From the Ark of History to the Arc of Reasoning
|
|
|
- Jason Hardy
- 5 years ago
- Views:
Transcription
1 From the Ark of History to the Arc of Reasoning William McCallum The University of Arizona & Illustrative Mathematics JMM, 2016
2 Themes Decluttering Attending to historically unattended leaps Distinguishing between objects, uses of those objects, and ways of viewing them (why not just call a ratio an ordered pair of numbers?)
3 The number line marked off in thirds GradeThemeaningoffractionsInGrades1and2,studentsusefractionlanguagetodescribepartitionsofshapesintoequalshares.2.G.In2.G.Partitioncirclesandrectanglesintotwo,three,orfourequalshares,describethesharesusingthewordshalves,thirds,halfof,athirdof,etc.,anddescribethewholeastwohalves,threethirds,fourfourths.Recognizethatequalsharesofidenticalwholesneednothavethesameshape.Gradetheystarttodeveloptheideaofafractionmoreformally,buildingontheideaofpartitioningawholeintoequalparts.Thewholecanbeacollectionofobjects,ashapesuchasacircleorrect-angle,alinesegment,oranyfiniteentitysusceptibletosubdivisionandmeasurement.Thewholeasacollectionofobjects!Ifthewholeisacollectionof4bunnies,thenonebunnyis14ofthewholeandbunniesis4ofthewhole.Gradestudentsstartwtihunitfractions(fractionswithnumer-ator1).Theseareformedbydividingawholeintoequalpartsandtakingonepart,e.g.,ifawholeisdividedinto4equalpartstheneachpartis14ofthewhole,and4copiesofthatpartmakethewhole.Next,studentsbuildfractionsfromunitfractions,seeingthenumer-atorof4assayingthat4iswhatyougetbyputtingofthe14 stogether..nf.1anyfractioncanbereadthisway,andinparticular.nf.1understandafraction1 asthequantityformedby1partwhenawholeispartitionedinto equalparts;understandafrac-tion asthequantityformedby partsofsize1.thereisnoneedtointroducetheconceptsof properfraction"and improperfraction"initially;5iswhatonegetsbycombining5partstogetherwhenthewholeisdividedintoequalparts.twoimportantaspectsoffractionsprovideopportunitiesforthemathematicalpracticeofattendingtoprecision(mp6): Specifyingthewhole.TheimportanceofspecifyingthewholeWithoutspecifyingthewholeitisnotreasonabletoaskwhatfractionisrepresentedbytheshadedarea.Iftheleftsquareisthewhole,itrepresentsthefraction2;iftheentirerectangleisthewhole,itrepresents4. Explainingwhatismeantby equalparts. Initially,studentscanuseanintuitivenotionofcongruence( samesizeandsameshape )toexplainwhythepartsareequal,e.g.,whentheydivideasquareintofourequalsquaresorfourequalrectangles.arearepresentationsof14ineachrepresentationthesquareisthewhole.thetwosquaresontheleftaredividedintofourpartsthathavethesamesizeandshape,andsothesamearea.inthethreesquaresontheright,theshadedareais14ofthewholearea,eventhoughitisnoteasilyseenasonepartoutofadivisionintofourpartsofthesameshapeandsize.studentscometounderstandamoreprecisemeaningfor equalparts as partswithequalmeasurement. Forexample,whenarulerisdividedintohalvesorquartersofaninch,theyseethateachsubdivisionhasthesamelength.Inareamodelstheyreasonabouttheareaofashadedregiontodecidewhatfractionofthewholeitrepresents(MP).Thegoalisforstudentstoseeunitfractionsasthebasicbuildingblocksoffractions,inthesamesensethatthenumber1isthebasicbuildingblockofthewholenumbers;justaseverywholenumberisobtainedbycombiningasufficientnumberof1s,everyfractionisobtainedbycombiningasufficientnumberofunitfractions.ThenumberlineOnthenumberline,thewholeistheunitinterval,thatis,theintervalfrom0to1,measuredbylength.Iteratingthiswholetotherightmarksoffthewholenumbers,sothattheintervalsbetweenconsecutivewholenumbers,from0to1,1to2,2to,etc.,areallofthesamelength,asshown.Studentsmightthinkofthenumberlineasaninfiniteruler.Thenumberline012456etc.Toconstructaunitfractiononthenumberline,e.g.1,studentsdividetheunitintervalintointervalsofequallengthandrecognizethateachhaslength1.Theylocatethenumber1onthenumberDraft,5/29/2011,commentatcommoncoretools.wordpress.com. The