In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

Footnotes

The Ordering for the Holiday Party task is rooted in number and has the potential to give students rich explorations by aligning numerical procedures with conceptual underpinnings.

Bartell, Tanya, AnitaWager, AnnEdwards, DanBattey, MaryFoote, and JoiSpencer. 2017. “Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice.” Journal for Research in Mathematics Education48, no. 1 (January): 7–21.

Bartell, Tanya, AnitaWager, AnnEdwards, DanBattey, MaryFoote, and JoiSpencer. 2017. “Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice.” )| false

Battista, Michael T.2017. “Mathematical Reasoning and Sense Making.” In Reasoning and Sense Making in the Mathematics Classroom: Grades 3–5. Reston, VA: National Council of Teachers of Mathematics.

Battista, Michael T.2017. “Mathematical Reasoning and Sense Making.” In )| false

Boaler, Jo. 2002. “Learning from Teaching: Exploring the Relationship between Reform Curriculum and Equity.” Journal for Research in Mathematics Education33, no. 4 (July): 239–58.

Boaler, Jo. 2002. “Learning from Teaching: Exploring the Relationship between Reform Curriculum and Equity.” )| false

Carpenter, Thomas P., Megan LoefFranke, and LindaLevi. 2003. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann.

Carpenter, Thomas P., Megan LoefFranke, and LindaLevi. 2003. )| false

Hiebert, James, and DianaWearne. 2003. “Developing Understanding through Problem Solving.” In Teaching Mathematics through Problem Solving: Grades 6–12, edited byRandall I.Charles (series ed.) and Harold L.Schoen (volume ed.). Reston, VA: National Council of Teachers of Mathematics.

Hiebert, James, and DianaWearne. 2003. “Developing Understanding through Problem Solving.” In )| false

Henningsen, Marjorie, and Mary KayStein. 1997. “Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning.” Journal for Research in Mathematics Education28, no. 5 (November): 524–49.

Henningsen, Marjorie, and Mary KayStein. 1997. “Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning.” )| false

Horn, Ilana Seidel. 2012. Strength in Numbers: Collaborative Learning in Secondary Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Jackson, Kara J., Emily C.Shahan, Lynsey K.Gibbons, and Paul A.Cobb. 2012. “Launching Complex Tasks.” Mathematics Teaching in the Middle School18, no. 1 (August): 24–29.

Jackson, Kara J., Emily C.Shahan, Lynsey K.Gibbons, and Paul A.Cobb. 2012. “Launching Complex Tasks.” )| false

Marcus, Robin, and James T.Fey. 2003. “Selecting Quality Tasks for Problem-Based Teaching.” In Teaching Mathematics through Problem Solving: Grades 6–12, edited byRandall I.Charles (series ed.) and Harold L.Schoen (volume ed.). Reston, VA: National Council of Teachers of Mathematics.

Marcus, Robin, and James T.Fey. 2003. “Selecting Quality Tasks for Problem-Based Teaching.” In )| false

National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). 2010. Common Core State Standards for Mathematics.Washington, DC: NGA Center and CCSSO. http://www.corestandards.org.

National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). 2010. )| false

Nolan, Edward C., Juli K.Dixon, George J.Roy, and JanetAndreasen. 2016. Making Sense of Mathematics for Teaching: Grades 6–8. Bloomington, IN: Solution Tree.

Nolan, Edward C., Juli K.Dixon, George J.Roy, and JanetAndreasen. 2016. )| false

Roy, George J., Sarah B.Bush, Thomas E.Hodges, and FarshidSafi. 2017. “Mathematics Discussions: Expectations Matter.” Mathematics Teaching in the Middle School23, no. 2 (October): 98–105.

Roy, George J., Sarah B.Bush, Thomas E.Hodges, and FarshidSafi. 2017. “Mathematics Discussions: Expectations Matter.” )| false

Smith, Margaret, and Miraim GamoranSherin. 2019. The 5 Practices in Practice: Successfully Orchestrating Mathematical Discussion in Your Middle School Classroom. Reston, VA: National Council of Teachers of Mathematics.

Smith, Margaret, and Miraim GamoranSherin. 2019. )| false

Smith, Margaret S., and Mary KayStein. 2018. 5 Practices for Orchestrating Productive Mathematics Discussions. 2nd ed.Reston, VA: National Council of Teachers of Mathematics

Smith, Margaret S., and Mary KayStein. 2018. )| false