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PRINICPLES TO ACTION Developing Worthwhile Mathematical Tasks Introduce self UCTM Leadership Conference 2015 Sue Womack, Ph.D. UCTM Post Secondary Board Member

Group Norms Start and End on Time Presume Positive Intentions Put Ideas on the Table Pause, Paraphrase, and Probe Pay Attention to Self and Others Balance Advocacy and Inquiry Dwell in possibility

many x Many people believe mathematicians relish giving unsolvable problems. That is a great opportunity to see students fail, but they could not be farther from the truth.

LEARNING GOALS: Discuss the degree of implementation of tasks Discuss quality of tasks in your district Examine 5 ways to improve tasks. Choose one to use with teachers at next professional development.

What Makes a Worthwhile Math Task? With a partner or trio, talk about characteristics of worthwhile math tasks Go to Answer Garden and post your words.[URL was here. It was set to expire in 1 day] 45 second timer

NCTM Task Criteria The problem has important, useful mathematics embedded in it. The problem requires higher-level thinking and problem solving. The problem contributes to the conceptual development of students. The problem creates an opportunity for the teacher to assess what his/her students are learning and where they are experiencing difficulty. The problem can be approached by students in multiple ways using different solution strategies. The problem has various solutions or allows different decisions or positions to be taken and defended. The problem encourages student engagement and discourse. The problem connects to other important mathematical ideas. The problem promotes the skillful use of mathematics. The problem provides an opportunity to practice important skills. National Council of Teachers of Mathematics. (2010). Research Brief on Problem Solving.

Degree of implementation Quality of tasks overall What IS YOUR SCHOOL’S/DISTRICT’S LEVEL OF USAGE OF RICH mathematical tasks? 4 minutes Degree of implementation Quality of tasks overall What are the successes? What are the concerns? These timers appear initially as a cream, coloured circle. The timer is initiated by clicking on, at which point the circle will fill up in a clockwise direction with the colour you see above. At the end of the time, a bell will sound. It is possible to change the timings of the timers by entering the animation settings and changing the timings of the relevant ‘Oval’. Note the timings have to be entered in seconds. It is possible to have multiple timers on the same slide as these work independently of each other.

VISUAL REPRESENTATION Mark where your school is on the spectrum of implementation of rich math tasks. Need adding machine tape & sticky flags High successful implementation Not yet begun

TEACHERS HEAR WRONG MESSAGE: So you don’t want me to teach the book? What is wrong with the book? So it doesn’t have to align to Utah Core Standards? So I can just do this everyday instead of teaching? So they don’t have to know basic facts or the steps to solving the problem? So I have them struggle with stuff they don’t know how to do?

FIVE EASY Development Tools for transforming textbook activities into worthwhile tasks relatively Low prep Can be used with ANY textbook or pacing map. Shifting thinking day by day

#1 Reduce the number of problems Big Ideas 7th Grade

Which uses the least amount of packaging? Each package has 24 cubes. http://blog.mrmeyer.com/category/3acts/page/2/

MAKE CLEAR CONNECTIONS TO PRACTICE STANDARDS

#2 OPEN up questions Test questions provide a RICH source of easily opened questions.

Deeper and More Rigorous Routine:  Find the difference between 23 and 7. Deeper and More Rigorous OPEN: The difference between two numbers is 16. What might the numbers be? Explain your thinking. This is a great place to give the answer. Have the students figure out the question.

Deeper and More Rigorous Routine: Find 3 + 4 and 5 + 4 and 3 + 7 and 1 + 6 etc. etc. (1st grade)  Find ways to make 7 with two numbers. Then write them in a pattern!    Deeper and More Rigorous OPEN:  

Deeper and More Rigorous Routine: Calculate 25 × 42. Deeper and More Rigorous OPEN IT UP WITH A PARTNER!

Possible WAY to Open Task OPEN: Calculate 25 × 42 in two different ways. Compare your ways with those of your friend.

OPEN IT UP WITH A PARTNER! CLOSED: OPEN IT UP WITH A PARTNER!

Possible WAY to Open Task OPEN: Remove the letters identifying sides that are the same. Describe the triangles and sort by characteristics

This skill is built through EXPERIENCE This skill is built through EXPERIENCE! This is a great collaboration discussion.

#3 Make Connections among representations Routine: Shade 2/3 of the figure. Worthwhile: Use a number line and an area model to show 2/3. Explain how the number line and the area model both show 2/3.

Select and describe one task that uses connections among representations

#4 Increase accessibility by adding a story context

https://www.illustrativemathematics.org/content-standards/tasks/50

https://grade5aglcommoncoremath.wikispaces.hcpss.org/Assessing+6.NS.1

#5 CREATE ARGUMENT!

PROVE OR DISPROVE   Sam says that multiplying is like adding a number over and over. Jonas isn’t sure. Explain to Jonas what Sam means using an example. 4 + 8 = 8 + 4 Keiko subtracted 17 from 23 and got 14 (23-17 = 14). Soraya got 6. How did they get their answers? Who got it right? Show how you decided.

What are some other examples of changing a routine task into a worthwhile task by using argument?

RECAP What are the 5 actions for transforming routine math tasks? Turn and tell a partner.

5 ACTIONS Reduce the number of problems. Open up questions Make connections among representations Add a story context. Create chances for argument.

IMPLEMENTATION STEPS Which of the 5 actions are the right NEXT step for your school/district?

Anyone can do well in math! Start video at 27 seconds