a presentation to the class on what they have done, and what they have learned. This can produce some fascinating sessions. Students even providing notes for the other students on their discoveries and how they work with worksheet and s to practise should this be desired. Be aware however, that even very capable students can find these investigations daunting, as they are unstructured, and they need to develop their own approach. If you feel that they need some initial support, an introductory session could be run. Activity 2 is probably the simplest of the investigations merely involving students looking for patterns and short cuts when adding, subtracting, multiplying and dividing powers. If this is restricted to just looking at what happens with whole numbers (as indices and bases) it is very manageable. The activity is an important one as too many students make erroneous assumptions about when the Great Index Law can be used, as they have never explored its limits. For
2 However even activity 2 may need to be scaffolded if students are unfamiliar with investigations or discovery in mathematics. This can be done by discussing with students what they think they should be looking at (what sorts of numbers etc), working on several sets of s of problems, looking for patterns in what is found, and by explaining how to write up the discoveries. A sheet providing guidelines for writing up an investigation is available for students to follow. (ref investigation sheet here) Investigations: PDF or Word
3 Indices investigation 1 You have already met powers. For 2 is an of a power. You have also been introduced to fractions, decimals and integers, and have been introduced to algebra with letters being used to stand for numbers. In this investigation you will be exploring what happens when these sorts of numbers (or pieces of algebra) are used in powers.. Task 1 Investigate powers with different types of numbers as their base. Write up your investigation in your book, showing each step of the investigation. Be prepared to explain what you have done, and present some of your findings to the class. AC EA AA AM AP+ Explanation When you learnt about powers you 'invented' them as a short way of writing repeated multiplications. instead of writing you can write 2 However, if you want to work out the value of 2 unless you memorise the answer, you still have to work it out the long way (by doing the multiplication) as there is no short cut to get straight from the 2 and the in the power 2 to the answer 16 Now it is fairly obvious that if you can write as 2, you should also be able to write and as include brackets to show that as (2) likewise for this is the base The task you have been set is to investigate such powers to see if there are any short cuts which will help you work out their values without having to multiply everything out the long way. Here is an to show you how to investigate different sorts of base doing the long way
4 27 6 summarising in power form often identifies the short cut In this there appears to be a short cut to do with using the index outside the bracket for both the numerator and denominator of the fraction. short cut 27 6 Most of this investigation can be done by trying different sorts of problems then looking for patterns and short cuts. Once you have identified a 'short cut', you should write a rule which (a) says how the 'short cut ' works (b) says when you are allowed to use it (c) gives an of its use This rule then needs to be tested on a series of questions which are answered using both the 'long' way and the 'short' way. (If both routes get the same answer, your rule is likely to be a good one.) Note  this task you have been given is too big to be solved without planning. The first thing you should do is decide how you are going to tackle the problem. Here are some guidelines that might help you. (1) Write down all the different types of base that you have to investigate. (Hint  there are lots of algebraic ones) (2) It is always easier to start with the simple stuff and gradually increase the level of difficulty. (Hint  what numbers are easy to deal with? What numbers might give you special results?) () Your overall approach needs to be systematic, carefully structured and wellexplained when dealing with fractional bases you should use different sorts of fractions like one third, three sevenths, nine fourths,... easiest 1 7 special as it has a one on top fraction with top number smaller than the bottom one
5 getting 9 fraction with top number bigger than the bottom one harder 5 6 negative fraction etc () Be careful in the way you set out your problems. (Hint  follow the format from the on page 2.) Finally, there is one thing you need to be aware of. In multiplying variables 1 x 21x 2 x 2 So with powers If you want to include the negative sign as part of the base you must use brackets therefore (2)
6 Indices investigation 2 Task It is possible to think of a power as a sort of number. If we do this we can explore what happens as we use them in problems. In this investigation, you are to investigate what happens when we try to add, subtract, multiply or divide powers. Write up your investigation in your book, showing each step of the investigation. Be prepared to explain what you have done, and present some of your findings to the class. AC EA AA AM AP Explanation When you operate on numbers you change them in some way. The four operations you know best are addition, subtraction, multiplication and division. If we look at how these operations change the numbers 2 and we find We see that each operation produces a different answer (and uses a different mathematical rule to get that answer.) In this investigation you are to investigate how powers work when they are added, subtracted, multiplied and divided. Once again, use the format from page 2 of the first investigation and look for any short cuts that will help you find the answers more quickly. Also use the same sort of strategy you used to investigate the different sort of bases. Remember to use the investigation flow diagram in writing up your work. Don't forget that finding there is no short cut for a certain type of problem is also an important discovery that you need to record.
