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Counting to Calculus
Math Building Blocks:
Basic math skills provide the floor of your math house, and the advanced math courses (Algebra, Geometry, Calculus) provide the ceiling in your house. In between your floor joists and the roof, lie five building blocks, which provide the cornerstones of your math house.
1. Numbers
2. Place Value System
3. Operations of Whole Numbers
4. Fractions and Decimals
5. Problem Solving
1 Questions: [email protected]
2 Questions: [email protected] www.rainbowresource.com
1. NUMBERS with Activities* by Developmental Stages:
Infant to 3 Years: • SingandRecitenumberstoyourchild. • Introducecountingandsorting.
Two to Three Years: • Childwillbegintoassociateanumberwith
the quantity. • Teachchildrentocountandsort. • Introducebasicmathlanguageinrelationship
to objects: under, over, behind, fast, heavy. • Teachchildtheiragewithfingers.
Three to Five Years: • Willdeveloptheabilitytocountto5items(possibly
10 items). • Willbegintorecognizewrittennumbers. • Willdeveloptheabilitytocountthenext
number in sequence. • BuildupontheCountandSortActivity. • Around3years,teachaddressandphonenumber. • Between5-6years,willbeabletocount1-100.May
be able to skip count by 10s to 100.
Six Years and Up: • Maybeabletocountto200. • SortingandClassifyingwillbecomemorecomplex. • Willbegintounderstandnumberrepresentation
on a number line. • Willbegintoassociatelesswithcounting(ie:7is
less than 8). • Perfecttimetointroduceskipcountingby2s,5s,10s. • Understandsordinaltermslikefirst,second,third.
*Pleasenote:theseareforreferenceonlyandnotindicativeofdevelopmentaldelaysorgiftedness.
Counting to Calculus
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2. PLACE VALUE SYSTEM Activities*:
Infant to 3 Years: • Counting.
Three to Five Years: • Mastercountingto100. • Teachchildtobuildnumbersconcretelywithsnap
cubes or connecting cubes (or items found at home). • Teachsetsof10afterproficientwithbuilding
numbers concretely.
Six Years and Up: • Stilloperatesinconcretethinking,somanipulatives
orvisualrepresentationsarecriticaltosuccess.Usemanipulatives to teach math concepts esp. place value.
• Willbegintounderstandplacevalueat7-8years.
3. OPERATIONS OF WHOLE NUMBERS Activities*:
Infant to 3 Years: • Between2-3years,willbegintounderstandsimple
addition using objects.
Three to Five Years: • Childrencontinuetodevelopunderstandingofsimple
addition-byage6,maybeabletoaddupto6objects. • Around5,willbeabletosolvesimplestoryproblems.
Six Years and Up: • From5-6years,childrenexperienceanexponential
growthintheirabilitytounderstandmorecomplexmath operations.
• Maybeabletoaddsmallnumbersintheirhead. • From7yearsandup,childrenwillbeabletoadd/subtractmultipledigit
numbers (using concrete objects) without borrowing or carrying. • Teachmorecomplexstoryproblemswithmanipulatives. • Buildonpreviousteachingsonsets.
*Pleasenote:theseareforreferenceonlyandnotindicativeofdevelopmentaldelaysorgiftedness.
Counting to Calculus
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4. FRACTIONS AND DECIMALS Activities*:
Familiarize children with process of parts to whole — this is a more abstract concept.
Infant to 3 Years: • Teachingandunderstandingshapesisfoundational.
Three to Five Years: • Beginningaround3years,childrencanbeintroducedtothepartstowholeconcept. –Shareachocolatebar. –Serveanunevennumberofcookies. – Help cut foods. –Coloringactivities(Paperplatescolor½,then½of½—or1/4).
Six Years and Up: • Showfractionalsizedifferenceswithfood. • Introducefractionmanipulatives
5. PROBLEM SOLVING Activities*:
Make a part of everyday.
Infant to 3 Years: • Explainpatterns—usuallybetween12-18monthswillbeabletorecognizesimple
patterns in daily routine. • Stringbeadsorusepegboardtogetherandfollowapattern.
Three to Five Years: • Begintounderstandsinglestepproblemsanddevelopmultistepproblemsolvingin
later preschool years (and beyond). • Buildonpatternactivitiesandenlisttheirhelpsortinglaundry.Makeitagame! • AllowfreeplaywithLEGO®andDUPLO®bricks. • Introducepuzzles. • Cooktogether. • Around4-5years,moredeductivereasoning.
