Train the Trainers

COMMON CORESTANDARDS

Harnett County SchoolsSpring, 2011

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We will examine the Common Core State Standards for Mathematics and discuss implications for all grade levels; and prepare for teacher training on the new standards.

Content Objectives

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We will analyze the CCSS for Mathematics through:◦ completion of a jigsaw activity.◦ examination of the Mathematical Practices.◦ evaluation of the grade level changes in grades

K-5.◦ evaluation of traditional mathematics problems.

Language Objectives

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When you think about using mathematics, what comes

to mind?

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On a note card, write a preconception about mathematics.

Write one explanation of how the preconception impacts instruction.

Preconceptions About Mathematics

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“Mathematics is about learning to compute” (Donovan& Bransford, 2005, p. 220).

“Mathematics is about following rules to guarantee correct answers” (Donovan & Bransford, p. 220).

“Some people have the ability to do math and some don’t” (Donovan & Bransford, p. 221).

Preconceptions About Mathematics

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Percent Responding with these Answers

Grades 7 12 17 12 and 17

1st & 2nd 5% 58% 13% 8%

3rd & 4th 9% 49% 25% 10%

5th & 6th 2% 76% 21% 2%

8 + 4 = [ ] + 5

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Types of Math Problems Presented

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How Teachers Implemented Making Connections Math Problems

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The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms.

The emphasis on understanding is evident in the steps of a typical Japanese lesson.

•Teacher instructs students in a concept or skills.

•Teacher solves example problems with the class.

•Students practice on their own while the teacher assists individual students.

•Teacher poses a thought provoking problem.

•Students and teachers explore the problem.

•Various students present ideas or solutions to the class.

•Teacher summarizes the class solutions.

•Students solve similar problems.

Lesson Comparison:Japan and United States

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Hong Kong had the highest scores in the most recent TIMMS.

Hong Kong students were taught 45% of objectives tested.

Hong Kong students outperformed US students on US content that they were not taught.

US students ranked near the bottom.

US students

‘covered’ 80% of TIMMS content.

US students were outperformed by students not taught the same objectives.

Hong Kong / US Data

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Mathematical Practices

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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.

Standards for Mathematical Practices

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Review the assigned Standards for Mathematical Practice.

Share with your table what your practice was about.

Discuss the following question:

What does this look like in ____ grade?

Mathematical Practices Jigsaw

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What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know?

What do you notice about the relationship between area and perimeter?

Math Time!

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Discuss the following at your table:

◦What thinking and learning occurred as you completed the task?

◦What mathematical practices were used?

◦What are the instructional implications?

Table Talk

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1. What is the area of this rectangle?2. What is the perimeter of this rectangle?

Compared to….

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10

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The value of the common core is only as good as the implementation of the mathematical practices.

What if we didn’t have a requirement for math – how would we lure students in?

~ Jere Confrey

Something to Think About

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Mile wide and inch deep does not work.

The task ahead is not so much about how many specific topics are taught; rather, it is more about ways of thinking.

To change students’ ways of thinking, we must change how we teach.

Lessons Learned

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Format and Structure of the

Common Core State Standards

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Mathematical Practices

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StandardsDomain

Grade

Level

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Standards

DomainConceptua

l Categories

Standards

Cluster

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Glossary and Tables

Common Core Resources

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Property Table

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What’s New, Better, and Different?

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Focus and coherence◦ Focus on key topics at each grade level◦ Coherent progression across grade level

Balance of concepts and skills◦ Content standards require both conceptual

understanding and procedural fluency

Mathematical practices◦ Fosters reasoning and sense-making in

mathematics

College and career readiness◦ Level is ambitious but achievable

Common Core Attributes

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Grade or course introductions give 2- 4 focal points

K-8 presented by grade level

Organized into domains that progress over several grades

High school standards presented by conceptual theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability)

Standards for Mathematical Content

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Teachers are the next step

If teachers just swap out the old standards and put the new CCSS in the old boxes:

◦ old systems and procedures◦ the old relationships◦ old instructional materials formats◦ old assessment tools

Old Boxes

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Grade level changes

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Kindergarten New to Kindergarten:

Fluently add and subtract within 5 (K.CC.5)

Compose and decompose numbers from 11 to 19 into tens and ones (K.NBT.1)

Non-specification of shapes (K.G)

Identify shapes as two-dimensional or three-dimensional (K.G.3)

Compose simple shapes to form larger shapes (K.G.6)

Moved from Kindergarten:Equal Shares (1.02)Calendar & Time

(2.02)Data Collection (4.01,

4.02)Repeating Patterns

(5.02)

