Thursday, November 29, 2018

Countdown to the Holidays!

You know how I love nrich.maths.org for rich problems to solve.  Well--today I saw that they have an advent calendar for elementary students.  Each day has a rich task that accompanies it.  The problems are not holiday based; only the design of the calendar is.

You might just refer to it as a holiday countdown calendar, but no matter what you call it, it should lead to some good student thinking!



Monday, November 26, 2018

3 Act Tasks: Have you tried them yet?



3 Act Tasks offer our students such an engaging opportunity to make sense of math! However, as teachers, sometimes we are afraid to try something new not knowing where it might take us and scared that something bad might happen.  I just heard an analogy recently about this being like being at the top of a rollercoaster:

via ytCropper


And, while it might have twists and turns and dropoffs, not to mention bugs in the face, it also brings an excitement and thrill that we rarely find doing a traditional math lesson. We need to think about putting ourselves in that precarious position at the top of the rollercoaster; it's what we ask our students to do on a regular basis so that they can grow.  We should try it, too!

3 Act Tasks are real-world problem-solving scenarios which require students to make sense of what to do.  During Act 1, they use the reading skills of visualizing, predicting, and inferring in a math context.  They figure out what they need to know to solve the problem. In Act 2, students work to solve the math question in a way that makes sense to them. They discuss their thinking with a friend and compare their answer to their estimate.  Act 3 is exciting because that is when they find out if they were on the right track!  


While they are working during Act 2, you are monitoring (and asking questions that help them understand--not helping too much).  You are monitoring to see the methods that students used in order to solve the problem.  During Act 3, it is your job to have students share ways that they solved the problem.  These should be sequenced so that you can show connections between different methods. Be clear on what your math target for the lesson was and be sure that your models and discussion help that math target to be evident to everyone.  You synthesize the learning at the end of the lesson.


3 Acts are very visual and often use videos to help students better understand the situation. They follow more of the format of "you do, we do, I do" rather than the traditional layout of "I do, we do, you do."


Typically, a 3 Act Task in K-2  about 20-30 minutes.  In 3-5, a task usually takes about 4o minutes.  As students get stronger and more comfortable, the time needed for a 3 Act might decrease.


I am happy to come and model a 3 Act Task for you and your class, but I know that many of you can do them without my support.  You just need to put yourself on the rollercoaster!


At the top of this blog, you will find a tab labeled 3 Act Tasks.  This will take you to a large number of standards-aligned tasks that I have organized using SMART Notebook (and sometimes Google slides).  They are by a variety of mathematicians; I just put all of the pieces together into one format.  You can also find more great tasks by clicking here or here or even by Googling 3 Act Tasks.


As always, share with me your questions, struggles, or successes and let me know how I can help!

Monday, November 19, 2018

Would You Rather? -- Holiday Edition



If you are looking for some problem solving to get your students thinking and proving themselves while mixing in some holiday cheer, maybe these Would You Rather problems will work for you!

Would You Rathers are something that students are very familiar with, and these just include a mathematical twist.  Students can choose whichever option they want, but they need to have a mathematical explanation of why that is what they chose or didn't choose.  They can be used with students of all ages and offer great opportunities for collaboration.

If you like these, you can find more like them at this site, but I am betting you can come up with some good ones of your own!

Holiday Would You Rather 1

Holiday Would You Rather 2

Holiday Would You Rather 3

Holiday Would You Rather 4

Holiday Would You Rather 5

Thursday, November 15, 2018

A Stepping Stone to a More Student-Driven Workshop

If you are still looking for ways to make your math workshop more about collaboration and problem-solving rather than about independent work and computation, a Week of Inspirational Math by Jo Boaler/Youcubed might just be the ticket!  If you have done any of these lessons before, you know how awesome they can be!  Well--she has recently posted her WIM #4!  That's right--4 weeks of math explorations and engaging lessons that you can use to build your mathematicians.

These engaging lessons are organized by grade level strands and are grouped into a week's worth of lessons.  They are great to use a week at a time, but you certainly could use them independently if you needed to.  They embody the paradigm shift in math education with a focus on growth mindset, visual math, patterns, and collaboration.

Besides that, each lesson will really engage your students for at least math period.  (Oftentimes, students keep working on the problem after class...) Each lesson begins with a video that you can show if you wish.  It helps to build the growth mindset in your students and presents them with mathematical thinking that helps them to see math is all around them.  After the video, there is a lesson (with full lesson-plan) that you can have students work on in small groups and share out with the class.  You can learn so much about your students as you circulate the room listening to their thinking, and they will learn so much about themselves as mathematicians!

With the craziness of the holidays, you might find a few days where some WIM activities are just the ticket, and they might cause you to begin rethinking your workshop!  They might be a good way to spend your math time during those days right before holiday break, but they might also be an awesome way to set the tone for 2019!

I have blogged about WIM before, but I can't tell you enough how much they can invigorate and change your classroom, your student's thinking, and your own thinking!  Time well spent!

Saturday, November 10, 2018

Building Collaborative Thinkers


Are you giving your students enough time to work with each other to solve problems?  This is an area of growth for many of us.  Consider the following problem.  How could you build it into your math workshop?  In what ways would you anticipate that your students would be able to prove their answer?

Thanksgiving in the US has been declared to be the fourth Thursday in November.  This year, Thanksgiving is the earliest date it can possibly be.  What is the latest date Thanksgiving can possibly be? Be prepared to prove your answer.

I'd love to hear your results!


Tuesday, October 30, 2018

The Last Number--an exploration



Just found this problem recently, and thought about what a great exploration it would be--for nearly any age!

Consider the string 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Cross out any two numbers in this list and add the difference to the end of the list. This new number is now part of the list. Continue the process of crossing out two number on the list and adding the difference until there remains only one number. What can you say about the last number? Explore. [from Richard Hoshino]


This problem offers a rich exploration of number while practicing basic subtraction facts. (Making it great for 2nd grade!).  

Once your students have a conjecture about the final number, can they try that conjecture out on a different string of numbers?  What happens when your string goes from 1-15?  How about a string from 3-12?  Can they figure out what the pattern is and why the difference ends up like it does?  Even if they can't, they should have some rich time practicing subtraction, working together, and looking for patterns!

Can you figure out what is happening?  If you are like me, you might spend a lot of your free time working on this problem to see if you can make sense of it!

Tuesday, October 23, 2018

Building Conceptual Understanding of Fractions

In 3rd, 4th, and 5th grades, fractions dominate much of our instructional time, and it is important that we work to help our students gain a firm grasp on the concepts of fractions. Going deep now will help them down the road as they use fractions in more complicated mathematical situations.

A reminder of the progression of fractions in elementary school by Graham Fletcher allows us to remember how important our models are:



Sometimes I'm afraid that teachers steer clear of fraction exploration because they are uncomfortable with them themselves.  Imagine all of the learning that could occur if we went out of our own comfort zone with our students?  

I have shared Fraction resources before in this blog.  I have also shared an exploration or two.  Here are some more resources that might help your students (and you) to make more sense of fractions.

When and when not to give the answer:  This Marilyn Burns' post offers an opportunity for your students to build their own understanding of fractions.

Fractions, Decimals, & Percentages:  A number talk which begins with fraction addition.

Exploring Fractions:  An article from nrich.maths.org which offers links to rich tasks that develop a deep understanding of fractions.

Illustrative Mathematics also has some resources that will help you better understand the horizontal progression of fraction skills.

Maybe you find one or two ideas above to help you stretch during your fractions unit--that's great!  Don't try to change everything all at once. As always, let me know if there is something I can do to help!