Using #GETMath to teach the Standards for Mathematical Practice

Some of you may have thought about using the Sums of Consecutive Numbers and joining in the #GETMath conversation but you're feeling stuck because you don't feel like the problem clearly connects to the content for your grade level.  (If you haven't heard about #GETMath, learn more here: http://bit.ly/1eybFKx)

This problem does not need to be (nor should it necessarily be) completed in one or two class periods.  Students can play with the problem during the month of February and share their observations once or twice each week.

This is an opportunity emphasize the Standards for Mathematical Practice!  

1. Make sense of problems and persevere in solving them.
• Sums of Consecutive Numbers has many different aspects to explore.  In introducing the problem to a 4th grade class, some students immediately thought to use more than two addends.  Another student made a conjecture that no even number could be made by only two addends.  The students were ready to get started and excited to look for patterns!  We created a chart where they can confirm or revise their findings and add additional observations.
2. Reason abstractly and quantitatively.
• Because this standard focuses on connecting real situations with symbolic representations, it is not really a standard that could be emphasized during this exploration.  
3. Construct viable arguments and critique the reasoning of others.
• As noted above, students were making conjectures about the patterns and working to prove or disprove their thinking.  As students continue working through the problem, they can add to the class chart.  We even plan to video chat with another 4th grade class - what a great opportunity to share our arguments and discuss our thinking about the problem!
4. Model with mathematics.
• As with SMP #2, this would not be the best standard to apply with the Sums of Consecutive Numbers problem.  Students might use a table to organize their thinking but they do not apply math to solve a real-world problem.
5. Use appropriate tools strategically.
• As with SMP #2 and #4, this would not be a strong standard to emphasize with this particular problem.  While the table or organizer used by students might be considered a tool, it would be a weak connection to this standard.
6. Attend to precision.
• In the Sums of Consecutive Numbers problem, students need to be sure that the numbers they use are indeed consecutive numbers and check to be sure the sum they find is accurate.  They also need to be able to communicate their thinking in a way that is clearly understood by others.  This would be a strong standard to emphasize with this problem!
7. Look for and make use of structure.
• The Sums of Consecutive Numbers problem provides students with an opportunity to notice and discuss the structure of mathematics.  For example, why can the odd numbers always be made by the sums of two consecutive numbers? 
8. Look for and express regularity in repeated reasoning.
• The Sums of Consecutive Numbers problem provides students with an opportunity to observe patterns and reason about generalizations.  For example, what numbers cannot be made by the sums of consecutive numbers?  Could you predict the next number that cannot be made as a sum of consecutive numbers?  Can you write a rule that will help you find all of the numbers that cannot be made by the sum of consecutive numbers?

The Sums of Consecutive Numbers problem has clear connections to five of the eight Standards for Mathematical Practice.  The CCSS emphasizes that the Standards for Mathematical Practice are as essential as the mathematical content.  While it would be difficult to emphasize five Mathematical Practices within your lesson, there are many opportunities for you to engage students in the Standards for Mathematical Practice through this problem. 

I hope you will join us and share your thinking at #GETMath!