12/9/2015
CESA #4’s State Title I Network Presents
Title I Teachers and
Friends: Small Group
Math Practices
Norms
*Agree to learn in a safe place
*Ask questions when they arise
*Honor technology and human
interaction
*Think forward about application
Objectives
To understand some of the research on small group math instruction
To build strategies for best practice in small group mathematics
To develop a sample workshop approach: time, materials, organization
Allow for planning time
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Introductions and a warm-up
Use exactly four 4's to form
every integer from 0 to 50,
using:
+, -, x, /, (), x2, and !
Whole Group:
Small Group:
teaching new concepts
practicing new skills
using manipulatives
introducing independent work
more questioning than telling
practicing new skills
using manipulatives
introducing independent work
providing intensive remedial instruction
more questioning than telling
The shift we need is more toward facilitating learning through thoughtful questioning
and away from telling and showing students what they need to learn.
Just like Guided Reading is a component of a Balanced
Literacy Program and does not replace Universal
instruction, “guided math” is a component does not replace
universal instruction.
How do you small group?
C.
A.
B.
D.
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What small group is
“A way to meet the needs of all of the kids in your classroom in a powerful
way that will accelerate learning.”
Debbie Diller, Making the Most of Small Groups (2007)
What small group is
Balanced mathematics:
Procedural Skill and Fluency
Conceptual Understanding
Application and Problem Solving
What small group is
❖an opportunity for students to hear other students’ thinking about their
mathematical problem-solving skills and strategies
❖provides strong support for struggling learners
❖provides extra challenges for proficient learners
❖allows students to demonstrate their understanding in a variety of ways
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What small group is
Planned, purposeful instruction based on data, assessment, observation from
multiple sources
What small group is
An opportunity for students to try out what was modeled in whole group
instruction….
...in a skillful way with instructional level problems.
Small group is an answer...
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What small group is connected to WI Initiatives
❏ an opportunity for kids
to do math with
engagement and
enthusiasm
Danielson’s Domain 3 Instruction
Component C, Engaging Students in
Learning
❏ Grouping of Students
Whatever the grouping, skilled teachers
decide it purposefully.
❏ The purpose is to maximize student
engagement in learning.
What small group is connected to WI Initiatives
❏ an opportunity for kids
to solve math problems
strategically
CCSS.MP - 5 Use appropriate tools
Strategically
CCSS.M 2.NBT.7
Add and Subtract within 1000, using concrete
models or drawings and strategies based on
place value, properties of operations...
What small group is connected to WI Initiatives
❏ an opportunity for kids
to engage in
meaningful,
invigorating
conversations about
math
CCSS.MP - 3 Construct viable arguments and
critic the reasoning of others
“There is a world of difference between a
student who can summon a mnemonic device
to expand a product such as (a+b)(x+y) and a
students who can explain where the
mnemonic comes from.”
CCSS for Math p.4
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What small group is connected to WI Initiatives
❏ an opportunity for kids
to solve real-world
tasks
CCSS.MP - 1 Make sense of problems and
persevere in solving them
CCSS.MATH.CONTENT.5.NF.B.6
Solve real world problems involving
multiplication of fractions and mixed
numbers
What small group is connected to WI Initiatives
❏ an opportunity for kids
to develop fact fluency
and automaticity
CCSS.MATH..3.OA.C.7
Fluently multiply and divide within
100.
CCSS.MATH.CONTENT.4.NBT.B.4
Fluently add and subtract multi-digit
whole numbers using the standard
algorithm.
8 Fluency standards K-5
What small group is NOT
A replacement for whole group, universal instruction
A daily occurrence for all students
The only method for differentiation
The best fit for all students all of the time
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What small group
is NOT
Make it & take it centers
Decreasing rigor
Lowering Expectations
Tracking
Brain Break
Top Ten Single Digit Numbers
Mathematics
is complicated.
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Rigor in CCSS
The CCSSM require a balance of:
Solid conceptual understanding
Procedural skill and fluency
Application of skills in problem solving situations
Pursuit of all three requires equal intensity in
time, activities, and resources.
Conceptual Understanding
Fluency
•The standards require speed and accuracy in
calculation.
•Teachers structure class time and/or small group time
for students to practice strategies to solve problems
(such as single-digit multiplication) so that they are
better able to apply strategies to understand and
manipulate more complex concepts
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strategy - fluency - automaticity
Tools of the Trade…..a little insider knowledge to help teachers
Progressions
Document from
Arizona
Mathematical
Practice
Standards
LESRA Framework for Mathematics
Instruction:
Launch (whole group)
Explore (small group)
Summarize (whole group)
Reflect (individual)
Apply (small group)
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concrete: doing stage - allows
students to physically manipulate
objects to solve a math problem
representational: seeing stage students use images (pictures or
drawings) to represent the objects to
solve a math problem
abstract: symbolic stage - students
solve the problem using numbers and
symbols
CRA: Concrete Representational Abstract
5 Tenants of Small Group
❏ Match to the individual mathematician
❏ Teach toward independence
❏ Teach strategies explicitly so that mathematicians
become proficient and skilled
❏ Value time spent, volume, and a variety of
tasks/problems
❏ Follow predictable structures and routines
5 Ways to Try Small Group:
Instructional Formats
Mathematics Domain Groups: Students grouped based on domain deficits
(Algebra Readiness, Geometry, Data & Measurement)
