Exploring Focus in the 2011 MA Curriculum Framework for Mathematics Exploration Activity: Examining the Critical Areas in Mathematics April 2011

Desired Outcomes In this activity, participants will: Become familiar with the Critical Areas for their grade level “Unpack” the big ideas, skills and concepts for at least one Critical Area. Understand how the Critical Areas help organize and bring focus to grade level standards. These are the desired outcomes for today’s activity. 2

Supporting changes in practice The new standards support improved curriculum and instruction due to increased: FOCUS, via critical areas at each grade level COHERENCE, through carefully developed connections within and across grades CLARITY, with precisely worded standards that cannot be treated as a checklist RIGOR, including a focus on College and Career Readiness and Standards for Mathematical Practice throughout Pre-K-12 The standards support improved educational opportunities because of these four key areas. They are more focused due to the use of 3-4 critical areas at each grade level. THIS IS OUR FOCUS FOR TODAY. They are more coherent through the use of domains and clusters that make explicit the connections of standards within and across grade levels. They are more clear because the language of the standards is much more precise. They detail various ways of understanding so that teachers will be more likely to ensure students attain deep conceptual understanding. The standards are more rigorous because they explicitly started with the goal of career and college readiness and backtracked to develop a body of knowledge to support this goal. The Standards for Mathematical Practice represent rich mathematical expertise that should be interwoven into genuine mastery of the content standards.

Critical Areas There are typically two to four Critical Areas for instruction in the introduction for each grade level or course. They bring focus to the standards at each grade by grouping and summarizing the big ideas that educators can use to build their curriculum and to guide instruction. The NCTM Focal Points were used as a model for the creation of the critical areas. http://www.nctm.org/standards

Example of a Critical Area _______________________________________________________________________________________ Kindergarten In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; and (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics. (1) Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in Kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away. (2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes. The Standards for Mathematical Practice complement the content standards at each grade level so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise. Example of a Critical Area Have each participant take out their MA Curriculum Frameworks for Mathematics. Explain that the Critical Areas are described at the beginning of each grade level (on the page before the Overview). Click. The short description of one Critical Area is highlighted. Explain that each Critical Area page begins with a short description. Click, the highlighting will disappear. Click. The full description of that Critical Area is now highlighted. For the warm up activity, participants will be given the short description and will be asked what they would expect to find in the full description.

Overview of Activities Warm up: We will consider the impact of focusing our teaching and learning on a few key areas in each grade level (or course) (10 minutes) Main Activity: In small groups, each person will search for standards within a grade level (or course) that connect to a particular Critical Area (20 min) Combine results and discuss (15 min) Debrief the experience as a whole group (10 min) Today’s activity will take about an hour. For the main activity, each of you are going to focus on one critical area. You will record the standards that fall within your critical area and then discuss with your group what how this grouping defines the big ideas in math for your grade. We will end by making some observations about the role of the critical areas in terms of focusing the new standards.

Warm-up Activity Please discuss in small groups and then share with the whole group: How will/could it improve teaching and learning in our school/district when each grade focuses on a few Critical Areas? Grade level PK K 1 2 3 4 5 6 7 8 # of Critical Areas Course Alg I Geo Alg II Math I Math II Math III # of Critical Areas 4 6 5 Ask participants to discuss this question in their small groups for about 5 minutes and then share out with the whole group for about 5 minutes. Time estimate: 10 minutes

Main Activity: Focusing on the Critical Areas Task 1: In small groups, each member chooses a focus Critical Area and reads the description in the Framework. Individually, read each content standard, marking the recording sheet with a: √ when a standard strongly matches your Critical Area and ? when you are not sure Task 2: Transfer individual data to the Grade-Level Recording Sheet. Task 1: Choose focus Critical Area and mark the Activity Recording Sheet. Note that this is somewhat subjective and there are no right answers. Try to make sure each Critical Area is chosen/assigned. If there are more critical areas than participants at a grade level, either combine groups and focus on one grade level or ask participants to start with one Critical Area and then work on a second one if there is time. If there are more participants than critical areas, more than one person can focus on the same critical area. Please note: The full description of the critical area is not listed on the recording sheet. Participants should read the full description in their frameworks. For this activity, they should be flipping between the standards and the Critical Areas. Task 2: Transfer individual data to the group’s recording sheet. (The group level recording sheet is the extra recording sheet at each table. Let participants know that you will be collecting the group recording sheet for each grade level at the end of the work today.) Time estimate: 20 minutes

Main Activity: Grade-level Discussion Group members share a brief summary of their focus Critical Area. Referring to the group’s recording sheet, discuss: Did every standard fall within a Critical Area? Are there standards that fall within more than one Critical Area? Do all the standards within a cluster fall within the same Critical Area? Grade-Level Discussion Questions Looking at the data collected on the group grade level recording sheet, participants will discuss the following questions (Questions are also listed on the recording sheet) in their small groups. Depending on timing and flow, you may want to ask each group to report out 1-2 interesting findings as well. Did every standard fall within a Critical Area? If your group has standards that do not fall within a Critical Area, read that standard and discuss the possible reasons. There will probably be a few standards that do not fall within any Critical Areas. Some possible reasons: the standard is laying the ground work for work in a future grade or the standard is the culmination of more focused work at an earlier grade level. If there are groups that did not finish task one, encourage them to work as a group to see if the standards without a match belong to the Critical Area that was not completed. Are there standards that fall within more than one Critical Area? Read that standard. Does it fall within each Critical Area equally or does it have a stronger connection to one area over another? Do all standards within a cluster fall within the same Critical Area? Share your rationale with the group. Time estimate: 15 minutes

Wrap-up Whole Group Discussion How do the Critical Areas help organize and bring focus to your grade level standards? How should we as a school (or district) use what we have learned today about Critical Areas in planning for the implementation of the new standards? Use these questions to guide a whole group discussion. Time estimate: 10 minutes

Feedback and Information To provide feedback on this activity as a facilitator or participant, or to find more activities and resources, go to the ESE’s Curriculum and Instruction page at: http://www.doe.mass.edu/candi/commoncore/