number line GradeThemeaningoffractionsInGrades1and2,studentsusefractionlanguagetodescribepartitionsofshapesintoequalshares.2.G.In2.G.Partitioncirclesandrectanglesintotwo,three,orfourequalshares,describethesharesusingthewordshalves,thirds,halfof,athirdof,etc.,anddescribethewholeastwohalves,threethirds,fourfourths.Recognizethatequalsharesofidenticalwholesneednothavethesameshape.Gradetheystarttodeveloptheideaofafractionmoreformally,buildingontheideaofpartitioningawholeintoequalparts.Thewholecanbeacollectionofobjects,ashapesuchasacircleorrect-angle,alinesegment,oranyfiniteentitysusceptibletosubdivisionandmeasurement.Thewholeasacollectionofobjects!Ifthewholeisacollectionof4bunnies,thenonebunnyis14ofthewholeandbunniesis4ofthewhole.Gradestudentsstartwtihunitfractions(fractionswithnumer-ator1).Theseareformedbydividingawholeintoequalpartsandtakingonepart,e.g.,ifawholeisdividedinto4equalpartstheneachpartis14ofthewhole,and4copiesofthatpartmakethewhole.Next,studentsbuildfractionsfromunitfractions,seeingthenumer-atorof4assayingthat4iswhatyougetbyputtingofthe14 stogether..nf.1anyfractioncanbereadthisway,andinparticular.nf.1understandafraction1 asthequantityformedby1partwhenawholeispartitionedinto equalparts;understandafrac-tion asthequantityformedby partsofsize1.thereisnoneedtointroducetheconceptsof properfraction"and improperfraction"initially;5iswhatonegetsbycombining5partstogetherwhenthewholeisdividedintoequalparts.twoimportantaspectsoffractionsprovideopportunitiesforthemathematicalpracticeofattendingtoprecision(mp6): Specifyingthewhole.TheimportanceofspecifyingthewholeWithoutspecifyingthewholeitisnotreasonabletoaskwhatfractionisrepresentedbytheshadedarea.Iftheleftsquareisthewhole,itrepresentsthefraction2;iftheentirerectangleisthewhole,itrepresents4. Explainingwhatismeantby equalparts. Initially,studentscanuseanintuitivenotionofcongruence( samesizeandsameshape )toexplainwhythepartsareequal,e.g.,whentheydivideasquareintofourequalsquaresorfourequalrectangles.arearepresentationsof14ineachrepresentationthesquareisthewhole.thetwosquaresontheleftaredividedintofourpartsthathavethesamesizeandshape,andsothesamearea.inthethreesquaresontheright,theshadedareais14ofthewholearea,eventhoughitisnoteasilyseenasonepartoutofadivisionintofourpartsofthesameshapeandsize.studentscometounderstandamoreprecisemeaningfor equalparts as partswithequalmeasurement. Forexample,whenarulerisdividedintohalvesorquartersofaninch,theyseethateachsubdivisionhasthesamelength.Inareamodelstheyreasonabouttheareaofashadedregiontodecidewhatfractionofthewholeitrepresents(MP).Thegoalisforstudentstoseeunitfractionsasthebasicbuildingblocksoffractions,inthesamesensethatthenumber1isthebasicbuildingblockofthewholenumbers;justaseverywholenumberisobtainedbycombiningasufficientnumberof1s,everyfractionisobtainedbycombiningasufficientnumberofunitfractions.ThenumberlineOnthenumberline,thewholeistheunitinterval,thatis,theintervalfrom0to1,measuredbylength.Iteratingthiswholetotherightmarksoffthewholenumbers,sothattheintervalsbetweenconsecutivewholenumbers,from0to1,1to2,2to,etc.,areallofthesamelength,asshown.Studentsmightthinkofthenumberlineasaninfiniteruler.Thenumberline012456etc.Toconstructaunitfractiononthenumberline,e.g.1,studentsdividetheunitintervalintointervalsofequallengthandrecognizethateachhaslength1.Theylocatethenumber1onthenumberDraft,5/29/2011,commentatcommoncoretools.wordpress.com. From whole numbers to fractions 6 etc.