Number Sense and Fact Fluency: Students grouped on number development
skills
Goal Setting Groups: groups of students with the same next steps
Previous Sequential Concepts: groups based on mastery of previous concepts;
common misconceptions
Other: what other ways might you group your math students?
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Conferring is the heart of the Workshop
Thinking Form
What does the teacher do:
Before
During
After
Conferencing in mathematics:
Two Purposes:
Immediate:
Future:
To differentiate the lesson to meet current needs of each student
For differentiation in lesson planning
Conferring provides the teacher an opportunity to gain insight into individual student
learning. Through kid watching, questioning, and explicit teaching, the teacher can
determine how to best meet the specific needs of students. It is also a time to set goals for
the student to further their understanding. By taking notes, the teacher has an opportunity
for reflection and future lesson planning.
Think about your students
Before: What sources of data do you
have for looking at the whole child as a
mathematician to match needs?
Which groups are needed?
Who can I meet the needs of in a group,
rather one-to-one, or through whole
group?
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During: What would an
observant teacher be
watching for in a lesson?
Evidence like...
After: What
documentation/indication
would work for you to
determine next moves?
Teachers
Small group instruction
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Students & Stations
Train and Practice
Create classroom rules for Math time:
•
What does working independently look/sound like?
•
What does small group instruction look/sound like?
•
What does work station work look/sound like?
•
What does transitioning look/sound like?
Train and Practice Some More!
Introduce the new activities in large group
You may need to train and practice periodically
throughout the year!
Always introduce and practice a new “writing” activity
before it goes in a math station!
Make sure you have taught the games at the game
workstation before putting them out!
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12/9/2015
Lesson Structures for Small Group
Another approach
One approach
Before: Number Development work,
warm up, Number Talks
During:
skill, strategy focus for the
lesson with teacher model and student testdrive
After: meaningful practice in
Mathematics, Number Development, writing
about mathematics
Connect & Compliment:
Tell children why they’ve been pulled
together, highlight their strengths, state
strategy for today’s lesson
Teach:
brief demonstration, shared
practice, or example
Engage:
coach student in skill
development as they try out the strategy
Link: invite students to continue working
independently, applying and reapplying the
strategy practiced in new contexts
Organizing Your Math Block
Daily 5 in Literacy? Daily 3-4 in Math!
10-15 minute lesson introduction, three 15 minute
workstations
Two days of whole group instruction, three days of
workstation?
Any other ideas?
one example
8:50-9:05 Warm-up or morning stretch
9:05-9:30 Guided Practice – Mini-lesson
Whole group setting
9:30-10:15 Math Groups
Three 15 min. groups or two 20 min. groups or continue whole group
Guided Math Instruction – with small groups on known or unknown content
Other students participate in independent practice (math work stations)
10:15-10:20 Wrap-up Session
Whole group setting
Review problem of the day, share, collect work, etc.
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Guided Math
20-30 Minutes
•Small group reteach,
conferencing &/or extension
•Collaborative problem-solving
•Center Activities
•Manipulative discovery and
connections
Think-Aloud
10-15
Minutes
Core Lesson
30-60
Minutes
Review/
Assessment
10-30 Minutes
Total Time
120 Minutes
Model thinking process for
problem solving & test-taking
strategies
•Whole group standards-based
lesson
•Review important concepts
•Reflect or Assess
10-15
Think-Aloud
Minutes
30-60
Core Lesson
Minutes
Model thinking process for
problem solving & test-taking
strategies
•Whole group standards-based
lesson
Review/
Assessment
10-30 Minutes
•Review important concepts
Guided Math
20-30 Minutes
Small group reteach,
conferencing &/or extension
•Reflect or Assess
•Collaborative problem-solving
•Center Activities
•Manipulative discovery and
connections
Total Time
120 Minutes
Math Work Stations
While you are providing small
group instruction, what are the
rest of the students doing?
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12/9/2015
Work Stations
Writing
Games
Number
Development
Fact
Fluency
Technology
Geometry
Math Stations Should…
Look Like:
Students are working with math ideas.
Students are taking turns nicely.
Students are talking with their partners about
math.
Materials are put back in their places.
Students are on task.
Students are using materials like the teacher
modeled.
Teacher is not interrupted while working with a
group.
Sound Like:
Quiet voices so others can learn.
Using math vocabulary.
Talking with just your partner.
Making choices together.
“Let’s try this together.”
Feel Like:
I can do it!
I like to solve problems.
Calm
I like math!
Active engagement
Geometry Puzzles Station
Pattern Blocks
Pentominoes
Cuisenaire Rods
Polydrons
Tangrams
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Games Station
Card Games
Dice Games
Dominoes
Board Games
Software
Technology Station
Free iPad Apps for Math
Xtra Math
Cool Math
IXL Math
learnzillion
youcubed
Adapted Mind
Fact Fluency
Incremental Rehearsal
Human Calculator
Odyssey Math
x
4
9
24
48
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Writing Stations
I used to think...but now I know…
If I was (1 cm high..)
What is (subtraction)?
Which is (larger/smaller)?
Provide directions to (add with like denominators; use a protractor)
Which is bigger: ⅓ or ½ ?
Equal groups? Equal sharing? Partitioning?
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Self-assessment for student learning
Math Haiku
Your turn to write
Consider what you have heard so far about small group math instruction and
math work stations.
Complete this statement:
I used to think….but now I know...
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Number Station
number work activities at each student's independent level

