Harnessing the Power of Modeling Tasks through the Lens of a Math - - PowerPoint PPT Presentation

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Harnessing the Power of Modeling Tasks through the Lens of a Math - - PowerPoint PPT Presentation

May 08, 2023 176 likes •1.38k views

Harnessing the Power of Modeling Tasks through the Lens of a Math Progression Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com/ Procedural Conceptual Fluency Understanding Application

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Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com/

Harnessing the Power of Modeling Tasks through the Lens of a Math Progression

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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
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Procedural Fluency Application Conceptual Understanding

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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
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SLIDE 6 Instructor’s Manual for Elementary and Middle School Mathema7cs Teaching Developmentally Sixth Edi7on - John A. Van de Walle (Virginia Commonwealth University)

students doing the solving and the sense making teacher showing a very conceptual approach top-down, rule oriented approach

3

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3 questions

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1 Billion Circles

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100 circles : minute 144,000 circles : day 1,000,000,000 would take 6944 days 19+ years with no sleep

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2nd Question

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Where does 1 billion go on the number line? 1 trillion

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Where does 1 billion go on the number line? 1 trillion

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5 8 6 x

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6 x 5 8

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Today’s Goals

  • Understand the structure of 3-act task and see how

they fit into the scope and sequence of a unit.

  • Explore the importance of progressional

understanding and how a good task can be used as formative assessment.

  • Numbers and Operations in Fractions
  • Understand the importance of an effective closing and

the role it plays in deciding our next move.

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How many orange wedges are in the bowl? Estimate

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How many orange wedges are in the bowl? What information do you need to know?

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Each orange wedges is a quarter.

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Graham had 5 oranges and cut them into quarters. How many orange wedges did Graham have?

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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
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Most asked questions:

  • How often 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?
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SLIDE 29 MTMS: Vol. 14, No. 9, May 2009-5 Prac7ces for Orchestra7ng Produc7ve Mathema7cs Discussions
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  • 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 Prac7ces for Orchestra7ng Produc7ve Mathema7cs Discussions
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5 oranges Each wedge is a quarter

?

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  • 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 order 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 Prac7ces for Orchestra7ng Produc7ve Mathema7cs Discussions
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SLIDE 42 1a-Counting Up 1b-Counting Up
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SLIDE 43 1-Counting Up 2a-Skip Counting 2b-Skip Counting 1b-Counting Up
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SLIDE 44 1-Counting Up 2a-Skip Counting 2b-Skip Counting 1b-Counting Up 3a-Multiplicative 3b-Multiplicative
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SLIDE 45 1-Counting Up 2a-Skip Counting 2b-Skip Counting 1b-Counting Up 3a-Multiplicative 3b-Multiplicative
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Group 1 Group 2 Group 3

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Unit Fractions

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Representation of a Fraction

1 a

unit fraction —

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3 4

Say this fraction

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3 4

Say this fraction three one-fourths

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3 = 1 + 1 + 1

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3 4 3 = 1 + 1 + 1 = + + 1 4 1 4 1 4

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What’s the Sum?

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What’s the Sum?

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What’s the Sum?

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SLIDE 70 Directions: Using the whole numbers 1-9 once each, create and place 4 fractions greater than 1 on the number line in the correct order. (fractions B & C are equal) CCSS.MATH.CONTENT.4.NF.A.2

Open Middle

A C B D
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Equivalent Fractions

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= = = 6 2 3 3 2

Equal Fraction

4

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W T F ?

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hat’s his raction

W T F ?

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It is possible to over-emphasize the importance of simplifying fractions in this way. There is no mathematical reason why fractions must be written in simplified form, although it may be convenient to do so in some cases.

http://commoncoretools.me/wp-content/uploads/2011/08/ccss_progression_nf_35_2013_09_19.pdf
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What about “the test”

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3 6 + is equal to which of the following? 1 6 4 12 a. b. c.

  • d. None of the above

8 12 3 6

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Equivalence Simplifying

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Comparing Fractions

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Which girl ate more apple?

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Which girl ate more apple? What information do you need to know?

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Pause I I

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twelfths eighths

Pause I I

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Apple Eat Off Act-3

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Big sister ate of an apple and little sister ate

  • f an apple. Which sister ate more apple?

10 12 7 8

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  • 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 order 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 Prac7ces for Orchestra7ng Produc7ve Mathema7cs Discussions
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S1 S6 S5 S4 S3 S2

Pause I I

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S3 S4 S1

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It Takes 3 to Prove it to Me

3

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1 3 4 4

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1 3 4 4

Common Denominator

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1 3 4 4

Common Denominator

5 3 6 4

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

2 4 4 6

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

2 4 4 6

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

2 4 4 6

Benchmark

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

2 4 4 6

Benchmark

2 2 3 5

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

2 4 4 6

Benchmark

2 2 3 5

Common Numerator

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1 3 4 4

Common Denominator

5 3 6 4

Missing Parts

2 4 4 6

Benchmark

2 2 3 5

Common Numerator

Unit Fraction Understanding Unit Fraction Understanding Unit Fraction Understanding
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8 4 11 7

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8 8 11 14

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gfletchy@gmail.com @gfletchy www.gfletchy.com/math-plus