Regional Educational Laboratory (REL) Midwest and the
Great Lakes West Comprehensive Center present
Making Connections:
Improving Mathematics Instruction and Interventions
Within a Response to Intervention Framework
Cathy Shide, www.movingtocommoncore.com
cathy.integrated@bluetie.com
FOCUS ON FLUENCY
BRIDGING THE GAPS
Developed by Cathy Shide, Consultant
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Goals for the
Session
•
•
•
Introduce the fluencies required at each
grade level in grades K-12 as specified in the
CCSSM
Understand that balanced emphasis requires
that teachers create opportunities for
students to develop fluencies
Understand how to apply the research to
develop fluency
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What is fluency?
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•
ABalancedApproach:Fluencyhttp://ww
w.youtube.com/watch?v=ZFUAV00bTw
A
Video of Authors of CCSSM
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What is fluency?
• Fluent in the Standards means “fast and
accurate.” It might also help to think of
fluency as meaning the same thing as
when we say that somebody is fluent in
a foreign language: when you’re fluent,
you flow. Fluent isn’t halting, stumbling,
or reversing oneself.
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Fluency is related to “quickness”, but it is not just
about time. It is about ease of use and
confidence in proceeding. For fact fluency, it is
about remembering facts with automaticity.
Procedural fluency is related to things you do
“without having to stop repeatedly to determine
next steps.” It enables students to get to
application, problem solving, and increased
complexity much faster. It facilitates the
development of deeper understanding. Fluency
helps students access their answers through
different vantage points.
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Fluencies from
Listserv question
• Computational fluencies – mental recall
of facts and beyond!
• Procedural fluencies – algorithms and
properties of arithmetic
• Conceptual fluencies – vocabulary!
• Representational fluencies
• Algebraic fluencies
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Grade
K
1
2
3
4
5
6
7
8
Required Fluency - http://engageny.org/wpcontent/uploads/2011/07/CCSSFluencies.pdf
Add/subtract within 5
K.OA.5
Add/subtract within 10
1.OA.6
Add/subtract within 20
2.OA.2
Add/subtract within 100 (pencil and paper)
2.NBT.5
Multiply/divide within 100
3.OA.7
Add/subtract within 1000
3.NBT.2
Add/subtract within 1,000,000
4.NBT.4
Multi-digit multiplication
Addition/subtraction of fractions
4.NBT.5
5.NF.1
Whole number and decimal operations
5.NBT.5
Multi-digit division
6.NS.1
Multi-digit decimal operations
6.NS.3
Operations with rational numbers
7.NS.1
Solve equations px + q = r, p(x + q) = r
7.EE.4a
Solve linear equations in one variable
8.EE.7
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High School Required Fluency PARCC Content Frameworks
Computing fluently with positive and negative fractions
and decimals.
Applying ratio reasoning in real-world and mathematical
problems
Solve real-world and mathematical problems involving
angle measure, area, surface area, and volume
Because important standards for college and career
readiness are distributed across grades and courses,
systems for evaluating college and career readiness
should reach as far back in the standards as Grades 6-8
A.REI.3
Solve linear equations and inequalities in one variable,
including equations with coefficients represented by
9
letters.
Computational
Fluency
• Multiply 16 x 35 mentally
• Only write an answer
• Share your strategies in your
table
• 384/16
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Strategies vs
Procedures
• Counting on
• Patterns
–Fact families
–Doubles
–Times 5, times 9,
square numbers
• Composing and
decomposing
numbers to . . .
– Make a ten
– Make a double
– Make a known fact
– Make friendly
numbers
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Fact fluency
development
• Follows the progression of learning
– concrete, representations or
pictures, abstract.
• Teacher needs to choose problems
strategically
• Time spent with strategies in
different context
Developed by Cathy Shide, Consultant
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Flash Cards &
Games
• Look at the games that are described in
the handout
• What fluency would the game help to
build in your students?
• How could this game be used or
modified to help struggling learners.
Developed by Cathy Shide, Consultant
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Math Wars
• A player takes two cards and adds the
numbers and records the sum.
• Next player repeats this process during his
turn
• The player with the highest sum gets the
cards.
• Continue play until all cards are done.
• See which player has the most cards.
• Make Adjustments to this game!
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“If a child can't
learn the way we
teach, maybe we
should teach the
way they learn.”
Ignacio Estrada
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Resources
• Number Talks – Helping Children Build
Mental Math and Computation Strategies,
Grades K-5, Sherry Parrish author, from Math
Solutions
• Number Talks http://www.insidemathematics.org/index.ph
p/classroom-video-visits/number-talks
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High School
Strategies
• Increasing Decreasing Quantities lesson
http://map.mathshell.org.uk/materials/lessons.php
?taskid=210&subpage=concept
• Pre-Assessment Probes – Uncovering Student
Thinking in Mathematics, Grades 6-12: 30 Formative
Assessment Probes for the Secondary Classroom
• Secondary Number Talks http://www.sandi.net/cms/lib/CA01001235/Centri
city/Domain/217/middle_level_bank.pdf
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Recommendation 2
• Instructional materials should
focus on whole numbers in K-5
and rational numbers grades 4-8
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Recommendation 3
• Instruction during the intervention
should be explicit and systematic. . .
. Models of proficient problem
solving, verbalization of thought
processes, guided practice,
corrective feedback, and frequent
cumulative review
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Recommendation 5
• Intervention materials should include
opportunities for students to work with
visual representations of mathematic
ideas and interventions should be
proficient in the use of visual
representations of mathematical ideas.
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Recommendation 6
• Interventions at all grade levels should
devote about 10 minutes in each session
to building fluent retrieval of basic
arithmetic facts.
–K-2 efficient counting
–2-8 = knowledge of properties of
arithmetic (page 90 of CCSSM)
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Recommendation 7
&8
• Monitor the progress of students
receiving supplemental instruction and
other students who are at risk.
• Include motivational strategies in tier 2
and tier 3 interventions
–Allow students to chart their progress
and to set goals for improvement.
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