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Whats In the Box? (Creative Techniques for Teaching Those Difficult Common Core State Standards) 2013 Making Connections Conference MS Gulf Coast Coliseum and Convention Center Friday, June 7, 2013 Marla Davis, Ph.D., NBCT, Office Director for Mathematics Office of Curriculum and Instruction 1

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1.Introducing New Vocabulary 2.Unpacking Grade Level Standards 3.Using Appropriate Tools Strategically 4.Preparing for the PARCC Assessment 2 Goals of this Session

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3 Introducing New Vocabulary Students do not learn how to speak mathematics by memorizing the definitions of new words, but they learn by hearing these words frequently and having many opportunities to use them in context.

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4 Introducing New Vocabulary Basic everyday language Rarely requires direct instruction Typically does not have multiple meanings Tier 1 High frequency May have multiple meanings Occurs across multiple domains Tier 2 Low frequency Context-specific May be subject to personal experience Tier 3

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5 Directions: Examine the question below and write your response on the lines provided. What does it mean to KNOW what a fraction is? _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ _______________________________________________ Introducing New Vocabulary

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6 For example, if fraction is a vocabulary word that students must learn in Grade 3, does knowing it mean they are able to: identify or recognize a fraction? model a fraction? describe a fraction? compare and contrast fractions with unlike numerators? explain where to place a fraction on the number line? determine when two fractions are equivalent? Introducing New Vocabulary

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Directions: In your groups, locate the three charts post on the wall closest to you. Review each vocabulary word. As a group, determine what does it mean for a student to know the indicated vocabulary word. (Hint: Ask yourself what should a student be able to do with the indicated word?) Repeat this exercise for the remaining two charts. 7 Activity #1

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8 Numbers (11-19) Number LineAngle This slide is left blank intentionally.

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9 Without saying a word or looking at another group member, complete the following task: 1.Locate a sheet of scratch paper. 2.Fold the paper in half. 3.Fold the paper in half again. 4.Tear the top right part of the paper off. 5.Hold your sheet of paper up for your entire group to see. What do you notice?

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Using the five guiding questions below, address this Essential Question: How is it that everyone read the exact same directions but obtained different results? What was the first thing you did when you saw the task? Can you demonstrate how you completed this task? At any time, were there any directions that seemed unclear or ambiguous? If so, which ones? Why? Should there be one correct solution/outcome? How does this task relate to teaching the CCSSM? 10

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11 Standard #1 (K.NBT.1) K. NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

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12 Unpacking K.NBT.1 Key Verbs (skill) Key Terms (vocabulary) This slide is left blank intentionally.

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13 Unpacking K.NBT.1 Key Verbs (skill) Key Terms (vocabulary) compose decompose using record understand compose decompose further ones objects drawings composition equation A student should be able to given -or- using Given -or- using a student should be able to

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Write three I Can statements for the standard K.NBT.1. ______________________________ Write three Essential Questions for the standard K.NBT.1. _______________________________ 14 Unpacking K.NBT.1

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15 This will be the first time that some students will move beyond the number 10 with representations. Special attention must be given to these numbers because they do not follow a consistent pattern in the verbal counting sequence: 11 and 12 are special number words. Teen means one ten plus ones. The verbal counting sequence for teen numbers is backwards. Teaching the teen numbers as one group of ten and extra ones is foundational to understanding both the concept and the symbol that represents each teen number. Unpacking K.NBT.1

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Directions: Locate the small box on your table. Select the grid paper and any other object(s) of your choice that could be used to teach and assess the standard K.NBT.1. Be prepared to share with the entire group. 16 Activity #2 Think outside the box!!

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17 Possible Strategy

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18 Assessment Item for K.NBT.1 Write an equation for the number that is modeled by the drawing on the left and justify your response.

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19 Place a check mark next to the Mathematical Practice(s) demonstrated in the Assessment Task for K.NBT.1. 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.

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20 Standard #2 (7.NS.1) 7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

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21 Unpacking 7.NS.1 Key Verbs (skill) Key Terms (vocabulary) This slide is left blank intentionally.

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22 Unpacking 7.NS.1 Key Verbs (skill) Key Terms (vocabulary) apply extend addition subtraction horizontal number line vertical number line rational number* A student should be able to given -or- using Given -or- using a student should be able to

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Write three I Can statements for the standard 7.NS.1. ______________________________ Write three Essential Questions for the standard 7.NS.1. _______________________________ 23 Unpacking 7.NS.1

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24 7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. What do the circled words indicate? What are the implications for instruction? assessment? Unpacking 7.NS.1

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Directions: Locate the small box on your table. Select the cash register tape and any other object(s) of your choice that could be used to teach and assess the standard 7.NS.1. Be prepared to share with the entire group. 25 Activity #3 Think outside the box!!

