A listener asked how would we structure our math class. In this episode Pam and Kim discuss the approach they'd take to provide their students with the best math education experience possible to learn Real Math and still meet their required standards and scope and sequence.
Talking Points:

• The Two-Third/One-Thirds rule
• Rich Tasks - see Episodes 102 and 103
• Test Prep?!
• Use instructional routines for spiral review
• Tune in to the next episode for examples

Registration for our workshops are open now! Sessions for everyone, K-12! Check them out!
https://www.mathisfigureoutable.com/workshops

The school year is starting! For this exciting time, Pam and Kim want to discuss what starting strategies can help you and your students to build thinking relationships and strategies rather than simply answer getting.
Talking Points:

• Problem Talks are great ways to pre-assess your students
• Partial strategies are a great starting place but we have to help students develop more sophisticated strategies
• The starting strategies for each major operation
• Students need lots of experience developing relationships through Problem Strings and Rich Tasks for strategies to be natural outcomes

Check out our free eBook to learn more about these strategies: https://www.mathisfigureoutable.com/big
And don't miss out on the You Can Change Math Class Challenge! https://www.mathisfigureoutable.com/change
Check out Episodes 10 and 12 of this podcast for more ideas about starting your school year.

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 games
• What you celebrate, answers or thinking, is what students will share
• How 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/change

Learn 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 line
• When 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 measurement
• What can you model on an open number line? Elapsed time, addition and subtraction of whole numbers and integers and more
• Is an open number line helpful for higher math concepts?

See episode 138 for more about subtraction pitfalls

Check 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 106
• Applying knowledge of whole number multiplication to decimals
• It's more about reasoning than shifting the decimal
• Reasoning in small steps builds understanding vs. just counting the decimals
• Reasonableness comes from keeping kids in reasoning land
• Language 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 money
• Students need to develop a few starting relationships before becoming more sophisticated
• Smart 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 Tanton
• Money 

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?