Middle School Geometry

Middle School GeometryMichelle Corbin, NBCT

Making Connections ConferenceBiloxi, MSJune 11th 13th, 2014Time: 2 hours

Materials Needed:1The 8 Mathematical PracticesDirections: Locate the Ziploc bag in the center of the table and empty its contents.

Work with your table mates to math the math practice with its big idea.Time: 5 minutes/5 minutes

Prep: Have cards printed and on cardstock in Ziploc bags. May be a good idea to have each tables pieces on a different color in case they get mixed up.

Talking Points:Explain the activity to the participants.Allow teams 2 minutes to match 2How Can we provide opportunities?Math Practice #1Never give up!Provide challenging problems and question effectively.

Math Practice #2Think through it!Provide opportunities for students to work together. Time: 2 minutes

Prep: NA

Talking Points:Review over the activity by going over the answers and expanding on HOW educators can ensure students have engaging practice with these standards regularly. 3How Can we provide opportunities?Math Practice #3Argue and PROVE your work!Provide opportunities for students to explain and justify their work.

Math Practice #4Manipulatives, equations, tables, etc.Allow student to show multiple methods of problem solving. Time: 2 minutes

Prep: NA

Talking Points:Review over the activity by going over the answers and expanding on HOW educators can ensure students have engaging practice with these standards regularly.

4How Can we provide opportunities?Math Practice #5Know when and how to use tools!Provide various tools regularly and encourage students to use them.

Math Practice #6Communicate all the details!Question students about the details while they are explaining. Time: 2 minutes

Prep: NA

Talking Points:Review over the activity by going over the answers and expanding on HOW educators can ensure students have engaging practice with these standards regularly.

5How Can we provide opportunities?Math Practice #7Connections across math topics!Point out ways to build mathematical understanding on prior knowledge.

Math Practice #8Identify patterns to create an algorithm for solving!Provide student explorations BEFORE teaching algorithms. Time: 2 minutes

Prep: NA

Talking Points:Review over the activity by going over the answers and expanding on HOW educators can ensure students have engaging practice with these standards regularly.

6

WHAT are you teaching?!?!

Otherwise known as the CONTENT STANDARDS in the Common CoreTime: 1 minute/

Prep: NA

Talking Points:Explain to the participants we will now investigate the content standards.

7

Time: 2 minutes

Prep: NA

Talking Points:Discuss the progression of the domains over time.Ask participants to discuss some observations with the flow.

8PARCC Model Content FrameworkMajor ClustersMajor focus

Supporting ClustersAssessed through major content

Additional ClustersInstrumental for next grade level, may not have a heavy correlation with another standard to be considered supporting.

Time: 4 minutes/

Prep: Copies of PARCC Model Content Framework at each table.

Talking Points:Explain that the PARCC Model Content Framework was created to shed further light on the content standards. Discuss that there are many informative pieces of information in the document, but for the purpose of today, we will be looking at the classification of clusters as major, supporting, and additional clusters. Major clusters will be heavily emphasized on the assessment and therefore should be heavy emphasis in instruction.Supporting clusters will be assessed through a major standard. An example of this is given further in the Model Content Framework document. Additional clusters are standards that may not have a strong correlation to another standard and therefore, are classified as additional. Assessment development will follow the same emphasis structure. 9 PARCC Test Blueprint (EOY/PBA)CalculatorsYes or NoFluency?

Math PracticesProcessHow?

ClarificationsAdditional insight

Time: 5 minutes

Prep: Copies of PARCC Test Blueprint at each table.

Talking Points:Explain that the PARCC test Blueprint was created to provide further clarification of the assessment of the standards. Discuss that we will be focusing on 3 areas of this document:If calculators will be allowed how is this helpful to us as educators?What math practices will be assessed What will this help us to do in our teaching of the concept?Further clarifications any extra information that will assist us in best preparing our students. Assessments will be written based on the information found in this document. 10Activity GoalsRecognize ways to incorporate the standards for mathematical practice in lessons.

Identify CCSS-M content standards in an activity or lesson.

Time: 2 minutes11Calculating volumeTake a moment and work with your table to calculate the volume of the figure to the right.

Volume = l(w)(h)5(6)(7)210 in3Time: 3 minutes12Understanding volumeDirections: Locate the Volume envelope and the pack of cubes in the center of the table.

Work with your team to build a model that could represent the information given on the card.

Complete one card at a time.Time: 7 minutes13VolumeOne Step furtherJoaquin wants to find the volume of his cereal box, but he only has inch cubes available. He measured the box and found that it was 7 incheswide, 11"tall, and 2 inchesthick.

With your team, determine how manycubes it will take to completely fill the cereal box.7.5(2) = 1511(2) = 222.5(2) = 515(22)(5) = 1,650 half-inch cubesTime: 7 minutes14Volume StrategiesHow manycubes fit in a 1 cube?

Using your answer from the previous problem, what is the volume of the cereal box measured in cubicinches?81,650 8 =206.25 inches3Time: 8 minutes

Prep:

Talking Points: Acube is not actually a standard unit of measure. Standard units of measure involve using units such as 1 inch, 1 centimeter, or 1 foot. Explore different units of measure in the following three problems.