strengthen their number work and problem solving skills, becoming more fluent in this strand

allow them to participate in a routine meant to strengthen skills

help them gain independent work skills/habits

allow them to work at their own levels and at their own pace – meeting each student’s needs.
Before and After
Ways to Make
Dash to the Century
Count by
Addition Card Draw
Meaningful Number Work
Number Work Focuses by Grade Level
*Start with the progressions document
*Use the standards to understand when students should develop mastery
(know from memory), apply strategies to solve, or demonstrate efficiency
with the standard algorithm
*Teach problem-solving in the whole group
Kindergarten
-Know number names and count sequence

Count to 100 by 1s

Count forward beginning from a given number within the known sequence (instead of having to begin with 1)

Understand the relationship between numbers and quantities; connect counting to cardinality

Count to answer, “how many?” questions about as many as 20 things
- Understand addition as putting together and adding to

Decompose numbers less than or equal to 10 into pairs in more than one way (10 frames)

For any number from 1-9, find the number that makes 10 when added to the given number (10 frames)
- Work with numbers 11-19 to gain foundations for place value

Compose and decompose numbers from 11-19 into ten ones and some further ones (10 frames)
- Analyze, compare, create and compose shapes

Compose simple shapes to form larger shapes
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Grade 1
Apply properties of operations as strategies to add and subtract
- Add and subtract within 20

Relate counting to addition and subtraction

Add and subtract within 20, demonstrating fluency for addition and subtraction
within 10
- Work with addition and subtraction equations

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are
true or false
- Extend the counting sequence

Read and write numerals in this range
- Understand place value

Understand that the two digits of a two-digit number represent amounts of tens and ones (10 frames)
- Reason with shapes and their attributes

Compose two-dimensional shapes to create a composite shape
Grade 2
Add and subtract within 20

Know from memory all sums of two one-digit numbers
- Understand place value

Understand that three digits of a three-digit number represent amounts of hundreds, tens, and ones

Count within 1,000; skip count by 5s, 10s, and 100s

Read and write numbers to 1,000 using base ten numerals, number names, and expanded form
- Use place value understanding and properties of operations to add and subtract

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900
Grade 3
Understand properties of multiplication and the relationship between multiplication and division

Apply properties of operations as strategies to multiply and divide

Understand division as an unknown-factor problem
- Multiply and divide within 100

Fluently multiply and divide within 100
- Use place value understanding and properties of operations to perform multi-digit arithmetic

Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of
operations, and/or the relationship between addition and subtraction

Multiply one-digit whole numbers by multiples of 10 in the range 10-90
- Develop understanding of fractions as numbers

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts

Understand a fraction as a number on the number line; represent fractions on a number line diagram

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size
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Grade 4
Gain familiarity with factors and multiples
- Generate and analyze patterns
- Generalize place value understanding for multi-digit whole numbers

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in
the place to its right
- Use place value understanding and properties of operations to perform multi-digit arithmetic

Fluently add and subtract multi-digit whole numbers using the standard operation
- Extend understanding of fraction equivalence and ordering

Compare two fractions with different numerators and different denominators
Grade 5
Write and interpret numerical expressions

Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols
Understand the place value system

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the
place to its right and 1/10 of what it represents in the place to its left

Read, write, and compare decimals to thousandths
Perform operations with multi-digit whole numbers and with decimals to hundredths

Fluently multiply multi-digit whole numbers using the standard algorithm
It’s Up to You!
It is always up to you as to how to use the time in your
math block. Just remember that you need to:
• address every student’s needs
• teach every student so he/she makes expected yearly
progress
• challenge every student in your classroom - high,
medium or low!
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Management Essentials: At your
table
What works:
★ Students in small group
What
works
for you?
★ Students out of small group
★ Whole room visual
Cues/Supports for routine
Plan, Dream, Implement, Reflect
Turn and Talk at your
table about what
you’d like to
implement.
What will you need?
What students will you target?
Who will you tell in your building/team/department?
What will be the measurement of your success in
implementation?
Plan to share out
Sources Cited and Resources for You
Debbie Diller, Making the Most of Small Groups (2007)
Marilyn Burns, Writing in Math Class (1995)
Cherly Rose Tobey, Mathematics Formative Assessment (2011)
Laney Sammons, Guided Math: A Framework for Mathematics Instruction 2010
Paula Kluth, From Tutor Scripts to Talking Sticks 2010
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Exit Ticket
We use your feedback.!
Thank you!
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