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Resource Packet

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Resource Packet

1. 1. GPB Fourth Grade Session Resource Packet GPB Fourth Grade Session Resource PacketYou will need the following materials while participating in the session:Fourth Grade Handouts (included in this packet)Color tiles, pattern blocks, grid paper, paperNote-taking materialsSession Format: Why CCGPS? How to read the standards Fourth Grade Overview What’s New in Fourth Grade Six Lenses Focus Activity- Pattern Block Fractions- http://illuminations.nctm.org/LessonDetail.aspx?ID=U113 Coherence Activity- Fourth Grade Handout 1- Pattern Block Angles Fluency Activity- Clear the Board- http://www.mathsolutions.com/documents/0-941355-75- 6_L.pdf Deep Understanding Activity- The Factor Game- http://www.mathsolutions.com/documents/978-1-935099-02-4_NL36_L1.pdf Application - Mathematizing Fourth Grade- Intro to Multiplication of Fractions- http://www.mathsolutions.com/documents/0-941355-64-0_L.pdf Balanced Approach Activity- Fourth Grade Handout 3- Ms. Guy’s Puppy Problem Suggestions and ResourcesSix Lenses-FocusCoherenceFluencyDeep UnderstandingApplicationsBalanced Approach Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 1 of 16 All Rights Reserved
2. 2. GPB Fourth Grade Session Resource Packet K-5 OverviewKindergarten • Know number names and the count sequence. • Count to tell the number of objects. • Compare numbers. • Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. • Work with numbers 11–19 to gain foundations for place value. • Describe and compare measurable attributes. • Classify objects and count the number of objects in categories. • Identify and describe shapes. • Analyze, compare, create, and compose shapes.1st Grade • Represent and solve problems involving addition and subtraction. • Understand and apply properties of operations and the relationship between addition and subtraction. • Add and subtract within 20. • Work with addition and subtraction equations. • Extend the counting sequence. • Understand place value. • Use place value understanding and properties of operations to add and subtract. • Measure lengths indirectly and by iterating length units. • Tell and write time. • Represent and interpret data. • Reason with shapes and their attributes.2nd Grade • Represent and solve problems involving addition and subtraction. • Add and subtract within 20. • Work with equal groups of objects to gain foundations for multiplication. • Understand place value. • Use place value understanding and properties of operations to add and subtract. • Measure and estimate lengths in standard units. • Relate addition and subtraction to length. • Work with time and money. • Represent and interpret data. • Reason with shapes and their attributes.3rd Grade • Represent and solve problems involving multiplication and division. Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 2 of 16 All Rights Reserved
3. 3. GPB Fourth Grade Session Resource Packet• Understand properties of multiplication and the relationship between multiplication and division.• Multiply and divide within 100.• Solve problems involving the four operations, and identify and explain patterns in arithmetic.• Use place value understanding and properties of operations to perform multi-digit arithmetic.• Develop understanding of fractions as numbers.• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.• Represent and interpret data.• Geometric measurement: understand concepts of area and relate area to multiplication and to addition.• Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.• Reason with shapes and their attributes.4th Grade• Use the four operations with whole numbers to solve problems.• Gain familiarity with factors and multiples.• Generate and analyze patterns.• Generalize place value understanding for multi-digit whole numbers.• Use place value understanding and properties of operations to perform multi-digit arithmetic.• Extend understanding of fraction equivalence and ordering.• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.• Understand decimal notation for fractions, and compare decimal fractions.• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.• Represent and interpret data.• Geometric measurement: understand concepts of angle and measure angles.• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.5th Grade• Write and interpret numerical expressions.• Analyze patterns and relationships.• Understand the place value system.• Perform operations with multi-digit whole numbers and with decimals to hundredths.• Use equivalent fractions as a strategy to add and subtract fractions.• Apply and extend previous understandings of multiplication and division to multiply and divide fractions.• Convert like measurement units within a given measurement system.• Represent and interpret data. Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 3 of 16 All Rights Reserved
4. 4. GPB Fourth Grade Session Resource Packet• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.• Graph points on the coordinate plane to solve real-world and mathematical problems.• Classify two-dimensional figures into categories based on their properties.Resources:Teaching Guides/CCGPS: https://www.georgiastandards.org/Pages/default.aspxhttps://portal.doe.k12.ga.us/Login.aspxRekenrek: http://www.mathlearningcenter.org/media/Rekenrek_0308.pdfOpen Number Line:http://www.uwosh.edu/coehs/mindsongmath/concepts/documents/Empty_Number_Line.pdfMath Solutions Free Resources: http://www.mathsolutions.com/index.cfm?page=wp9&crid=122VandeWalle, “Teaching Student-Centered Mathematics, 3-5” (Sent to every GA elementary school,Fall 2011)Unit 1 Fourth Grade Webinar, 3:15, May 9, 2012 Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 4 of 16 All Rights Reserved
5. 5. GPB Fourth Grade Session Resource Packet Take out the pattern block pieces and put circle on overhead.By looking at the common geometric shapes of pattern blocks students canexplore angles and their combinations, as well as lay some foundations forfurther study in geometry and the use of circle graphs.Angles are formed by two rays that intersect at a point called the vertex.The unit of measurement for angles was created by the Babylonians, and isformed by dividing a circle into 360 equal parts.By placing pattern blocks around the center of the circle so that theircorners (vertices) touch the center, students can determine the measure ofthe various angles formed by the corners of the different shapes. Forexample, with squares......and triangles. Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 5 of 16 All Rights Reserved
