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AgendaCCSS Standards for Mathematical Practice

CCSS Grade Level Overviews DifferentiationVan Hiele & Mosaic Puzzles Menu Slices and FALs LunchBreakout Groups

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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.

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Grouping the Practices

William McCallum

Standards for Mathematical PracticeTucson, April 2011

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+Grouping the Practices

SMP Pairs1 & 6 ; 2 & 3 ; 4 & 5 ; 7 & 8

Discuss with your SMP partner the similarities and differences between the two practices in the K-1 posters and then the middle school posters.

Discuss with your SMP partner why these two practices have been grouped together.

Share highlights of your partner talk with your table.

Whole group discussion

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+Geometry Across Grade Levels

In your team of 8:Read one of the overview handouts (K/1;

2/3; 4/5, 6, 7, 8, Algebra, Geometry)Circle, underline, or, highlight any

geometry concepts and other big ideas that support geometrical reasoning.

Share the progression of geometry with your table, beginning with the K/1 overview.

Popcorn share out and clarifying questions.

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+ CCSS-Mathematics

Content standards:paint the Big Picture of the domainflesh out the domainare not a checklistare independent of California’s 1997 math standards

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+Differentiation

Please read Malcolm Swan’s Improving Learning in Mathematics: Challenges and Strategies

Discuss at your table: highlights from the article. anything that resonated with you. questions that arose while reading .

Whole Group Debrief

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+Setting the Stage for Geometry

Take a few minutes to think about and represent in some way [diagraming, webbing, listing, organizing] what you believe are the big ideas in Geometry.

Pair/Share your ideas with an elbow partner

Group Popcorn Sharing

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+Setting the Stage for Geometry

Please read the excerpts from Van de Walle and Burns.

Discuss at your table: highlights from the article. anything that resonated with you. questions that arose while reading .

Whole Group Debrief

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+Van Hiele Levels

“I believe that development is more dependent on instruction than on age or biological maturation and that types of instructional experiences can foster, or impede, development.”

-Pierre M. van HieleTeaching Children Mathematics

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+Van Hiele Levels

Please read Van Hiele’s Levels of Geometric Reasoning

Level 0 RecognitionLevel 1 AnalysisLevel 2 Informal DeductionLevel 3 Formal DeductionLevel 4 Rigor

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+Level 0

Shapes are what they look like

Students recognize and name figures based on the global visual characteristics of the figure. It’s a square because it looks like a house.

These shapes go together because they’re pointy or they’re fat.

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+Work of 10th grader

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+Work of 10th grader

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+Instruction at Level 0

Sorting and Classifying-see how shapes are alike and different

Variety of shapes- minimize the effect of irrelevant features. Build activities around specific properties so students start to understand and see them naturally.

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+Questions at Level O

Let’s see if that’s true for other rectangles.

Can you draw a triangle that does not have a right angle?

In general students should be challenged to see if observations made about a particular shape apply to other similar shapes.

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+Level 1- Analysis

Students start to see classes of shapes (instead of a rectangle, all rectangles)

Start to see properties of shapes or list of attributes

They have trouble with subcategories or sifting through the attributes, such as seeing that squares are also rectangles, quadrilaterals, parallelograms.

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+What’s a rectangle?

6th graders were asked: Can a parallelogram be both a rectangle and a rhombus?

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+What’s a rectangle?

6th graders were asked: Can a parallelogram be both a rectangle and a rhombus?

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+What’s a rectangle?

6th graders were asked: Can a parallelogram be both a rectangle and a rhombus?

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+Student Finds Correct Attributes25

+Student Finds Correct Attributes

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+ Other Students

Did not notice that Blobbies had 4 sides.

Failed to notice that Blobbies had circles in the middle or thought all shapes with circles in the middle were Blobbies.

Students used irrelevant properties like parallel sides.

Students couldn’t sort with 2 attributes.

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+Instruction at Level 1

Focus on properties rather than mere identification.

Think about classes: all rectangles, all prisms.

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+Questions at Level 1

Questions that involve reasoning: If the sides of a four-sided shape are all congruent, will you always have a square? How do you know?

Can you find a counterexample? How do you know?

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+ Instruction at Level 2

Make and test hypotheses and conjectures.

Examine properties of shapes to determine necessary and sufficient conditions.

Use language of informal deduction: all, some, none, if-then, what if, etc.

Encourage students to attempt informal proofs.

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+Implications for Instruction

HandoutStudents working at the recognition or visual level needed activities like…

Students working at this analysis stage need activities like…

Students working at abstraction or informal deduction are ready for…

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+Mosaic Puzzle

Please cut out the puzzle pieces and explore their relationships.

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+Mosaic Puzzle

Find all the pieces that can be made from two other pieces.

Find all the pieces that can be made from three other pieces.

How many different shapes can be made with a pair of pieces?

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+Mosaic Puzzle

What two shapes make a parallelogram?What other two pieces make this shape?

Do they also work flipped over?Can you make a parallelogram with three pieces? Hint: Try pieces 1,2 and 5; make it in a different way with these 3 pieces. Also try pieces 1,2, 5 flipped over

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+

BREAK Time !!

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+ Problem of the Month (POM) and SlicesSVMI morning sessions provide:

Opportunities to experience the development of specific mathematical content through the grade levels.

POMs and Menu Slices provide: multiple entry points to mathematics opportunity for extension, development,

and differentiation an opportunity to analyze and synthesize

the progression of mathematics within domains

September and October POMs

November and December Menu Slices

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+G

eometry

Menu Slices

Choose a color from the pile on your table.

Go to corresponding color Menu Station2- and 3- Dimensional ShapesLocation and PositionTransformations and SymmetryVisualization, Spatial Reasoning, and Modeling

Work through all the activities in the slice.

Complete the Learning Log

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+G

eometry

Menu Slices

Return to your table.

Share Learning Log for the Slice you experienced with your table.

Whole Group Discussion

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Lunch

Please be back in 45 minutes

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+Breakout Sessions

K-2

3-5

6-8

Algebra - HS

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+3-5 afternoon session

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+Spatial VisualizationNumber Talks

Dot Patterns

• 2-D Geometry

• 3-D Geometry

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Dot PatternsDot Patterns

How Many Dots?

How did you see it?

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2-D Geometry2-D GeometryWhat are the shapes?

How did you see them?

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+ 3-D Geometry3-D GeometryHow many cubes?

How did you see them?

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+ Teacher TechniquesTeacher Techniques• Individual Think Time

• Signals - e.g. Use of Thumbs

• Pair/Share

• Whole Group Share Out

• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk

• 3 x 5 Card Formative Assessment: two different strategies for solving problem

• And the conversation continues …

• Individual Think Time

• Signals - e.g. Use of Thumbs

• Pair/Share

• Whole Group Share Out

• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk

• 3 x 5 Card Formative Assessment: two different strategies for solving problem

• And the conversation continues …

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+Teacher ToolsTeacher Tools

• Overhead Transparencies

• Charts

• Butcher Paper Recordings

• White Boards

• Document Reader

• Smart Boards

• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk

• And the conversation continues …

• Overhead Transparencies

• Charts

• Butcher Paper Recordings

• White Boards

• Document Reader

• Smart Boards

• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk

• And the conversation continues …

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+4 Triangle Problem

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+Roping in Quadrilaterals

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+MARS tasks related to Geometry

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+MARS for next time (Measurement)

Work the task

Think about where your students will be successful

Predict misconceptions

Administer the task to your students

Bring back the work in December.

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