4 Connection between division and fractions Why is 5 5?
5 From Fractions to Ratios
6 From Equivalent Ratios to Proportional Relationships cups grape cups peach cups grape cups peach
7 From Proportional Relationships to Linear Functions
8 MP8: Look for and express regularity in repeated reasoning Moving from the table and the graph to the equation for each 1 unit you move to the right, move up 2 5 of a unit. when you go 2 units to the right, you go up 2 2 when you go units to the right, you go up 2 when you go 4 units to the right, you go up 4 2 when you go x units to the right, you go up x 2 starting from p0, 0q, to get to a point px, yq on the graph, go x units to the right, so go up x 2 therefore y x 2 5
Progressions for the Common Core State Standards in Mathematics
Progressions for the Common Core State Standards in Mathematics c Common Core Standards Writing Team 8 The Progressions are published under the Creative Commons Attribution (CC BY) license For information
Multiplication to Ratio, Proportion, and Fractions within the Common Core
Multiplication to Ratio, Proportion, and Fractions within the Common Core Karen C. Fuson 1, Sybilla Beckmann 2 1 Northwestern University, Professor Emerita 2 Department of Mathematics, University of Georgia
Putnam County Schools Curriculum Map 7 th Grade Math Module: 4 Percent and Proportional Relationships
Putnam County Schools Curriculum Map 7 th Grade Math 2016 2017 Module: 4 Percent and Proportional Relationships Instructional Window: MAFS Standards Topic A: MAFS.7.RP.1.1 Compute unit rates associated
Course Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
GRADE LEVEL: SEVENTH SUBJECT: MATH DATE: CONTENT STANDARD INDICATORS SKILLS ASSESSMENT VOCABULARY ISTEP
GRADE LEVEL: SEVENTH SUBJECT: MATH DATE: 2015 2016 GRADING PERIOD: QUARTER 2 MASTER COPY 10 8 15 CONTENT STANDARD INDICATORS SKILLS ASSESSMENT VOCABULARY ISTEP COMPUTATION Unit Rates Ratios Length Area
Lesson 1 6. Algebra: Variables and Expression. Students will be able to evaluate algebraic expressions.
Lesson 1 6 Algebra: Variables and Expression Students will be able to evaluate algebraic expressions. P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable
Part Mark Answer Further Information. Part Mark Answer Further Information Award 1 mark for 20, 15, 35 or. Part Mark Answer Further Information
Cambridge International Examinations Cambridge Checkpoint MATHEMATICS 1112/01 Paper 1 For Examination from 2014 SPECIMEN MARK SCHEME MAXIMUM MARK: 50 This document consists of 11 printed pages and 1 blank
UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet
Name Period Date UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet 20.1 Solving Proportions 1 Add, subtract, multiply, and divide rational numbers. Use rates and proportions to solve problems.
Grade 4. COMMON CORE STATE STANDARDS FOR MATHEMATICS Correlations
COMMON CORE STATE STANDARDS FOR MATHEMATICS Standards for Mathematical Practices CC.K 12.MP.1 Make sense of problems and persevere in solving them. In most Student Edition lessons. Some examples are: 50
Grade: 4 Lesson Title: Equivalence and Comparison of Fractions
How do we know if fractions are equivalent, if not how do we compare their relative sizes? Targeted Content Standard(s): 4. NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by
7 Mathematics Curriculum
New York State Common Core 7 Mathematics Curriculum GRADE Table of Contents 1 Percent and Proportional Relationships GRADE 7 MODULE 4... 3 Topic A: Finding the Whole (7.RP.A.1, 7.RP.A.2c, 7.RP.A.3)...
Core Learning Standards for Mathematics Grade 6
Core Learning Standards for Mathematics Grade 6 Write and evaluate numerical expressions involving whole-number exponents. Write, read, and evaluate expressions; identify parts of an expression using mathematical
Exploring bivariate data Student Activity Sheet 4; use with Exploring Interpreting linear models
1. What is Hooke s Law? 2. What item in the science experiment is being used to simulate a spring? 3. Fill in the table (for number of marbles = {0, 5, 10, 15}) with the data collected during the science
4, 5, 6, 7, 8, 9, 10, 11, 12
Question 1 11 Plus Mathematics - Practice Taster In the number 7,251 - The 5 is worth 50 What is the value of the number 1? What is the value of the number 7? What is the value of the number 2? Question
Example. h + 8 < -13 and b 4 > -6 Multiplying and dividing inequalities
Unit 2 (continued): Expressions and Equations 2 nd 9 Weeks Suggested Instructional Days: 10 Unit Summary (Learning Target/Goal): Use properties of operations to generate equivalent expressions. CCSS for
Unit 4: Proportional Reasoning 1
Subject Mathematics Grade 7 Unit Unit 4: Proportional Reasoning Pacing 5 weeks plus 1 week for reteaching/enrichment Essential Questions How can constants of proportionality (unit rates) be identified?
