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Warm Up
2012-2013 CIE
2012 State Math Assessments
The Structure is the Standards
Shift 2 – Coherence
Erin’s Problems
Break
Learning Progressions
Practice with Progression
NCTM Article – Part III - Teaching in Grades 3 & 4
Please remove the document on the left hand side of the folder titled:
New York State PreK - 8 Common Core Learning Standards for
Mathematics What is in this document and how can we
use it to help in our planning?
PK-8 Math CCLS
How can you use a calculator with a broken 7 key to solve the following equation?
Warm Up
= 4 x 7
•Explain your strategy to your neighbor?
Guiding Questions◦What does it mean to deepen and
broaden the citywide instructional expectations?
◦How might I begin planning for next year?
◦Why are three specific competencies from Danielson’s Framework called out and why where they selected?
2012-2013 Citywide Instructional Expectations
What did we see in the math assessments that◦we expected? ◦was surprising? ◦was particularly challenging for students?
What are the instructional implications? How will we prepare our students to
handle the increased rigor?
What can we take away from this year’s state math assessments?
Instructional Next StepsNoticings
Article by Phil Daro, Bill McCallum & Jason Zimba
Read the article and HIGHLIGHT or underline at least 3 (x > 3) items that resonate with you.
The Structure is the Standards
Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
Shift 2 - Coherence
Erin has 6 boxes. Each box has 7 caterpillars in it. How many caterpillars does Erin have?
Problem A
Erin has 6 beetles. She has 7 times as many caterpillars as beetles.
How many caterpillars does Erin have?
Problem B
As a table, discuss how Problems A and B are alike and different.
Use the Venn Diagram to help you chart the similarities and differences.
Compare and Contrast
Read the two word problems. Then answer the questions below. (Worksheet
Provided)
1. What single equation can be used to answer both questions? Use words or diagrams to explain why this equation answers both questions.
2. What do the numbers in your equation mean when it is used to solve problem A?
3. What do the numbers in your equation mean when it is used to solve problem B?
Erin’s Problems
Use the following questions to guide your discussion:1. What changed when Problems A and B were
combined and the three questions were added? 2. What was challenging as you worked on this
problem? Why? What was easy?3. What CCLS is this task aligned to and why?4. How can this support you in your work as a
coach/lead teacher?
Aligning Erin’s Problem
GUIDING QUESTIONS:◦What are the Common Core Learning
Progressions?
◦How can we use them to deepen our understanding of the CCLS and the sequence of teaching and learning that prepares students for success?
Learning Progressions
The Common Core State Standards in mathematics were built on progressions.◦ Narrative documents describing the progression
of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.
◦ These documents were spliced together and then sliced into grade level standards. From that point on the work focused on refining and revising the grade level standards.
Introduction of the Learning Progressions
They can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics.
This would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks.
Introduction of the Learning Progression
Read the selected sample of “Progressions for the Common Core State Standards in Mathematics”
As you read, identify 2 to 4 significant sentences or phrases from the text.
Choose one of them and write it on an index card.
Put the index cards face down in the middle of the table and mix them up.
Each person selects a card, reads the sentence or phrase and comments on it.◦ *If you choose your own, put it back face down.
Brief reading of the Progressions
The answer is 15 boxes. Write three word problems as tools to build learning from one grade to the next. ◦ *Ignore the directions at the top of the handout.
Practice
What did you learn about trying to create word problems that progress from grade to grade?
Did you encounter any difficulties? Were there any “aha” moments?
Share
Part 3 of 5 By Angela T. Barrow and Shannon Harmon
NCTM Article – Part II – Getting Started in Grades K-2
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