7 Indices investigation Task Investigate powers with different types of number as their base. Write up your investigation in your book, showing each step of the investigation. Be prepared to explain what you have done, and present some of your findings to the class. AC EA AA AM AP+ Explanation In this investigation you are to look at what happens to powers and their values when the indices are things other than natural numbers. (For, if the index is an integer or fraction). However, in investigating various types of index, it will not be possible (initially) to do the problem 'the long way'. 1 2 just what does mean? Consequently you must use other tactics to find the values of such powers. One technique is to use a calculator, the other is to look at patterns. A third could involve the use of a computer and a spreadsheet. Extending this pattern allows you to develop values and expanded forms for zero and negative indices. Powers of ? Furthermore, if your development is systematic, graphing your information will often provide you with useful results. When investigating decimal indices there are 2 basic approaches you can adopt. (a) (b) change the base but keep the index the same i e 1, 2,,, 5, 6, 7, 8, 9, etc keep the base the same but change the index i e,,,,,,,, etc
8 Both approaches use a system and form a pattern  and produce interesting results when graphed (try it.) You may even be able to explain some weird calculator results by using some of the graphs you draw. By the way, one thing that can happen in this investigation is that you don't always find short cuts which you could use to work out answers much more quickly and easily... Instead you might discover some interesting relationships between powers and other sorts of numbers. (If you want a clue, or to find out more about these other sorts of number, try to find out about the topics of logarithms and/or surds.) Also, sort through your sets of results carefully, as only one or two of the indices you are likely to investigate will give you the clues you need to find the links. As with the first of the indices investigations, to successfully complete this task you will need to plan your approach carefully. Here are some suggestions that might help you construct your strategy. (1) Write down all the different types of index that you should investigate (2) Use sets of problems and create patterns and sequences in them () Use a calculator () Start with the easiest types of problem (5) Think of any special numbers that may produce special results when they are used as indices. Extension Investigate powers with different types of indices and bases. Are there any special rules for evaluating something like 2 1 or 5 2 etc (The problems in this part shouldn't be too difficult, but should be enough to show what happens when the different sorts of indices and bases are combined.)
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
More informationAlgebra 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.
More informationPreAlgebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value
Syllabus PreAlgebra A Course Overview PreAlgebra is a course designed to prepare you for future work in algebra. In PreAlgebra, you will strengthen your knowledge of numbers as you look to transition
More informationMathematics 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
More informationTOPICS 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
More informationUNIT 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
More informationMathematics 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
More informationGrade 5 + DIGITAL. EL Strategies. DOK 14 RTI Tiers 13. Flexible Supplemental K8 ELA & Math Online & Print
Standards PLUS Flexible Supplemental K8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 14 RTI Tiers 13 1520 Minute Lessons Assessments Consistent with CA Testing Technology
More informationUsing Proportions to Solve Percentage Problems I
RP71 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
More informationAre 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,
More informationAlignment of Australian Curriculum Year Levels to the Scope and Sequence of MathUSee Program
Alignment of s to the Scope and Sequence of MathUSee Program This table provides guidance to educators when aligning levels/resources to the Australian Curriculum (AC). The MathUSee levels do not address
More informationChapter 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
More informationMODULE 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
More informationAGS THE GREAT REVIEW GAME FOR PREALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS
AGS THE GREAT REVIEW GAME FOR PREALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic
More informationGrade 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
More informationMultiplication 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.
More informationStacks Teacher notes. Activity description. Suitability. Time. AMP resources. Equipment. Key mathematical language. Key processes
Stacks Teacher notes Activity description (Interactive not shown on this sheet.) Pupils start by exploring the patterns generated by moving counters between two stacks according to a fixed rule, doubling
More informationPage 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Subtopic: General. Grade(s): None specified
Curriculum Map: Grade 4 Math Course: Math 4 Subtopic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community
More informationWhat 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
More informationCharacteristics of Functions
Characteristics of Functions Unit: 01 Lesson: 01 Suggested Duration: 10 days Lesson Synopsis Students will collect and organize data using various representations. They will identify the characteristics
More informationExtending 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
More informationAlgebra 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
More informationLet s think about how to multiply and divide fractions by fractions!
