Clarify Their Own Thinking Consider and Test Other Strategies Investigate and Apply Math...
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Transcript of Clarify Their Own Thinking Consider and Test Other Strategies Investigate and Apply Math...
Why Number Talks?
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.
Number TalksCharacteristics
5-15 minutes
Think-Pair-Share
Wait Time- Emphasize Thinking Over SpeedWait 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 IdeasDifferent 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
Classroom DiscussionsEmphasize Talk!
Sample PromptsI 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+2x5Compensation
28+29 = (28-1) + (29+1)= 27+30
+10 +10 +10
27 37 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•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
• 2x6
• 3x5x2
• 5x2x6
1 Problem- Many Strategies
12+19
CompensationMake 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 form12+19=( 10+2) +(10+9)
Use associative property to add 10’s and 1’s
10+10=20 2+9=1120+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=3232-1=31
1 Problem- Many Strategies12x15
Decomposing and The Associative Property
Decompose The Factors12=3x4 15=3x5
12x15=3x4x3x5
Rearrange to friendlier numbers 12x15=(4x5)x (3x3)
Recompose with friendlier numbers12x15=20x912x15=180
1 Problem- Many Strategies
12x15
Distributive Property
Distribute 12 Groups of 15 Into Friendly Groups- 10 Groups of 15 +2 Groups of 1512x15= (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 Strategies12x15
Doubling and Halving
Double 1 Factor and Halve The Other12x15=6x30
Decompose 30 Into 3x106x30= 6x3x10
Use associative property to multiply a basic fact and multiple of 10
6x3=1818x10=180
Accountability
Smaller Number Talks
Signal most efficient strategy
Posters of Strategies Used
Exit Problems
Weekly Computation Assessment
Day 1 – Problem TalkTed 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 month- 3x5
Then we have to find out he saves in a year- (3x5) x12
Day 2 – Number Talk3x5
15x12
K-2 Classrooms: Big Ideas
Developing Number SenseRelationships
Magnitude
Effect of operations
Mental Math
Estimation
Conservation of #
Developing Fluency With Small NumbersMore 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 ClassroomsDeveloping Number Sense
Relationships
Magnitude
Effect of operations
Mental Math
Estimation
Conservation of #
Place Value
Developing FluencyMore 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 relationships5 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 Factors40/8 = 40 / (4x2) = (40/4) / 2 = 10/2 = 5