laying the foundation for single-digit addition & subtraction fluency grades k-2 and beyond...
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Laying the Foundation for Single-Digit Addition & Subtraction Fluency Grades K-2 and Beyond
Common Core Leadership for MathematicsJune 21, 2011DeAnn Huinker & Melissa HedgesUniversity of Wisconsin-Milwaukee
Common Core Leadership in Mathematics Project
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
K-8 DomainsK 1 2 3 4 5 6 7 8
Counting & Cardinality
Ratios & Proportional
Relationships
Operations & Algebraic ThinkingExpressions &
Equations
Number & Operations in Base Ten The Number System
Number & Operations -
FractionsFunctions
Measurement & DataStatistics & Probability
Geometry
K-8 Content Domains, CCSSM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Domain Progressions - Number
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Learning Intentions
We are learning to… Understand how fluency with single-digit addition
& subtraction develops and progresses in CCSSM.
Read & interpret the cluster of CCSSM standards related to adding and subtracting within 20.
We will know we are successful when we can… Understand the strategies students use for solving
single-digit addition and subtraction problems.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Getting started…
Mentally compute the answer to the following…
1005 – 998
54 + 48
No pencil or paper please!
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Turn and share your reasoning.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Reflecting on your homework reading, compare the definitions of a computational strategy versus algorithm.
Did you use a strategy or an algorithm?
What do you understand about number relationships that allow you to mentally compute answers?
Discuss
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
A Content Standards ProgressionGrade 1
Page 15 of the CCSSM.
Read the OA domain for Grade 1:“Operations and Algebraic Thinking” 1.OA.1-8
As you read, mark the following:
familiar ideas: ✓surprising ideas: ! confusing ideas: ?
Then turn and share a ✓ or ! and a ?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
A Content Standards ProgressionGrade 2
Page 19 of the CCSSM.
Read the 2.OA.1 and 2.OA.2
In what ways do the grade 2 standards build from the grade 1 standards?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
A Content Standards ProgressionGrade K
Read pages 11-12 of CCSSM:K.CC.4a-c, K.OA.3, K.OA.4, and K.NBT.
In what ways do these standards in kindergarten lay the foundation for learning single-digit addition and subtraction problems?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Dot Patterns & Ten Frames
Play “Flash”How many dots did you
see?How did you see it?
What’s the math?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Dot Pattern
How many dots?How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
How many dots?How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
How many dots?How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Ten Frames
Ten frames show relationships of small numbers to five and ten, in particular, drawing attention to the role of 10.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
How many dots?How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
How many dots?How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
How many dots?How did you see it?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Laying a foundation for understanding
Morgan, Dot Plates, & Ten Frames
Enjoy!
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Through the lens of the Math Content
What does Morgan understandabout number?
K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings…
K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings...
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Through the lens of the Math Content
What is the difference between K.OA.3 and K.OA.4 in the classroom?
What value does this foundation have for our middle and high school students?
K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., use objects or drawings…
K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., using objects or drawings...
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Building Understanding Through Context
How might a student solve this problem?
There were 6 cookies on the plate. Mom put 5 more cookies on the plate. How many cookies are on the plate now?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Progression toward fluency
Methods for solving single-digit problemspp. 36-38 of the OA progressions document
Level 1: Direct Modeling
Level 2: Counting on
Level 3: Convert to an Easier Problem
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Level Jigsaw
Form Groups of Three. Number off 1-3.
Read and highlight your assigned level.
Using examples, teach your colleagues how student thinking and reasoning would sound at your level.
#1s read & teach Level 1
#2s read & teach Level 2
#3s read & teach Level 3
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Grade 1: Content Standard 1.OA.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
Use strategies such as
• counting on
• making ten
• decomposing a number leading to a ten
• using the relationship between addition & subtraction
• creating equivalent but easier or known sums
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Strategies for Single Digit Addition
Counting on.
Make a ten.
Use an easier “equivalent” problem.
Transform the
problem in some wayUse fives
Use a helping fact
Use doubles
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
8 + 6
Strategies:Make a ten.Use a double.Use fives.Use some other
equivalent problem.
Put 8 counters on your first frame & 6 counters on your second frame.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Make a ten: 8 + 6
How could you make a ten?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Make a ten: 8 + 6
How could you make a ten?
Move 2 counters to the top frame.
Write an equation.
8 + 6 = 8 + 2 + 4 = 10 + 4 = 14
Then you have 10 and 4 more counters.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Use a double: 8 + 6
What doubles might you use?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Use a double: 8 + 6
What doubles might you use?
Write an equation.
8 + 6 = 6 + 6 + 2 = 12 + 2 = 14
Reason 6 + 6 = 12; then add 2 more.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Use fives: 8 + 6
Can you see some fives? Where?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Use fives: 8 + 6
Can you see some fives? Where?
Reason: 5 + 5 is 10; need to add 3 more and 1 more.
Write an equation.
8 + 6 = 5 + 5 + 3 + 1
= 10 + 4 = 14
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
7 + 9 9 + 8 6 + 7
Select a problem. Tell an addition story. Draw a strategy card for the group. Everyone uses ten frames and counters to reason
through the strategy and writes an equation(s) that shows the reasoning.
Share, compare, and discuss as a group. Repeat with another strategy card for the the same
problem or a new problem.
Reflect: Which strategies seem to work best for each problem?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011
Learning Intentions
We are learning to… Understand how fluency with single-digit addition
& subtraction develops and progresses in CCSSM.
Read & interpret the cluster of CCSSM standards related to adding and subtracting within 20.
We will know we are successful when we can… Understand the strategies students use for solving
single-digit addition and subtraction problems.