Constructing Task: Fraction Clues
Constructing Task: Fraction Clues STANDARDS FOR MATHEMATICAL CONTENT MCC4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction
Can the number be represented as a fraction? What are the different categories of numbers? CPM Materials modified by Mr. Deyo
Common Core Standard: 8.NS.1, 8.NS.2, 8.EE.2 Can the number be represented as a fraction? What are the different categories of numbers? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.4 What Kind
GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: Read (in standard form) whole numbers. whole numbers Equivalent Whole Numbers
CRAWFORDSVILLE COMMUNITY SCHOOL CORPORATION 1 GRADE LEVEL: FOURTH GRADE SUBJECT: MATH DATE: 2019 2020 GRADING PERIOD: QUARTER 1 MASTER COPY 1 20 19 NUMBER SENSE Whole Numbers 4.NS.1: Read and write whole
Standards for Mathematical Practice
Common Core State Standards Mathematics Student: Teacher: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively Standards for Mathematical Practice 3. Construct
Using Tables of Equivalent Ratios
LESSON Using Tables of Equivalent Ratios A table can be used to show the relationship between two quantities. You can use equivalent ratios to find a missing value in a table. EXAMPLE A The table shows
7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular)
7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular) Unit #1 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers;
BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals BIG IDEA 1:
BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals Multiplying and Dividing Decimals Explain the difference between an exact answer and an estimated
Unit 4.4 Representing Images
Unit 4.4 Representing Images Candidates should be able to: a) Explain the representation of an image as a series of pixels represented in binary b) Explain the need for metadata to be included in the file
Module 1. Ratios and Proportional Relationships Lessons Lesson #15 You need: pencil, calculator and binder. Do Now:
Module 1 Ratios and Proportional Relationships Lessons 15 19 Lesson #15 You need: pencil, calculator and binder. Do Now: 1. The table gives pairs of values for the variables x and y. x 1 2 3 y 3 6 9 Determine
Unit 2: Ratio & Proportion Applications
Time Frame: Approximately 3-4 Weeks Connections to previous learning: In Grade 6, students develop an understanding of ratio and proportion using ratio tables, tape diagrams, and double number lines. Focus
What role does the central angle play in helping us find lengths of arcs and areas of regions within the circle?
Middletown Public Schools Mathematics Unit Planning Organizer Subject Geometry Grade/Course 10 Unit 5 Circles and other Conic Sections Duration 16 instructional + 4 days for reteaching/enrichment Big Idea
8.EE. Development from y = mx to y = mx + b DRAFT EduTron Corporation. Draft for NYSED NTI Use Only
8.EE EduTron Corporation Draft for NYSED NTI Use Only TEACHER S GUIDE 8.EE.6 DERIVING EQUATIONS FOR LINES WITH NON-ZERO Y-INTERCEPTS Development from y = mx to y = mx + b DRAFT 2012.11.29 Teacher s Guide:
Number Systems and Fractions
Number Systems and Fractions Section 1: Fractions A. Adding and Subtracting Fractions The rule: When adding or subtracting fractions find a common denominator in order to add or subtract the fractions.
1. Write the fraction that each tile represents, if 1 (one) is represented by the yellow tile. Yellow Red Blue Green Purple Brown
Fraction Tiles Activity Worksheet In this activity you will be using fraction tiles to explore relationships among fractions. At the end of the activity your group will write a report. You may want to
Math 7 Notes - Part A: Ratio and Proportional Relationships
Math 7 Notes - Part A: Ratio and Proportional Relationships CCSS 7.RP.A.: Recognize and represent proportional relationships between quantities. RATIO & PROPORTION Beginning middle school students typically
What is the expected number of rolls to get a Yahtzee?
