“We live in a time of vast changes that
include
accelerating
globalization,
mounting quantities of information, the
dominating influence of science and
technology, and the clash of civilizations.
Those changes call for new ways of learning
and thinking in school, business, and the
professions.”
-Howard Gardner
Five Minds for the Future (2007)
http://www.corestandards.org
Phase 1 (2011-2012)
Phase 2 (2012-2013)
Full Implementation
Grade K
Phase 3 (2013-2014)
Full Implementation
Begin Implementation of
Literacy Standards in ALL
Content Areas for Grades
6-12
Grades K-1
Full Implementation of
Literacy Standards in ALL
Content Areas for Grades
6-12
Full Implementation
Grades K-2
Phase 4 (2014-2015)
Full Implementation
Grades K-12
Implementation of a
Blended Curriculum (CCSS
and Supplemental NGSSS PARCC Assessments
Aligned to FCAT 2.0 and
Aligned to CCSS
EOCs) for Grades 3-12
Begin Implementation of
Rich and Complex Text and
Informational Text for
Continue Implementation
Grades K-12
of Rich and Complex Text
and Informational Text for
Grades K-12
Continue Implementation
of Rich and Complex Text
and Informational Text for
Grades K-12
http://www.fldoe.org/bii/pdf/CCSS-ImplementationTimeline.pdf
3
“The Standards for Mathematical Practice are unique in
that they describe how teachers need to teach to ensure
their students become mathematically proficient. We were
purposeful in calling them standards because then they
won’t be ignored.” - Bill McCallum
Develops dispositions and habits of mind
“Characteristic of an educated person”
• Precision in thought
• Precision in the use of language and terms
• Precision of argument
• Sense making happens through conversations
-Jason Zimba
http://youtu.be/9pKcO9E4Flw
5
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
6
Performance Task:
Open you Common Core
Book to the Standards for
Mathematical Practice
Read through the Practices
Think of a few questions that
you might use to help
students develop these habits
of mind.
1. Make sense of problems and persevere in
solving them
What is the problem asking?
How would you describe the problem?
How would you describe what you are trying to find?
What information is given in the problem?
What steps have your already tried?
What might you change?
What is another strategy that you might try?
How might you use one of your previous problems to
help you?
How else might you organize… represent.. show…?
How will you know if your answer makes sense?
2. Reason abstractly and quantitatively
What do the numbers used in the problem
represent?
What is the relationship of the quantities?
What is the relationship between ___ and ____?
How is ___ related to ___?
What properties might you use to find a solution?
How do you know your answer is reasonable?
3. Construct viable arguments and
critique the reasoning of others
How did you decide what the problem was asking you to
find?
How did you test whether your approach worked?
What other methods did you try? Did they work? Why
or why not?
What can you tell us about a different method?
How does your representation support your work?
What were you considering when …?
How can you be sure that …?
What evidences would support your solution?
4. Model with mathematics
What model could you construct to represent
the problem?
What are some ways to represent the
quantities?
How would it help to create a diagram, graph,
table …?
What are some ways to visually represent …?
What formula might apply in this situation?
How would you change your model if….?
5. Use appropriate tools strategically
You’ve heard of smart
computers? Well, these are
graduated cylinders.
What could you use to help solve the problem?
What mathematical tools can be used to visualize and
represent the situation?
What can using a ____ show us that ____ may not?
In which situation might it be helpful to use … a graph
..., number line…, rule…, diagram …, calculator …,
manipulative?
In what situations might it be more informative or helpful
to use...?
Why did you decide to use___ ?
6. Attend to Precision
How are you showing the meaning of the quantities?
What symbols or mathematical notations are important
in this problem?
What mathematical language…, definitions…,
properties can you use to explain … ?
How can you mathematical terms (vocabulary) in your
explanation?
What does that mean?
7.Look for and make sense of structure
What do you notice when…?
What patterns do you find in…?
How does this relate to … ?
In what ways does this problem connect to
other mathematical concepts?
What rule did you use to solve this
problem?
How is this like… ?
Explain how this strategy works in other situations?
What do you notice about…?
What is happening in this situation?
What would happen if… ?
What mathematical rule applies to this situation?
What predictions or generalizations can this pattern
support?
What mathematical consistencies do you notice?
