GPB Third Grade Session Resource Packet. You will need the following materials while participating in the session:

Transcription

1 GPB Third Grade Session Resource Packet You will need the following materials while participating in the session: Third Grade Handouts (included in this packet) Connecting cubes, color tiles, 2 color counters (or 2 colors of cubes), tracing paper or patty paper, 2 paper clips Note-taking materials Session Format: Why CCGPS? How to read the standards Third Grade Overview What s New/Different in Third Grade Six Lenses Focus Activity- True or False? Coherence Activity- Third Grade Handout 1- My Monkey Fluency Activity- Third Grade Handout 2- Multiplication Four Across Deep Understanding Activity- Third Grade Handout 3- Score It! Application - Mathematizing Third Grade Balanced Approach Activity- Third Grade Handout 4- Ms. Guy s Puppy Problem Suggestions and Resources Six Lenses- Focus Coherence Fluency Deep Understanding Applications Balanced Approach Feb 28, 2012 Page 1 of 24

2 K-5 Overview Kindergarten 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 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. Feb 28, 2012 Page 2 of 24

3 3rd Grade Represent and solve problems involving multiplication and division. 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. Feb 28, 2012 Page 3 of 24

4 Convert like measurement units within a given measurement system. Represent and interpret data. 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: Dot Cards and Ten Frames: _frame_package2005.pdf Rekenrek: Open Number Line: Math Solutions: Free lessonshttp:// Video clipshttp:// Exemplars.com: Free taskshttp:// NZMaths: Numeracy resourceshttp://nzmaths.co.nz/numeracy-projects VandeWalle texts, Teaching Student-Centered Mathematics K-3 and Teaching Student-Centered Mathematics 3-5 sent to each elementary school in Fall (1 copy of each, per school) Feb 28, 2012 Page 4 of 24

5 (Handout 1) My Monkey I shared a bag of grapes with my monkey. I ended up with 17 more grapes than my monkey and my monkey had 29. How many grapes were in the bag to begin with? Use a number line to find and explain the answer. Feb 28, 2012 Page 5 of 24

6 Multiplication Four Across (Handout 2) Materials: Two paper clips and several two color counters. Number of Players: 2 Directions: The first player takes the two paper clips and places them on the row of digits appearing below the grid, either on two different digits or on the same digit (being able to put them on the same digit allows for multiplying a digit by itself). He or she multiplies the two numbers together, produces a product, and places a two-color counter over that product on the game board. The second player moves ONE of the paper clips to a different digit, produces a product and places a two-color counter over that product on the game board. Play alternates in this way, each player moving only one marker at a time to a different digit, until one player has captured four squares in a row (horizontally, vertically, or diagonally) Feb 28, 2012 Page 6 of 24

7 STANDARDS ADDRESSED (Handout 3) PRACTICE TASK: SCORE IT! (Adapted from NC Math and from MCC3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. STANDARDS FOR MATHEMATICAL PRACTICES 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE Students often struggle with finding shapes if the shape looks different than what is typical seen. In this activity, students are encouraged to find the triangles, quadrilaterals, pentagons, and hexagons seen in two different figures. This will help to continue to build student s spatial sense and geometric reasoning. It takes many experiences with shapes to be able to move develop these skills with students. ESSENTIAL QUESTIONS How might finding shapes within other shapes help me in life? Can you provide an example of a non-regular pentagon or hexagon? Do quadrilaterals have to look like rectangles? How do you know? MATERIALS Printed copies of the Student Sheet OR Use technology to Display Student Sheet Math Journal or paper to keep track of number of shapes and total score Feb 28, 2012 Page 7 of 24

8 GROUPING Individual or Partner TASK DIRECTIONS Students will find all of the shapes in Figure A (triangles, quadrilaterals, pentagons, and hexagons) and Figure B (rectangles that include the special case: square.) Some students might be able to solve this by simply tracing over the shape with their pencils. Others might need to draw the shapes on paper. For the struggling student, you may want to get tracing paper or lightweight paper to have students trace of the lines to find all of the shapes. FORMATIVE ASSESSMENT QUESTIONS/PROMPTS How could you make sure you find all of the shapes within other shapes? How do you think this type of task helps you for the future? Do you struggle with finding shapes that were not regularly shaped? DIFFERENTIATION Extension Allow students to create another type of figure like either A or B. Once they know how many shapes are in their large shape, allow other students to solve for the answer. Intervention Suggestions: Tracing paper or lightweight paper to trace the lines; colored pencils and have student change colors for each type of shape; allow student to have their own Copier Paper that has either Figure multiple times (to cut out or trace over) Feb 28, 2012 Page 8 of 24

