M ATH C OMMITTEE Mathematical Shifts Mathematical Practices

M ATH S HIFTS 1. Focus: Focus strongly where the standards focus. 2. Coherence: Think across grades and link to major topics. 3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.

F OCUS Is …. Fewer topics taught for longer Related content Solid conceptual understanding Procedural skill Math application Is not …. Many topics taught fast Unrelated content Rules with no understanding

C OHERENCE Is…. Links topics across grades Connect content within a grade Coherent progressions Building new understandings on solid foundations Is not…. Random topics done at random times New standards without the necessary foundation

R IGOR Is …. Fluency: Speed and accuracy Solid conceptual understanding Application of skills in problem solving Real-world problems and tasks Is not…. Lots of homework More problems A set of mnemonics Teaching students “how to get the answer”

8 M ATHEMATICAL P RACTICES

M ATHEMATICAL P RACTICES  The mathematical practices describe ways in which the students should engage with mathematics  The mathematical practices should connect to mathematical content in mathematics instruction.

T ABLE A CTIVITY Match the “I can” statements with the MP Each MP has 8 “I can” statements

I can try many times to understand and solve a math problem I can think about the math problem in my head first I can make a plan, carry out my plan and evaluate its success I can take numbers and put them in a real-world context I can look for entry points for a solution I can write and solve an equation from a word problem I can check my answers and determine if it makes sense I can use properties to help solve problems I can monitor my progress I can make sense of quantities and their relationships I can look for clue words I can manipulate equations I can picture the situation I can create an understandable representation of the problem solved I can explain the problem to myself I can represent symbolically Make sense of problems and persevere Reason abstractly and quantitatively

I can make a plan and discuss the strategy with other students I can use math symbols and numbers to solve problems I can make conjectures I can recognize math in everyday life I can use examples and non- examples I can estimate to make problems easier I can identify flawed logic I can use pictures to solve problems I can show how I got my answer I can analyze relationships mathematically to draw conclusions I can understand and use definitions I can interpret results I can defend my mathematical reasoning I can identify important quantities and use tools to show relationships I can ask questions to clarify I can simplify problems with diagrams, tables and flowcharts Construct a viable argument Model with mathematics

I can use math tools to solve problems I can check to see if my calculations are correct I can make an organized list I can use precision when communicating my ideas I can decide what tool will be most helpful I can calculate accurately I can use technology to deepen my understanding I can correctly use math vocabulary I can use a graphing calculator I can speak, read, write and listen mathematically I can strategically use estimation to detect errors I can state the meaning of symbols I know when to use a table I can accurately label axis and measures I can use a protractor I can calculate efficiently Use appropriate tool strategically Attend to precision

I can use what I already know about math to solve a problem I can use a strategy that I used before to solve another problem I can determine a pattern I can identify calculations that repeat I can shift perspective I can look for general methods I can see complicated things as being composed of smaller objects I can maintain oversight of the process, while attending to the details I can sort shapes by attributes I can evaluate the reasonableness of results I can see how numbers are put together I can recognize repeated subtraction as division I can use the distributive property I can find short cuts I can use dimensions to calculate area I can notice repeated strategies Look for and make use of structure Look for and express regularity

T ABLE A CTIVITY #2 Look at the class task/activity. Decide which 2 mathematical practices are addressed in the task.

B E I NTENTIONAL !