Math is Figure-Out-Able!

We've got another one of our favorite routines for you today! In this episode Pam and Kim demonstrate the Relational Thinking routine, a routine that helps students understand equivalence and become more comfortable with relational strategies. Thanks to the   Cognitively Guided Instruction group for introducing us to this routine!Talking Points:Examples of the routine for all four operationsWhat does the equal sign really mean?Strategies based on equivalence: Give and Take, Constant Difference, Doubling and Halving, Equivalent RatioResources:Find examples of Relational Thinking problems here: https://www.mathisfigureoutable.com/relational-thinkingFind our Developing Mathematical Reasoning info graphics here:  https://www.mathisfigureoutable.com/blog/development-4

There are a lot of great instructional routines out there, and today we want to highlight As Close as it Gets. In this episode Pam and Kim discuss how to use this instructional routine in your classroom and how it can help your students get mathematizing with estimation!Talking Points:A routine to help students learn what Real Math estimation is through reasoning.ExamplesTeacher moves to introduce the routine and common pitfallsWhy do we use the routine?Where to find help for your classroomLearn more about this powerful routine here: https://www.mathisfigureoutable.com/instructionalroutines

Are your students dumb or smart? Fast or slow? Under achiever or advance achiever? Or are they just your students with varying experiences? In this episode, Pam and Kim discuss labels, and the effect they have on you as teachers and your students. They propose a different way to look at your students so that you can provide opportunities and experiences for all students so that they continue to learn and love math.Talking Points:The problem with labels.What do we believe about learning?Focus on providing experience rather than natural talent or ability.      

How can we take what students already know and leverage that to make other mathematical connections? You've probably heard us mention that you should know your content and know your kids, but there's a lot of meaning behind that. In this episode Pam and Kim go in deep on how knowing your content and your kids support effective teaching practices and maximize learning for students.Talking Points:We need to know beyond our standards.Why we need to look vertically and horizontally at our standard's landscape?How knowing our students can help target their individual zone of proximal development.

We did it! We made it to episode 73! Why is that an important milestone? Just cause it's Kim's favorite number :-). In this episode Pam and Kim take the opportunity to highlight some important milestones in the Math is Figure-Out-Able movement. We're so grateful you're a part of it!Talking Points:Pam and Kim's favorite numbersTwitter followers and MathStratChatYou Can Change Math Class ChallengePam and Kim as colleaguesPodcastOnline Workshops What's coming up next?

Facilitating a Problem String is tricky business, so Pam and Kim take the time in this episode to provide some do's and don'ts that anyone can learn from.Talking Points:What is a Problem String?How long should a Problem String last?Can Problem Strings be given in a worksheet or as a bell ringer?Does everyone share during the Problem String?How do I know which students should share and in what order? What if all of my students aren't using the strategy?What if I don't understand a student's strategy?How do I write Problem Strings?If you want to hear more about Problem Strings, check out Episode 163. 

What makes Problem Strings different from other sequences of problems? In this episode Pam and Kim get into the nitty gritty on how Problem Strings work and what sets them apart.Talking Points:Defining Problem StringsThe "Why or Purpose" - What sets a Problem String apart from just a list of problems?The "How" - How are Problem Strings facilitated differently from a textbook lesson or rich task?An exampleIf you want to hear more about Problem Strings, check out Episode 163. Find examples of Problem Strings (including video!) at https://www.mathisfigureoutable.com/ps

Problem Strings are meant to build off each other so that the math is always moving forward. That's why we've decided to build off the last episode with another Problem String! In this episode Pam and Kim find the equation of some lines using relationships and develop powerful strategies for more sophisticated thinking.Talking Points:You don't have to have lots of recent experience to notice the patterns.Problem Strings to notice patterns and relationships between the x values and the y values.How the relationships between the x values and the y values help you think and reason about slope and y intercept.Algebra is Figure-Out-Able!!

We've talked a lot about the types of reasoning we need to help students develop, but a lot of teachers believe that there comes a point in higher math where reasoning just won't cut it. In this episode Pam and Kim tackle functional reasoning, and demonstrate that algebra can be so much more than memorized steps.Talking Points:Is using the procedure of finding slope, plugging into a formula, etc the most efficient?The importance of working with intuitionExamples of using patterns that you notice to find the equation of a line without formulasIntuitively finding the equation of a line in standard form

In Episode 67 revisited the Development of Mathematical Reasoning (DMR) and we described how students can solve addition problems with Counting Strategies. What about the addition algorithm and multiplication and division problems? In this episode Pam and Kim explore the Development of Mathematical Reasoning even further, and discuss how important it is that we help students become more sophisticated. It's more than just answer getting. And stay tuned to the end for a freebie!Examples of solving addition problems with bigger numbers using Additive Reasoning.Examples of solving multiplication problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.Examples of solving division problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.Brand new free infographics of the Development of Mathematical Reasoning.Videos of students solving problems using the different types of reasoning to help you use the DMR in your classroom to identify where your students are in their reasoning.Find the infographics here: https://www.mathisfigureoutable.com/blog/development-4