Harnessing the Power of the Purposeful Task Graham Fletcher - - PowerPoint PPT Presentation

▶
harnessing the power of the purposeful task
SMART_READER_LITE
LIVE PREVIEW

Harnessing the Power of the Purposeful Task Graham Fletcher - - PowerPoint PPT Presentation

Sep 18, 2022 155 likes •1.17k views

Harnessing the Power of the Purposeful Task Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com ? 3 Questions ? 1 Billion Circles 1 Billion Circles 100 circles : minute 144,000 circles : day

slide-1
SLIDE 1 Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com

Harnessing the Power of the Purposeful Task

slide-2
SLIDE 2

?

3 Questions

slide-3
SLIDE 3

1 Billion Circles

?

slide-4
SLIDE 4
  • 100 circles : minute
  • 144,000 circles : day
  • 1,000,000,000 would take 6944 days
  • 19+ years with no sleep

1 Billion Circles

slide-5
SLIDE 5

?

2nd Question

slide-6
SLIDE 6
slide-7
SLIDE 7 Where does 1 billion go on the number line? 1 trillion
slide-8
SLIDE 8 Where does 1 billion go on the number line? 1 trillion
slide-9
SLIDE 9

?

What is mathematical modeling What is modeling with mathematics

slide-10
SLIDE 10
slide-11
SLIDE 11 Today’s Goals
  • Understand the structure of 3-act task and see
how they fit into the scope and sequence of a unit.
  • Investigate mathematical modeling (SMP #4)
  • Explore the importance of progressional
understanding and how a good task can be used as formative assessment.
  • Multiplication
  • Understand the importance of an effective closing
and the role it plays in deciding our next move.
slide-12
SLIDE 12 Procedural Fluency Conceptual Understanding Application
slide-13
SLIDE 13

Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

slide-14
SLIDE 14

Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

slide-15
SLIDE 15

Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

slide-16
SLIDE 16

Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

slide-17
SLIDE 17

Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

slide-18
SLIDE 18

17 12 fewer

slide-19
SLIDE 19

17 12

slide-20
SLIDE 20

17 12

W T F ?

slide-21
SLIDE 21

17 12

W T F ?

hat’s he ive
slide-22
SLIDE 22 Current Research
slide-23
SLIDE 23
slide-24
SLIDE 24
slide-25
SLIDE 25

65%

slide-26
SLIDE 26 65% of children entering primary school today will ultimately end up working in completely new job types that don’t yet exist. http://reports.weforum.org/future-of-jobs-2016/chapter-1-the-future-of-jobs-and-skills/

“ ”

slide-27
SLIDE 27 Early mathematics competency predicts later reading achievement better than early literacy skills.
  • A. Szekely. Unlocking Young Children’s Potential: Governors’ Role in Strengthening Early Mathematics Learning
(Washington, D.C.: National Governors Association Center for Best Practices, October 28, 2014).

“ ”

slide-28
SLIDE 28
slide-29
SLIDE 29
slide-30
SLIDE 30

You little plucker!

John SanGovanni, NCTM ‘16
slide-31
SLIDE 31 number John SanGovanni, NCTM ‘16

You little plucker!

slide-32
SLIDE 32
slide-33
SLIDE 33
slide-34
SLIDE 34
slide-35
SLIDE 35
slide-36
SLIDE 36
slide-37
SLIDE 37
slide-38
SLIDE 38
slide-39
SLIDE 39
slide-40
SLIDE 40

?

slide-41
SLIDE 41

58 Packages

slide-42
SLIDE 42

14

slide-43
SLIDE 43

The Big Reveal

slide-44
SLIDE 44
slide-45
SLIDE 45 Graham had 58 packages of Skittles. Each package had 14 Skittles. How many Skittles did Graham have?
slide-46
SLIDE 46