Standard or Benchmark Aligned
to Course Description
• Guides the development of
the lesson beginning with the
desired outcome
Learning Goals
Engaging Lesson
Formative, Interim, and/or
Summative Assessments
• Includes appropriate and
meaningful activities that engage
students in the learning process,
address common
misconceptions, and incorporate
higher-order thinking skills
• Describes what students should
know and be able to do
• Includes essential questions and
• Rubrics to define levels of
knowledge acquisition
• Provides multiple sources of
student data to guide decisions
about adjusting instruction
and/or providing interventions
25
Course Requirements and Standards
“Chunks” or Big Ideas
Major Learning Goals
Progression Scales for Major Learning
Goals
Progress Monitoring Assessments
26
Follow precisely a multistep procedure when
carrying out experiments, taking measurements,
or performing technical tasks.
LACC.68.RST.3.7
Integrate quantitative or technical information
expressed in words in a text with a version of that
information expressed visually (e.g., in a
flowchart, diagram, model, graph, or table).
LACC.68.WHST.1.1 Write arguments focused on discipline-specific
content.
LACC.68.WHST.1.1b Support claim(s) with logical reasoning and
relevant, accurate data and evidence that
demonstrate an understanding of the topic or text,
using credible sources.
LACC.68.RST.1.3
MACC.7.G.2.6
MACC.7.EE.2.3
Solve real-world and mathematical problems involving area, volume and surface area of
two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes,
and right prisms.
Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.
MACC.7.EE.2.4
Use variables to represent quantities in a real-world or mathematical problem, and construct
simple equations and inequalities to solve problems by reasoning about the quantities.
MACC.7.EE.2.4a
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q,
and r are specific rational numbers. Solve equations of these forms fluently. Compare an
algebraic solution to an arithmetic solution, identifying the sequence of the operations used
in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm.
What is its width?
MACC.8.G.3
Solve real-world and mathematical problems involving volume of cylinders, cones and
spheres.
Know the formulas for the volume of cones, cylinders, and spheres and use them to solve
real-world and mathematical problems.
Describe qualitatively the functional relationship between two quantities by analyzing a
graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a
graph that exhibits the qualitative features of a function that has been described verbally.
MACC.8.G.3.9
MACC.8.F.2.5
SC.8.N.1.1 Define a problem from the eighth grade curriculum using
appropriate reference materials to support scientific
understanding, plan and carry out scientific investigations of
various types, such as systematic observations or
experiments, identify variables, collect and organize data,
interpret data in charts, tables, and graphics, analyze
information, make predictions, and defend conclusions.
SC.8.P.8.2 Differentiate between weight and mass recognizing that
weight is the amount of gravitational pull on an object and is
distinct from, though proportional to, mass.
SC.8.P.8.3 Explore and describe the densities of various materials
through measurement of their masses and volumes.
Kent Treadgold
7th grade
Density
https://www.teachingchannel.org/videos/teaching-density?fd=1#
http://youtu.be/iHFHzjjHNsg
Task: As you view the
video, Making Sense of
Density, record where
you see the Standards for
Mathematical Practice
being infused.
Florida Common Core
– http://www.fldoe.org/schools/ccc.a
sp
– http://www.fldoe.org/schools/Blast
Off.asp
Common Core State Standards for
Mathematics
– http://www.corestandards.org
CPALMS
– http://www.floridastandards.org
Parent Roadmaps to Common
Core Standards
– http://cgcs.schoolwires.net/domain
/36
Parents' Guides to Student Success
– http://www.pta.org/4446.htm
The Teaching Channel
– https://www.teachingchannel.org
Inside Mathematics
– http://www.insidemathematics.or
g/index.php/common-corestandards
Illustrative Mathematics
– http://illustrativemathematics.org
Tools for the Common Core
– http://commoncoretools.me/
31
http://www.corestandards.org
The Need…
“Few will have the greatness to bend
history itself; but each of us can work
to change a small portion of events,
and in the total of all those acts will
be written the history of this
generation.”
– Robert F. Kennedy
Bureau of Curriculum and Instruction
Dr. Karol Yeatts
Director-Office of Mathematics and Science
karol.yeatts@fldoe.org
Dr. Jackie Speake
Science Curriculum Specialist
Jackie.speake@fldoe.org