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? Memorize in Minutes: The Times Tables by Alan Walker
This is Mr. Fletcher’ s book! Hands off!
👄 👎
Dirty monkeys smell bad 👄 👎 Does McDonald’s sell cheeseburgers? ?
81 47 3819 - 376 59 - 47 12 Mentally…please
Today’s Goals • 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.
Procedural Conceptual Fluency Understanding Application http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
Before 2010 Procedural Conceptual Fluency Understanding Application http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
Procedural Fluency Laddy Regedanz (6/23/08)
2010-Today Procedural Conceptual Fluency Understanding Application http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
Procedural Conceptual Fluency Understanding Application http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
? Math Games
Games Procedural Conceptual Fluency Understanding Application http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
How many Skittles are in the jar?
Estimate = Educated Guess
A strategic choice of a number Estimate = Educated Guess
SKITTLES PEOPLE 0-200 10 201-400 75 401-600 60 601-800 10 >800 10
58 Packages
14 Skittles : Pack
14 Skittles : pack 58 Packages
4b-Partial Products 5-Partial Products 3-counting on Cut up one sheet and place them in a progression or order. 4a-Partial 2-doubling Where the Lattice goes 1-Skip Products counting
Ah-ha or New Idea Change or Difference ? Lingering Questions Dig Deeper
Write an equation that matches the model
Where does this learning start?
Arrange all the radios so there is the same number of radios on each shelf. You can add shelves or remove shelves if needed.
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?
How many radios would you need to to have the same number on each shelf?
1 2 3 4 5
What is the fewest number of tiles you could use to make an array?
1 Tile What is the fewest number of tiles you could use to make an array?
What is the fewest number of tiles you could use to make an array?
15 radios on 3 shelves 15 radios on 4 shelves
15 radios on 3 shelves 15 radios on 4 shelves
15 radios on 3 shelves 15 radios on 4 shelves 3 4
15 radios on 3 shelves 15 radios on 4 shelves 3 5 3 4 3
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
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
Write an equation that matches the model
Write an equation that matches the model
290 radios shared on 13 shelves 22 radios per shelf 13 shelves 4 radios left over
290 radios shared on 13 shelves 12 radios per shelf 13 shelves 4 radios left over
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 of shelves. Each of the shelves can hold 7 radios and 2 are left over so you move 2 spaces on the board.
Assessing Student Learning How many way can you shelve 36 radios?
How many little Post-its to make the Big Pad?
Student Learning
Consolidating the Learning in Congress
32 3 2 x 3 3
Area Model
20 3 60 20 400 23 x 22 2 40 6
2 3 3 3 9 2 2 2 3 x 3 3 3 2 6 4 3 3 9
x 3 4 4x 12 4(x = 3)
x 7 2 x X 7x (x + 8)(x + 7) 8 8x 56
x 3 x 2 2 (x + 3) = x + 6x + 9 3
? Divison
Strip Model Diagramming
Ah-ha or New Idea Change or Difference ? Lingering Questions Dig Deeper
Additive Multiplicative Thinking Thinking
Strip Model Diagramming
What If?
16 + 23
16 + 23
16 + 23
16 + 23
16 + 23
Catch Me if You Can
Sounds of Imagining Numbers
Ah-ha or New Idea Change or Difference ? Lingering Questions Dig Deeper
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