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

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 – 8 th ) 1

10/9/19 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 … What message do they have in common? Montessori Piaget Bruner Dienes Skemp Dewey Vygotsky 2

10/9/19 3 types of Learners Visual/ Middle Abstract/ verbal Group Linear learners learners • Fast • Need time to think • A mix • Memorize easily • Memorization is hard • Might struggle with • Often good at seeing written representation relationships, creative solutions Therefore, All Our Work Has 3 Levels: • Level One: Concrete/Pictorial • Level Two: Transfer to the Abstract • Level Three: Challenge Problems 3

10/9/19 GRADING Examples of the 3 Levels 4

10/9/19 FINAL GRADE FINAL GRADE FINAL GRADE Level 1 Level 2 Level 3 OR OR Points score out of Points score out of Points score out of 32 34 32 36 32 37 SGRs SGRs SGRs 22 24 22 24 22 24 HW HW HW Quizzes, Quizzes, Quizzes, 16 18 16 18 16 18 Level 1 Level 1 Level 1 Quizzes, Quizzes, Quizzes, 18 20 18 24 18 28 Level 2 Level 2 Level 2 Quizzes, Quizzes, Quizzes, 0 4 0 4 10 4 16 Level 3 Level 3 Level 3 92 96 92 112 92 123 TOTAL TOTAL TOTAL FINAL FINAL FINAL 96% 83% 76% GRADE GRADE GRADE A B C 5

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10/9/19 ASSESSMENT Every test/quiz has ALL 3 levels. All students must do Levels 1&2. Level 3 is optional, if time . Test/Quiz Breakdown: Although everyone does all three levels, they are graded at a different % on questions from the 3 levels. Level One: Level Two: Transfer to Level Three: Concrete/Pictorial the Abstract Challenge Accessible to all At grade level: more For fastest • • • students, since it is algorithms and more workers visual, not word problems abstract. 9

10/9/19 TEACHING Each Grade Level has 2 or 3 “Non-negotiables” • 5 th th : : Fractions – at at leas ast pictorial ally • 6 th th : Fractions, Signed numbe bers, solving equations (at least pictorially) pi • 7 th th : Equations with fractions, signed numbe bers, per percen ents, r , ratios th : • 8 th : Graphing Equations, , systems of equations, , monomials 10

10/9/19 In the Classroom Concrete Pictorial Challenge ! Level ONE, ! 5 th Grade 1! ! 1 1 2 ! 2 ! ! 1 1 1 3 ! 3 ! 3 ! What do ! 1 1 1 1 you see? 4 ! 4 ! 4 ! 4 ! ! 1 1 1 1 1 5 ! 5 ! 5 ! 5 ! 5 ! ! 1 1 1 1 1 1 6 ! 6 ! 6 ! 6 ! 6 ! 6 ! ! 1 1 1 1 1 1 1 1 8 ! 8 ! 8 ! 8 ! 8 ! 8 ! 8 ! 8 ! ! 1 1 1 1 1 1 1 1 1 9 ! 9 ! 9 ! 9 ! 9 ! 9 ! 9 ! 9 ! 9 ! ! 1 1 1 1 1 1 1 1 1 1 10 ! 10 ! 10 ! 10 ! 10 ! 10 ! 10 ! 10 ! 10 ! 10 ! ! 1 1 1 1 1 1 1 1 1 1 1 1 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! 12 ! ! 11

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10/9/19 Transferring to the Abstract Fog Stone Isle 13

10/9/19 WHAT ABOUT CHALLENGE? 14

10/9/19 Level ONE Level ONE = 15

10/9/19 Level Subtraction? ONE Transfer to the Level TWO Abstract SUBTRACTION 16

10/9/19 Level TWO LEVEL THREE 17

10/9/19 Level THREE 1 Two 600 ml pitchers contain vinegar. One pitcher is 3 2 full and the other pitcher is full. Oil is added to fill each 5 pitcher completely, and then both pitchers are poured into one large container. What fraction of the mixture in the large container is vinegar? th Gr 6 th th /7 /7 th Grade 18

10/9/19 Level ONE, 6 th Grade ???? 1/6 1/6 1/6 1/6 1/6 = ½ of what? 1 19

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10/9/19 Level ONE 1 1 2 x + 6 = 9 6 th / 7 th Grade 2( x + 3) − 1 1 1 2 x = 3 2 x = 9 1 2 x = 1 x = 2 21

10/9/19 Mr.Mathematics.com CHALLENGE Critical thinking Company Books and eBooks 22

10/9/19 -15 +4 -10 = ? SIXTH GRADE HOT AND COLD CUBES - LEVEL ONE After an increase of 12%, Wyatt’s new salary Level ONE, After an increase of 12%, Wyatt’s new salary was 7 th Grade was $8.90 per hour. What was his old salary? $8.90 per hour. What was his old salary? Use a calculator, and round to the nearest (rounded to the nearest penny) penny. Hint: 100% ! 112% ! ? ! 8.90 ! 23

10/9/19 c) Kyle spent 15% of his allowance money on a football. If the football cost $60, how much money did he start with? 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 60 OR…. 60 = .15 of what? Sentence: 60 = .15 x …. Level ONE, 6 th 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? 24

10/9/19 Level TWO, 7 th Grade Level THREE, 7 th Grade Source: AOPS 25

10/9/19 th Gr 8 th Grade 26

10/9/19 Level ONE, Graph the coordinates. x y 8 th Grade Then find the slope and -2 3 the y-intercept. 0 1 y 6 5 2 -1 4 3 4 -3 2 1 x x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Level ONE, 8 th Grade 8 + 2x = 40 3 x x 8 40 40 40 Equations? 120 E: 40 Ÿ 3 = 120 for 2 ‘ x ’ units + 8 120 – 8 = 112 for 2 ‘ x ’ units 112 112 ÷ 2 = 56 per unit S: x = 56 27

10/9/19 Level TWO, 8 th Grade y 6 5 4 2. Graph by any method: 3 y = 3 x - 2 2 1 y = - ½ x + 4 x x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Level THREE, 8 th Grade 28

10/9/19 Where to find Challenge 29

10/9/19 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 online: the-pi-project.com https://bit.ly/2TQ6EwF 30