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First Grade New to 1st Grade:

Properties of Operations -Commutative and Associative (1.0A.3)

Counting sequence to 120 (1.NBT.1)

Comparison Symbols (<, >) (1.NBT.3)

Defining and non-defining attributes of shapes (1.G.1)

Half-circles, quarter-circles, cubes (1.G.2)

Relationships among halves, fourths and quarters (1.G.3)

Moved from 1st Grade: Estimation (1.01f)Groupings of 2’s, 5’s

and 10’s to count collections (1.02)

Fair Shares (1.04)Specified types of data

displays (4.01)Certain, impossible,

more likely or less likely to occur (4.02)

Sort by two attributes (5.01)

Venn Diagrams (5.02)Extending patterns

(5.03)

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Second Grade New to 2nd Grade:

Addition with rectangular array (2.OA.4)

Count within 1,000 by 5s, 10s, 100s (2.NBT.2)

Mentally add and subtract by 10 & 100 (2.NBT.8)

Measurement concepts (2.MD.2, 2.MD.4, 2.MD.5, 2.MD.6,)

Money (2.MD.8)Line Plots, Picture

graphs, bar graphs (2.MD.9, 2.MD.10)

Moved from 2nd Grade:Estimation (1.01e,

1.04b)Temperature (2.01b)Cut and rearrange 2-D

and 3-D figures (3.02)Symmetric and

congruent figures (3.03a, 3.03b)

Venn diagrams and pictographs (4.01)

Probability (4.02)Repeating and

growing patterns (5.01)

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Third Grade New to 3rd

Grade:◦Area and

perimeter (3.MD.5, 3.MD.6, 3.MD.7, 3.MD.8)

Moved from 3rd Grade:◦Permutations and

combinations (4.02, 4.03)◦Rectangular

coordinate system (3.02)◦Circle graphs

(4.01)

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Fourth Grade New to 4th Grade:

◦ Factors and multiples (4.OA.4)◦ Multiply a fraction by

a whole number (4.NF.4)

◦ Conversions of measurements within the same number system (4.MD.5, 4.MD.6,

4.MD.7)◦ Lines of symmetry

(4.G.3)

Moved from 4th Grade:◦ Coordinate system

(3.01)◦ Transformations (3.03)◦ Line graphs and bar

graphs (4.01)◦ Data-median, range,

mode, comparing data sets (4.03)

◦ Probability (4.04)◦ Number relationships

(5.02, 5.03)

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Fifth Grade New to 5th grade:

◦ Patterns in zero when multiplying (5.NBT.2)

◦ Extend understanding of multiplication and division of fractions (5.NF.3, 5.NF.4, 5.NF.5, 5.NF.7)

◦ Conversions of measurements within the same system (5.MD.1)

◦ Volume (5.MD.4, 5.MD.5◦ Coordinate System

(5.G.1, 5.G.2)◦ Two-dimensional figures-

hierarchy (5.G.3, 5.G.4)◦ Line plot to display

measurements (5.MD.2)))

Moved from 5th grade:◦ Estimate measure of

objects from one system to another system (2.01)

◦ Measure of angles (2.01)◦ Describe triangles and

quadrilaterals (3.01)◦ Angles, diagonals,

parallelism and perpendicularity (3.02, 3.04)

◦ Symmetry-line and rotational (3.03)

◦ Data-stem-and-leaf plots, different representations, median, range, and mode (4.01, 4.02, 4.03)

◦ Constant and varying rates of change (5.03)

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Traditional Question:If you have 6 pieces of candy and your brother gives you 2 more, how many pieces of candy do you have now?

More open-ended:You have 6 pieces of candy, your brother gives you 2 pieces today and 2 pieces tomorrow. Draw a picture to show how many pieces you will have in all. Can you share the pieces equally between yourself and 3 friends? Why or why not?

Changing Tasks: Low Level to High Level

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Traditional Question:If you earned $380 for 2 weeks of work, how much will you earn in 15 weeks?

Changing Tasks: Low Level to High Level

Kate earns $380 every two weeks. She thinks she will earn enough in 15 weeks to pay for a used car that costs $3000. Write an explanation to convince Kate that this is or is not true.

More Open-ended:Kate earns $380 for 2 weeks of work, how much will she earn in 15 weeks? Explain how you arrived at your answer.

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Write up a traditional math problem that you would find at your grade level.

Revise the question so it is more open-ended and rigorous.

Your Turn!

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As Cathy Seeley said: In your math class, who is doing the

talking? Who is doing the math?

Classroom Instruction

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QUESTIONS

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Next Steps