Lesson 1: Defining Quantities

Algebra 1 – Unit 2 – Cycle 2

Lesson 1: Defining Quantities

Todayyourstudentcalculateddifferentquantitiesinreal-worldproblems.Heorsheexplainedwhat informationeachunitineachquantitiesgivesandhowthatmeasurehelpsothersthatare involvedin that situation.In thereal world,answersareusuallynotjustnumbers;theyareusuallyquantities—number withunits.Unitsareusedinour worldeveryday.For example,bananasmaycost39 centsperpound

atthegrocerystore.Ifyoupurchase5bananasthatweighatotalof 1.4pounds,youwillspend0.55centsonbananas.

Yourstudentshouldbeableto answerthesequestionsaboutquantities:

1) Whatis anotherquantityyoucoulduse in this problem?Whatinformationwillitgive you?

2) Explainhowyoucoulduseeachunitofmeasure.Wouldsomepeopleinthissituationfinda differentmeasuremorehelpfulthanothers?

Herearesomeideasto workwithquantities:

1) Whataresomequantitiesyoucancalculateabouttheworldaroundyou?Thinkabouteventsthat takeplaceinyourschoolor community.Can youmeasurethenumberof peoplewhopassby yourhome?Whatabouttheamountof electricityyourhomeuses?

2) Doyouhearquantitiesonthenewsorradioorreadaboutthem online?Whattypesof quantities dopeopleuseto describeeventsinour world?Can youexplainwhattheunitsmean?

Algebra 1 – Unit 2 – Cycle 2

Lesson 2: Quantities in Scientific Notation

Todayyourstudentperformedoperationsinscientificnotation.Scientificnotationisanabbreviatedwayofwritingverylargeandverysmallnumbers.Anyvaluecanberepresentedthisway;itsimplymeansthe productofanumberbetween1and10timesapowerof10.Forexample,8iswritteninscientificnotation 8 x 101.Scientificnotationisnotonlyausefulshorthandforrepresentingverylargeandverysmallnumbers(like0.00000000000034235),butitalsoallowsforquickercomparisonsandoperationson valueslikethis.

Understandingthevalueofanumberinscientificnotationcanhelpyourstudentmakesenseofmany differentphenomenaintheworld.Forexample:HowfarawayistheMoon?Howmuchfartherawayisthe neareststar?Inaddition,thesecomputationalproblemsincludedfraction,decimal,andexponentoperationskillsyourstudenthasalreadylearned.Buildingtheseskillshelpsyourstudentasheorshedelvesdeeperintoalgebrathisyear.

Yourstudentshouldbeabletoanswerthesequestionsaboutscientificnotation:

1) Whataresomeexamplesoftimesthatitismoreappropriatetousescientificnotation?Arethere timesthatscientificnotationisnotaseasytouse?

2) Canreplacingthenumberwithasimplernumberhelpyouseehowtosolveit?

3) Whatisyourplanforsolving?

4) Doesyouranswermakesense?Whyorwhynot?

Herearesomeideastoworkwithscientificnotation:

1) Identifynumbersinyoureverydaylifecanbeexpressedinscientificnotation.

2) Video:Introductiontoscientificnotation

3) Video:Multiplyinginscientificnotation

radicals/scientific-notation/v/multiplying-in-scientific-notation

Algebra 1 – Unit 2 – Lesson 3

Lesson 3: Accuaracy with Quantities

Todayyourstudentconsideredaccuracywhenworkingwithquantities.Forexample,yourstudent exploredreportingameasurementaccuratelybypayingattentiontothescaleof themeasurementused.

Inaddition,heorshealsolearnedabouttheaccuracyof givenmeasurementsbypayingattentiontothe numberof significantdigits.Thenumberof significantfigures,orsignificantdigits,tellsushowprecisethe measurementis. Yourstudentidentifiedthenumberof significantfiguresfordifferentquantitiesand roundedtotheappropriatenumberof significantfiguresafterperformingmultiplicationanddivision.

Yourstudentshouldbeableto answerthesequestionsaboutsignificantdigits:

1) Howmanysignificantdigitsdoesthisnumberhave?Howdoyouknow?

2) Explainwhyit importantto knowaboutsignificantfigures.

3) Howaccurateis thismeasuredquantity?Howdo youknow?

Herearesomeideasto workwithsignificantdigits:

1) WatchaCrashCourseVideoonSignificantDigits:

2) Findtheareaof aroom in yourhome.Write yourareausingthecorrectnumberof significantfigures.

3) ReviewsignificantfiguresonKhanAcademy:Video:SignificantFigures

Video:Moreon SignificantFigures

on-significant-figures

Video:Addingand SubtractingwithSignificantFigures

and-subtraction-with-significant-figures

Video:MultiplyingandDividingwithSignificantFigures

and-dividing-with-significant-figures

Practice:SignificantFigures

Algebra 1 – Unit 2 – Cycle 2

Lesson 4: Quantities in Complex Problem

Todayyourstudentwrotecomplicatedexpressionsforcontextualsituations.Yourstudentfirstlookedat theproblemtoseewhatthesituationwasabout.Thenyourstudentdeterminedifheorsheneededto defineanyvariablesin orderto writetheexpression.Sometimestherearemultiplewaystocorrectlywrite anexpressiontorepresentasituation.Thiswillprepareyourstudentto writeandsolveequationsin order tosolvereal-worldproblems.

Yourstudentshouldbeableto answerthesequestionsaboutwritingcomplicatedexpressions:

1) What’sgoingoninthesituation?

2) Whatvariablesandnumbersdo youknow?

Whatvariablesdoyouneedto define?

3) Whatarethetermsintheexpression?Whataretheconstants?

4) Isthereanotherway youcouldwritethisexpression?

Herearesomeideasto workwith writingcomplicatedexpressions:

1) Writeanalgebraicexpressionto describeareal-lifesituation.Itcouldbe

about yourlife,school, community,orworld!

2) Watcha videotoreviewtranslatingbetweenexpressionsandmathstatements.