Learning Progressions and Fluency for Multiplication and Division - - PowerPoint PPT Presentation

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Learning Progressions and Fluency for Multiplication and Division - - PowerPoint PPT Presentation

Mar 07, 2023 49 likes •1.06k views

Learning Progressions and Fluency for Multiplication and Division gfletchy@gmail.com @gfletchy www.gfletchy.com What is the value of this picture? Memorize in Minutes: The Times Tables by Alan Walker What is the value of this picture?

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gfletchy@gmail.com @gfletchy www.gfletchy.com

Learning Progressions and Fluency for Multiplication and Division

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What is the value of this picture?

Memorize in Minutes: The Times Tables by Alan Walker
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SLIDE 3 Memorize in Minutes: The Times Tables by Alan Walker

What is the value of this picture?

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This is Mr. Fletcher’ s book! Hands off!

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👎

👄

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?

Does McDonald’s sell cheeseburgers? Dirty monkeys smell bad

👎

👄

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47 3819

  • 376

59

  • 47

12 81

Mentally…please

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  • Explore the scalability of conceptual

understanding with the progression of division and multiplication

  • Multi-vision: the ability to recognize, understand,

and leverage the relationship between multiplication and division

  • Identify ways to be more intentional and

purposeful when engaging students in games.

  • We’ll poke a couple of the sleeping bears in our

practice.

Today’s Goals

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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

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/

Before 2010

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Procedural Fluency

Laddy Regedanz (6/23/08)
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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/

2010-Today

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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
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?

Math Games

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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/

Games

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How many Skittles are in the jar?

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Estimate = Educated Guess

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Estimate = Educated Guess

A strategic choice

  • f a number
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SKITTLES PEOPLE 0-200 10 201-400 75 401-600 60 601-800 10 >800 10

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58 Packages

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14 Skittles : Pack

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14 Skittles : pack 58 Packages

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2-doubling 1-Skip counting 3-counting on 4a-Partial Products 4b-Partial Products 5-Partial Products

Where the Lattice goes

Cut up one sheet and place them in a progression or order.

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Ah-ha or New Idea Change or Difference Lingering Questions

?

Dig Deeper

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Write an equation that matches the model

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Where does this learning start?

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Arrange all the radios so there is the same number of radios on each shelf. You can add shelves or remove shelves if needed.

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Questions to Consider

How many ways could you arrange the radios on the shelf? How many radios per shelf? How many shelves? Did you find all the possible arrangements? What did you notice? What did you wonder?

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How many radios would you need to to have the same number on each shelf?

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1 4 5 2 3

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What is the fewest number of tiles you could use to make an array?

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What is the fewest number of tiles you could use to make an array? 1 Tile

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What is the fewest number of tiles you could use to make an array?

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15 radios on 3 shelves 15 radios on 4 shelves

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15 radios on 3 shelves 15 radios on 4 shelves

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15 radios on 3 shelves 15 radios on 4 shelves

3 4

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15 radios on 3 shelves 15 radios on 4 shelves

3 4 5 3 3

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SLIDE 59 7/6/2019 View online: Bridges in Mathematics Grade 4 - Teachers Guide | Bridges Educator Site https://bridges.mathlearningcenter.org/view/br4-tg#144 1/1
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7/6/2019 View online: Bridges in Mathematics Grade 4 - Teachers Guide | Bridges Educator Site https://bridges.mathlearningcenter.org/view/br4-tg#144 1/1

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Write an equation that matches the model

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Write an equation that matches the model

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290 radios shared on 13 shelves

13 shelves 22 radios per shelf 4 radios left over

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290 radios shared on 13 shelves

13 shelves 12 radios per shelf 4 radios left over

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Remainder Race

Roll two 10-sided dice and create the smallest number of radios possible using the digits. Roll the 6-sided dice to represent the number of shelves. Example: A 7 and 3 are rolled and 37 is created to create the number of radios that need to go on the shelves. A 5 is rolled to represent the number

  • f shelves. Each of the shelves can hold 7 radios

and 2 are left over so you move 2 spaces on the board.

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Assessing Student Learning

How many way can you shelve 36 radios?

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How many little Post-its to make the Big Pad?

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Student Learning

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Consolidating the Learning in Congress

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32 3 3 2 3 x

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Area Model

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20 3 20 2 400 40 60 6 23 x 22

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3 9 2 3 6 3 4 9 2 2 3 2 3 2 3 3 x 3 3

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x 4x 12 4(x = 3) 4 3

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x 7 x 8 X 8x 7x 56 (x + 8)(x + 7)

2

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(x + 3) = x + 6x + 9

2 2

x 3 x 3

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Divison

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Strip Model Diagramming

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Ah-ha or New Idea Change or Difference Lingering Questions

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Dig Deeper

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Multiplicative Thinking Additive Thinking

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Strip Model Diagramming

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What If?

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16 + 23

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16 + 23

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16 + 23

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16 + 23

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16 + 23

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Catch Me if You Can

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Sounds of Imagining Numbers

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Ah-ha or New Idea Change or Difference Lingering Questions

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Dig Deeper

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gfletchy@gmail.com @gfletchy www.gfletchy.com

Learning Progressions and Fluency for Multiplication and Division