Math in Action Jennifer Griffin HPS Curriculum Conference January 2014

Session Learning Targets I can facilitate the Standards for Mathematical Practice. I can explore strategies for implementing the Mathematical Practices

What does it mean to be Mathematically Proficient?

Table Talk Are students who can remember formulas or memorize algorithms truly mathematically proficient, or are there other skills that are necessary? Is the correct answer the ultimate goal of mathematics, or do we expect a greater level of competence?

With new standards, mathematical practices are elevated to essential expectations, changing our view of math to encompass more than just content. The goal is now to apply, communicate, make connections, and reason about math content rather than simply compute.

What are The Standards for Mathematical Practice?

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?

The Holiday Tree The Partin family counted the different types of ornaments on the town’s holiday tree. Here is a list of what they saw. – Stars 24 – Gingerbread men 14 – Snowflakes 12 – Reindeer 18 – Candy Canes 6 Six of the reindeer had red noses. What fraction of the reindeer has red noses? Tell how you would get the answer.

The Partin family counted the different types of ornaments on the town’s holiday tree. Here is a list of what they saw. – Stars 24 – Gingerbread men 14 – Snowflakes 12 – Reindeer 18 – Candy Canes 6 What fraction of the ornaments were snowflakes? What fraction of the ornaments were edible? If 6 of the stars were silver, what fraction of the stars were not silver?

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. Traditional Problems or Rich Problems?

Reflecting on strengthening student problem solving experience... 1.Do I routinely provide opportunities for my students to share their solutions and processes with partners, groups, and the whole class? 2.Do I show my students that I value process (how they did it) rather than simply the correct answer? 3.Do I pose problems that require perseverance? Do I use thoughtful questions to guide and encourage students as they struggle with problems?

Exploring Standard Two 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?

Headline Stories Newspaper Headlines give an idea of what the news story is about. An equation is like a newspaper headline. Short and to the point. The headline is to the news story as the equation is to the word problem. Helps teachers see understandings and misconceptions.

Headline Stories Headline: 52 ÷ 4 =  Headline stories can be as easy or as difficult as you make them. Students might be asked to write problems about equations that include fractions, decimals, percents, or variables.

Variations Draw a picture to show... Work in pairs and post Create a book with each page containing a different story about the equation Reverse it Match it: The equation on one card and story on the other. (in pairs or as a class) Question it: the answer is 10, the problem is...(write the word problem.)

Number Partners Find a number partner that makes What are some modifications for this task?

Pinch Cards 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?

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

Understanding the Standard What do we do in the classroom to get students to justify their answer and defend their process for finding the answer? How do we help students understand math skills and concepts so they can construct viable arguments. How do we help students consider and judge the reasonableness of other answers and strategies?

Eliminate It Four math concepts or facts Students state which one item to eliminate and why Examples: AddSubtract MultiplyJoin

Examples RectangleCylinder CircleTriangle

Create Your Own

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

Agree or Disagree? Jim has 12 pencils and Annie has 8. Jim has more than Annie and are the only ways to make is an even number. 6 tens and 3 ones is the same as 5 tens and 13 ones. 3 jars of peanut butter for $7.50 is a better deal than 4 jars of peanut butter for $10.20.

Constructing Arguments What is the difference between an assertion and an argument?

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.

Number Talks A five to ten minute conversation about specific mathematical strategies for computation that build upon key foundational ideas of mathematics with a focus on number relationships and number theory. Students share and defend their solutions, strategies, and collective reasoning.

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Key Components of Number Talks 1.Classroom environment and community 2.Classroom discussion 3.The teacher’s role 4.The role of mental math 5.Purposeful computation problems

Benefits of Sharing and Discussing Computation Strategies Students have the opportunity to: 1.Clarify their own thinking. 2.Consider and test other strategies to see if they are mathematically logical. 3.Investigate and apply mathematical relationships. 4.Build a repertoire of efficient strategies. 5.Make decisions about choosing efficient strategies for specific problems.

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Shifting By changing my question from “What answer did you get?” to “How did you solve that problem?” I was able to understand how they were making sense of mathematics.

Four Procedures and Expectations Essential to Number Talks 1.Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions. 2.Provide appropriate wait time for the majority of students to access the problem. 3.Accept, respect, and consider all answers. 4.Encourage student communication throughout the number talks.

Student Interactions I agree with _____________ because _____. I do not understand ____________. Can you explain this again? I disagree with _____________ because _____________. How did you decide to _________________?

A Teacher’s Perspective

Number Webs

Questions? Comments?

Evaluate

Resources and Acknowledgements Denise Schultz, Department of Public Instruction Putting the Practices Into Action, O’Connell and SanGiovanni Number Talks, Parrish

What do you want to know more about?

Exploring Standard 5 Use appropriate tools strategically.

Understanding the Standard What are the tools used by our students? Why is it important to use tools? Tools enhance our students’ mathematical power by assisting them as they perform tasks. The ability to select appropriate tools is and important reasoning skill.

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 and 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, 59cents/lb X 0 X What comes next 3, 7, 15, 31, ____

How do we get there? Use tools appropriately Number lines (it’s close to...) Rulers (broken ruler, magnified inch) Mental Math – Number Partners – In my head?

Provide Tools It is important to provide opportunities for students to select the appropriate tool. They should select the tool and then be able to use it effectively.

Folding Paper Fold the strip in half. Open it, and mark ½ at the center fold. Refold the strop in half and fold it in half again. Label ¼, 2/4, ¾ on the three folds.

Questions Are the sections equal in size? Do the fraction labels make sense? Why? Where is 0? Why? Why are 1/2 and 2/4 on the same fold?

Folding Paper Refold the paper and then fold it in half one more time. Open the paper, place a mark on each fold and indicate what each of the new marks represent.

Folding Paper Why is there more than one fraction on some folds? Does it make sense thatthose fractions are on the same fold? Why? Which of those fractions is easiest to understand? Would you say 1/2 or 2/4, or 4/8? Why?