Fall 2013 Putting the Mathematical Practices Into Action

Norms Listen as an Ally Value Differences Maintain Professionalism Participate Actively

Session Outcome Understand the Standards for Mathematical Practice Explore strategies for implementing the Standards effectively

What has been your biggest challenge with the implementation of The Standards for Mathematical Practice?

Overarching habits of mind of a productive Mathematical Thinker

Exploring Standard 1 Make Sense of Problems and Persevere in Solving them.

Understanding the Standard What do we do each day in our classroom to build mathematical thinkers? What do we do to keep our students actively engaged in solving problems? How do we help our students develop positive attitudes and demonstrate perseverance during problem solving?

What questions could you ask? Shipley Aquarium Admission Cost Adults - $8.00 Children (ages 3 and over) - $6.50 Children (ages 2 and under) – Free

Traditional Problems vs. Rich Problems We can ask questions that stifle learning by prompting a quick number response. –What is the answer to number 3 on your worksheet? –What is 5 x 4? We can ask questions that promote discussion, thinking, and perseverance.

Sort the math questions. Check your arrangement on page 22

Exploring Standard 6 Attend to precision.

Understanding the Standard Why is precision important in mathematics? What does it mean to be precise? What can we do in the classroom to promote precise communication in mathematics?

Estimate and Exact Buying bags of candy to put in party treat bags Measuring the dimensions of the doorway to install a screen door Buying pizzas for a class party Buying carpeting for a living room floor

Estimation Skills 5 x 8/

Sort and Label

Exploring Standard 2 Reason abstractly and quantitatively.

Understanding the Standard What can we do in our classrooms each day to help students build a strong understanding of numbers (quantities)? How do we help students convert problems to abstract representations? What can we do to help students understand what numbers stand for in a given situation?

How Do We Get There? Translate the Symbol Expression Webs Pinch Cards

Expression Webs A > B

Translate the Symbol 4 dollars and 10 cents is greater than 4 dollars and 5 cents One-fourth of 16 is 4 Doubling a number then adding six more

Translate the Symbol 12 = x = 6 3 x 4 > 2 x 5

Which Is More Challenging? 4 dollars and 10 cents is greater than 4 dollars and 5 cents One-fourth of 16 is 4 Doubling a number then adding six more 12 = x = 6 3 x 4 > 2 x 5

Pinch Cards Pinch cards are an all-pupil response technique. There were 6 soccer teams in the league and 12 players on each team. How many players were in the league? The 4 members of the High Rollers Bowling Team scored 120, 136, 128, and 162. What was the team’s mean score? page 41

Pinch It There were 6 soccer teams in the league and 12 players on each team. How many players were in the league? The 4 members of the High Rollers Bowling Team scored 120, 136, 128, and 162. What was the team’s mean score?

Avoiding Key Words Key words are misleading. Many problems have no key words. The key word strategy sends a terribly wrong message about doing mathematics. A sense making strategy will always work. Van de Walle & Lovin (2006)

Video of Key Words

Exploring Standard 3 Construct viable arguments and critique the reasoning of others.

How Do We Get There? Eliminate It Agree or Disagree?

Eliminate It! As a group, decide on the concept that should be eliminated with reasoning or math data to back up your decision. There may be more than one way to eliminate an item! Create your own.

Agree or Disagree? 75% is more than 2/3. Tell why you agree or disagree.

Assertion vs. Argument Assertion: a statement of what students want us to believe without support or reasoning. –The answer is correct “because it is,” “because I know it,” or “because I followed the steps.” Argument: a statement that is backed up with facts, data, or mathematical reasons Constructing viable arguments is not possible for students who lack an understanding of math skills and concepts.

Is this true? 19+6 = 20+5

Exploring Standard 4 Model with mathematics.

Assessment Tips Tell me what your model represents. Why did you choose this model? Did creating a model help you any way? If so, how? Did you get any insights by looking at your model? Is there another way you might model this problem or idea? How? Page 75

Exploring Standard 5 Use appropriate tools strategically.

Which tool is more efficient? There is often more than one tool that will work for a task, but some tools are more efficient than others.  Paper & Pencil  Mental Math  Calculator

Solve using your assigned tool! 1.5 x x 15 3.Estimate the cost of 2 $3.75 each $3.20 each $1.79 gal 59 cents/lb x 0 x What comes next 3, 7, 15, 31, ___ 6.A local TV store had a sale on TV’s. They sold 7 for $1, each. They made a profit of $ on each TV. What did the store pay for the 7 TVs? A. $1,183.00C. $13, B. $10, D. $11,899.65

In My Head? (Mental Math) Do I use paper & pencil or do it in my head? –734 x 82 –63 x 4 –1/4 + 2/8 –930 ÷ 3 Students need to identify tools that increase their efficiency with math tasks.

What questions do you have?

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