# data[].attributes.body
Grades K - 12

# data[].attributes.body
Grades 5 - 8

# data[].attributes.body
Grades K - 6

# data[].attributes.attachment_link.keywords[]
good questions for math teaching: why ask them and what to ask

# data[].attributes.attachment_link.keywords[]
mathematics - study and teaching (elementary)

# data[].attributes.attachment_link.keywords[]
education / teaching methods & materials / mathematics

# data[].attributes.attachment_link.keywords[]
teaching methods & materials - mathematics

# data[].attributes.attachment_link.title
Good Questions for Math Teaching: Why Ask Them and What to Ask, K-6

# data[].attributes.attachment_link.description
Do you think it makes sense to split a day into twenty-four hours? Would another number have been a better choice? "Good questions" promote students' mathematical thinking and understanding. These best-selling books offer a wealth of sample questions and guidance on how to creat...

# data[].attributes.body
Grades K - 12

# data[].attributes.body
Grades K - 12

# data[].attributes.attachment_link.readable_text
We understand that it's challenging for teachers to find resources to support students in building an enduring understanding of mathematics. Only the IM Certified Experience helps teachers catalyze mathematical proficiency with an engaging and inclusive approach that lifts students up to the skills, understandings, and practices that will stay with them for a lifetime. IM K-12 Math gives you exclusive access to engaging content and professional learning and to an inclusive community.

Help students become lifelong math learners. Preview IM K-12 Math™.

# data[].attributes.attachment_link.title
Illustrative Mathematics | K-12 Math | Resources for Teachers & Students

# data[].attributes.attachment_link.description
We understand that it's challenging for teachers to find resources to support students in building an enduring understanding of mathematics. Only the IM Certified Experience helps teachers catalyze mathematical proficiency with an engaging and inclusive approach that lifts students up to the skills, understandings, and practices that will stay with them for a lifetime.

# data[].attributes.body
Grades 3 - 12

# data[].attributes.attachment_link.readable_text
Shamrocks in Ireland are actually be 3-leafed white clover, trifolium repens. If you are lucky , you can sometimes find a four-leafed clover. How rare is finding a 4-leafed clover? How hard do you have to look? What size area of clover must you examine to find one?

Class Opener

We know the saying "Spring forward, fall back".

What does this expression mean?
Early Sunday morning, March 14th at 2 am, we will change our clocks to read 3 am and start Daylight Savings Time.

Will you wake up and go to sleep earlier or later on Sunday?

What kind of chart or picture could you draw to help you compare before and after Daylight Savings Time has begun?

Will your Sunday seem longer or shorter?

How do you expect that you will feel?

8 Activities for π day !

Celebrate π in your school and in your math class with activities that demonstrate how π was derived; visually show why π makes sense; show a surprising place where π is used; increase students ability to measure and long divide; applauds the talent of people who can memorize large strings of numbers; and lets students just have fun.

PiDay-ClassOpener - Puzzle to ponder with a surprising outcome.

For members: PiDayClassOpenerSolution.pdf

What is Pi?.pdf - The logic of finding the perimeters of inscribed and circumscribed polygons as the number of sides to the polygons increase.

For members: What is Pi-solution.pdf

HatSize.pdf -Hat size is a measure of the diameter of your head ... but how do you measure that ... through your ears?
Clicking on the above image will take you to Brian's movie of making Hot chocolate.
Act I - Watch the movie. Making hot chocolate movie or by clicking on the picture above. What do you notice and wonder?

Act II - What information would be helpful to figure out how many 1/4 teaspoons you need? How many 1/4 teaspoons are equivalent to a whole teaspoon? How can you visualize this? What math models this problem? If helpful check out this online fraction bar tool.

This "Last Great Race on Earth" will start on Sunday, March 7th at 2pm near Willow, Alaska.

The race route has been changed to be safer for all those involved. Each checkpoint will be visited twice to reduce the number of volunteers and staff needed to serve the dogs and mushers.

If you were a musher, how would you rethink your plans?

The activity: Iditarod2021.pdf

Last year, Dunkin Donuts offered a great deal for getting two breakfast sandwiches at a pretty low cost.

Check out their poster for the sandwich costs and pictures.

Can you figure out the cost of each sandwich's components?

