Mathematics Summit

Southern Indiana Deanery: Focus on Mathematics Instruction

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Standards for the Day

• Deepen understanding of new Common Core State Standards for mathematics

• Create understanding of using multiple representations and approaches to problem solving

• Apply a variety of strategies to support and promote the learning of mathematics

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Agenda

DAY II• Analysis of New Common Core State Standards• Using Multiple Representations to Develop Deeper

Understanding • Using Number lines and manipulatives to support

conceptual understanding

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Quick Write

From our time together yesterday,

What ideas, strategies, concepts, routines do you want to revisit as you plan your classroom for the upcoming year? Which do you want to focus on initially? & How do you plan on accomplishing this?

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Reasoning Abstractly and Quantitatively

• 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

• Working in non-grade level groups (2-3)

Divide 365÷4 (by hand) using three different methods.

(Keep in mind, we are developing reasoning and sense-making, and multiple approaches/methods

to use with our students )

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Method 1 of ∞

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Method 2 of ∞

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Method 3 of ∞

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Method 4 of ∞

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Method 5 of ∞

112/4 = 28

112/4 = 28

112/4 = 28

24/4 = 6 5/4 = 1 R1

365 = 112+112+112+24+5 = 28+28+28+6+1+¼ = 91¼ 4 4

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Common Core State Standards for MathematicsK-8 Mathematics Content

DOMAINS Counting & Cardinality

Operations & Algebraic Thinking

Number & Operations in Base

Ten

Measurement & Data Geometry

Number & Operations:

Fractions

Ratios & Proportional Relationships

The Number System

Expressions & Equations

Statistics & Probability Functions

K X X X X X

1 X X X X

2 X X X X

3 X X X X X

4 X X X X X

5 X X X X X

6 X X X X X

7 X X X X X

8 X X X X X

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

6 7 8

Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems

Analyze proportional relationships and use them to solve real world and mathematical ‐problems.

The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Compute fluently with multi digit numbers ‐and find common factors and multiples.

Apply and extend previous understandings of numbers to the system of rational numbers.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Expressions and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one variable ‐equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Use properties of operations to generate equivalent expressions.

Solve real life and mathematical problems ‐using numerical and algebraic expressions and equations.

Work with radicals and integer exponents. Understand the connections between

proportional relationships, lines, and linear equations.

Functions Define, evaluate, and compare functions. Use functions to model relationships

between quantities.

Geometry Solve real world and mathematical ‐problems involving area, surface area, and volume.

Draw, construct and describe geometrical figures and describe the relationships between them.

Solve real life and mathematical problems ‐involving angle measure, area, surface area, and volume.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand and apply the Pythagorean Theorem.

Solve real world and mathematical ‐problems involving volume of cylinders, cones, and spheres.

Statistics and Probability

Develop understanding of statistical variability.

Summarize and describe distributions.

Use random sampling to draw inferences about a population.

Draw informal comparative inferences about two populations.

Investigate chance processes and develop, use and evaluate probability models.

Investigate patterns of association in bivariate data.

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Content Analysis

In grade level groups:

• Identify new content for your grade level

• Identify different opportunities for using multiple representations, approaches, number forms

• Develop a priority list of content & approaches to be developed during the transition period.

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Content Analysis

In school groups:

• Outline content priorities at each grade level

• Identify both major and minor shifts

• Shift emphases – decide that teachers will pay more attention to x and y in 2011-2012 and less attention to z

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Quick Write

Based on this morning’s conversations, what do you want to remember? How have you added any more thinking to the routines/processes that you are planning on implementing this year?

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Working with Manipulatives

• Don’t assume that students make the connections between the different forms/representations of the problems

• As with any process, students need to develop understanding of the process prior to attempting to learn new material.

You must be intentional in doing this!

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

How do we represent in mathematics?

Number

Algebra

Graphical

Sentence

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

CTL, Mathematical Literacy

21

Grade Level Content

Working in multi-grade groups work throughseveral of the problems on the page.

What does it look like?How do the ideas progress across the grades?How do I support, develop student skills in this area?

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Literacy in Mathematics

Vocabulary Development

Reading

Writing2Speaking/ Listening

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Community Wiki

sidmath.pbworks.com

Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction

August 3, 2011

Community Wiki

sidmath.pbworks.com

By the way, what is a Wiki?

rodaniel@ctlonline.org