Honors Precalculus The Yahtzee Problem Name Bolognese Period A Yahtzee is rolling 5 of the same kind with 5 dice. The five dice are put into a cup and poured out all at once. Matching dice are kept out
Ratios and Proportions in the Common Core NCCTM State Mathematics Conference
Ratios and Proportions in the Common Core NCCTM State Mathematics Conference Robin Barbour robin.barbour@dpi.nc.gov www.ncdpi.wikispaces.net 11/1/11 2 Ratios and Proportions 6.RP Understand ratio concepts
Incoming Advanced Grade 7
Name Date Incoming Advanced Grade 7 Tell whether the two fractions form a proportion. 1. 3 16, 4 20 2. 5 30, 7 42 3. 4 6, 18 27 4. Use the ratio table to find the unit rate in dollars per ounce. Order
STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. OPTIONAL CHALLENGE QUESTIONS:
STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 1. 18 6x = 2x + 6 2. z = 84 6z 3. 3 f = 6f + 24 4. 3(2 + m) = 2(3 m) 5. 4(2y 1) + 5 = 3y + 1 1. Solve the equation:
Year 7A Mathematics Homework Autumn Term
Year 7A Mathematics Homework Autumn Term Week 1 2 3 Name : 4 5 Teacher: Class: Target: 6 7 8 9 10 The blank sheets should be used for working out Negative Numbers Top tip: Use these to help you! Equations
Week of December 12 th to December 16 th, nd 9 weeks 7 th Grade Math (Periods 4, 5, 6)
Week of December 12 th to December 16 th, 2016 2 nd 9 weeks 12/12 Review for Midterm Exam Modules 1-7 Exam Review Modules 1-7 12/13 Review for Midterm Exam Exam Review Modules 1-7 Modules 1-7 12/14 Midterm
7 Mathematics Curriculum
Common Core 7 Mathematics Curriculum GRADE Table of Contents Percent and Proportional Relationships GRADE 7 MODULE 4 Module Overview... 3 Topic A: Finding the Whole (7.RP.A., 7.RP.A.2c, 7.RP.A.3)... Lesson
1 of Lesson Alignment Guide Mathematics Cranston Public Schools
Multiplyig Fractions 2.2 (Note: There have been changes to the scope and sequence of units 2.2 and 2.3) 1 of 4 1-4 5.NF.4a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts;
Solving Linear & Graphing Inequalities
Solving Linear & Graphing Inequalities Sep 7 11:06 PM 1 Open circle on the graph means that the inequality will be greater than or less than. > or < Closed circle on the graph means that the inequality
STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 2. z = 84 6z z = 12 OPTIONAL CHALLENGE QUESTIONS:
STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 1. 18 6x = 2x + 6 x = 3 2. z = 84 6z z = 12 3. 3 f = 6f + 24 f = 3 4. 3(2 + m) = 2(3 m) m = 0 5. 4(2y 1) + 5 = 3y
Correlation of USA Daily Math Grade 5 to Common Core State Standards for Mathematics
Correlation of USA Daily Math Grade 5 to Common Core State Standards for Mathematics 5.OA Operations and Algebraic Thinking (Mondays) 5.OA.1 Use parentheses, brackets, or p. 1 #3 p. 7 #3 p. 12 Brain Stretch
Roberto Clemente Middle School. Summer Math Packet For students entering Math 7
Roberto Clemente Middle School Summer Math Packet For students entering Math 7 Name: 1. Write each expression in the correct column. Equal to 5.4 Equal to 5.42 2.36 + 3.06 2.16 + 3. 36 2.71 2 1.80 3 9.53
An Overview of Mathematics 4
An Overview of Mathematics 4 Number (N) read, write, represent, and describe whole numbers to 10 000 using concrete materials, pictures, expressions (e.g., 400 + 7), words, place-value charts, and symbols
6th Grade. Slide 1 / 215. Slide 2 / 215. Slide 3 / 215. Fraction & Decimal Computation. Fraction and Decimal Computation
Slide 1 / 215 Slide 2 / 215 6th Grade Fraction & Decimal Computation 2015-10-20 www.njctl.org Fraction and Decimal Computation Slide 3 / 215 Fraction Division Long Division Review Adding Decimals Subtracting
HIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT
HIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT Accelerated 7 th Grade Math Second Quarter Unit 3: Ratios and Proportional Relationships Topic C: Ratios and Rates Involving Fractions In Topic C,
LEVEL 9 Mathematics Observation
LEVEL 9 Mathematics Observation Student: Assessment Date: Grade in School: Concepts Evaluated Score Notes. Applying the concept of slope to determine rate of change Equation of a line: slope-intercept
Mathematics (Project Maths Phase 2)
013. M9 Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination 013 Mathematics (Project Maths Phase ) Paper 1 Higher Level Friday 7 June Afternoon :00 4:30 300 marks
I can. Compute unit rates. Use ratios and finding unit rate in context.
EngageNY 7 th Grade Module 1 Topic A: Proportional Relationships 7.RP.2a Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship,
Diocese of Erie Mathematics Curriculum Third Grade August 2012
Operations and Algebraic Thinking 3.OA Represent and solve problems involving multiplication and division 1 1. Interpret products of whole numbers. Interpret 5x7 as the total number of objects in 5 groups
Game Rules. Wild Card Fractions (Game 3-12) Object: Win the most cards by comparing fractions and explaining comparisons.
