Breaking Down The Common Core S 8 Mathematical Practice Standards

Bonisiwe Shabane
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breaking down the common core s 8 mathematical practice standards

The Common Core mathematical practice standards are the foundation for mathematical thinking and practice for students as well as guidance that helps teachers modify their classrooms to approach teaching in a way that develops... Think of these standards as a guide to creating a more complex and absorbing learning experience that can be applied to everyday life, instead of being left in the classroom. The first Common Core mathematical practice standard is found in almost every math problem across the board. It means that students must understand the problem, figure out how to solve it, and then work until it is finished. Common Core standards encourage students to work with their current knowledge bank and apply the skills they already have while evaluating themselves in problem-solving. This standard is easily tested using problems with a tougher skill level than already mastered.

While students work through more difficult problems, they focus on the process of solving the problem instead of just getting to the correct answer. When trying to problem solve, it is important that students understand there are multiple ways to break apart the problem in order to find the solution. Using symbols, pictures or other representations to describe the different sections of the problem will allow students to use context skills rather than standard algorithms. This standard is aimed at creating a common mathematical language that can be used to discuss and explain math as well as support or object others’ work. Math vocabulary is easily integrated into daily lesson plans in order for students to be able to communicate effectively. “Talk moves” are important in developing and building communication skills and can include such simple tasks as restating a fellow classmate’s reasoning or even supporting their own reason for agreeing or disagreeing.

Prompting students to participate further in class mathematical discussion will help build student communication skills. Math doesn’t end at the classroom door. Learning to model with mathematics means that students will use math skills to problem-solve real world situations. This can range from organizing different types of data to using math to help understand life connections. Using real world situations to show how math can be used in many different aspects of life helps math to be relevant outside of math class. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill... Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.

They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify...

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a... Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly... Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.

They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it... Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies.

Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.

They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. The dust has finally settled, and it looks like Common Core math is here to stay. After countless political battles (and more than one Common Core math meme floating around social media), the initiative that incorporates techniques like cooperative learning and active learning has settled into the American education system. Prodigy offers common Core-aligned math practice that your students will love.

