Welcome to Welcome to Everyday MathematicsEveryday Mathematics

University of Chicago School University of Chicago School Mathematics ProjectMathematics Project

Why do we need a Why do we need a new math program?new math program?

60% of all future jobs have not even 60% of all future jobs have not even been created yetbeen created yet80% of all jobs will require post 80% of all jobs will require post secondary education / training.secondary education / training.Employers are looking for candidates Employers are looking for candidates with higher order and critical thinking with higher order and critical thinking skillsskillsTraditional math instruction does not Traditional math instruction does not develop number sense or critical develop number sense or critical thinking. thinking.

Research Based CurriculumResearch Based CurriculumMathematics is more meaningful when it is rooted in real Mathematics is more meaningful when it is rooted in real life contexts and situations, and when children are given life contexts and situations, and when children are given the opportunity to become actively involved in learning. the opportunity to become actively involved in learning.

Children begin school with more mathematical Children begin school with more mathematical knowledge and intuition than previously believed. knowledge and intuition than previously believed.

Teachers, and their ability to provide excellent Teachers, and their ability to provide excellent instruction, are the key factors in the success of any instruction, are the key factors in the success of any program. program.

Curriculum FeaturesCurriculum Features

Real-life Problem SolvingReal-life Problem Solving

Balanced InstructionBalanced Instruction

Multiple Methods for Basic Skills PracticeMultiple Methods for Basic Skills Practice

Emphasis on CommunicationEmphasis on Communication

Enhanced Home/School PartnershipsEnhanced Home/School Partnerships

Appropriate Use of TechnologyAppropriate Use of Technology

Lesson ComponentsLesson Components

Math MessagesMath Messages

Mental Math and ReflexesMental Math and Reflexes

Math Boxes / Math JournalMath Boxes / Math Journal

Home linksHome links

ExplorationsExplorations

GamesGames

Alternative AlgorithmsAlternative Algorithms

Learning Goals

AssessmentAssessment

Grades primarily reflect mastery of secure Grades primarily reflect mastery of secure skillsskills

End of unit assessmentsEnd of unit assessments

Math boxesMath boxes

Relevant journal pagesRelevant journal pages

Slate assessmentsSlate assessments

Checklists of secure/developing skillsChecklists of secure/developing skills

ObservationObservation

What Parents Can Do to HelpWhat Parents Can Do to Help

Come to the math nightsCome to the math nightsLog on to the Log on to the Everyday Mathematics Everyday Mathematics website or website or the the South Western Math Coach’s South Western Math Coach’s web siteweb siteRead the Family letters – use the answer key to Read the Family letters – use the answer key to help your child with their homeworkhelp your child with their homeworkAsk your child to teach you the math games and Ask your child to teach you the math games and play them.play them.Ask your child to teach you Ask your child to teach you the new algorithmsthe new algorithmsContact your child’s teacher Contact your child’s teacher with questions or concernswith questions or concerns

Partial SumsPartial Sums

An Addition AlgorithmAn Addition Algorithm

268+ 483

600Add the hundreds (200 + 400)

Add the tens (60 +80) 140Add the ones (8 + 3)

Add the partial sums(600 + 140 + 11)

+ 11751

785+ 6411300Add the hundreds (700 + 600)

Add the tens (80 +40) 120Add the ones (5 + 1)

Add the partial sums(1300 + 120 + 6)

+ 6

1426

329+ 9891200 100

+ 18

1318

An alternative subtraction algorithm An alternative subtraction algorithm

In order to subtract, the top number must be larger than the bottom number 9 3 2

- 3 5 6 Start by going left to right. Ask yourself, “Do I have enough to take away the bottom number?” In the hundreds column, 9-3 does not need trading.

12

13

Move to the tens column. I cannot subtract 5 from 3, so I need to trade.

12 8

Now subtract column by column in any order

5 6 7

Move to the ones column. I cannot subtract 6 from 2, so I need to trade.

Let’s try another one together

7 2 5

- 4 9 8

15

1211 6

Now subtract column by column in any order

2 7 2

Start by going left to right. Ask yourself, “Do I have enough to take away the bottom number?” In the hundreds column, 7- 4 does not need trading.

Move to the tens column. I cannot subtract 9 from 2, so I need to trade.

Move to the ones column. I cannot subtract 8 from 5, so I need to trade.

Now, do this one on your own.

9 4 2

- 2 8 7

12

313 8

6 5 5

Last one! This one is tricky! 7 0 3

- 4 6 9

13

9 6

2 4 3

10

Partial Products Partial Products Algorithm for Algorithm for MultiplicationMultiplication

Calculate 50 X 60

67X 53

Calculate 50 X 7

3,000 350 180 21

Calculate 3 X 60

Calculate 3 X 7 +Add the results 3,551

To find 67 x 53, think of 67 as 60 + 7 and 53 as 50 + 3. Then multiply each part of one sum by each part of the other, and add the results

Calculate 10 X 20

14X 23

Calculate 20 X 4

200 80 30 12

Calculate 3 X 10

Calculate 3 X 4 +Add the results 322

Let’s try another one.

Calculate 30 X 70

38X 79

Calculate 70 X 8

2, 100 560 270 72

Calculate 9 X 30

Calculate 9 X 8 +Add the results

Do this one on your own.

3002

Let’s see if you’re right.

Partial QuotientsPartial QuotientsA Division AlgorithmA Division Algorithm

The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. You might begin with multiples of 10 – they’re easiest.

12 158There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240)

10 – 1st guess

- 12038

Subtract

There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess

3 – 2nd guess- 36

2 13

Sum of guesses

Subtract

Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )

Let’s try another one

36 7,891100 – 1st guess

- 3,6004,291

Subtract

100 – 2nd guess

- 3,600

7 219 R7

Sum of guesses

Subtract

69110 – 3rd guess

- 360 331

9 – 4th guess

- 324

Now do this one on your own.

43 8,572100 – 1st guess

- 4,3004272

Subtract

90 – 2nd guess

-3870

15199 R 15

Sum of guesses

Subtract

4027 – 3rd guess- 301

1012 – 4th guess

- 86