15Volume StrategiesLook back at your strategy for determining the number of 1 inch cubes it will take to fill the box from our first problem, (slide 12).

Calculate the volume (measured in cubic inches) of Joaquins cereal box using this strategy. Did you get the same volume as in part (b) of this problem? Why or whynot?7.5(11)(2.5) = 206.25 inches3Time: 8 minutes

Prep:

Talking Points: Acube is not actually a standard unit of measure. Standard units of measure involve using units such as 1 inch, 1 centimeter, or 1 foot. Explore different units of measure in the following three problems.

16Reflecting on our goalsWhich Mathematical Practice(s) were used in the activity? Provide a complete justification for each MP you identify.

Which content standard(s) were addressed in these activities?6.G.2 Time: 5 minutes17Sample PARCC Items EOY 6.G.2

5400Sample PARCC Items EOY 6.G.2

38164Three-Dimensional FiguresA cross section of a three-dimensional solid (an object that has length, width, and height) is the figure obtained when the solid is intersected or sliced by a plane.Time: 1 minute20Three-Dimensional FiguresUsing clay, make a rectangular prism or cube.Each person in your team should make a slightly differentprism.

Use your string to slice the rectangular prism by holding it tightly and pulling it through the solid. Place the newly created face made by the slice that came from the inside of the rectangular prism on your paper and trace the resulting shape. What is the name of yourshape?Time: 8 minutes21Three-Dimensional FiguresWhich of the following shapes can you make by slicing your prism in different ways? Before making a new slice, reshape yourprism.TriangleSquareRectangleTrapezoidParallelogramPentagonHexagonOctagonCircleTime: 6 minutes22Three-Dimensional FiguresNow make a rectangular pyramid. Again, each person in your team should make a slightly different pyramid.

Using your string, what other shapes can you make by slicing your pyramid in different ways? What shapes are impossible to make? How do the types of shapes that you can make with the rectangular pyramid compare to the types of shapes that you made with the rectangular prism?Time: 6 minutes23Three-Dimensional FiguresUse the pyramid shown at left to answer the questions below.

If the pyramidwere sliced vertically, what would the resulting cross sections look like? Sketch them.If the pyramid were sliced horizontally, what would the resulting cross section look like? Sketch it.

Time 5 minutes24Reflecting on our goalsWhich Mathematical Practice(s) were used in the activity? Provide a complete justification for each MP you identify.

Which content standard(s) were addressed in these activities?7.G.3 Time: 5 minutes25Sample PARCC Items EOY 7.G.2

Proving PythagorasThe picture to the left represents the grass area in my backyard. The width of the grass area is 10 yards and the length of the grass area is 10 yards. How much total grass do I mow?100 square yardsProving PythagorasI want to have a pool put in the backyard as shown. If the total area of the pool is 20 square yards, how much grass will I be cutting after the pool is installed?100 20 = 80 square yardsProving PythagorasWhat if I move the pool to this location? How much grass will I have to mow?The amount will stay the same since the area of the total grass and the area of the pool are staying the same.100 20 = 80 square yardsProving PythagorasWhat if I wanted to split the pool into two equal sections?No matter how we move or cut a figure, as long as we have the same size, it will always have the same area.Proving PythagorasWhat is the area of the inner green square?

What is the area of the outer square?

Can we rearrange the triangles in some way to PROVE a2 + b2 = c2?c2bacbacbacbac(a + b)231Proving PythagorasWork with your team to figure out a way to rearrange and/or cut the triangles in some way to PROVE a2 + b2 = c2 using the manipulatives on the tables. bacbacbacbac32Proving PythagorasWhat is the area of the green space now?

bacbacbacbacc233Proving PythagorasWhat is the area of the green space now?

bacbacbacbacc234Proving PythagorasWhat is the area of the green space now?

Can you rename it in any way?

bacbacbacbacc2a2 + b2b2a235Proving PythagorasWhat area does this shape represent in relationship to a, b, and c?

a2 + b2bbaa36Proving PythagorasUse your original triangles as a tracing tool on your model of a2 + b2 as shown at the left.

Cut along the traced lines.

Now can you rearrange the shapes to model the area as c2?

bacbac37Proving PythagorasCut, move, and replace.

bacbac38Proving PythagorasCut, move, and replace again.

bacbac39Reflecting on our goalsWhich Mathematical Practice(s) were used in the activity? Provide a complete justification for each MP you identify.

Which content standard(s) were addressed in these activities?8.G.6Time: 5 minutes40Evidence Tables for 8.G.6Not specifically identifiedIt is found encompassed in the C claims 8.C.5.3Apply geometric reasoning in a coordinate setting, and/or use coordinates to draw geometric conclusions. Content Scope: Knowledge and skills articulated in 8.G.BMathematical Practices: 2, 3, 5Calculator will be allowedCredits and ResourcesCollege Preparatory Mathematicswww.cpm.org

PARCCwww.parcconlne.org

Contact InformationMichelle Corbin, NBCTMathematics SpecialistDesoto County Schools

michelle.corbin@dcsms.org(662)449-7203 office(901)238-8828 cell