The activity: Dunkin'sGo2s.pdf

CCSS: 6.EE, 7.EE, 8.EE, HSA

# data[].attributes.attachment_link.description
Shamrocks in Ireland are actually be 3-leafed white clover, trifolium repens. If you are lucky , you can sometimes find a four-leafed clover. How rare is finding a 4-leafed clover? How hard do you have to look? What size area of clover must you examine to find one?

# data[].attributes.body
Grades 6 - 12

# data[].attributes.attachment_link.description
Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for ‘Career and College Readiness’ at High School Grades 9 and above. Some lessons are focused on developing math concepts, others on solving non-routin…

# data[].attributes.body
Grades 2 - 12

# data[].attributes.attachment_link.description
ASKING STUDENTS TO CHOOSE A PATH AND JUSTIFY IT

# data[].attributes.body
Grades 3 - 12

# data[].attributes.attachment_link.description
Top menu: NT = Number Talks PT = Pattern Talks (hover over NT to see)

# data[].attributes.body
Grade 3 - 12

# data[].attributes.attachment_link.readable_text
The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online.

The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math 9 (Integrated), Math 10 (Integrated), and Math 11 (Integrated) are from Pearson. Other Scope and Sequences were developed by me, modeling a similar visual style.
Grade 3 CCSS PrBL Curriculum Map Grade 4 CCSS PrBL Curriculum Map Grade 5 CCSS PrBL Curriculum Map Grade 6 CCSS PrBL Curriculum Map Grade 7 CCSS PrBL Curriculum Map Grade 8 CCSS PrBL Curriculum Map Math 9 (Integrated) CCSS PrBL Curriculum Map Math 10 (Integrated) CCSS PrBL Curriculum Map Math 11 (Integrated) CCSS PrBL Curriculum Map Algebra 1 CCSS PrBL Curriculum Map Geometry CCSS PrBL Curriculum Map Algebra 2 CCSS PrBL Curriculum Map
Be sure to check back often as these curriculum maps are bound to change when new cool activities are added on math blogs worldwide. I'll be adding more and more curriculum maps in due time. Also, if you have a favorite particular task that isn't here (or just comments in general), let me know in the comments!

For more on Problem Based learning, you can check out my previous posts on the topic.

- Geoff

# data[].attributes.attachment_link.title
Common Core Problem Based Curriculum Maps

# data[].attributes.attachment_link.description
The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online. The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math...

# data[].attributes.body
Grades 6 - 12

# data[].attributes.attachment_link.keywords[]
mathalicious lessons teach standards-based math through real-world topics that students care about.

# data[].attributes.attachment_link.description
Mathalicious lessons teach standards-based math through real-world topics that students care about.

# data[].attributes.body
Grades 6 - 12

# data[].attributes.body
Grades K - 12

# data[].attributes.attachment_link.description
My growing list of free real world problem-based lessons for grades 2 through high school. Includes links to download multimedia and teacher guide.

# data[].attributes.body
Grades K - 12

# data[].attributes.attachment_link.readable_text
Thursday evening I asked Frank Noschese (@fnoschese) and Elizabeth (@cheesemonkeysf) a question about whether they thought there was any value in students using a reductive, drill-and-kill math practice exercise platform, provided that it was accompanied by rich tasks and assessments in a classroom that demands synthesis and critical thinking, and provides students with opportunities to develop mathematical habits of mind.

I received a reply, but I'm more interested in a tangential question @NatBanting asked in the middle of the exchange:

@mjfenton Curious: what makes a task "rich" in your eyes? I'm trying to synthesize my view.

- Nat Banting (@NatBanting) August 16, 2013

I've been throwing that phrase ("rich tasks") around a lot more lately, in tweets, blog posts, workshops, and conversations at school and at home (my wife is either amazingly longsuffering or genuinely interested-maybe both?-when it comes to talking about math education). So what exactly is a "rich task"? What do other people have in mind when they use the phrase? What do I mean when I use it?

I told Nat that I'm still working that out in my own mind, but I think it's time to clarify what I mean, if for no other reason than to have a better sense of what I'm looking for when I try to find, adapt, and/or create rich tasks for my own students.

Here's What I Do Mean

A rich mathematical task is one that...

1. Has a low floor and a high ceiling. The first of many ideas I've stolen from others, this one from so many sources I don't even know who to credit anymore. Most recently, Dan Meyer has me thinking about this in his Makeover Monday series. The bottom line: everyone can start, no one can truly say they've exhausted the problem's potential (at least not in a 50-minute period).

