Transcript Common Core 6th and 7th Grade Math

Common Core
Grades 6 – 8 Math
Stacy Wozny
[email protected]
February 18th, 2013
Workshop Norms
O Listen as a friend
O Value differences
O Maintain professionalism
O Limit sidebar conversations
O Limit use of technology
O Participate actively
O Work cooperatively
Warm-Up
O Complete at least one of the three
problems for your grade level on the
handout.
O What specific Common Core
Standards are addressed by the
problem you chose?
O What mathematical practices are
addressed by the problem you
chose?
Exploring Resources: NRICH (http://nrich.maths.org)
www.nrichmaths.org
The challenges in generating rich
mathematical tasks/problems are:
O Being mathematical and sustaining the focus
on mathematics
O Believing that all students can engage in
mathematical inquiry and are learning
O Balancing the freedom, discussion and
frustrations that go with rich activity with the
need to support students to understand new
ideas.
Goal of the Session
O Explore and Experience tasks/problems
that align with the Common Core
Standards
What does it mean to
understand mathematics?
"Understand" is used in these
standards to mean that students can
explain the concept with mathematical
reasoning, including concrete
illustrations, mathematical
representations, and example
applications.
Dr. James Williams, NCCTM, October, 2011
What does it mean to
understand mathematics?
Students who understand a concept can
a. use it to make sense of and explain
quantitative situations (see SMP 1, 2,
and 4)
b. incorporate it into their own
arguments and use it to evaluate the
arguments of others (see SMP 1, 3)
Dr. James Williams, NCCTM, October, 2011
What does it mean to
understand mathematics?
Students who understand a concept
can:
c. bring it to bear on the solutions to
problems (see SMP 1, 4, and 8)
d. make connections between it and
related concepts (see SMP 1, 2, 3,
4, 7, and 8)
Dr. James Williams, NCCTM, October, 2011
Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving
them
6. Attend to precision
2. Reasoning
and
3. Explaining
4. Modeling
and
5. Using tools
Adapted from work of William McCallum
7.Seeing structure
and
8. Generalizing
Common Core Domains and Clusters
6th Grade
Ratios and
Proportional
Relationships
7th Grade
Ratios and
Proportional
Relationships
8th Grade
Functions
• Understand ratio concepts and use ratio reasoning
to solve problems.
• Analyze proportional relationships and use them to
solve real-world and mathematical problems.
• Define, evaluate, & compare functions.
• Use functions to model relationships between
quantities.
Proportional Reasoning
O Complete your grade level problem.
O If time permits, complete another
problem from a different grade
level.
Proportional Reasoning
O What specific Common Core
Standards are addressed by your
problem?
O What mathematical practices are
addressed by your problem?
O How can you assess student
understanding from this problem?
Common Core Domains and Clusters
6th Grade
Probability &
Statistics
7th Grade
Probability &
Statistics
8th Grade
Probability &
Statistics
• Develop understanding of statistical variability.
• Summarize and describe distributions.
• Draw informal comparative inferences about two
populations.
• Investigate patterns of association in bivariate data.
Age Gauge
O Guess each person’s age as the
slide show plays.
O Record the name and guess on
the handout.
Age Gauge
O How can we determine who is the
best guesser?
Age Gauge
O Using this collected data, what
questions might you ask your
students?
Age Gauge
Using your differences:
O Find the measures of center and
measures of variability for your
data.
O Who is the best guesser at your
table and why?
O What does the perfect guesser look
like?
Age Gauge
Representation of data:
O With a partner, create a stacked box
plot
O Based on the results, determine the
best guesser.
O What does the representation look
like for the perfect guesser?
Age Gauge
Representation of data:
O How can a scatter plot answer the
question of who is the best guesser?
O Make a scatter plot showing (actual
age, guessed age)
O What does the representation look
like for the perfect guesser?
O What is the linear equation for the
perfect guesser?
Age Gauge
Representation of data:
O Informally fit a straight line to your
data.
O Informally write an equation for
your line.
O Interpret the slope within the
context of the problem.
O Write a statement about your
guessing based on your scatter plot
and equation.
Age Gauge
Representation of data
O Who is the best guesser in your
group?
O Write an argument defending your
choice for the best guesser in your
group.
Age Gauge
O How could you facilitate a whole
class comparison?
O What mathematical practices are
addressed by this task?
O What specific content standards are
covered in this task?
O How does this task assess student
understanding?
3-ACT MATH
O Act One
Introduce the central conflict of your
story/task clearly, visually, viscerally, using
as few words as possible.
O Act Two
The protagonist/student overcomes
obstacles, looks for resources, and develops
new tools.
O Act Three
Resolve the conflict and set up a sequel or
extension.
From http://blog.mrmeyer.com/?p=10285
3-ACT MATH
File Cabinet ACT 1:
ACT 2: What do you want to know from
ACT 1? What questions could be asked
from ACT 1?
ACT 3: The result
From Andrew Stadel 3-Act Math Tasks
3-ACT MATH
Taco Cart ACT 1:
ACT 2: What information would be
useful to know here? What questions
could be answered from Act 1?
ACT 3: The result
From Dan Meyer 3-Act Math Tasks
3-ACT MATH
Ticket to Ride ACT 1:What questions
could be answered from Act 1?
ACT 2: What information would be
useful to know here?
Link 1, 2, 3, 4, 5
ACT 3: The result
From Dan Meyer 3-Act Math Tasks
3-ACT MATH
O How could you use 3-ACT Math in your
classroom?
O What are the advantages to using 3ACT MATH?
O What mathematical practices are
demonstrated when students
experience 3-ACT MATH?
Common Core Domains and Clusters
6th Grade
Geometry
7th Grade
Geometry
8th Grade
Geometry
• Solve real world and mathematical problems
involving area, surface area, and volume.
• Solve real world and mathematical problems
involving angle measure, area, surface area, and
volume.
• Solve real world and mathematical problems
involving volume of cylinders, cones, and spheres.
Geometry
O Complete at least one of your grade
level problems.
O How does this problem assess
student understanding?
O What mathematical practices are
addressed by this problem?
O What specific content standards are
covered in this problem?
Wrap-Up
O Reflect on your instruction: How can you use
problems/tasks to make the connection among the
Standards for Mathematical Practice and the
Common Core Standards?
O On a post-it note: What do you need for future
professional development?