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:
More informationFractionWorks Correlation to Georgia Performance Standards
Cheryl Keck Educational Sales Consultant Phone: 8004455985 ext. 3231 ckeck@etacuisenaire.com www.etacuisenaire.com FractionWorks Correlation to Georgia Performance s Correlated to Georgia Performance
More informationMath 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
More informationMathUSee Correlation with the Common Core State Standards for Mathematical Content for Third Grade
MathUSee 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 MathUSee
More informationEdexcel GCSE. Statistics 1389 Paper 1H. June Mark Scheme. Statistics Edexcel GCSE
Edexcel GCSE Statistics 1389 Paper 1H June 2007 Mark Scheme Edexcel GCSE Statistics 1389 NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional
More informationCreating a Test in Eduphoria! Aware
in Eduphoria! Aware Login to Eduphoria using CHROME!!! 1. LCS Intranet > Portals > Eduphoria From home: LakeCounty.SchoolObjects.com 2. Login with your full email address. First time login password default
More informationTabletClass Math Geometry Course Guidebook
TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course
More informationHOLMER 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
More informationCAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4Year Subgroup: none Test Date: Spring 2011
CAAP Content Analysis Report Institution Code: 911 Institution Type: 4Year Normative Group: 4year Colleges Introduction This report provides information intended to help postsecondary institutions better
More informationInvestigate the program components
Investigate the program components ORIGO Stepping Stones is an awardwinning core mathematics program developed by specialists for Australian primary schools. Stepping Stones provides every teacher with
More informationBittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: AddisonWesley.
Course Syllabus Course Description Explores the basic fundamentals of collegelevel mathematics. (Note: This course is for institutional credit only and will not be used in meeting degree requirements.
More informationRendezvous with Comet Halley Next Generation of Science Standards
Next Generation of Science Standards 5th Grade 6 th Grade 7 th Grade 8 th Grade 5PS13 Make observations and measurements to identify materials based on their properties. MSPS14 Develop a model that
More informationPedagogical 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
More informationAnswers To Hawkes Learning Systems Intermediate Algebra
Answers To Hawkes Learning Free PDF ebook Download: Answers To Download or Read Online ebook answers to hawkes learning systems intermediate algebra in PDF Format From The Best User Guide Database Double
More informationPearson Grade 8 Practice And Homework
Pearson Grade 8 And Free PDF ebook Download: Pearson Grade 8 And Download or Read Online ebook pearson grade 8 practice and homework in PDF Format From The Best User Guide Database 3rd Grade EOG Prep.
More informationsuccess. It will place emphasis on:
1 First administered in 1926, the SAT was created to democratize access to higher education for all students. Today the SAT serves as both a measure of students college readiness and as a valid and reliable
More informationFocus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multidigit whole numbers.
Approximate Time Frame: 34 weeks Connections to Previous Learning: In fourth grade, students fluently multiply (4digit by 1digit, 2digit by 2digit) and divide (4digit by 1digit) using strategies
More informationAfm Math Review Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database
Afm Math Free PDF ebook Download: Afm Math Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database C++ for Game Programming with DirectX9.0c and Raknet. Lesson 1.
More informationMay 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
More informationWritten by Wendy Osterman
PreAlgebra 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
More informationMathematics Success Grade 7
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,
More informationSt Math Teacher Login
St Math Login Free PDF ebook Download: St Math Login Download or Read Online ebook st math teacher login in PDF Format From The Best User Guide Database Ace Arms. Login Instructions. : karlahill6. Student:
More informationIf we want to measure the amount of cereal inside the box, what tool would we use: string, square tiles, or cubes?
String, Tiles and Cubes: A HandsOn Approach to Understanding Perimeter, Area, and Volume Teaching Notes Teacherled discussion: 1. PreAssessment: Show students the equipment that you have to measure
More informationFourth 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 kindergarten5 utilize a
More informationRIGHTSTART 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
More informationMathematics. Mathematics
Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in
More informationCommon 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
More informationSouth 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
More informationFunctional Skills Mathematics Level 2 assessment
Functional Skills Mathematics Level 2 assessment www.cityandguilds.com September 2015 Version 1.0 Marking scheme ONLINE V2 Level 2 Sample Paper 4 Mark Represent Analyse Interpret Open Fixed S1Q1 3 3 0
More informationMental Computation Strategies for PartWhole Numbers
Mental Computation Strategies for PartWhole Numbers Annaliese Caney and Jane M. Watson University of Tasmania Abstract Mental strategies used by school students in solving problems involving operations
More informationBENCHMARK 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
More informationAssessment Requirements: November 2017 Grade 5
1 Assessment Requirements: November 2017 Grade 5 Your son starts his exams on 15 November 2017 Please ensure that he has the following at school EVERY DAY during the assessment week: A complete pencil
More informationShockwheat. Statistics 1, Activity 1
Statistics 1, Activity 1 Shockwheat Students require real experiences with situations involving data and with situations involving chance. They will best learn about these concepts on an intuitive or informal
More informationDiagnostic Test. Middle School Mathematics
Diagnostic Test Middle School Mathematics Copyright 2010 XAMonline, Inc. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by
More informationEDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 4. Working with measures
EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 4 Working with measures SECTION G 1 Time 2 Temperature 3 Length 4 Weight 5 Capacity 6 Conversion between metric units 7 Conversion
More informationCalculators in a Middle School Mathematics Classroom: Helpful or Harmful?