3-Act Tasks

Act 1:
  • Real world problem or scenario presented
  • What do you notice? What do you wonder?
  • Make estimates
Act 2:
  • Identify missing variables and missing variables to solve
  • Define solution path using variables
Act 3:
  • Solve and interpret results of the solution
  • Validate answer
slide-47
SLIDE 47 Most asked questions:
  • How often should we use 3-Act Tasks?
  • When should we use 3-Act tasks? How do
they fit into the scope of a unit?
  • How long does one task usually take?
  • What if we don’t have the time?
slide-48
SLIDE 48 Standards for Mathematical Practice
  • 1. Make sense of problems and persevere in solving them.
  • 2. Reason abstractly and quantitatively.
  • 3. Construct viable arguments and critique the reasoning of
  • thers.
  • 4. Model with mathematics.
  • 5. Use appropriate tools strategically.
  • 6. Attend to precision.
  • 7. Look for and make use of structure.
  • 8. Look for and express regularity in repeated reasoning.
slide-49
SLIDE 49 Standards for Mathematical Practice
  • 4. Model with mathematics.
slide-50
SLIDE 50 What is mathematical modeling? What is modeling with mathematics?
slide-51
SLIDE 51 What ISN’T mathematical modeling
  • The use of manipulatives does not ensure that
modeling with mathematics is taking place.
  • If the mathematics is not contextualized, modeling
with mathematics cannot exist.
  • Modeling with mathematics does not mean, “I do,
we do, you do.”
slide-52
SLIDE 52 Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw
  • conclusions. They routinely interpret their mathematical results
in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Model with Mathematics
slide-53
SLIDE 53 Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw
  • conclusions. They routinely interpret their mathematical results
in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Model with Mathematics
slide-54
SLIDE 54 Contextualized Decontextualized Real-World Problem Validate Answer Solve & interpret results Define a solution path using variables Identify missing variables Make assumptions & estimates Mathematical Modeling in the Elementary Grades
slide-55
SLIDE 55 Contextualized Decontextualized Real-World Problem Validate Answer Solve & interpret results Define a solution path using variables Identify missing variables Make assumptions & estimates Mathematical Modeling in the Elementary Grades
slide-56
SLIDE 56 Contextualized Decontextualized Real-World Problem Validate Answer Solve & interpret results Define a solution path using variables Identify missing variables Make assumptions & estimates Mathematical Modeling in the Elementary Grades
slide-57
SLIDE 57
slide-58
SLIDE 58
  • 1. Anticipating student responses to challenging mathematical tasks;
  • 2. Monitoring students’ work on and engagement with the tasks;
  • 3. Selecting particular students to present their mathematical work;
  • 4. Sequencing the student responses that will be displayed in a specific
  • rder and;
  • 5. Connecting different students’ responses and connecting the responses
to key mathematical ideas.

5

The practices are: MTMS: Vol. 14, No. 9, May 2009-5 Prac8ces for Orchestra8ng Produc8ve Mathema8cs Discussions
slide-59
SLIDE 59

14 Skittles 58 Packages

slide-60
SLIDE 60 Identify and name the strategy used, then place the student work in order in terms of efficiency (least to greatest)
slide-61
SLIDE 61
slide-62
SLIDE 62 Sequence the order students will share during the closing.
slide-63
SLIDE 63
slide-64
SLIDE 64
slide-65
SLIDE 65
slide-66
SLIDE 66
slide-67
SLIDE 67
slide-68
SLIDE 68
slide-69
SLIDE 69
slide-70
SLIDE 70 Identify and name the strategy used, then place the student work in order in terms of efficiency (least to greatest)
slide-71
SLIDE 71 1-skip counting
slide-72
SLIDE 72 1-skip counting 2-doubling
slide-73
SLIDE 73 2-doubling 1-skip counting 3-counting on
slide-74
SLIDE 74 2-doubling 1-Skip counting 3-counting on 4a-Partial Products 4b-Partial Products
slide-75
SLIDE 75 2-doubling 1-Skip counting 3-counting on 4a-Partial Products 4b-Partial Products 5-Partial Products
slide-76
SLIDE 76 2-doubling 1-Skip counting 3-counting on 4a-Partial Products 4b-Partial Products 5-Partial Products

?

slide-77
SLIDE 77 2-doubling 1-Skip counting 3-counting on 4a-Partial Products 4b-Partial Products 5-Partial Products Where the Lattice goes
slide-78
SLIDE 78 Which student work samples do you share? Why?
slide-79
SLIDE 79
slide-80
SLIDE 80
slide-81
SLIDE 81
slide-82
SLIDE 82

Area Model

slide-83
SLIDE 83
slide-84
SLIDE 84

4 (x + 3)

slide-85
SLIDE 85
slide-86
SLIDE 86
slide-87
SLIDE 87

?

2 Questions

slide-88
SLIDE 88 Surface Area of an Apple
slide-89
SLIDE 89
slide-90
SLIDE 90 Approximately 0.25”
slide-91
SLIDE 91 2.5” 2.25”
slide-92
SLIDE 92
slide-93
SLIDE 93 8.13” 2.25” 2.5”
slide-94
SLIDE 94
slide-95
SLIDE 95

Redemption Time

slide-96
SLIDE 96
slide-97
SLIDE 97 Height Diameter Red Green Circumference 3.63” 8.5” 3.25” 2.25” 2.5” 11.5”
slide-98
SLIDE 98
slide-99
SLIDE 99
slide-100
SLIDE 100
slide-101
SLIDE 101 Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com/scoe2018

Harnessing the Power of the Purposeful Task