Clarify Their Own Thinking
Consider and Test Other Strategies
Investigate and Apply Math Relationships
Develop Multiple Strategies and Choose the Most
Efficient One
Number Talks
Strings- Give students a series of smaller problems that
build on each other to teach a particular strategy.
Focused Problem- 1 bigger problem that allows
students to explore how to solve the problem in
different ways- develops flexible and efficient thinking.
5-15 minutes
Think-Pair-Share
Wait Time- Emphasize Thinking Over Speed
Wait until most students feel they have at least one strategy
Students who solve problem quickly are encouraged to solve
problems in more than 1 way
Accept All Ideas
Different Strategies develop flexible thinking and build on
understanding of number relationships
Wrong answers lead discussion to focus on important strategies
and clear up common misconceptions
Sample Prompts
I agree with ____________ because__________.
I disagree with__________ because__________.
I do not understand____________. Can you please
explain again?
Why did you decide to_________________?
Getting Started
Start with smaller problems
Offer strategies from former students
It’s ok to put an answer on the back burner
5-15 minutes
Be patient
Building Mathematical
Relationships
Writing Problems Horizontally
199 + 199
+1 +1
200 + 200 = 400
-2
398
Vertical problems encourage standard algorithm
Building Mathematical Relationships
Anticipate Student Answers and Name Them:
28+29
Friendly Numbers or Landmarks
25+23=25+25-2= 50-2=48
7x5= 5x5+2x5
Compensation
28+29 = (28-1) + (29+1)= 27+30
+10
27
+10
37
+10
47
57
Breaking Numbers Into Place Value
(20+8)+ (20+9) = (20+20) + (8+9) = 40+17 = 40 +10 + 7 = 50 +7 = 57
Strings
- a series of smaller problems that teach a pattern, strategy, etc….
•
7+3
• 3+4
• 7+3+4
• 7+7
Strings
- a series of smaller problems that teach a pattern, strategy, etc….
•
3x5
• 2x6
• 3x5x2
• 5x2x6
•Clarify Their Own Thinking
•Tyler realized his mistake and did the 2nd one
correctly
•Consider and Test Other Strategies
•Investigate and Apply Math Relationships
•Associative property
•Develop Multiple Strategies and Choose the Most
Efficient One
•3x (5x2) is more efficient than (3x5)x2
1 Problem- Many Strategies
12+19
Compensation
Make a 12 a friendly number by subtracting 2. Add 2 to 19 to compensate.
12+19= 10 + 21
(12-2) + (19+2)
1 Problem- Many Strategies
12+19
Place Value
Rewrite numbers in expanded form
12+19=( 10+2) +(10+9)
Use associative property to add 10’s and 1’s
10+10=20 2+9=11
20+11=31
1 Problem- Many Strategies
12+19
Friendly Landmarks
Adjust 12 and 19 to make the friendly landmarks of 10 and 19.
12-2=10 and 19+1=20
10+20=30
Readjust numbers back
30+2=32
32-1=31
1 Problem- Many Strategies
12x15
Decomposing and The Associative Property
Decompose The Factors
12=3x4
15=3x5
12x15=3x4x3x5
Rearrange to friendlier numbers
12x15=(4x5)x (3x3)
Recompose with friendlier numbers
12x15=20x9
12x15=180
1 Problem- Many Strategies
12x15
Distributive Property
Distribute 12 Groups of 15 Into Friendly Groups- 10 Groups of 15 +2 Groups of 15
12x15= (10 x 15) + (2 x 15) = 150+30=180
Or
Distribute 15 Groups of 12 Into Friendly Groups- 10 Groups of 12 + 5 Groups of 12
12x15= (12 x 10) + (12 x 5)= 120 +60=180
1 Problem- Many Strategies
12x15
Doubling and Halving
Double 1 Factor and Halve The Other
12x15=6x30
Decompose 30 Into 3x10
6x30= 6x3x10
Use associative property to multiply a basic fact and multiple of 10
6x3=18
18x10=180
Accountability
Smaller Number Talks
Signal most efficient strategy
Posters of Strategies Used
Exit Problems
Weekly Computation Assessment
Day 1 – Problem Talk
Ted is saving money for a new bike. He deposits money at
his bank three times a month. Each time he goes, he deposits
$5. How much will he have saved in a year.
First we have to figure out how much he saves in a month3x5
Then we have to find out he saves in a year- (3x5) x12
Day 2 – Number Talk
3x5
15x12
K-2 Classrooms: Big Ideas
Developing Number Sense
Relationships
Magnitude
Effect of operations
Mental Math
Estimation
Conservation of #
Developing Fluency With Small Numbers
More than memorizing facts…understanding number relationships
Subitizing
Making 10’s
K-2 Classrooms: Tools
Dot Cards
Rekenreks (Bead models)
5 Frames and 10 Frames
Number Lines
Number Grids
K-2 Classrooms: Strategies
Counting on/ Counting Back
Counting chunks
Finding 10’s
Compose and Decompose
Place Value
Doubles/ Near Doubles
Compensation
3-5 Classrooms
Developing Number Sense
Relationships
Magnitude
Effect of operations
Mental Math
Estimation
Conservation of #
Place Value
Developing Fluency
More than memorizing facts…understanding number relationships
Properties
Connecting Mathematical Ideas
3-5 Classrooms: Addition And Subtraction Strategies
Counting on/ Counting Back
Counting chunks
Finding 10’s
Compose and Decompose
Place Value
Doubles/ Near Doubles
Compensation
3-5 Classrooms: Multiplication Strategies
Area Models
Repeated addition
Skip Counting
Doubling and Halving and related relationships
5 x 4 = 10 x 2
Partial Products
Landmarks and Friendly Numbers
Decomposing Factors into Smaller Factors
3-5 Classrooms: Division Strategies
Area Models
Repeated subtraction
Sharing out (picture models)
Multiplying Up (Partial products)
Partial Quotients
Proportional Reasoning (halving and halving)
200/4 = (200/2) / (4/2) = 100/2 = 50
Decomposing Factors into Smaller Factors
40/8 = 40 / (4x2) = (40/4) / 2 = 10/2 = 5