Six Years and Up: • Deductivereasoningblossomsbetween6-7years. • Recognizestheideaofequalorsameas. • Developsalgebrasense. • Greattimetointroduceestimating.
*Pleasenote:theseareforreferenceonlyandnotindicativeofdevelopmentaldelaysorgiftedness.
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ADDITIONAL SUPPORTS in our Math House:
Infant to 3 Years: • GEOMETRY AND SPATIAL SENSE –Most1-yearolds,willunderstandthatahiddenobjectstillexits.PlayPeekABoo
to reinforce this concept. –Introduceshapes,useShapeSorters. –KnobPuzzles. –3-5-piecepuzzles. –Crafts. –Teachinto,over,under,aroundetc.outdoorsusingplayequipment. –Buildtentswithboxes,chairs/cushionsetc. • MEASUREMENT SKILLS –Teachconceptstall,shortandbig,small. –Freeplaywithbuckets-encouragepouring. • CALENDAR AND WEATHER – Introduce weather related terminology. –Readfunchildren’sbookstogether(seeHelpful Resources,page7). • TIME AND MONEY – Introduce terminology daytime, night time primarily. –Won’tgraspmoneyconcepts,butcantalkshapesofcoins,size,etc.
Three to Five Years: • GEOMETRY AND SPATIAL SENSE –Puzzles. –Shapesintheworldaroundthem. –LEGO®andDUPLO®bricks,Tangramsetc. • MEASUREMENT SKILLS –Bucketplay-talkaboutmoreandless.Introducedifferentshapecontainers. –Around5years,introducemeasuringcups(1cup,½,and1/4whenready). –Compareobjectsize. • CALENDAR AND WEATHER –Between4-5yearsintroducedaysoftheweekandrelatedactivities. –Around5years,beginteachingmonths,weeksandyears. –TeachCalendarandWeatherconceptstogether.
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Three to Five Years (continued): • TIME AND MONEY –Around3years,willunderstand“before”and“after”. –Setascheduleasmuchaspossible. –Around5years,introducetheconceptsofhourandhalf-hour. –With3-yearolds,begintointroducecoins:size,shape,howitfeelstotouch.
Six Years and Up: • GEOMETRY AND SPATIAL SENSE –Puzzlesbuildgeometryandspatialsense. – Allow to look at a shape for a couple minutes, remove it, and then have them draw it –Willbeabletorecognizeshapesregardlessoforientationorsize. –Around7years,willuseandunderstandvarioustermsthatdescribephysicalloca-
tions. • MEASUREMENT SKILLS –Around6years,readytomovebeyondbasicdescriptivewordsforsize.Introduce
measurementofthingsaroundthehousewithotherhouseholditems(eg:pencils—norulers yet). Create simple graphs.
– Cook together. • CALENDAR AND WEATHER –Between6-7years,willmasterdaysoftheweek,months,seasons. –Talkmoreaboutweather-createaweathergraphforthemonth. • TIME AND MONEY – Begin to tell time by hour; half hour. –Workonskipcountingby5s(introducetimein5-minuteincrements). –Teachmoneyconceptsastheyrelatedtovalue-willbeabletounderstandtheconcept
that4quartersequalsone-dollarbill.
Counting to Calculus
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Counting to Calculus
HELPFUL RESOURCES
Websites & Videos:
• PBS Parents Interactive http://www.pbs.org/parents/child-development/
• Math Wars Video http://ourhomeschoolforum.com/videos/workshops/math-wars/
• Saxon Math 101 Video http://ourhomeschoolforum.com/videos/workshops/saxon-math-101/
• World Book Typical Course of Study https://www.worldbook.com/typical-course-of-study.aspx
Books & More:
• It’s Snowing Gail Gibbons • It’s Raining Gail Gibbons • Snowy DayEzraJackKeats • Good Night MoonMargaretWiseBrown • Early Bird: Weather(EvanMoor) • Dr. Wright’s Kitchen Table Math Book 1 • Dr. Wright’s Kitchen Table Math Book 2 • Dr. Wright’s Kitchen Table Math Book 3 • What your ______Grader Needs to Know • On Core Mathematics • Spectrum Math workbooks • Right Brain Math • Games for MathPeggyKaye • PizzaFractionFun • FractionCircles
MATH CURRICULUM COMPARISON CHART
This chart was assembled by Rainbow Resource Curriculum Consultants and is intended to be a comparative tool based on our own under-standing of these programs and is not necessarily reflective of publishers' opinions. Some designations are "best fit," not absolute.