Game Rules GAME Fractions (Game -) Object: Win the most cards by comparing fractions and explaining comparisons. How to Play:. Each player draws five cards. Place a privacy barrier between you. Take turns
Common Core Math Tutorial and Practice
Common Core Math Tutorial and Practice TABLE OF CONTENTS Chapter One Number and Numerical Operations Number Sense...4 Ratios, Proportions, and Percents...12 Comparing and Ordering...19 Equivalent Numbers,
Grade 2 Math Unit 6 Measurement and Data
Grade 2 Math Unit 6 Measurement and Data 2.MD.1 UNIT OVERVIEW Grade 2 math instructions centers arond 4 Critical Focus Areas. This unit addresses work in Critical Focus Area #3, Using standard units of
Module 1 Study Guide
1. John is filling a bathtub that is 18 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take ten more minutes for the water to reach the
GREATER CLARK COUNTY SCHOOLS PACING GUIDE. Grade 4 Mathematics GREATER CLARK COUNTY SCHOOLS
GREATER CLARK COUNTY SCHOOLS PACING GUIDE Grade 4 Mathematics 2014-2015 GREATER CLARK COUNTY SCHOOLS ANNUAL PACING GUIDE Learning Old Format New Format Q1LC1 4.NBT.1, 4.NBT.2, 4.NBT.3, (4.1.1, 4.1.2,
= 5th_Grade_Math (5th_Grade_Math) What is the perimeter of the triangle shown in the drawing? A. 1,258. B C D. 1.
Name: Date: 1. What is the perimeter of the triangle shown in the drawing? 2. 7.548 6 = 1,258. 125.8 12.58 1.258 1 3. 12.08 1.7 = 2,053.6 205.36 20.536 2.0536 4. White Mountain National Forest covers more
NUMBERS & OPERATIONS. 1. Understand numbers, ways of representing numbers, relationships among numbers and number systems.
7 th GRADE GLE S NUMBERS & OPERATIONS 1. Understand numbers, ways of representing numbers, relationships among numbers and number systems. A) Read, write and compare numbers (MA 5 1.10) DOK 1 * compare
Unit 9: May/June Solid Shapes
Approximate time: 4-5 weeks Connections to Previous Learning: Students have experience studying attributes and names of flat shapes (2-dimensional). Focus of the Unit: Students will extend knowledge of
7 Days: August 17 August 27. Unit 1: Two-Dimensional Figures
1 st Trimester Operations and Algebraic Thinking (OA) Geometry (G) OA.3.5 G.1.1 G.1.2 G.1.3 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent
Alex Benn. Math 7 - Outline First Semester ( ) (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days
Math 7 - Outline First Semester (2016-2017) Alex Benn (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days 0.1 Classroom Rules Multiplication Table Unit 1 Measuring
PMI 6th Grade Ratios & Proportions
Unite Rate Packet.notebook December 02, 2016 www.njctl.org PMI 6th Grade Ratios & Proportions 2016 09 19 www.njctl.org www.njctl.org Table of Contents Click on the topic to go to that section Writing Ratios
Pearson's Ramp-Up Mathematics
Introducing Slope L E S S O N CONCEPT BOOK See pages 7 8 in the Concept Book. PURPOSE To introduce slope as a graphical form of the constant of proportionality, k. The lesson identifies k as the ratio
You could identify a point on the graph of a function as (x,y) or (x, f(x)). You may have only one function value for each x number.
Function Before we review exponential and logarithmic functions, let's review the definition of a function and the graph of a function. A function is just a rule. The rule links one number to a second
Year End Review. Central Tendency 1. Find the mean, median and mode for this set of numbers: 4, 5, 6, 3, 7, 4, 4, 6, 7 mean. median.
Math 8 Name: Year End Review Central Tendency 1. Find the mean, median and mode for this set of numbers: 4, 5, 6, 3, 7, 4, 4, 6, 7 mean median mode Operations with Fractions 2. Solve. Show all your work.
