Math is Figure-Out-Able!

How can you make changes in your math classroom to help your students do more Real Math? In this episode Pam and Kim describe some first steps, and bigger steps, you can take to transform your math class. Talking Points: Creating a safe mathematical community conducive for Real Math to happen Wait time - "Do you want time or help?"Where are you on the continuum to make some or lots of changes?Tips on where to start wherever you are on the continuum Using Problem Strings, I Have, You Need, MathStratChat and other instructional routines and gamesWhat you celebrate, answers or thinking, is what students will shareHow to transform your curriculum if you're super gung-ho See also Episode 136 for more discussion about helping students.Don't miss out on the You Can Change Math Class Challenge! Register today at https://www.mathisfigureoutable.com/changeLearn more about I Have, You Need by listening to episode 7, or visit us at https://www.mathisfigureoutable.com/blog/i-have-you-need

We sure loved discussing the open number line model last week, but have you ever heard of the double open number line? In this episode Pam and Kim discuss how the double open number line can be used to develop Proportional Reasoning and to think and reason about rates.Talking Points:A Problem String to reason about unit rates and model on a double open number lineWhen could an double open number line be helpful in middle school and high school?When is a ratio table more versatile than a double open number line?What other concepts can a double open number line be helpful for students?The percent bar is a double open number line?Check out our free download on Double Number Lines: https://mathisfigureoutable.com/double

The open number line is not just a powerful tool for computation, but it's an amazing model for developing all sorts of mathematical concepts! In this episode Pam and Kim discuss how to help students develop the open number line in a natural and meaningful way.Talking Points:What is an open number line vs a closed number line?Are number lines, closed or open, discrete models and why does it matter?Why shift to a measurement model vs a discrete model?What are some common errors students make when we use the traditional way of teaching measurement?We suggest a rich task by Cathy Fosnot to help students develop an understanding of the open number line through measurementWhat can you model on an open number line? Elapsed time, addition and subtraction of whole numbers and integers and moreIs an open number line helpful for higher math concepts?See episode 138 for more about subtraction pitfallsCheck out Cathy Fosnot's amazing rich task:  https://www.heinemann.com/products/e01010.aspx

Multiplying decimals can be fun! In this episode Pam and Kim tackle several gnarly problems like 0.77 x 2.4, and have a blast doing it. Talking Points: Building reasoning allows students to be flexible and have fun with decimal multiplication Kim uses percent and money to solve 0.77 x 2.4 with confidence (no need for a calculator) Pam represents her thinking on a ratio table for 0.77 x 2.4 Different strategies for 0.77 x 0.24? What about 7.7 x 0.24? Why is thinking and reasoning so important?

Being able to scale comfortably is important for both whole and decimal numbers. And just as there are more sophisticated ways to handle scaling with whole numbers, we can also be more sophisticated scaling decimals! In this episode Pam and Kim describe how we can help students become comfortable with decimal multiplication using their understanding of whole number multiplication and then scaling.Talking Points:Reflecting on the more sophisticated strategy from Ep 106Applying knowledge of whole number multiplication to decimalsIt's more about reasoning than shifting the decimalReasoning in small steps builds understanding vs. just counting the decimalsReasonableness comes from keeping kids in reasoning landLanguage to focus on and language to avoid

How can we help students make sense of decimal multiplication? In this episode Pam and Kim run through two beginning Problem Strings that will get students feeling comfortable and understanding the world of multiplying decimals.Talking Points:Which models are helpful Decimals and moneyStudents need to develop a few starting relationships before becoming more sophisticatedSmart Partial Products with decimals

We've gotten a ton of questions about decimals. In this episode Pam and Kim discuss three different models and why they are great for questioning and building relationships, but may or may not be good for computation.Talking Points:Base Ten Materials Exploding Dots by James TantonMoney 

Most students can scale up by ten as they begin to multiply larger numbers and that is a great starting place for students. In this episode Pam and Kim discuss a more sophisticated way of scaling numbers in multiplication problems. Talking Points:How beginning learners will use multiplying by 10 in double digit multiplication problems.How more sophisticated students deal with smaller numbers then scale up.How this applies to middle school students.How can Five is Half of 10 be used with more sophisticated thinking?

Often people misunderstand what this game we call mathematics is and feel they aren't good enough to play. In this episode Pam and Kim discuss how students need the opportunity to experience and play in the real game of mathematics.Talking Points:Mathematizing is not about speedPam, the basketball playerIt's not about memorizing disconnected rules and procedures.Kim, the teacher pleaser Experience and opportunities are important so kids have choicesWe need all students in the game of mathIs there such a thing as a "math gene" or natural talent?All students have different talents to bring to the tableTake the Math Perspective Quiz to find more about your perspective of math class and instruction.All students have talents to bring to the table

It's our two year anniversary! We are so grateful you've spent this time with us. In this episode Pam and Kim discuss openly things they've learned and how they've grown during their journey as math teacher educators.Talking Points:It's not 'Pam Math', it's Real Math and developing mathematicians!Coaching teachers is about mentoring, not just tellingThe importance of a common vocabulary - Check out Episodes 58 and 101Empowering teachers and leaders through Journey and Journey LeaderDeep dive online workshops for Kindergarten through middle schoolBuilding Powerful Linear Functions for high school coming soon!