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26 Possible Strategy Without using any tools, brainstorm about the following questions: –What point must be clearly indicated first? –Where would 16 be on your number line? –Where would 4 have to be? –Where would you place the number a? What about the number b? –Does a relationship exist between the numbers a andb? –How can you plot the numbers a and b on your number line?

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27 Possible Strategy (continued) Directions: Select two separate tools (other than a ruler). Let your first tool represent the length a. Let your second tool represent the length b.

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28 Possible Strategy (continued) Directions: Place the following ten numbers on your number line and discuss your work as a team. ab -a-b b – aa – b a + b b + a ½a ¾b

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29 Given the number line above, create a list of expressions that would yield a negative value. Provide a complete justification for each of your responses. Assessment Item for 7.NS.1

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30 Place a check mark next to the Mathematical Practice(s) demonstrated in the Assessment Task for 7.NS.1. 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.

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31 Directions: On a Post-it note, draw a symbol or small picture that depicts how your feelings have changed about introducing new vocabulary words to your student. (Be creative! ) Place your Post-it note on the back door.

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4.MD.5a, 5b Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 32 Standard #3 (4.MD.5a, 5b)

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33 Unpacking 4.MD.5a, 5b Key Verbs (skill) Key Terms (vocabulary) This slide is left blank intentionally.

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34 Unpacking 4.MD.5a, 5b Key Verbs (skill) Key Terms (vocabulary) recognize share understand consider intersect use measure turns angles intersect rays endpoint reference (to a circle) circular arc A student should be able to given -or- using Given -or- using a student should be able to

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Write three I Can statements for the standard 4.MD.5a and 4.MD.5b. ______________________________ Write three Essential Questions for the standard 4.MD.5a and 4.MD.5b. _______________________________ 35 Unpacking 4.MD.5a, 5b

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36 Sample Progression of 4.MD.5a, 5b 4 th year CCSS High School Course (F-TF.3) : Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number. 8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 4.MD.5a: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. 4.MD.5b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

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Directions: Locate the small box on your table. Select any object(s) of your choice that could be used to teach and assess the standard 4.MD.5a and 4.MD.5b. Be prepared to share with the entire group. 37 Activity #4 Think outside the box!!

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38 Assessment Item for 4.MD.5a,5b Create two separate assessment items for the diagram (angles 1-4) above. Use the space below to record your response.

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39 Place a check mark next to the Mathematical Practice(s) demonstrated in the Assessment Task for 4.MD.5a,5b. 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.

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40 Key Note about 4.MD.5a,5b The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same.

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Directions: Take a few minutes to reflect on todays presentation. In the space provided, identify how this session has impacted your perception in the following areas. 41 Reflections Planning Instruction Assessment

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CCSSM Exemplar Assessment Prototypes 42 PARCC http://www.parcconline.org/samples/item-task-prototypes Smarter Balanced (SBAC) http://www.ode.state.org.us/serach/page/?id=3747 Illustrative Mathematics (IM) www.illustrativemathematics.org Mathematics Assessment Resources Service (MARS) http://map.mathshell.org/materials/lessons.php New York City Dept of Education (NYC) http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsSt udentWork/default.htm

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CCSSM Resources 43 Common Core Website www.corestandards.org PARCC Assessment Administration Guidance http://www.parcconline.org/assessment-administration-guidance PARCC Grade Level Assessment Blueprints and Test Specifications http://www.parcconline.org/assessment-blueprints-test-specs Progression Documents for CCSSM http://math.arizona.edu/~ime/progressions/ PARCC Model Content Frameworks for Mathematics http://www.parcconline.org/parcc-model-content-frameworks SEDL CCSSM Support Videos http://secc.sedl.org/common_core_videos/

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MDE Resources 44 Office of Curriculum and Instruction www.mde.k12.ms.us/ci MDE iTunes U (archived webinars) www.mde.k12.ms.us/itunes MDE Common Core Website www.mde.k12.ms.us/ccss CCSS and PARCC training materials https://districtaccess.mde.k12.ms.us/commoncore/ Curriculum and Instruction Listserv http://fyt.mde.k12.ms.us/subscribe/subscribe_curriculum.html

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MDE Contact Information 45 Office of Curriculum and Instruction 601.359.2586 Nathan Oakley – Director of Curriculum and Instruction noakley@mde.k12.ms.us Dr. Marla Davis – Office Director for Mathematics mdavis@mde.k12.ms.us

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