Math 1: Algebra, Geometry and Statistics Ms. Sheppard-Brick
Exit Ticket 32 Chapter 3 Quiz 3 Review Students Will Be Able To: Determine whether the slope of a line is positive, negative, zero, or undefined Find the slope of a line between two points. Find the slope
http://www.math.utah.edu/~palais/sine.html http://www.ies.co.jp/math/java/trig/index.html http://www.analyzemath.com/function/periodic.html http://math.usask.ca/maclean/sincosslider/sincosslider.html http://www.analyzemath.com/unitcircle/unitcircle.html
What Is Leaps and Bounds? A Research Foundation How to Use Leaps and Bounds Frequently Asked Questions Components
Contents Program Overview What Is Leaps and Bounds? A Research Foundation How to Use Leaps and Bounds Frequently Asked Questions Components ix x xiv xvii xix Teaching Notes Strand: Number Number Strand
LECTURE 8: SPECIAL PRODUCTION FUNCTIONS, PART II ANSWERS AND SOLUTIONS. True/False Questions
LECTURE 8: SPECIAL PRODUCTION FUNCTIONS, PART II ANSWERS AND SOLUTIONS True/False Questions False_ The elasticity of scale of a fixed proportions production function is not defined because the fixed proportions
Station Activities. for Mathematics Grade 6
Station Activities for Mathematics Grade 6 WALCH EDUCATION The classroom teacher may reproduce materials in this book for classroom use only. The reproduction of any part for an entire school or school
Cambridge Secondary 1 Progression Test. Mark scheme. Mathematics. Stage 9
Cambridge Secondary 1 Progression Test Mark scheme Mathematics Stage 9 DC (CW/SW) 9076/8RP These tables give general guidelines on marking answers that involve number and place value, and units of length,
Accuplacer Math Packet
College Level Math Accuplacer Math Packet 1. 23 0 2. 5 8 5-6 a. 0 b. 23 c. 1 d. None of the above. a. 5-48 b. 5 48 c. 5 14 d. 5 2 3. (6x -3 y 5 )(-7x 2 y -9 ) a. 42x -6 y -45 b. -42x -6 y -45 c. -42x -1
Pyle Middle School Summer Math Packet Incoming C2.0 Math 7
Pyle Middle School Summer Math Packet Incoming C2.0 Math 7 Dear Student and Parent, The purpose of this packet is to provide a review of objectives that were taught the previous school year and provide
Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics F-H Approximately 14 days Begin around January 9 th
HIGLEY UNIFIED SCHOOL DISTRICT 2016/2017 INSTRUCTIONAL ALIGNMENT Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics F-H Approximately 14 days Begin around January
Year 9 mathematics test
Ma KeY STAGe 3 Year 9 mathematics test Tier 5 7 Paper 1 Calculator not allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start.
Problem of the Month What s Your Angle?
Problem of the Month What s Your Angle? Overview: In the Problem of the Month What s Your Angle?, students use geometric reasoning to solve problems involving two dimensional objects and angle measurements.
MS.ETS1.A: Defining and Delimiting Engineering Problems. MS.ETS1.B: Developing Possible Solutions
MS.ETS1.A: Defining and Delimiting Engineering Problems The more precisely a design task s criteria and constraints can be defined, the more likely it is that the designed solution will be successful.
3.4 The Single-Loop Circuit Single-loop circuits
25 3.4 The Single-Loop Circuit Single-loop circuits Elements are connected in series All elements carry the same current We shall determine The current through each element The voltage across each element
Rosa Parks Middle School Summer Math Packet Incoming C2.0 IM
Rosa Parks Middle School Summer Math Packet Incoming C2.0 IM Student Name: Teacher Name: Date: Dear Student and Parent, The purpose of this packet is to provide a review of objectives that were taught
Summer Math Assignment 2017 Briggs Chaney Middle School For Students Entering C2.0 Investigations into Mathematics
Summer Math Assignment 2017 Briggs Chaney Middle School For Students Entering C2.0 Investigations into Mathematics This summer math booklet was developed to provide students an opportunity to review math
Before How does the painting compare to the original figure? What do you expect will be true of the painted figure if it is painted to scale?
Dilations LAUNCH (7 MIN) Before How does the painting compare to the original figure? What do you expect will be true of the painted figure if it is painted to scale? During What is the relationship between
Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics D-H Approximately 25 days Begin around January 4 th
HIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT Fourth Grade Quarter 3 Unit 5: Fraction Equivalence, Ordering, and Operations Part 2, Topics D-H Approximately 25 days Begin around January 4 th In
Prolegomena. Chapter Using Interval Notation 1
Chapter 1 Prolegomena 1.1 Using Interval Notation 1 Interval notation is another method for writing domain and range. In set builder notation braces (curly parentheses {} ) and variables are used to express
GREATER CLARK COUNTY SCHOOLS PACING GUIDE. Algebra I MATHEMATICS G R E A T E R C L A R K C O U N T Y S C H O O L S
GREATER CLARK COUNTY SCHOOLS PACING GUIDE Algebra I MATHEMATICS 2014-2015 G R E A T E R C L A R K C O U N T Y S C H O O L S ANNUAL PACING GUIDE Quarter/Learning Check Days (Approx) Q1/LC1 11 Concept/Skill
Aim #35.1: How do we graph using a table?
A) Take out last night's homework Worksheet - Aim 34.2 B) Copy down tonight's homework Finish aim 35.1 Aim #35.1: How do we graph using a table? C) Plot the following points... a) (-3, 5) b) (4, -2) c)
Example: The graphs of e x, ln(x), x 2 and x 1 2 are shown below. Identify each function s graph.
