(03) Integers 3: Multiply and Divide within 100
Topic outline

Essential Questions
 How do multiplication and division and multiplication help us solve problems? What types of problems?
 How can we represent our thinking about multiplication and division?
 How are multiplication, division, addition, and subtraction all related? How do we know when to use each?
 How can we use one multiplication fact to determine another?
 How can we use one division fact to determine another?
 Which multiplication and division facts should be memorized? And when is it OK or better to estimate or use a strategy or a calculator?
Links

I will...
 Do the Introduction to Equal Groups.
 Play The Pizza Game and variations on it.
 Do leveled picture drills for Equal Sets
 Do JUMP Division Worksheets  Visuals
So I can...
 Translate fluently between manipulatives, pictures, and stories.
 Parse and describe equal grouping situations in terms of number of groups, amount per group, and total.
As assessed by...
[Coming soon]

I will...
 Play area games!
 How Close to 100?
 YouCubed instructions
 Normal gameboard
 Create variations on your own grid paper
 Area Battle [How Many Rows? How Many in Each Row?]
 YouCubed instructions
 Gameboard printout
 Create variations on your own grid paper
 How Close to 100?
 Solve problems with areas & arrays. [Under construction]
So I can...
 Translate fluently between manipulatives, pictures, and stories.
 Parse and describe equal row situations in terms of number of rows, amount per row, and total.
As assessed by...
[Coming soon]
 Play area games!

I will...
 Model equal jump problems on a number track [Select document B in the left panel then press "Recompile"].
So I can...
 Translate fluently between manipulatives, pictures, and stories.
 Parse and describe equal jump situations in terms of number of steps, amount per step, and total.
As assessed by...
[coming soon]

I will...
[coming soon]
So I can...
 Translate fluently between all visual representations of equal sets.
 Generate and describe examples of how they correspond.
 Show commutativity in all groups, rows, and arrays.
As assessed by...
[coming soon]

[coming soon]

I will..
 Play the Factor Game.
 Play Last to Zero.
 Do Leveled Drills for Remainders
 Drill solving and representing remainders in groups, rows, and jump situations. [Under construction.]
 Do JUMP Mult & Div Review, with Remainders
 Learn to use the words "multiple" and "factor" and how they relate to remainders and divisibility. I'll be able to describe all the divisibility rules and create examples to show them.
So I can...
 Explain and demonstrate with my own examples when and why remainders occur, what they are, and how to interpret them in context for all previous representation.
 Explain my reasoning using the words “multiple” and “factor”.
 Use equations to record my thinking about remainders.
As asssessed by...
2.9.2 Students will be fluent in solving division equations with and without remainders (15 solutions per minute, 95% accuracy, can do orally as teacher or tutor writes). Remainder Drills  Division Only
2.9.3 Students will be fluent in solving equations involving remainders and determine a corresponding multiplication or division statement. Example: \( 7 \div 2 = 3\ R1 \iff 2 \times 3 + 1 = 7 \)
2.9.4 Students will be able to generate examples of all of the above.

I will...
 Do leveled drills on equations.
 Master fact families for multiplication and division.
 Level 4b  Write Equations
 Representing Multiplication & Division Template
 All Structures Word Problems (except ratios and rates)
So I can...
 Translate fluently between previous representations, repeated addition and repeated subtraction equations, and multiplication and division equations.
 Recognize and explain when to multiply and when to divide.
 Show and explain the relationship between all operations.
As assessed by...
[coming soon]
 Do leveled drills on equations.

I will...
 Skip Counting
 Scorecard
 Drill pages
 Mr DeMaio's Multiplication Songs (actually skip counting).
 TicTacToe Products
So I can...
 Count by 2, 5, and 10 up to 10 groups, without reference to ones. I use automatic recall or addition strategies instead.
 Show my thinking with manipulatives, number tracks and/or number lines, aloud, and in written sequences and tables.
 Use skip counting to solve equations and I always pick the easier skip count when possible.
As assessed by...
[coming soon]
 Skip Counting

I will...
 Mr DeMaio's Multiplication Songs (actually skip counting)
 Figure out Which Number Doesn't Belong [source: Mindtrap's "Geometrical Riddles"]
So I can...
 Count fluently by 3, 4, and 9 up to 10 groups, without reference to ones. I use automatic recall or addition strategies instead.
 Show my thinking with manipulatives, number tracks and/or number lines, aloud, and in written sequences and tables.
 Use skip counting to solve equations and I always pick the easier skip count when possible.
As assessed by...
[coming soon]

I will...
 Mr DeMaio's Multiplication Songs (actually skip counting)
So I can...
 Count fluently by 6, 7, and 8, up to 10 groups, without reference to ones. I use automatic recall or addition strategies instead.
 Show my thinking with manipulatives, number tracks and/or number lines, aloud, and in written sequences and tables.
 Use skip counting to solve equations and I always pick the easier skip count when possible.
As assessed by...
[coming soon]


I will...
 Print the Times Tables and track my progress on it.
 Practice Incremental Multiplication Facts (will have to create a new copy for each student).
 Learn the patterns of the 6 and 9 times table, then drill them.
 Play!
 Do progressive fact drills
 Zak Facts
 Rocket Math [uploaded to Bravo Math servers, not Google Drive]
So I can...
 I can demonstrate automatic recall for the 0, 1, 2, and 10 times tables.
 I can demonstrate fluency in multiplying by 10 then dividing by 2 and/or using recall for the 5 times table.
 I can apply the distributive property for the 9, 6, and 3 times tables. I can represent my thinking in a variety of ways.
As assessed by...
[coming soon]

I will...
 Play Meteor Multiplication.
 Drill the Factors of 100.
 Learn the Factors of 60
 3 Clocks Per Page
 Factors of 60 Drills [coming soon!]
 Practice Incremental Multiplication Facts.
I can...
 Use repeated doubling strategies for the 4 and 8 times table.
 Demonstrate automatic recall, fluency in strategies and/or mnemonics, for all remaining times table facts.
 Demonstrate automatic recall for all factor pairs of 60 and 100.
As assessed by...
[coming soon]

I will...
 Play Meteor Multiplication
 Play variations on TicTacToe
 Tic Tac Toe Products
 The Product Game
 Do × & ÷ Fact Drills
 Distributive Property Drills
 Practice Incremental Multiplication Facts.
So I can...
 Demonstrate such fluency in all of the previous strategies and/or have such automatic recall for all times table facts that looking up answers, drawing, guessing, or counting all slow me down.
 Demonstrate flexibility and fluency in using strategies to multiply and divide within 100. I can record my thinking with equations and diagrams.
 Apply my skills in context and create a visual if necessary.
As assessed by...
[coming soon]

I will...
[coming soon]
So I can...
 I can translate fluently between direct models (linear and discrete), pictures, words, and counting.
 I can compare quantities using subtraction and division, record my thinking with equations, and interpret appropriately in context.
As assessed by...
[coming soon]

I will...
[under construction]
 Craig Bartonrecommended ratios/proportion thing, N6
 Desmos: Balloon Float
 Desmos: Pizza Toppings
 Thinking in Rates
 Multiply or Divide? All Structures
I can...
 Use multiplication and division to solve simple applications involving ratios and rates.
 Succeed at rich problems and mini numeracy tasks by myself.
As assesssed by...
[coming soon]