9 Student Sheet Direction: Use Figure A and find all of the triangles, quadrilaterals, pentagons and hexagons. Once you believe you have found all of the shapes, give the appropriate amount of points to each shape found. Total your score to see if you get the correct score! Score This Figure: 2 points for Triangles 3 points for Quadrilaterals 4 points for Pentagons 5 points for hexagons Figure A Directions: Use Figure B and find all of the rectangles. Remember what you have learned about rectangles and squares. Do you see any shapes that are similar to each other? Figure B Feb 28, 2012 Page 9 of 24

10 Copier Sheet: Print to give each student their own copy of the design. Feb 28, 2012 Page 10 of 24

11 Copier Sheet: Print to give each student their own copy of the design. Feb 28, 2012 Page 11 of 24

12 Teacher Answer Key for Figure A: Figure A: There are 5 triangles, 3 quadrilaterals, 3 pentagons, 2 hexagons for a total of 41 points. Triangles: Quadrilaterals: Feb 28, 2012 Page 12 of 24

13 Pentagons: Hexagons: Teacher Answer Key for Figure B: 14 solutions Feb 28, 2012 Page 13 of 24

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15 Miss Guy's Puppy Problem (Handout 4) Miss Guy has a very energetic puppy. The puppy loves to play outdoors, so Miss Guy decided to build a pen to allow her pet to be outside while she is at school. She just happens to have 50 feet of fencing in her 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 to support your solution. Feb 28, 2012 Page 15 of 24

16 Grade Levels 3-5 Miss Guy's Puppy Problem Miss Guy has a very energetic puppy. The puppy loves to play outdoors, so Miss Guy decided to build a pen to allow her pet to be outside while she is at school. She just happens to have 50 feet of fencing in her 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 to support your solution. Context This task was given to students after a unit on measurement. Two of the major concepts addressed in this unit were those of area and perimeter. The two fourth grade classes were given a menu of problems to choose from. This was the most popular problem, perhaps because Miss Guy actually has a new puppy. What This Task Accomplishes This problem directly addresses the concepts of area and perimeter and is a good assessment of student mastery and understanding of these concepts. There is the opportunity for students to discover the relationship between area and perimeter. This task also provides students with a real-world application of the skills they have been developing in class. What the Student Will Do Students were given a choice to work independently or in groups. Most students began by sketching rectangles and figuring dimensions that would total 50 feet. Few students were able to discover the size for a square pen, 12 1/2 feet per side, but many were able to find the 12 x 13 foot pen. Calculators were used to compute the areas of the pens. A group of students used the side of the house as one side of the pen, which resulted in an alternative solution to the problem, with a larger area. Time Required for Task Two 45-minute periods Miss Guy's Puppy Problem Copyright, Exemplars. All rights reserved. Feb 28, 2012 Page 16 of 24

17 Interdisciplinary Links Students could research the recommended pen sizes for dogs, horses, sheep or any other animal and compare the fencing types. It might be interesting to discuss grazing requirements of farm animals and plans for rotating pastures with area farmers. Teaching Tips Most students needed to make a lot of sketches of rectangles. Having a puppy they knew about starring in the problem helped motivate students to find the largest possible area. Suggested Materials Graph paper Calculators Rulers Tiles Possible Solutions The pen with the most area is 12 1/2 feet x 12 1/2 feet. 12 feet x 13 feet is the largest pen possible when using whole numbers. If the student uses the side of the house as one side of the pen, answers will vary. Benchmark Descriptors Novice A solution that shows an incomplete understanding or inability to solve the problem. A solution that does not use 50 feet of fencing or address the areas of potential pens. Reasoning is lacking or inaccurate. It is not clear what the student did to solve the task. Apprentice A solution that attempts to address the area of the pens using 50 feet of fencing, but is incomplete or incorrect in the final result. A solution which shows some understanding of the problem, but has a weak or random explanation or strategy. The student lacks communication about what was done to solve the task. Practitioner A solution that shows understanding of the perimeter and area aspects of the problem. A solution in which the student is able to apply fundamentals of multiplication and addition to calculate the area and perimeter of the pens. The student finds the largest possible pen either in whole numbers or using fractions and supports the answer. The student is able to communicate with some clarity what was done to solve the problem and why. Expert A solution that shows understanding of the perimeter and area aspects of the problem. A solution in which the student is able to apply fundamentals of multiplication and addition to calculate the area and perimeter of the pens. The student finds the largest possible pen either in whole numbers or using fractions and supports the answer. The student is able to communicate with some clarity what was done to solve the problem and why. Miss Guy's Puppy Problem Copyright, Exemplars. All rights reserved. Feb 28, 2012 Page 17 of 24

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24 Expert Feb 28, 2012 Page 24 of 24