Sense of Wonder and curiosity is innately wired in human beings.
http://www.5280math.com/noticing-and-wondering/
http://robertkaplinsky.com/lessons/
There are a number of resources available as sources of great, engaging mathematics tasks.
Michigan-developed MAISA CCSSI Units (Michigan Association of Intermediate School Administrators – Common Core State Standards Initiative)
Grades: kindergarten through high school
The MAISA project has taken the CCSS-M and CCSS-ELA standards and placed them in units of study for all grades K-11. The mathematics units include a unit plan, a detailed model lesson from the unit, one or more formative assessment tasks, and a wealth of other resources. The units are made available through MAISA’s Atlas curriculum management software’s public site.
Jerry Burkhart’s “Creative Math Prompts” provide visual prompts for exploring “What do you wonder?” “What do you know?” See also his “Problems That Never End”.
Jo Boaler and her youcubed team at Stanford University have created and gathered a number of tasks across all grade levels. Since fall 2015, the team has also created a “Week of Inspirational Math” with the idea of kicking off the school year with highly engaging rich mathematics tasks.
Grades: kindergarten through high school
MathHooks.com – intriguing “hooks” for each of the grades 7 and 8 mathematics standards to help teachers kick off lessons through inquiry.
EMATHS – Excellent Michigan-produced tasks and units for Algebra 1, Geometry, and Algebra 2. The professional learning is also great, and along with the tasks, can change teaching and learning to enrich mathematical understanding and competence.
Mathematics Assessment Project – from MARS (Mathematics Assessment Resources Service)
Grades: Mainly 6-8 and high school
See the Index of Classroom Challenges for 100 lessons in total. See the Index of Summative Tasks for middle and high school novice, apprentice, and expert tasks.
A 1993 NSF funded mathematics assessment project, Balanced Assessment included teams from Harvard, the University of California, Michigan State University, and the University of Nottingham. It was ahead of its time in creating tasks (rather than “problems”) for students to engage in, explore, and develop and provide evidence of deep understanding. Tasks are available at all grade levels, and have since been published by Corwin Press and by Teachers’ College Press.
Grades: kindergarten through high school
NRICH – Enriching Mathematics – from the University of Cambridge
Grades: kindergarten through high school; Select the “Teachers” menu option and choose from Early Years, Primary, or Secondary.
Inside Mathematics – Includes “Problems of the Month” and “Performance Assessment Tasks”, along with other helpful resources for teachers and professional learning providers.
Graphing Stories: Fifteen seconds at a time A collection of short video clips illustrating various types of change for students to graph. Not a “rich task” in itself, but the site takes the “heavy lifting” of providing suitable edited video clips for teachers to use as part of a task.
Grades: Middle school and high school
101 Questions provides a wealth of photos and video clips to inspire asking great mathematical and statistical questions. These graphics can help kick off a rich investigation.
Grades: mainly middle and high school; some suitable for upper elementary.
National Science Digital Library – Includes mathematics tasks. Choose MATHEMATICS as the “subject” and the grade level you are interested in viewing.
National Council of Supervisors of Mathematics – NCSM has published a new version of its “Great Tasks for Mathematics” (original set of problems released in the 1990s). Two books.
Grades: K-5 (“NCSM Great Tasks for Mathematics K-5”) and 6-12 (“NCSM Great Tasks for Mathematics 6-12”)
Dan Meyer’s Three-Act Math Tasks – For background on using Three-Act Mathematical Stories, read Dan’s blog here.
3-Act Math Problems – Inspired by Dan Meyer. An innovative way of approaching and enriching mathematics problems; many sites are noted in this LiveBinder.
Grades: Mainly middle school and high school.
Achieve the Core – Includes mathematical tasks along with other resources of interest to teachers.
Emergent Math – Includes CCSS Problem-Based Curriculum Units, along with links to the mathematical tasks within the units.
(Fee-based) Mathalicious has a number of tasks tagged to standards. They have now organized some tasks into units to assist teachers with embedding rich tasks into lessons throughout the course.
Grade levels: Grade 6 through High School
PBS provides over 1900 math-related itemsto spark ideas for rich tasks. Most of the entries here are not fully-developed tasks, but inspirations or launches for tasks. Use the filter provided to explore what’s available for your grade(s).
Grade levels: Pre-K through High school
Illustrative Mathematics has released an excellent mathematics curriculum resource for grades 6 through 8. It has received a nearly perfect score from EdReports.org. See also the other rich tasks at the website.
Math Landing: Resources and Tools for Elementary Math Specialists and Teachers. Grades: K-5. Check out the Classroom Collections. Grouped by Standard of Mathematical Practice.
Estimation 180 provides photos which teachers can use a prompts for estimating and developing number sense. Many of these photos could serve as prompts for Number Talks or Math Talks. The site provides lessons, other activities, and other resources.
Grade Levels: kindergarten through high school
CIC Task Library (Complex Instruction Consortium) – Tasks for High School – You may need to sign in with a Google account. Once in the site, click on CONSORTIUM, and then on TASK LIBRARY.
East Midlands (U.K.) Math Tasks – A collection of tasks along with teacher guides.
Grade levels: kindergarten through high school
North Carolina has developed a number of tasks as part of their Department of Education curriculum support. They are posted by grade level. Look under the “Compiled Documents”.
Click on the grade level to visit:
kindergarten 1st grade 2nd grade
K-2 Formative Tasks Overview
3rd grade 4th grade 5th grade
Grades 3-5 Formative Tasks Overview
6th grade 7th grade 8th grade
Grades 6-8 Middle Grades Overview
North Carolina High School Resources – “Math Resources for Instruction” documents provide or link a suggested task for each standard. Look in the purple “Instructional Resources” box of the table.
Rich learning tasks from New Zealand. See also their “Counting Collections” resources.
Resources to help plan for and implement these great math tasks for teaching and learning:
Thinking Through a Lesson Protocol (TTLP)
The Thinking Through a Lesson Protocol
For a number of “math in real life” resources (not necessarily rich tasks), visit Math in Daily Life from Annenberg (Learner.org)