University of Nebraska  Lincoln DigitalCommons@University of Nebraska  Lincoln Action Research Projects Math in the Middle Institute Partnership 72008 Calculators in a Middle School Mathematics Classroom:
More informationPRIMARY 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
More informationMissouri Mathematics GradeLevel Expectations
A Correlation of to the Grades K  6 G/M223 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley Mathematics in meeting the
More informationThis 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
More informationLESSON PLANS: AUSTRALIA Year 6: Patterns and Algebra Patterns 50 MINS 10 MINS. Introduction to Lesson. powered by
Year 6: Patterns and Algebra Patterns 50 MINS Strand: Number and Algebra Substrand: Patterns and Algebra Outcome: Continue and create sequences involving whole numbers, fractions and decimals. Describe
More informationNCSC Alternate Assessments and Instructional Materials Based on Common Core State Standards
NCSC Alternate Assessments and Instructional Materials Based on Common Core State Standards Ricki Sabia, JD NCSC Parent Training and Technical Assistance Specialist ricki.sabia@uky.edu Background Alternate
More informationFoothill 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:
More informationFractions Division And Multiplication Multiple Choice Test
Fractions Division And Multiplication Multiple Free PDF ebook Download: Fractions Division And Multiplication Test Download or Read Online ebook fractions division and multiplication multiple choice test
More informationBackwards 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
More informationIntroduction. Chem 110: Chemical Principles 1 Sections 4052
Introduction Chem 110: Chemical Principles 1 Sections 4052 Instructor: Dr. Squire J. Booker 302 Chemistry Building 8148658793 squire@psu.edu (sjb14@psu.edu) Lectures: Monday (M), Wednesday (W), Friday
More informationJulia Smith. Effective Classroom Approaches to.
Julia Smith @tessmaths Effective Classroom Approaches to GCSE Maths resits julia.smith@writtle.ac.uk Agenda The context of GCSE resit in a post16 setting An overview of the new GCSE Key features of a
More informationStandard 1: Number and Computation
Standard 1: Number and Computation Standard 1: Number and Computation The student uses numerical and computational concepts and procedures in a variety of situations. Benchmark 1: Number Sense The student
More informationThe 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...
More informationFunctional 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
More informationDublin City Schools Mathematics Graded Course of Study GRADE 4
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, technologysupported
More informationa) analyse sentences, so you know what s going on and how to use that information to help you find the answer.
Tip Sheet I m going to show you how to deal with ten of the most typical aspects of English grammar that are tested on the CAE Use of English paper, part 4. Of course, there are many other grammar points
More informationGCE. Mathematics (MEI) Mark Scheme for June Advanced Subsidiary GCE Unit 4766: Statistics 1. Oxford Cambridge and RSA Examinations
GCE Mathematics (MEI) Advanced Subsidiary GCE Unit 4766: Statistics 1 Mark Scheme for June 2013 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing
More informationCase study Norway case 1
Case study Norway case 1 School : B (primary school) Theme: Science microorganisms Dates of lessons: March 2627 th 2015 Age of students: 1011 (grade 5) Data sources: Pre and postinterview with 1 teacher
More informationDeveloping a concretepictorialabstract model for negative number arithmetic
Developing a concretepictorialabstract model for negative number arithmetic Jai Sharma and Doreen Connor Nottingham Trent University Research findings and assessment results persistently identify negative
More informationCentre for Evaluation & Monitoring SOSCA. Feedback Information
Centre for Evaluation & Monitoring SOSCA Feedback Information Contents Contents About SOSCA... 3 SOSCA Feedback... 3 1. Assessment Feedback... 4 2. Predictions and Chances Graph Software... 7 3. Value
More informationKeystone Algebra 1 Open Ended Practice
Keystone Algebra 1 Open Ended Practice Free PDF ebook Download: Keystone Algebra 1 Practice Download or Read Online ebook keystone algebra 1 open ended practice in PDF Format From The Best User Guide Database
More informationActivity 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
More informationBig Ideas Math Grade 6 Answer Key
