Transitioning to the Common Core State Standards – Mathematics Pam Hutchison firstname.lastname@example.org
AGENDA • Party Flags • Overview of CCSS-M • Standards for Mathematical Practice • Standards for Mathematical Content • Word Problems and Model Drawing • Math Facts • Quick review – Addition and Subtraction Facts • Strategies – Multiplication and Division Facts • Area Models and Multiplication
Expectations • We are each responsible for our own learning and for the learning of the group. • We respect each others learning styles and work together to make this time successful for everyone. • We value the opinions and knowledge of all participants.
Erica is putting up lines of colored flags for a party. The flags are all the same size and are spaced equally along the line. 1. Calculate the length of the sides of each flag, and the space between flags. Show all your work clearly. 2. How long will a line of n flags be? Write down a formula to show how long a line of n flags would be.
CaCCSS-M • Find a partner • Decide who is “A” and who is “B” • At the signal, “A” takes 30 seconds to talk • Then at the signal, switch, “B” takes 30 seconds to talk. “What do you know about the CaCCSS-M?”
CaCCSS-M “What do you know about the CaCCSS-M?” Using the fingers on one hand, please show me how much you know about the CaCCSS-M
National Math Advisory PanelFinal Report “This Panel, diverse in experience, expertise, and philosophy, agrees broadly that the delivery system in mathematics education—the system that translates mathematical knowledge into value and ability for the next generation — is broken and must be fixed.” (2008, p. xiii)
Common Core State Standards Developed through Council of Chief State School Officers and National Governors Association
How are the CCSS different? The CCSS are reverse engineered from an analysis of what students need to be college and career ready. The design principals were focusand coherence. (No more mile-wide inch deep laundry lists of standards)
How are the CCSS different? Real life applicationsand mathematical modelingare essential.
How are the CCSS different? • The CCSS in Mathematics have two sections: • Standards for Mathematical CONTENT • and • Standards for Mathematical PRACTICE • The Standards for Mathematical Content are what students should know. • The Standards for Mathematical Practice are what students should do. • Mathematical “Habits of Mind”
Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.
CCSS Mathematical Practices REASONING AND EXPLAINING Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS Model with mathematics Use appropriate tools strategically OVERARCHING HABITS OF MIND Make sense of problems and persevere in solving them Attend to precision SEEING STRUCTURE AND GENERALIZING Look for and make use of structure Look for and express regularity in repeated reasoning
CCSS Mathematical Practices • Cut apart the Eight Standards for Mathematical Practice (SMPs) • Look over each Taxedo image and decide which image goes with which practice • The more frequently a word is used, the larger the image • Using the Standards for Mathematical Practice handout…did you get them right? • Glue the Practice title to the appropriate image. • What did you notice about the SMPs?
Reflection • How are these practices similar to what you are already doing when you teach? • How are they different? • What do you need to do to make these a daily part of your classroom practice?
Supporting the SMP’s • Summary • Questions to Develop Mathematical Thinking Common Core State Standards Flip Book • Compiled from a variety of resources, including CCSS, Arizona DOE, Ohio DOE and North Carolina DOE • http://katm.org/wp/wp-content/uploads/ flipbooks
Content Standards • Are a balanced combination of procedure and understanding. • Stressing conceptual understanding of key concepts and ideas
Content Standards • Continually returning to organizing structures to structure ideas • place value • properties of operations • These supply the basis for procedures and algorithms for base 10 and lead into procedures for fractions and algebra
“Understand” means that students can… • Explain the concept with mathematical reasoning, including • Concrete illustrations • Mathematical representations • Example applications
Organization K-8 • Domains • Larger groups of related standards. Standards from different domains may be closely related.
Domains K-5 • Counting and Cardinality (Kindergarten only) • Operations and Algebraic Thinking • Number and Operations in Base Ten • Number and Operations-Fractions (Starts in 3rd Grade) • Measurement and Data • Geometry
Organization K-8 • Clusters • Groups of related standards. Standards from different clusters may be closely related. • Standards • Defines what students should understand and be able to do. • Numbered
Model Drawing • A strategy used to help students understand and solve word problems • Pictorial stage in the learning sequence of concrete – pictorial – abstract • Develops visual-thinking capabilities and algebraic thinking.
Steps to Model Drawing • Read the entire problem, “visualizing” the problem conceptually • Decide and write down (label) who and/or what the problem is about • Rewrite the question in sentence form leaving a space for the answer. • Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem H
Steps to Model Drawing • Chunk the problem, adjust the unit bars to reflect the information in the problem, and fill in the question mark. • Correctly compute and solve the problem. • Write the answer in the sentence and make sure the answer makes sense.
Missing Numbers 1 Mutt and Jeff both have money. Mutt has $34 more than Jeff. If Jeff has $72, how much money do they have altogether? H
Missing Numbers 2 Mary has 94 crayons. Ernie has 28 crayons less than Mary but 16 crayons more than Shauna. How many crayons does Shauna have?
Missing Numbers 3 Bill has 12 more than three times the number of baseball cards Chris has. Bill has 42 more cards than Chris. How many baseball cards does Chris have? How many baseball cards does Bill have?
Missing Numbers 4 Amy, Betty, and Carla have a total of 67 marbles. Amy has 4 more than Betty. Betty has three times as many as Carla. How many marbles does each person have?
Representation • Getting students to focus on the relationships and NOT the numbers!
Teaching for Understanding Telling students a procedure for solving computation problems and having them practice repeatedly rarely results in fluency Because we rarely talk about how and why the procedure works.
Teaching for Understanding • Students do need to learn procedures for solving computation problems • But emphasis (at earliest possible age) should be on why they are performing certain procedure
Learning Progression Concrete Representational Abstract
Research • Students who learn rules before they learn concepts tend to score significantly lower than do students who learn concepts first • Initial rote learning of a concept can create interference to later meaningful learning