common core grades 6 – 8 math stacy wozny [email protected] february 18 th, 2013
TRANSCRIPT
Workshop NormsOListen as a friendOValue differencesOMaintain professionalism
OLimit sidebar conversationsOLimit use of technology
OParticipate activelyOWork cooperatively
Warm-UpOComplete at least one of the three
problems for your grade level on the handout.
OWhat specific Common Core Standards are addressed by the problem you chose?
OWhat mathematical practices are addressed by the problem you chose?
Exploring Resources: NRICH (http://nrich.maths.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 SessionOExplore 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 cana. 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
1. Make sense of problems and persevere in solving them6. Attend to precision
2. Reasoning and3. Explaining
4. Modeling and5. Using tools
7.Seeing structure and8. Generalizing
Adapted from work of William McCallum
Standards for Mathematical Practice
Common Core Domains and Clusters
6th Grad
e Ratios and Proportiona
l Relationshi
ps
• Understand ratio concepts and use ratio reasoning to solve problems.
7th Grad
e Ratios and Proportiona
l Relationshi
ps
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
8th Grad
e Functions
• Define, evaluate, & compare functions.• Use functions to model relationships between
quantities.
Proportional ReasoningOComplete your grade level problem.
O If time permits, complete another problem from a different grade level.
Proportional ReasoningOWhat specific Common Core
Standards are addressed by your problem?
OWhat mathematical practices are addressed by your problem?
OHow can you assess student understanding from this problem?
Common Core Domains and Clusters
6th Grad
e Probability
& Statistics
• Develop understanding of statistical variability.• Summarize and describe distributions.
7th Grad
e Probability
& Statistics
• Draw informal comparative inferences about two populations.
8th Grad
e Probability
& Statistics
• Investigate patterns of association in bivariate data.
Age Gauge
OGuess each person’s age as the slide show plays.
ORecord the name and guess on the handout.
Microsoft PowerPoint Presentation
Age Gauge
OHow can we determine who is the best guesser?
Age Gauge
OUsing this collected data, what questions might you ask your students?
Age GaugeUsing your differences:OFind the measures of center and
measures of variability for your data.
OWho is the best guesser at your table and why?
OWhat does the perfect guesser look like?
Age GaugeRepresentation of data:OWith a partner, create a stacked box
plotOBased on the results, determine the
best guesser. OWhat does the representation look
like for the perfect guesser?
Age GaugeRepresentation of data:OHow can a scatter plot answer the
question of who is the best guesser?OMake a scatter plot showing (actual
age, guessed age)OWhat does the representation look
like for the perfect guesser?OWhat is the linear equation for the
perfect guesser?
Age GaugeRepresentation 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.OWrite a statement about your
guessing based on your scatter plot and equation.
Age GaugeRepresentation of dataOWho is the best guesser in your
group?OWrite an argument defending your
choice for the best guesser in your group.
Age GaugeOHow could you facilitate a whole
class comparison?
OWhat mathematical practices are addressed by this task?
OWhat specific content standards are covered in this task?
OHow does this task assess student understanding?
3-ACT MATHO Act One
Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.
O Act TwoThe protagonist/student overcomes obstacles, looks for resources, and develops new tools.
O Act ThreeResolve 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 MATHOHow could you use 3-ACT Math in your
classroom?OWhat are the advantages to using 3-
ACT MATH?OWhat mathematical practices are
demonstrated when students experience 3-ACT MATH?
Common Core Domains and Clusters
6th Grad
e Geometry
• Solve real world and mathematical problems involving area, surface area, and volume.
7th Grad
e Geometry
• Solve real world and mathematical problems involving angle measure, area, surface area, and volume.
8th Grad
e Geometry
• Solve real world and mathematical problems involving volume of cylinders, cones, and spheres.
GeometryOComplete at least one of your grade
level problems.OHow does this problem assess
student understanding?OWhat mathematical practices are
addressed by this problem?OWhat specific content standards are
covered in this problem?
Wrap-UpO 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?