2. Has multiple entry points, invites use of multiple representations. Student A starts by exploring numerically, Student B begins by investigating graphically, Student C jumps in by reasoning algebraically, and I don't have to tell two of them that their approach is a dead end because-even if they don't always make it-there is fruitful territory a little further down the path in any of their approaches.

3. Has multiple solution paths, provides opportunity for rich discussion. If there's only one way to solve the task students lose out on the rich discussion of making connections between various approaches and teachers lose the opportunity to build a mathematically coherent, concrete-to-abstract storyline as they orchestrate these discussions.

4. Integrates multiple topics. I owe a lot of what I'm thinking here to a single word Daniel Schneider used in a post about assessment. After my initial foray into standards based grading left me dissatisfied with an overly fractured curriculum, I'm now placing a high priority (philosophically, at least) on tasks and assessments that bring multiple topics together. A rich task, in my estimation, should demand that students wrestle with multiple topics from multiple domains (if I can use the term in the CCSSM sense).

5. Engages student interest, is mathematically/cognitively challenging. I'm a little mixed up here, because I believe engaging students' interest is massively important, but I'm not ready to throw away tasks that fail to generate buzz among students if I know they nevertheless provide great opportunities for exploration and discussion.

Here's What I Don't Mean

To clarify what I think a rich task is, I'll share a few thoughts on what I think a rich task is not:

1. A well-crafted, but constrained guided-discovery activity. I value this kind of activity, but when students are guided along a specific path to a specific goal, it pushes the lesson into a different category for me.

2. A thoughtfully constructed lecture or an engaging presentation. If the instructor is doing the heavy lifting during class, I would say the students are not engaged in a rich mathematical task. I'm not opposed to heavy lifting, especially in preparation outside of class, but students need to play an active, central role in exploring/solving/reporting if I'm going to use the "rich task" label for an activity.

3. A challenging problem for which students already have a tried-and-true method. I have a large stack of started-but-not-finished books, some related to math and education, others not. George Polya's How To Solve It is on the list, though I've read enough of it to be provoked and inspired, particularly by the distinction Polya provides between a problem (solution/method not known) and an exercise (solution/method already known).

I'll Close with a Link...

Incidentally, after typing out the post, I Googled "what is a rich mathematical task" and found this.

...And an Invitation

I would love to hear what you think are the key characteristics of a rich mathematical task. Drop a line in the comments or send me a line on Twitter.

# data[].attributes.attachment_link.description
Thursday evening I asked Frank Noschese (@fnoschese) and Elizabeth (@cheesemonkeysf) a question about whether they thought there was any value in students using a reductive, drill-and-kill math practice exercise platform, provided that it was accompanied by rich tasks and assessments in a classroom that demands synthesis and critical thinking, and provides students with opportunities to develop...

# data[].attributes.attachment_link.description
2016 Aug 6. Here is video of this task structure implemented with elementary students. 2013 May 14. Here's a brief series on how to teach with three-act math tasks. It includes video. 2013 Ap...

# data[].attributes.body
Grades 3 - 12

# data[].attributes.body
Grades K - 12

# data[].attributes.attachment_link.description
Inquiry Maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement (called a prompt). The website has resources for secondary school teachers.

# data[].attributes.body
Grades K - 12

# data[].attributes.attachment_link.description
STEM Learning Ltd offers the largest collection of learning resources for teachers and educators of science, technology, engineering, computing and mathematics in the UK.

# data[].attributes.headline
Open Middle:Challenging Math Problems Worth Sharing

# data[].attributes.subject
Open Middle:Challenging Math Problems Worth Sharing

# data[].attributes.body
Grades K - 12

# data[].attributes.body
Grades K - 12

# data[].attributes.attachment_link.readable_text
Students

In case you missed our Primary and Secondary Challenges during the summer break, we are continuing to feature them, so you can enjoy them for another month

Your Solutions

See if your solutions to our recent problems have been published
Primary
Secondary

For regular updates, sign up for our Newsletter

# data[].attributes.attachment_link.title
NRICH - Mathematics Resources for Teachers, Parents and Students to Enrich Learning

# data[].attributes.attachment_link.description
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

# data[].attributes.body
Grades K - 12