Daniel J. Brahier (brahier@bgsu.edu)BGSU/St. Rose School

Wednesday, 22 May 2013

Mathematics Grades 3-5iEvolve

Characteristics of the CCSS-Math

Fewer, clearer, and higher

Aligned with college and career expectations

Internationally benchmarked

Include rigorous content and application of higher-order skills

Evidence- and/or research-based

Build upon strengths and lessons of current state standards

Promote collaboration among states for instruction, resources, assessment, and professional development

So, what IS “mathematics”?

A. Something that you “know”B. Something that you “do”C. All of the above!

Mathematics is a VERB – something you “do”

NCTM Process Standards (1989)

1.Problem Solving

2.Reasoning and Proof

3.Communication

4.Connections

5.Representation

Standards for Mathematical Practice

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.

Student Responses

Students rarely, if ever, answer a question “wrong.” Instead, they give a “correct” answer to a different question than we thought we were asking!

How do you “know” these?

7 + 86 + 68 + 5

How do you “know” these?

7 + 86 + 68 + 5

Knowing Basic Facts

How do you visualize 3 x 5?

Which of these is/are most accurate? Which reveal misconceptions?

How do you find the answer?

160 x 50

What do you know about each?

A. 14.7 ÷ 1.05B. 126.68 ÷ 0.97C. 164 x 0.76

Where does the decimal go:27.49 x 8.31 = 2284419

Butterfly Multiplication

Why does this work???

Scientific and Engineering Practices (NSTA, 2012)

1. Asking questions and defining problems2. Developing and using models3. Planning and carrying out investigations4. Analyzing and interpreting data5. Using mathematics and computational thinking6. Constructing explanations and designing

solutions7. Engaging in argument from evidence8. Obtaining, evaluating, and communicating

information

Practices of Math AND Science

Which is true about the Standards for Math Practice?

A. They are of equal importance.

B. They should be emphasized in an equitable manner at each grade level (similar time devoted to each).

C. They vary in importance at different grade levels.

Which is true about the Standards for Math Practice?

A. They are of equal importance.

B. They should be emphasized in an equitable manner at each grade level (similar time devoted to each).

C. They vary in importance at different grade levels.

An Old Joke

•How do you kill a blue elephant?•With a blue elephant gun.•How do you kill a white elephant?•With a white elephant gun?•No, you first strangle the

elephant until it turns blue and then use the blue elephant gun you already have!

Chinese Proverb

Give me a fish and I eat for a day.Teach me to fish and I eat for a lifetime.

Practices

Emphasis on the Mathematical Practices is equivalent to teaching our students “how to fish”!

Domains for Grades 3-5

Operations and Algebraic ThinkingNumber and Operations in Base TenNumber and Operations – FractionsMeasurement and DataGeometry

Big Ideas (“Critical Areas”) in Grade 3

Understanding of multiplication and division strategies up to 100

Understanding of fractions, particularly unit fractions (numerator = 1)

Understanding of rectangular arrays and area

Describing/Analyzing two-dimensional shapes

Big Ideas in Grade 4

Understanding/Fluency with multi-digit multiplication and division with quotients having multiple digits

Fractions – equivalence, add/subtract with same denominator, multiply by whole numbers

Analyzing/Classifying geometric shapes based on parallel sides, symmetry, etc.

Big Ideas in Grade 5

Understanding/Fluency with adding/subtracting fractions and general idea of multiplying/dividing fractions

Decimals, including fluency in decimal operations up to hundredths

Developing an understanding of volume in three-dimensional shapes

What Develops Conceptual Understanding?

Engage Students in Productive Struggle

Productive Struggle

Making Mathematical Relationships Explicit

The Next Generation Assessments

Prototype Item – Grade 4 (Part A)

Prototype Item – Grade 4 (Part B)

Prototype Item – Grade 4 (Part C)

Daniel J. Brahier (brahier@bgsu.edu)BGSU/St. Rose School

Wednesday, 22 May 2013

Mathematics Grades 3-5iEvolve