Big Ideas Math Grade 6 Answer Key Free PDF ebook Download: Big Ideas Math Grade 6 Answer Key Download or Read Online ebook big ideas math grade 6 answer key in PDF Format From The Best User Guide Database
More informationPhysics 270: Experimental Physics
2017 edition Lab Manual Physics 270 3 Physics 270: Experimental Physics Lecture: Lab: Instructor: Office: Email: Tuesdays, 2 3:50 PM Thursdays, 2 4:50 PM Dr. Uttam Manna 313C Moulton Hall umanna@ilstu.edu
More informationMath 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 (CAS504) 8 9am & 1 2pm daily STEM (Math) Center (RAI338)
More informationP a g e 1. Grade 5. Grant funded by:
P a g e 1 Grade 5 Grant funded by: P a g e 2 Focus Standard: 5.NF.1, 5.NF.2 Lesson 6: Adding and Subtracting Unlike Fractions Standards for Mathematical Practice: SMP.1, SMP.2, SMP.6, SMP.7, SMP.8 Estimated
More informationDMA CLUSTER CALCULATIONS POLICY
DMA CLUSTER CALCULATIONS POLICY Watlington C P School Shouldham Windows User HEWLETTPACKARD [Company address] Riverside Federation CONTENTS Titles Page Schools involved 2 Rationale 3 Aims and principles
More informationSecret Code for Mazes
Secret Code for Mazes ACTIVITY TIME 3045 minutes MATERIALS NEEDED Pencil Paper Secret Code Sample Maze worksheet A set of mazes (optional) page 1 Background Information It s a scene we see all the time
More informationThe Flaws, Fallacies and Foolishness of Benchmark Testing
Benchmarking is a great tool for improving an organization's performance...when used or identifying, then tracking (by measuring) specific variables that are proven to be "S.M.A.R.T." That is: Specific
More informationAP Statistics Summer Assignment 1718
AP Statistics Summer Assignment 1718 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic
More informationGRADE 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 0304 Grade 5 Pre Assessment
More informationPearson Mymathlab Answer Key Math 110 Amu
Mymathlab Answer Key Math 110 Amu Free PDF ebook Download: Mymathlab Math 110 Amu Download or Read Online ebook pearson mymathlab answer key math 110 amu in PDF Format From The Best User Guide Database
More informationGCSE Mathematics B (Linear) Mark Scheme for November Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education
GCSE Mathematics B (Linear) Component J567/04: Mathematics Paper 4 (Higher) General Certificate of Secondary Education Mark Scheme for November 2014 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge
More informationAPES Summer Work PURPOSE: THE ASSIGNMENT: DUE DATE: TEST:
APES Summer Work PURPOSE: Like most science courses, APES involves math, data analysis, and graphing. Simple math concepts, like dealing with scientific notation, unit conversions, and percent increases,
More informationSouth Carolina College and CareerReady Standards for Mathematics. Standards Unpacking Documents Grade 5
South Carolina College and CareerReady Standards for Mathematics Standards Unpacking Documents Grade 5 South Carolina College and CareerReady Standards for Mathematics Standards Unpacking Documents
More informationTABE 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
More informationSTUDENTS' RATINGS ON TEACHER
STUDENTS' RATINGS ON TEACHER Faculty Member: CHEW TECK MENG IVAN Module: Activity Type: DATA STRUCTURES AND ALGORITHMS I CS1020 LABORATORY Class Size/Response Size/Response Rate : 21 / 14 / 66.67% Contact
More informationFoothill College Fall 2014 Math My Way Math 230/235 MTWThF 10:0011:50 (click on Math My Way tab) Math My Way Instructors:
This is a team taught directed study course. Foothill College Fall 2014 Math My Way Math 230/235 MTWThF 10:0011:50 www.psme.foothill.edu (click on Math My Way tab) Math My Way Instructors: Instructor:
More informationTitle: George and Sam Save for a Present By: Lesson Study Group 2
Research Aim: Title: George and Sam Save for a Present By: Lesson Study Group 2 Team Members: Jan Arslan, Lindsay Blanchard, Juneanne Demek, Hilary Harrison, Susan Greenwood Research Lesson Date: Tuesday,
More informationLab 1  The Scientific Method
Lab 1  The Scientific Method As Biologists we are interested in learning more about life. Through observations of the living world we often develop questions about various phenomena occurring around us.
More informationAP Chemistry
AP Chemistry 20162017 Welcome to AP Chemistry! I am so excited to have you in this course next year! To get geared up for the class, there are some things that you need to do this summer. None of it is
More informationFirst 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
More informationDEVM F105 Intermediate Algebra DEVM F105 UY2*2779*
DEVM F105 Intermediate Algebra DEVM F105 UY2*2779* page iii Table of Contents CDE Welcomev Introduction xiii
More information