Links to Rigorous Tasks
http://www.openmiddle.com This website allows you to browse by grade level by DOK for both skills and concepts and strategic thinking.
http://nzmaths.co.nz/problem-solving New Zealand Maths has Six Problem Solving Levels organized by strands. The problems allow for multiple problem solving strategies and could provide for exciting student discourse as they compare and contrast approaches to solving the problems.
http://nrich.maths.org/frontpage Enrich mathematics is a website designed by the University of Cambridge. The problems are open ended and require multiple steps.
http://illustrativemathematics.org/content-standards Click on grade level and the specific domain to find tasks
Achieve the Core
Achieve the core has wonderful tasks designed for specific key mathematical ideas. More tasks continue to be added.
Internet for Classrooms: Math tasks for 3rd -5th grade students linked to Common Core Math Standards.
Engaging discourse requires rigorous tasks!
Guide Principle #1 from the California Mathematics Frameworks states: “For students to achieve mathematical understanding, instruction and learning must balance mathematical procedures and conceptual understanding. Students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting, thought-provoking situations. Student understanding is further developed through ongoing reflection about cognitively demanding and worthwhile tasks.”
Cognitively demanding tasks require a higher level of depth of knowledge (DOK). There are many great websites that have problems written for students at DOK levels 2 and 3. These problems can be used to make sure students truly have a deep understanding of a concept vs. understanding the steps to solve a specific type of a problem.
Implementing a Rigorous Task
PRIOR TO LESSON:
1st: What do I want students to deeply understand? What is the Big Mathematical Idea?
2nd: What background knowledge might students need prior to launching the task?
3rd: Is there any vocabulary that is necessary for engaging in the task?
4th: What misconceptions may arise?
5th: What questions can I be prepared to ask to move thinking forward vs. giving away the process to solve the task?
6th: How can I personalize the task to make it relevant to my students?
7th: How do I provide multiple entry points? Do I need to differentiate the task for specific students?
Example of introducing a juicy problem or rigorous task
Based on the mathematical understandings and outcomes desired for all students, have individuals share out in a sequence that will make the learning accessible to all students. Moving from the most concrete to more abstract is often a good strategy. As students share, compare and contrast the strategies, making connections between pictures and numbers, graphs and charts, etc. Focus students on the relationships between the drawings and equations, and the relationship between the story and the drawings, numbers, charts, etc.