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©2019
MATHPrograms
Grades Religious Content Price Range
PK K 1 2 3 4 5 6 7 8 9 10 11 12 Christian N/Secular $ $$ $$$
Saxon K-3 * • • • • • •Saxon 3-12 * • • • • • • • • • • • •Bob Jones • • • • • • • • • • • • • • •Horizons (Alpha Omega) * • • • • • • • • • • •LIFEPAC (Alpha Omega) * • • • • • • • • • • • • • • •Switched-On Schoolhouse/Monarch (Alpha Omega) • • • • • • • • • • • •Math•U•See * • • • • • • • • • • • • • • • •Primary Math (US) (Singapore) * • • • • • • • • •Primary Math Standards Edition (SE) (Singapore) * • • • • • • • • •Primary Math Common Core (CC) (Singapore) • • • • • • • •Dimensions (Singapore) • • • • • • • • • • • •Math in Focus (Singapore Approach) * • • • • • • • • • • •Shaping Maths • • • • • • • •Christian Light Math • • • • • • • • • • • • • •Life of Fred • • • • • • • • • • • • • •A+ Tutorsoft Math • • • • • • • • • • •Starline Press Math • • • • • • • • • • • •ShillerMath • • • • • • • • • • •enVision Math • • • • • • • • •McRuffy Math • • • • • •Purposeful Design Math (2nd Ed.) • • • • • • • • •Go Math • • • • • • • • •Making Math Meaningful • • • • • • • • • • •RightStart Mathematics * • • • • • • • • • •MCP Mathematics • • • • • • • • •Conventional (Spunky Donkey) / Study Time Math • • • • • • • • • •Liberty Mathematics • • • • •Miquon Math • • • • •Math Mammoth (Light Blue series) * • • • • • • • • •Ray's Arithmetic • • • • • • • • • •Ray's for Today • • • • • • •Rod & Staff Mathematics • • • • • • • • • •Jump Math • • • • • • • • • •ThemeVille Math • • • • • • •Beast Academy (from Art of Problem Solving) • • • • • • •Strayer-Upton Practical Arithmetic • • • • • • • •Prentice Hall Math • • • • • • •Art of Problem Solving * • • • • • • • • •Paradigm Accelerated • • • •Principles of Mathematics • • • •A Fresh Approach • • • • • • •Jacobs Math • • • • • • Foerster Math • • • • • •VideoText • • • • • • •Math Lessons for a Living Education • • • • • • • • • •Mathematical Reasoning • • • • • • • • • • • • •Developmental Math • • • • • • • • • • •Math Power Basics • • • • • • • • •
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This chart was assembled by Rainbow Resource Curriculum Consultants and is intended to be a comparative tool based on our own under-standing of these programs and is not necessarily reflective of publishers' opinions. Some designations are "best fit," not absolute.
Placement tests are available on our website for programs marked with an ('*').Find them at: http://www.rainbowresource.com/searchspring.php?q=math+placement+tests
www.rainbowresource.com
©2019
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Approach Manipulatives Teacher Involvement CCSSNotes
Spiral Sequential Conceptual/Topical Req Opt RRC kit Low Med High Aligned
• • • • Scripted teacher manuals.
• • • Teaching tutorials available separately.
• • Paper manipulatives included & used in K-2.
• • • •• •• • SOS is computer-based. Monarch is online only.
• • • • Mastery-based. Optional songs some Christian content.
• • •• • • Pre-CCSS CA aligned.
• • • •• • • • Tests in 2019. Grades 1-5.
• • • • •• • • • 2013 syllabus. Singaporean money. Metric measurement.
• • Suggested manipulatives for lower grades.
• • Brief Christian references in elementary level.
• • Computer-based.
• • Pre-CCSS, CA standards aligned.
• • • Manipulatives. Discovery, Montessori approach.
• •• • • •
• • • • Mastery Sequential.
• • • Virtual manipulatives.
• • •• • • • •
• • Modified Sequential.
• • •• • Consumable workbooks.
• • • Mastery & skill-based. Uses Cuisenaire rods.
• • • B & W or color versions available.
• •• • • Up to level 8 in the works.
• •• • • Mastery-based.
• • • Manipulatives are used at all levels.
• •• • No Teacher Guide.
• •• • Recommended for gifted students.
• •• •• •• • Teaching tutorials available separately.
• • Teaching tutorials available separately.
• • DVD-based.
• • • Charlotte Mason approach.
• •• • • Skill-based levels.
• • Written at 4th grade level / for struggling students.