Familiar Functions - 1 Transformation of Functions, Exponentials and Loga- Unit #1 : rithms Example: The graphs of e x, ln(x), x 2 and x 1 2 are shown below. Identify each function s graph. Goals: Review
Year 1 Objectives: Number 1
Year 1 Objectives: Number 1 Objective 1:Counting: to 1, forwards and backwards, from any given number Count on from to 2 Count on from to 5 Counting: to 1, forwards and backwards, from any given number
Lesson 16: The Computation of the Slope of a Non Vertical Line
++ Lesson 16: The Computation of the Slope of a Non Vertical Line Student Outcomes Students use similar triangles to explain why the slope is the same between any two distinct points on a non vertical
3.4 Start Thinking. 3.4 Warm Up. 3.4 Cumulative Review Warm Up
3.4 Start Thinking Equations are useful because they give you a way to represent what happens to y when the value of x is changed. Think of a situation you can represent with x and y. Write an equation
TONBRIDGE SCHOOL. Year 9 Entrance Examinations for entry in 2016 MATHEMATICS. Saturday, 7th November 2015 Time allowed: 1 hour Total Marks: 100
Name:... School: TONBRIDGE SCHOOL Year 9 Entrance Examinations for entry in 2016 MATHEMATICS Saturday, 7th November 2015 Time allowed: 1 hour Total Marks: 100 Instructions: THIS IS A NON-CALCULATOR PAPER
Copyright 2014 Edmentum - All rights reserved.
Study Island Copyright 2014 Edmentum - All rights reserved. Generation Date: 03/05/2014 Generated By: Brian Leslie Unit Rates 1. Tanya is training a turtle for a turtle race. For every of an hour that
Wednesday, May 4, Proportions
Proportions Proportions Proportions What are proportions? Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar
Grade 4. Number and Operations - Fractions 4.NF COMMON CORE STATE STANDARDS ALIGNED MODULES 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 4 Number and Operations - Fractions 4.NF.1-2 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES 2012 COMMON CORE STATE STANDARDS ALIGNED MODULES
3rd Grade Math Unit 1 8/18. # of Days: 7. Assessment: Fluency with Addition & Subtraction 3.MD.A.1 MP 1, 2, 3, 4, 5, 6 3.MD.A.
Math Unit 1 # of Days: 7 8/18 Fluency with Addition & Subtraction. 3.MD.A.1 MP 1, 2, 3, 4, 5, 6 3.MD.A.2 MP 1, 2, 4, 5 3.NBT.A.2 3.OA.D.8 MP 1, 2, 3, 4, 5, 6 3.OA.D.9 MP 3, 6, 7, 8 3.MD.B.3 MP 2, 4 Tell
Learning Experience: Angle Circles. When planning, include the following: Models (Concrete Semi-Concrete Semi-Abstract Abstract) Problems/Situations
Learning Experience: Angle Circles When planning, include the following: Models (Concrete Semi-Concrete Semi-Abstract Abstract) Problems/Situations Questions AKS: 40.MD.5 recognize angles as geometric
SM3 Lesson 2-3 (Intercept Form Quadratic Equation)
SM3 Lesson 2-3 (Intercept Form Quadratic Equation) Factor the following quadratic expressions: x 2 + 11x + 30 x 2 10x 24 x 2 8x + 15 Standard Form Quadratic Equation (x + 5)(x + 6) (x 12)(x + 2) (x 5)(x
Summer Mathematics Review Upcoming 7 th Graders Show your Work!
Understand ratio concepts and use ratio reasoning to solve problems. 1. What is the ratio of triangles to circles? 2. What is the ratio of moons to pentagons? 3. For every 6 hotdogs sold at the malt shop,
Number and Operations Fractions
Number and Operations Fractions Standards Entry Points Access Skills 3 Page 59 Pages 60 61 Pages 60 62 4 Pages 63 64 Page 65 67 5 Pages 68 69 Page 70 72 MATHEMATICS 58 CONTENT AREA Mathematics DOMAIN Number
Core Connections, Course 2 Checkpoint Materials
Core Connections, Course Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn exactly the same way at the same time. At
Explain how you found your answer. NAEP released item, grade 8
Raynold had 31 baseball cards. He gave the cards to his friends. Six of his friends received 3 cards Explain how you found your answer. Scoring Guide Solution: 6 x 3 cards = 18 cards 7 x 1 card = 7 cards
4-3 Add and Subtract Like Fractions. Add or subtract. Write in simplest form. SOLUTION: SOLUTION: SOLUTION: SOLUTION:
1. Add or subtract. Write in simplest form. 2. 3. 4. esolutions Manual - Powered by Cognero Page 1 5. 6. 7. In Mr. Navarro s first period class, of the students got an A on their math test. In his second