Elementary Mathematics

Worked with base 10 blocksflat = 100long = 10unit = 1ex: 87 would consist of 8 longs and 7 unitsIdentified skills needed in mathreadingrelationshipsgroupingcountingsortingmemorizingrecognizingadding/subtracting Number Sense Foundationcounting/skip countingcardinality: remembering the same number that was counted without recounting1:1 response: knowing one itemsubitizingex: from 5 to 10 to horizontal to vertical 10 and eventually into a tower of 10 block

Aug. 30I add six to eleven, and get five. Why is this correctSept. 1What is the smallest number that increases by 12 when it is flipped and turned upside down?Numbers that can be flipped and turned outside down examples: 0, 1, 6, 8, 9, 11Answer: 86, when it is turned upside down and flipped, it becomes 98, which is 12 more than 86

This week was focused on adding/subtracting with numbers of bases that were not 10. We did this through "changing" the base number using the base 10 blocks.Example:https://online.math.uh.edu/Math2303-unpaid/ch1/s15/2303-Section-15.pdf 31four - 13four3 longs, 1 unit - 1 long, 3 unitsAction: take 1 long and 3 units from 31four = 12four

No class Sept. 6Sept. 8Brain TeaserWarm upNaming - quick viewWhat makes a good algorithm?Explaining additionHW

No class Sept. 6Sept. 8A company packages bottles of olive oil to sell. It costs $1.50 to make a full bottle. If the bottle is one dollar MORE than the olive oil, how much would the olive oil cost?Bottle = olive oil + $1 moreOlive oil = .25 = $1.25Together the total is $1.50 because $0.25 + $1.25

What makes a "good" algorithm?Reinforces base 10 ideasRefer back to 10 (ten)Repeatable Grows with math skills as they get harderEfficient and shortConsistency to get it right

Sept 13Brain teaserWarm upReview: what makes a good algorithm?Alternative algorithmsFriendly NumbersTrade offScratchHWSept. 15Review from 9/13Friendly numbersTrade OffNew - scratchHW

9/13A car's odometer shows 72927 miles, a palindromic number. What are the minimum miles you would need to travel to form another palindromic number?Palindromic: numbers/words that are the same when spelled backwards - ex: mom, wow, HannahAnswer: 72927 + 110 = 73037

Friendly Numbersa. Never have to carry a 1b. Make 0's in both numbersc. End in 0Example Problems:Base 10 137 + 423 = 130 + 430 (7+3=10) = 560 1 flat, 3 longs + 4 flats, 3 longs Base 8 (goal is to get to eight) 250eight + 430eight (5+3=8) 200 + 600 = 800 2 flats + 6 flatsBase 9 18nine + 31nine 20nine + 30nine = 50nine 2 longs + 3 longsTrade off Goal is to get as many 0'sNever have to carry a oneMake 0 in one of the numbersTake/trade just a little to make 0Example Problems:Can't make both to a zero 24 + 49 (take 1 from the 4 and add it to the 9 to make 10) 23 + 50 = 73 15seven + 43seven (take 2 from the 3 and add to the 5 to make 7) 17seven + 41seven17 converts into 2 longs or 20seven 20seven + 41seven = 61seven 168 + 439 (take 1 from the 8 and add to the 9) 167 + 440 (add the 6 to the 4 in tens place to make 500) 107 + 500 = 607

Tues. Sept. 20Brain teaserReviewScratch MethodNew Contentsubtracting with different basesHomework assignmentThurs. Sept. 22Brain TeaserNot borrowing but convertingReviewNew contentAlternative algorithmsexpanded formleft to rightlattice methodHomeworkStudy guide for exam #1

Sept. 20How many plus signs should be placed between the digits of 987,654,321 to get to a total of 99, and where should the plus signs be?9+8+7+65+4+3+2+1=99 Sept. 22How can you give someone $63 using six bills without using any one dollar bills?1 = $501 = $54 = $2

Scratchstart with first number and count up to base 10Examples:23541six + 31354six 1123541six31354six55335six5nine + 6nine (take 4 from 6 and add to 5 to make 9)1 long nine + 2 units nine = 12nine12 24 35 16 5 (6 becomes 5 because 4+5+1=10) 25 0 (5 becomes a 0 because 5+5=10) 03 04107Subtracting with Different Bases5six - 3six = 2six..... - ... (these 3 cancel out) *what you take from one side, you take from the other

Alternative Algorithms Expanded Form25 + 13 *Place value base 1020+5 + 10+310+330 + 8 = 38236 +157200 + 30 + 6100 + 50 + 7300 + 80 + 13 = 393Left to Right in the place value46 + 3170 7771536 + 43275000 800 50 135863

Sept. 27Brain teaserWarm upLattice methodIntro to multiplication - buildingHWExam #1 and mind map updateSept. 29No classWork on review for exam #1

Brain TeaserWhen my father was 31, I was 8 years old. Now he is twice as old as me. How old am I?31-8= 23 23x2= 46

Lattice MethodExamples: 48 +27 /1/ (write 15 as I say it) /6/5 (Add diagonal) 75 456 +248 /1/1/ (carried 1's) /6/9/4 704Multiplication - buildingWarm up:3x4adding three, four times4 groups of 33 groups of 4Examples: 2x5 = 10Group 1 xxxxxGroup 2 xxxxx2 rows of 5 columns 7x3 = 21Group 1 xxxxxxxGroup 2 xxxxxxx (array)Group 3 xxxxxxx3 rows of 5 columns Group 1 xxxGroup 2 xxxGroup 3 xxxGroup 4 xxxGroup 5 xxxGroup 6 xxxGroup 7 xxx7 rows of 3 columns

AgendaOct. 3Exam #1Oct. 6No Class

Week 14: No class Nov. 22Nov. 29Review Exam #2Dec. 1Final Exam

Nov. 15Review for Exam #2Nov. 17Exam #2

Review Notes

Nov. 8Brain TeaserReviewIntegersBuild with countersShow with diagramsNov. 10Brain TeaserReviewAdding Integers (2 digit numbers)

Nov. 1 (No in-person class)DivisionIntro to Alternate Algorithms Video #1Long DivisionRepeated SubtractionDivide UpDivisibility Rules Video #2HomeworkNov. 3 (review from Nov. 1)Division - Alt. AlgorithmsstepsDivisibility RulesHomework

Oct. 25Brain TeaserAlternative AlgorithmsExpanded FormLeft to RightLatticeHomeworkOct. 27No Class

A half is a third of it, what is it?Answer

Oct. 18 - Day 1Topic of the day: SubtractionAlternative AlgorithmExpanded FormEqual AddendsOct. 20 - Day 2Brain TeaserWarm Up4 CornersMultiplicationAutomaticityAlternative AlgorithmsHomework

Oct. 18Use the numbers 2, 3, 4, 5 and the symbols + and = to make a true math equationAnswer: 3+4=2+5Oct. 20If eggs are 12 cents a dozen, how many eggs can you get for $1.00?Answer 100 eggs

Oct. 18 NotesOct. 20 NotesWhat do I remember about learning multiplication facts for the first time?learning to memorize the times tablelearning rules for certain numbers (ex: 0, 1, 2, 5 etc)flash cardsskip countingWhat sorts of lessons/activities do I remember?flash cardstimed testshand tricksWhat was my favorite part of practicing/learning the facts?gamestimed testsWhat was my least favorite?competitions

Oct. 13Back from Fall BreakWarm upArea Model"good" algorithmpossible misconceptions with FOILExam ResultsHW

Area Model Expanded formNotes from my notebook