Continuum of Understanding
Students go through a general continuum of understanding for multiplication, division, and other operations (see anchor chart we created in class). (Direct Modeling --> Counting --> Derived Numbers --> Known Facts) The value in this is encouraging metacognition about math strategies, helping students understand that these stages are important for their own understanding and necessary to go through in order to reach that end goal.

Also notable in any new conceptual understanding, new information should presented Concrete --> Verbal -->Abstract/Sybmolic.

Loops and Groups (Bridges Math Curriculum, Copyrighted) similar as Circle and Stars by Marilyn Burns - create your own game!

Structured Array (see below)

Arrays fully visible

Arrays partial screen showing group markers and items in each group

Arrays partially screened showing only group markers

Verbal tasks

Multiplication Construct 3

100 Dot Structured Array - 100 Dot Array and Screen - Use this and a screen to build any size array that you want. Fantastic tool for multiplicative thinking.

100 Dot Array, Student Version (print and make an L-shaped screen) - Using the structured array, you can make any desired array. You can then use the screens to gradual screen the number in each group and group markers. Always watch for how students are counting: are they perceptual replacing the dots? Are they stress or skip-counting? Are they using something they know and building on?

Activities and Games to Support Verbal Sequences of Multiples (provide quantitative support in form of dot cards, dice patterns, etc. to begin)

Class Count Arounds (verbal, BUZZ, Pop, etc.) -Get creative. Remember to count both forwards and backwards.

Treasure Hunt (see AVMR Book for instructions, Course 2) - This is a great independent math activity. You can use the same cards to play Garbage.

Disappearing Numerals(red MR Book) - Write the multiples of any given number. Read the numberals forward and backward. Then, cross/cover one numeral. Read forward and backwards again. Continue process until all numerals are covered. Great independent sequencing practicing.

These students would benefit from relational tasks now. Use the structured array and question to really stretch student thinking!

100 Dot Structured Array - 100 Dot Array and Screen - Use this and a screen to build any size array that you want. Fantastic tool for multiplicative thinking.

100 Dot Array, Student Version (print and make an L-shaped screen

http://mindfull.wordpress.com/2011/02/06/introducing-multiplication-with-understanding/ helps show how all the facets of understanding our connected.

Continuum of UnderstandingStudents go through a general continuum of understanding for multiplication, division, and other operations (see anchor chart we created in class). (Direct Modeling --> Counting --> Derived Numbers --> Known Facts) The value in this is encouraging metacognition about math strategies, helping students understand that these stages are important for their own understanding and necessary to go through in order to reach that end goal.

Also notable in any new conceptual understanding, new information should presented Concrete --> Verbal -->Abstract/Sybmolic.

Multiplication Construct 1Multiplication Construct 2Lemonade StandLoops and Groups (Bridges Math Curriculum, Copyrighted)similar as Circle and Stars by Marilyn Burns - create your own game!Multiplication Construct 3Activities and Games to Support Verbal Sequences of Multiples(provide quantitative support in form of dot cards, dice patterns, etc. to begin)Class Count Arounds (verbal, BUZZ, Pop, etc.) -Get creative. Remember to count.both forwards and backwardsTreasure Hunt(see AVMR Book for instructions, Course 2) - This is a great independent math activity. You can use the same cards to play Garbage.Disappearing Numerals(red MR Book) - Write the multiples of any given number. Read the numberals forward and backward. Then, cross/cover one numeral. Read forward and backwards again. Continue process until all numerals are covered. Great independent sequencing practicing.Numeral Tracks- Practice counting forward and backwards by any numeral. You can do Disappearing Numerals with this as well.SMART Board for Numeral Tracks and Dot StripsGames

These students would benefit from relational tasks now. Use the structured array and question to really stretch student thinking!Multiplication Construct 4Using Multiplicative Language Ideas in ClassInstructionFluently double a number –doubling up to 100Fluently half a number –halving numbers up to 100Multiplication Construct 5Multi-digit Work and continued practice for fluency.

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