laying the foundation for single-digit addition & subtraction fluency grades k-2 and beyond...

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.