Start today! Beginning in 2010, the Common Core State Standards Initiative(CCSSI) aimed to change the way American students were taught English language arts and mathematics by countering low test scores, inconsistent learning standards and a curriculum... Of the 45 states (plus the District of Columbia and the Department of Defense Education Activity) that fully implemented Common Core by 2015, 24 chose to revise some aspects of the program but still... ��<�{'Qg���\:��GT-����ɐ�� �|3$)f��k� 9Hh5�h�נPR~w�in�5��`O F5��r0�`mu�ֻ�}���A��:������4��O�c�z���e̓8M�H���=`I*:�=*��#��=T4�<�(鸁���FFW&~iH$��@MOU{Fٓ�L�\��Q�dF�Rlvy���/>�"$nj� i���?dMj�x��a+���==�T\ʤ5�wc1�c��3�V��w��L}� *T�����h����KS�Ȇ��ԕli��*o�?�#�*��.�OS��&NxKih��m&���^���y�`�CFG��UR�¾}���֒ ~_%�6 �o��N ����WBT�؄�'J��\�q@r�ҺP��@t��Д BrDx]2��l&�R$���%˗�H�ra˗.@"��#�:�ATt��R�j��㪙�&Gd R.I+��7p��Z��b]�3�{-i*:��`X삧,fSUXr\.�{kb��3�?��j�>Թ��=ND}�ƙWO� ����|)8�D����-V�r�Mè����6:I�O�PXYV�ˎ0&~H�>�*R!��eB�A���R����T�����F��i��gn�]�L�]�k�[��0�� �[\0�c�O�?eS{n�W�-�Q���̎K�iiS�Z (��=�^�R���ߜp���?28���~�n���* OV{�i ޣ�4[H�&�o�5���QZ%J�������TZ��`�>�fk-�$�=#��V�� �i�c��3=T�=�&K� ��+��S0�恜�<#4���d�E�5kӴ�A3�*�G}��w����gJ���0 � SK6���=?DJ����q�\]o�s3�[ֳ7�k���Ԫ���K���~I�l���ER;�˻�{x-kl���Z��t�`?ʞ� ��?�0?�5ٍ�8�^�����}�%5-l�;["}�@YU�b1��mpꎨ͡�����S�@��!�י�����Ɠ|�C��~�U���״=ť���Eӹ�(��玈��.-�M9����-� u'�)x\R'���]��`�ǝǜ��H�I���V֫bԩ���~� �aO�U-�I �n-[�߉�r:J�[W\4�g���u*�@�kb9= �Qe[b 63�J;�W��< ��`�L�u��cv�g��Z� ���s+o[��G���@��uZEř�p �.�gZ��9� �N"�lN{(5 xUw�L�#�@�T��J�6����E��/㑜"�[�xi���O���tư��٘�N��K74r?%Mmp�T0��{��S�/�!���m��;*��S.p�O ���۴VH��*��u��s8�B��R�,�H�N��۠��'���� ��Cd�9��N��p�Ke�'������ 2F������q�... ��L�!��dg{.m&������,���F��HY-�׷e�sj�~��F�?�H��� ���~��jKzN;�D�l��o�k��z&��y���h�5��$6&�B8�z�( K��m<2��k�HB�u�;��O0H���4D��-B*B��d`S��WD��Z7R5� ���/:tN$�N����ʎ�����FG=���v8� ���9R�Ӑ��l��H�� ��l��(�P@#M5�q�;���.�W8����x@8����z�܇��R�cC��!�p>�����]��e5�-š��815����D�N��D�����`��sߴKa1Ռ�FDƖ�y������K���80WW� �Xy�H��^y��q��1��0#'��Wَb:aH�R��=Ħ��7c(a���FBꔼ� A��ʈ�a<�D��p�Ԡ_�'ӺmG2�4�*���Ϻs��G��B;���1����ޟܥ�6�H�P�sIH$�>�@�C��~� 0t�n'o*Sn#���T�=A����}F�������Nfe-�Y$�����X �H����];e��+�1�t�'��%� f}� m):)��������PUh h�s�O��:r�!k�5�pq.�`7� M�S���bA��R� kN�����I��U6V�i�۴�+�����{b�A��m�o� '��1!��A��� �����J�50��p�U5T��$�����W�k�9̏�SEeiN��L��v*��-!���׏� eln�W;KD��7V��kD��~H��m2�� ��PU�߸>��L����~�Q����>�����_�܎O�,�K�W�mZ�|���~H�w����c���W���kN{}zU�����D�Q&��%��>T7q:{��\�7cs�"'�f�m,��Y�+��'>����%;�,t�l��b@�V�kZMFd��U�[CkA� ���m޽ �`�0��������7<�n״K��ꁩ|ns�0:�*KZ���3�ʂ��Oi{� w'���j�ئ��#�Q��,�6��0�����s�t))ܶ���.3���r��^��0���2�I�Q�ˆpq캭*o�2Zz`|��@+�W�{=Dr?"��}M�� � �;}�Z�e"Z�I"`�|���������?T�a%�u���d��<_�I�d�ᘈī N���V�����!4{ߊ�ִI�T���[g\Ø=`�v|���Jl�2x�?D=Zf�k����J��n��U!�A�Q�.�ZL��`����5���T4��x�'=�if�.��d�W��}:l.p�����(cZ��6��Nx�u3�c �pB�Ɠ��$3�'��[�Т%�bu�M� ,힓� ���U�y�u�@ӿ���."�����A�}��Gn��W_�YY���)��)�n'�1���t*��گ�?9Rj~ƣeќ� Y}���a�������n�.��$v�At�^1����@�� ����1�4p������/-kv�ّ�}� �h�-;�=�R�uj�[%�v���T�T�o���(��+t��\�˧�#��u]6������^!�<�*Ґ�s�G�Ut�ի cO������P� m�!�!��Ds����|&��þ��˿��GѦ���� ʙվ!�?!������$�{=iKT�a��϶nGO���4�1��rB���;�B��㟆�k@)�*{�tG�Ҁi>��m>���'��K�^��]:��vߚ{t�����6���١���w�CQv�c}R��V��7... � �Ԁw�S��Ӽ�IN�l6������\�碈��0�l G)���=?�f�#i��+�f]��9@#�����-4�,�O�p~ߢhii�ޅև4�t��������7/��pH��@���e�t���B)���GC�I��)��u`�C�=����s�����;�5F��]T���[�=�~O�v��� �Ȕ�/��Do�:�-##�CR�i�n�0Q-�%H39��Z��v?�0=�m�� �,a�bxg���]Nh��j�~� u ��ZF W�<�N�'�(�2y�&IF�q���{jNy�\xI�v���ڣ���uq�ߟ����L�[�UB2�ʭk؝���QdW�z3���m]���<5,BW-�M �C��D�3g�}R�dtM5�PD�jz���>���yL�p?P�P�=N�:��Q�S${rB�@p��fP��*�p�!I�˗$��R��@t%H T$�*�.\B���˗ ���B�.J�E� W 9rD�MsS� "!r���- ar���rR2b3��J*6�S$Obr�B2�[�2��=��)*��v�����\�PeH�t�)�ӕ���"��cGH� 98�s�u�����f�����19 �=����@���&=�o)����Q�NZ�����,����,�4��y{��H�9F]�cӃ$D�R�8�۪������Ӗ����%}�&�Ө6� t�@��i5�阜�* Z��Wi��:����[� �3�S�l�&]�<����Sx���M���a��U��%ۦ1�ϲ �W���" s���[g����z@�'%Ci�]5��Y�:{(�'9��FbR[�mg �>}�Ƙڄ�#힫)��|)�tp8̭Um}���tN;�2ܣj���~���tx�SQ�׶2[��X���f{c��DV��\�5��Gӄ�Bؽ>�)�L $���.�3��@�3��kPA���^�̩ a�z�=��a[T[�`�w�&{�M� ݴ�0�� F�csg<��6����87gx�Bk�t�$c�@��?.T��k�����v)� i9�D颓O���I������3�t8wʴ-e���H��4��k�u60�3 �>П��6�w��"6��#i�,l�q�xT��Qp�C��3�™� >�gN��,��|�lo&�i�=�^iO  ��v�}J�<�G��o@?�5��0;A?D�uR�OHP�V�a�-���A���n��cˬ6��� k�� 6��M0...

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