Hudson Valley RAEN Painted Cube Workshop July 24, 2015 - Final
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Hudson Valley RAEN Common Core Math Workshop July 24, 2015 Presenter: Patricia Helmuth
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Transcript of Hudson Valley RAEN Painted Cube Workshop July 24, 2015 - Final
Hudson Valley RAEN
Common Core Math WorkshopJuly 24, 2015
Presenter: Patricia Helmuth
The Standards for Mathematical Practice
...are a redefinition and a guide for what it means to do math and what it means to be a mathematically proficient student. The 8 Mathematical Practices (MPs) are what students should be doing in our classes at every level. Phil Daro, one of the writers of the CC math standards has said the MPs are a way to define the content of students mathematical character. Too many of our students say, "I am not a math person". They say that because to them, being a math person means already knowing the math content.
The 8 Standards of Mathematical Practice are a way of redefining what it means to be a "math person" - it's not how much math content you know, but more about your attitudes and what you do to make sense of and learn math.
The Standards of Mathematical Practice represent the ideal place for teachers and programs to begin their work to align mathematics instruction with the Common Core.
http://cunycci.pbworks.com/w/page/58415851/Math
MP 1: Make Sense of Problems and Persevere in Solving Them
Students…● Can explain the meaning of a problem and look for entry points to its
solution.● Analyze givens, constraints, relationships, and goals.● Plan a solution pathway rather than simply jumping into a solution
attempt.● Consider similar problems● Try special cases and simpler forms of the original problem in order to
gain insight into its solution.● Monitor and evaluate their progress and change course if necessary.● Check their answers to problems using a different method than the one
they used to solve the problem.● Continually ask, “Does this make sense?”● Understand the approaches of others to solving complex problems● Identify similarities and differences between different approaches.
http://cunycci.pbworks.com/w/page/69135418/Make%20sense%20of%20problems%20and%20persevere%20in%20solving%20them
Open-Ended and Non-Routine
Math Problems Should:
1. Have a low entry and high ceiling2. Promote discussion3. Allow/require students to make decisions4. Allow for different approaches and/or different solutions5. Be “problematic”6. Be accessible and extendable
Presenting problems before offering explanations so students “learn on the job” as opposed to showing them how to solve a problem and then giving them a similar problem to solve.
Mathematical Learning in the Common Core EraNYSED Common Core/TASC Math Teacher Learning & Leadership Institute
2/3 x 3/4 =
Create a real-world situation for the following problem:
2/3 x 3/4 Solve the problem you have created without using a rule, and explain your answer.
http://cunycci.pbworks.com/w/page/67582593/Mathematical%20Tasks%20with%20High%20Cognitive%20Demands
Cognitive Complexity
The Painted
Cube
Using 1-centimeter red cubes, Sally builds a 3 by 3 cube. Sally paints all of the faces of the of the big cube yellow. Then she breaks it back down into 1-centimeter cubes.
❏ How many of the 1-centimeter cubes have no yellow faces at all?
❏ Exactly one face painted yellow?
❏ Exactly two faces painted yellow?
❏ Exactly three faces painted yellow?
❏ More than three faces painted yellow?
http://nrich.maths.org/2322
Planning QuestionsDescribe how you solved the problem.
Can you think of any other way to solve the problem?What DOK Level do you think this is?
What would you want students to get from working on this problem?
What challenges do you think students would have in solving this problem?
What questions could you ask to support a struggling student?
Break Time
Open-Ended and Non-Routine
Math Problems Should:
1. Have a low entry and high ceiling2. Promote discussion3. Allow/require students to make decisions4. Allow for different approaches and/or different solutions5. Be “problematic”6. Be accessible and extendable
Presenting problems before offering explanations so students “learn on the job” as opposed to showing them how to solve a problem and then giving them a similar problem to solve.
Mathematical Learning in the Common Core EraNYSED Common Core/TASC Math Teacher Learning & Leadership Institute
Extension Activity #11. Begin by working on the table by yourself2. Compare your results with someone else3. Discuss how you know the table is correct4. Make a list of what you would want your students
to get out of this activity5. Make a list of problems you think your students
encounter in this activity6. What questions could you ask to facilitate
productive struggle?7. Share Out
Extension Activity #21. Each group chooses a card2. Create a graph that would represent the number of faces painted that is
on your card3. Does your graph represent a cubic, quadratic, constant, or linear
relationship? How do you know?4. Does your graph represent a function? How do you know?5. Can you create a rule for your graph that would predict the number of
faces painted for any side length?6. Discuss what you would want your students to get out of this set of
activities including vocabulary.7. Discuss any misconceptions of difficulties you think your students might
encounter with this activity.8. Discuss questions you could ask to facilitate productive struggle.9. Share Out
Reflection1.What math did we “do”?2.How do you think this activity can benefit
students?3.What connections between mathematical
concepts can this activity help students to “see”?
4.How will you use this activity in your class?
Student Created List
Contact Information
Patricia HelmuthAdult Numeracy Consultant and EducatorHudson Valley Staff Developers Regional Network
845-798-7869