6. 6. GPB Fourth Grade Session Resource PacketHow many degrees are in the corners shown around the centers of thesecircles?Can you use known angles to determine unknown angles?Give groups pattern blocks, paper plates and chart paper to show theirwork and share with class. Explain how you solved the angle problem!(This is in the back of Cloak for a Dreamer) Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 6 of 16 All Rights Reserved
7. 7. GPB Fourth Grade Session Resource PacketMiss Guys Puppy Problem (Handout 4)Miss Guy has a very energetic puppy. The puppy loves toplay outdoors, so Miss Guy decided to build a pen to allowher pet to be outside while she is at school. She justhappens to have 50 feet of fencing in her basement thatshe can use for the pen.What are some of the ways she can set up the pen thatuses all the fencing?What are the dimensions of the rectangular pen with themost space available for the puppy to play?Write a letter to Miss Guy explaining her choices andwhich pen you would recommend she build. Be sure toshow how you made your decisions and include amathematical representation to support your solution. Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 7 of 16 All Rights Reserved
8. 8. GPB Fourth Grade Session Resource PacketGrade Levels 3 - 5Miss Guys Puppy ProblemMiss Guy has a very energetic puppy. The puppy loves to play outdoors, so Miss Guy decided to build apen to allow her pet to be outside while she is at school. She just happens to have 50 feet of fencing inher basement that she can use for the pen.What are some of the ways she can set up the pen that uses all the fencing?What are the dimensions of the rectangular pen with the most space available for the puppy to play?Write a letter to Miss Guy explaining her choices and which pen you would recommend she build.Be sure to show how you made your decisions and include a mathematical representation tosupport your solution.ContextThis task was given to students after a unit on measurement. Two of the major concepts addressedin this unit were those of area and perimeter. The two fourth grade classes were given a menu ofproblems to choose from. This was the most popular problem, perhaps because Miss Guy actuallyhas a new puppy.What This Task AccomplishesThis problem directly addresses the concepts of area and perimeter and is a good assessment of studentmastery and understanding of these concepts. There is the opportunity for students to discover therelationship between area and perimeter. This task also provides students with a real-world application ofthe skills they have been developing in class.What the Student Will DoStudents were given a choice to work independently or in groups. Most students began by sketchingrectangles and figuring dimensions that would total 50 feet. Few students were able to discover the sizefor a square pen, 12 1/2 feet per side, but many were able to find the 12 x 13 foot pen. Calculators wereused to compute the areas of the pens. A group of students used the side of the house as one side ofthe pen, which resulted in an alternative solution to the problem, with a larger area.Time Required for TaskTwo 45-minute periodsMiss Guys Puppy ProblemCopyright ©, 2003. Exemplars. All rights reserved. Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 8 of 16 All Rights Reserved
9. 9. GPB Fourth Grade Session Resource PacketInterdisciplinary LinksStudents could research the recommended pen sizes for dogs, horses, sheep or any other animal andcompare the fencing types. It might be interesting to discuss grazing requirements of farm animals andplans for rotating pastures with area farmers.Teaching TipsMost students needed to make a lot of sketches of rectangles. Having a puppy they knew about starringin the problem helped motivate students to find the largest possible area.Suggested Materials Graph paper Calculators Rulers TilesPossible SolutionsThe pen with the most area is 12 1/2 feet x 12 1/2 feet. 12 feet x 13 feet is the largest pen possiblewhen using whole numbers. If the student uses the side of the house as one side of the pen, answerswill vary.Benchmark DescriptorsNoviceA solution that shows an incomplete understanding or inability to solve the problem. A solution that does not use 50 feet offencing or address the areas of potential pens. Reasoning is lacking or inaccurate. It is not clear what the student did to solve thetask.ApprenticeA solution that attempts to address the area of the pens using 50 feet of fencing, but is incomplete or incorrect in the final result. Asolution which shows some understanding of the problem, but has a weak or random explanation or strategy. The student lackscommunication about what was done to solve the task.PractitionerA solution that shows understanding of the perimeter and area aspects of the problem. A solution in which the student is able toapply fundamentals of multiplication and addition to calculate the area and perimeter of the pens. The student finds the largestpossible pen either in whole numbers or using fractions and supports the answer. The student is able to communicate with someclarity what was done to solve the problem and why.ExpertA solution that shows understanding of the perimeter and area aspects of the problem. A solution in which the student is able toapply fundamentals of multiplication and addition to calculate the area and perimeter of the pens. The student finds the largestpossible pen either in whole numbers or using fractions and supports the answer. The student is able to communicate with someclarity what was done to solve the problem and why.Miss Guys Puppy ProblemCopyright ©, 2003. Exemplars. All rights reserved. Georgia Department of Education Dr. John D. Barge, State School Superintendent Feb 16, 2012 Page 9 of 16 All Rights Reserved
10. 10. GPB Fourth Grade Session Resource Packet Novice Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 10 of 16 All Rights Reserved
11. 11. GPB Fourth Grade Session Resource Packet Novice Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 11 of 16 All Rights Reserved
12. 12. GPB Fourth Grade Session Resource Packet Apprentice Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 12 of 16 All Rights Reserved
13. 13. GPB Fourth Grade Session Resource Packet Apprentice Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 13 of 16 All Rights Reserved
14. 14. GPB Fourth Grade Session Resource Packet Apprentice Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 14 of 16 All Rights Reserved
15. 15. GPB Fourth Grade Session Resource Packet Practitioner Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 15 of 16 All Rights Reserved
16. 16. GPB Fourth Grade Session Resource Packet Expert Georgia Department of EducationDr. John D. Barge, State School Superintendent Feb 16, 2012 Page 16 of 16 All Rights Reserved