Finding a fraction of something can be a tricky concept. In this episode Pam and Kim run through two strings that help reason about using fractions as operators. Talking Points: How are unit fractions related like halves, fourth and eighths? Scaling and Over Strategy with unit fractions Fractions as operators Why is scaling a unit fractions critical? Knowing that three fourths is the same as three 1/4s? Knowing non-unit fractions from fractions is a precursor. Thinking of fractions only as part-...
Jan 30, 2024•24 min•Ep. 189
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 24, 2024. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Jan 25, 2024•7 min
Does it really matter what we call the whole? In this episode Pam and Kim take a closer look at fraction problems where the unit matters. Talking Points: Kim and the beach How can there be 2 possible answers to the question "What is 1/2?" Focusing on the unit Naming the unit What happens when the unit changes? Help students focus on the unit, changing the unit, and finding a fractional amount of that new unit Even test writers struggle with fractions Re-unitizing will support students to reason ...
Jan 23, 2024•34 min
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 17, 2024. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Jan 18, 2024•6 min
How many people do you know that shy away from fractions? In this episode Pam and Kim discuss why teaching students to use step by step procedures to solve fraction problems actually leaves them not able to think about fractions at all. Talking Points: We love hearing your stories! What kind of reasoning do fractions engage? What happens when students learn to mimic steps rather than reason about fractions? What does reasoning about fractions look like? Are least common denominators really that ...
Jan 16, 2024•29 min•Ep. 187
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 10, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Jan 11, 2024•6 min
Minus-minus, plus-plus, or is integer subtraction actually figureoutable? In this episode Pam and Kim use a Problem String to build real understanding of integer subtraction. Talking Points: The importance of having multiple contexts Seeing the negative symbol as "opposite of" Using distance Understanding takes time, but is so worth it! See Episodes 181-183 for more about Integer operations. See Ep 242 for more information on Integer Multiplication Check out our social media Twitter: @PWHarris I...
Jan 09, 2024•32 min•Ep. 186
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 3, 2024. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all o...
Jan 04, 2024•7 min
Tracking students and sorting them into 'higher'/'lower' tracks is a topic that we have really, really firm feelings about. In this episode Pam and Kim discuss the unintended consequences of tracking students and offer some ideas to consider. Talking Points Who does tracking benefit, who does it hurt? Distaste for the vocabulary used to describe tracks of kids Everyone can do more real math than fake math From our experience as a teacher From our experience as a parent From a student's perspecti...
Jan 02, 2024•38 min
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 27, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all...
Dec 28, 2023•9 min
Happy holidays! Pam and Kim invite you to revisit Ep 87, it's super important! How do you navigate teaching math that is figure-out-able if your standards include the teaching of algorithms? Talking Points: All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems. Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year. St...
Dec 26, 2023•26 min•Ep. 184
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 20, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all...
Dec 21, 2023•6 min
Can integer subtraction feel intuitive without rote memory? In this episode Pam and Kim delve into a Problem String and explore integer subtraction relationships. Talking Points: Integer chips? Students reason about subtracting integers Distance versus removal Problem String subtracting integers in context When context is less helpful Don't go to rules, stay in reasoning See Episodes 149 and150 for more about distance vs removal See Ep 242 for more information on Integer Multiplication Check out...
Dec 19, 2023•30 min•Ep. 183
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 13, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all...
Dec 14, 2023•5 min
Mimicking rules for integer operations does not help students become doers of Real Math, and frankly doesn't often stick in their long term memory. In this episode Pam and Kim walk through a Problem String that helps students develop an intuitive understanding of integer addition! Talking Points: Exploring the beach as a context Equations and number lines in context Carefully chosen numbers to avoid distracting cognitive load Subtraction symbol or adding a negative? Parentheses or not? Let stude...
Dec 12, 2023•26 min•Ep. 182
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 6, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Dec 07, 2023•7 min
How can we help students reason about integers? In this episode Pam and Kim discuss fun and natural ways to explore and understand both positive and negative integers. Talking Points: The Pen/Pencil argument continues 5th graders can reason about integers Games do develp understanding of integers Clothes line math with integers Exploring four useful contexts for integers See Ep 242 for more information on Integer Multiplication Check out our social media Twitter: @PWHarris Instagram: Pam Harris_...
Dec 05, 2023•35 min
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 29, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all...
Nov 29, 2023•5 min
How do you label fractions on an open number line? How do you label a fraction of a candy bar? How many cuts do you make to cut a candy bar into fourths? Pam and Kim invite you to revisit episode 138, this time with an ear towards fractions. Do your students ever get confused about counting obects vs counting distance? In this episode 138 Pam and Kim use a Problem String to help build intuition about everyday subtraction problems. Talking Points: Experience a Problem String to build relationship...
Nov 28, 2023•27 min•Ep. 180
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 22, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all...
Nov 23, 2023•8 min
What does it mean when we say 'fake math' or 'less sophisticated'? Pam and Kim discuss how learning Real Math is empowering and opens a whole new world of understanding. Talking Points: Are squared numbers an important thing to own? The Matrix It takes experience to understand perspectives Martians Doing 'fake math' or using a 'less sophisticated' way of thinking does not make the person fake or unsophisticated Real math is empowering and can open up a new reality! Check out our social media Twi...
Nov 21, 2023•31 min•Ep. 179
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 15, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all...
Nov 16, 2023•7 min
We can be our own kids' best teachers, even when it comes to gnarly division problems. In this episode Pam and Kim relay their experiences exploring decimal division with their own kids. Talking Points: A tool for holding your thinking - a ratio table It's not about how much you can hold in your head Help them start with what they know Problem Strings are not about answering just the last problem It isn't about being able to solve every problem It's about owning the major relationships in order ...
Nov 14, 2023•30 min•Ep. 178
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 8, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Nov 09, 2023•6 min
Recorded live from NCTM! Pam and Kim discuss some of their experiences and takeaways from the 2023 National Council of Teachers of Mathematics conference. Talking Points: Travel stories As kids grow, teachers grow as well Know your content know your kids to choose Problem Strings for your students Tools that focus on answer getting stifle students reasoning Using a neutral response to keep students and adults continue their thinking We all need to understand the content - teachers and learning C...
Nov 07, 2023•32 min
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 1, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Nov 02, 2023•6 min
Place value is so much more than labeling digits. In this episode Pam and Kim dive into place value and common teaching practices that are necessary, but not enough. Talking Points: A fascination with the macabre Typical place value labeling and additional things you can think about to develop place value Precise questioning yields deeper place value thinking What are Exploding Dots? More about our place value system Practicing expanded notation is not enough You can register for the Place Value...
Oct 31, 2023•28 min•Ep. 176
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 25, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Oct 26, 2023•6 min
Division is figure-out-able! In this episode Pam and Kim discuss the most sophisticated strategy for division and precursors that students can begin developing in the fourth grade! Talking Points: An Equivalent Ratios Problem String Precursor relationships Scaling up or Scaling down What makes Equivalent Ratios the most sophisticated strategy for division 4th grade can begin to reason about division using the "bigger, smaller thing" to reason about division 5th grade can begin to reason about eq...
Oct 24, 2023•29 min•Ep. 175
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 18, 2023. Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies. Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Want more? Check out the archive of all ...
Oct 19, 2023•6 min
