the-pi-project.com Kathleen Jalalpour and Corrinne Lieu BLOG : - - PDF document

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the-pi-project.com Kathleen Jalalpour and Corrinne Lieu BLOG : - - PDF document

Dec 17, 2022 198 likes •513 views

10/9/19 the-pi-project.com Kathleen Jalalpour and Corrinne Lieu BLOG : Follow a year in 5 th grade, week by week. https://singapore-math-blog.com/ or Google : Off the Beaten Math, the Pi Project Keys Middle School, Palo Alto, CA ( 5 th

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10/9/19 1

Kathleen Jalalpour and Corrinne Lieu

the-pi-project.com

Keys Middle School, Palo Alto, CA (5th – 8th)

BLOG: Follow a year in 5th grade, week by week. https://singapore-math-blog.com/

  • r Google: “Off the Beaten Math”, the Pi Project
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1/3 of our students were ending up the remedial math track. .

The long-term consequences are fateful.

Tracking damages students who are tracked into the low track; it damages schools and ultimately, society as a whole.

Back to our college textbooks…

Vygotsky Piaget Dewey Dienes Montessori Skemp Bruner

What message do they have in common?

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3 types of Learners

Abstract/ Linear learners Middle Group Visual/ verbal learners

  • Fast
  • Memorize easily
  • Might struggle with

written representation

  • Need time to think
  • Memorization is hard
  • Often good at seeing

relationships, creative solutions

  • A mix

Therefore, All Our Work Has 3 Levels:

  • Level One: Concrete/Pictorial
  • Level Two: Transfer to the Abstract
  • Level Three: Challenge Problems
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Examples of the 3 Levels

GRADING

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FINAL GRADE FINAL GRADE FINAL GRADE

Level 1 OR Level 2 OR Level 3

Points score

  • ut of

Points score

  • ut of

Points score

  • ut of

SGRs

32 34

SGRs

32 36

SGRs

32 37

HW

22 24

HW

22 24

HW

22 24

Quizzes, Level 1

16 18

Quizzes, Level 1

16 18

Quizzes, Level 1

16 18

Quizzes, Level 2

18 20

Quizzes, Level 2

18 24

Quizzes, Level 2

18 28

Quizzes, Level 3 Quizzes, Level 3

4 10

Quizzes, Level 3

4 16

TOTAL

92 96

TOTAL

92 112

TOTAL

92 123

FINAL GRADE

96%

FINAL GRADE

83%

FINAL GRADE

76%

A B

C

4

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ASSESSMENT

Every test/quiz has ALL 3 levels.

All students must do Levels 1&2. Level 3 is optional, if time.

Level One: Concrete/Pictorial

  • Accessible to all

students, since it is visual, not abstract. Level Two: Transfer to the Abstract

  • At grade level: more

algorithms and more word problems Level Three: Challenge

  • For fastest

workers

Test/Quiz Breakdown: Although everyone does all three levels, they are graded at a different % on questions from the 3 levels.

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TEACHING

Each Grade Level has 2 or 3 “Non-negotiables”

  • 8th

th :

: Graphing Equations, , systems of equations, , monomials

  • 7th

th: Equations with fractions, signed numbe

bers, per percen ents, r , ratios

  • 6th

th: Fractions, Signed numbe

bers, solving equations (at least pi pictorially)

  • 5th

th:

: Fractions – at at leas ast pictorial ally

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In the Classroom

Concrete Pictorial Challenge

! ! 1! ! 1 2 ! 1 2 ! ! 1 3 ! 1 3 ! 1 3 ! ! 1 4 ! 1 4 ! 1 4 ! 1 4 ! ! 1 5 ! 1 5 ! 1 5 ! 1 5 ! 1 5 ! ! 1 6 ! 1 6 ! 1 6 ! 1 6 ! 1 6 ! 1 6 ! ! 1 8 ! 1 8 ! 1 8 ! 1 8 ! 1 8 ! 1 8 ! 1 8 ! 1 8 ! ! 1 9 ! 1 9 ! 1 9 ! 1 9 ! 1 9 ! 1 9 ! 1 9 ! 1 9 ! 1 9 ! ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! 1 10 ! ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! 1 12 ! !

Level ONE, 5th Grade

What do you see?

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Fog Stone Isle Transferring to the Abstract

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WHAT ABOUT CHALLENGE?

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Level ONE

=

Level ONE

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Level ONE

SUBTRACTION

Transfer to the Abstract

Level TWO

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Level TWO LEVEL THREE

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Two 600 ml pitchers contain vinegar. One pitcher is full and the other pitcher is full. Oil is added to fill each pitcher completely, and then both pitchers are poured into

  • ne large container.

What fraction of the mixture in the large container is vinegar?

1 3

2 5

Level THREE

6th

th/7

/7th

th Gr

Grade

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Level ONE, 6th Grade

1/6 1/6 1/6 1/6 1/6

????

= ½ of what?

1

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2(x +3)− 1 2x = 9 11

2x +6=9

11

2x =3

1 2x =1

x =2

Level ONE 6th / 7th Grade

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Mr.Mathematics.com

CHALLENGE

Critical thinking Company Books and eBooks

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SIXTH GRADE

  • LEVEL ONE

HOT AND COLD CUBES

  • 15 +4 -10 = ?

After an increase of 12%, Wyatt’s new salary was

$8.90 per hour. What was his old salary? (rounded to the nearest penny)

100%! 112%!

8.90! ? !

Hint:

Level ONE, 7th Grade

After an increase of 12%, Wyatt’s new salary was $8.90 per hour. What was his old salary? Use a calculator, and round to the nearest penny.

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c) Kyle spent 15% of his allowance money on a football. If the football cost $60, how much money did he start with?

Sentence:

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 60

60 = .15 of what? 60 = .15 x ….

OR….

Level ONE, 6th Grade

The ratio of a steel cable to a rope is 8:3. The total length of the two, end-to- end, is 176 m. How long is the rope?

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Level TWO, 7th Grade Level THREE, 7th Grade

Source: AOPS

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8th

th Gr

Grade

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x

  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

1 2 3 4 5 6 y 6 5 4 3 2 1

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6

x

Graph the coordinates. Then find the slope and the y-intercept.

x y

  • 2

3 1 2

  • 1

4

  • 3

Level ONE, 8th Grade

8 + 2x 3 = 40

E: 40 Ÿ 3 = 120 for 2 ‘x’ units + 8 120 – 8 = 112 for 2 ‘x’ units 112 ÷ 2 = 56 per unit S: x = 56

Equations?

40 40 40 120

8

x x

112

Level ONE, 8th Grade

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x

  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

1 2 3 4 5 6 y 6 5 4 3 2 1

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6

x

  • 2. Graph by any method:

y = 3x - 2 y = - ½ x + 4

Level TWO, 8th Grade Level THREE, 8th Grade

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Where to find Challenge

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VE VERDICT

  • Improvement in achievement for our most

vulnerable students.

  • Greater ownership of their own work.
  • Improved preparedness for algebra
  • Minimal parent opposition because of the

availability of challenge.

THANK YOU!

Kathleen Jalalpour and Corrinne Lieu email: ThePiProject@gmail.com

  • nline: the-pi-project.com

https://bit.ly/2TQ6EwF