For the Learning trajectory assignment I reviewed the 2nd grade math curriculum as presented by Bridges Mathematics Curriculum. I picked three lessons from Unit 3 Module 2 (Adding and Subtracting on the Number Line) that I felt would encourage students mathematical skill development. For the course of this write-up, I will be referring to the information presented in my Learning Trajectory as I investigate further the content of these lessons.
2. Big Idea and Connection to CCSSM: In my Learning Trajectory, I determined the big idea of Unit 3 Module 2 of the 2nd grade Bridges Mathematics Curriculum to be “Skip counting, rather than counting up, is a more efficient strategy for solving double digit addition and subtraction equations. Number lines facilitate the use of skip counting.” I believe it also worthy to not that Common Core State Standards for 2nd grade dictate that students must capable of skip-counting as noted in Standard 2.NTB.A.2 “Skip-count by 5s, 10s, and 100s.” (Common Core, 2010)
As well as skip-counting, it is necessitated by the 2nd grade CCSS’s that students have the capacity to utilize a number line, as noted in Standard 2.MD.B.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, and represent whole-number sums and differences within 100 on a number line diagram. (Common Core, 2010) In cumulation, the two standards noted above are encouraging that students develop skills to add and subtract numbers on a number line, utilizing the skip-count strategy. These standards are what generate the big idea of the three lessons I have decided to analyze for this project.
3. Conceptual Understandings Addressed: The curriculum anticipates that as students progress through these lessons, their conceptual understandings of solving addition and subtraction problems via counting strategies and number line usage will be developed. Throughout all three lessons the students will be provided with varying levels of activities aimed at enhancing the skills mentioned above. For example, students may be asked to identify age differences based on people age data that was recorded on a number line. Eventually, students will also strive to understand why skip counting can be considered a more efficient strategy than counting up when working on problems. It should be understood that when the problem includes numbers with a wide range between the two, that the type of confusion and mistake making that might happen with traditional the count up strategy can be surpassed with the use of skip counting.
4. Procedural Fluency Addressed: We see procedural fluency being addressed in these lessons when students are asked to know how to determine the distance between two numbers on a number line. Students use many different strategies, but they must describe their individual processes and also utilize a teacher provided strategy. For example, when counting, students must remember what numbers to verbalize next in the oral string of words.
5. CCSSM Mathematical Practices: The CCSSM Mathematical Practice that pertains to this set of lessons the most, is number four: “Reason abstractly and quantitatively” (Common Core, 2010). This mathematical practice discusses how students are able to identify the relationships between numbers and use that information to solve across various contexts. Students are given many story problems to solve throughout all three lessons, problems which can all be solved if they understand how to draw out the information from the problem and work solely with the critical numerical information.
6. Connections to Later Big Ideas: In my Learning Trajectory assignment, I identified two big ideas later big ideas that the present three helped students become prepared for. The first later big idea is “using pattern knowledge to fill in missing numbers on a number line.” The big idea of these lessons is that students are utilizing information from a story problem to help them fill in missing information on a number line. Eventually students will recognize patterns and be able to create equations to help fill in missing information more efficiently. The second later big idea identified in my Learning Trajectory is “Use bundling to solve addition and subtraction equations.” This big idea builds on the big idea for these lessons because it requires students to use physical grouping strategies, which bring the skip counting to life. For example, students will be asked to determine the amount of sticks in a collection of bundles. In order to solve this students will need to employ addition and subtraction strategies such as skip counting from the earlier lessons.
7. Prerequisite Skills: In my Learning Trajectory I identified two prerequisite skills that would be essential to student success in the three lessons | chose. The first prerequisite skill is the understanding of how to create addition and subtraction equations. The second prerequisite skill is to understand place values. This connects to the big idea of skip counting. In these three lessons students are asked to evaluate distances between plots on a number line by using various strategies, including skip counting. The Common Core State Standards has students in 2nd grade begin working with addition and subtraction strategies. In the standard 2.0A.A. 1 students are asked to “Represent and solve problems involving addition and subtraction.” (Common Core, 2010).