NCTM Standards Standard 3: Geometry Grades 3-5. NCTM Standards Standard 4: Measurement Grades 3-5

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1 Overview In program #4, students use Color Tiles to create the 12 possible pentomino shapes. These pentomino pieces are used by students to help them understand perimeter and area. Student spatial sense and problem solving are exercised as they look at the pentomino shapes they created to check for congruency and attempt to solve puzzles creating rectangles NCTM Standards Standard 3: Geometry Grades 3-5 Analyze characteristics and properties of two- and three dimensional geometric objects. Understand and demonstrate congruence Recognize the usefulness of transformations and symmetry in analyzing mathematical situations. Describe a motion or series of motions that will show that two figures are congruent Identify and describe line of symmetry in various two-dimensional shapes NCTM Standards Standard 4: Measurement Grades 3-5 Understand attributes, units and systems of measurement. Identify attributes such as length and area and know the type of unit and tool needed to measure each attribute Apply a variety of techniques, tools, and formulas for determining measurements. Determine the perimeter and area of shapes by counting segment, square units or cubic units. California State Standards: Grade 3 Measurement & Geometry 1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects: 1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. 1.3 Find the perimeter of a polygon with integer sides. California State Standards: Grade 4 Measurement & Geometry 1.0 Students understand perimeter and area: 1.1 Measure the area of rectangular shapes by using appropriate units 1.2 Recognize that the rectangles (shapes) having the same area can have different perimeters. 1.3 Understand that rectangles (shapes) that have the same perimeter can have different areas; 3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems: 3.3 Identify congruent figures 3.4 Identify figures that have bilateral and rotational symmetry TEAMS Mathematics Geometry In My World Program 4 1

2 Materials Color Tiles, per group of 4 students - one set per pair of students SAS#4.1 - one per student SAS#4.2 - one per student + transparency 1 grid paper - several per student Centimeter grid paper - several per student Student journals Scissors Colored pencils, markers or crayons Pre-viewing Activities Students sitting in groups of 4. Geometry In My World Telecast Outline Welcome Focus Discussion Activity #1 DLI CT S DLI CT S Discussion Activity #2 DLI CT S Introduction Students construct pentomino shapes using Color Tiles. These shapes will be used to review area and perimeter. Constructing Introduces the activity Facilitates activity Arrange 5 Color Tiles into pentominoes Introduces unique pentomino shapes Facilitates activity, checks for understanding Cut out pentomino shapes and check for congruency Call-in with the number of unique shapes they found Discuss the 12 pentomino shapes Symmetry What is the difference between area and perimeter? and Introduces activity Facilitates activity Work in groups to determine and record the area and perimeter of each pentomino TEAMS Mathematics Geometry In My World Program 4 2

3 Discussion Looking for a pattern Activity #3 and Rectangles DLI Introduces activity CT Facilitates activity S Use pentomino pieces to create rectangles from different numbers of pentominoes. Students record rectangles on centimeter grid paper and fill in SAS#4.1 DLI Symmetry - Bilateral and Rotational Journal Writing What did you learn about perimeter and area? KEY DLI: Distance Learning Instructor CT: Classroom Teacher S: Students Telecast Activities Activity #1 Description Materials Advanced Preparation Lesson Implementation Constructing Students arrange 5 Color Tiles into a pentomino. Groups try to find as many pentominoes shapes as possible. The Hands-on activity will be divided into two segments. Color Tiles per group 1 grid paper Scissors Duplicate 1 grid paper - several per student The Distance Learning Instructor introduces the activity by describing what a pentomino is. The Classroom Teacher facilitates the activity asking students to verify their shapes and questions students on finding unique (not-congruent) pentominoes. During the first students arrange 5 Color Tiles so that each square has at least one of its side completely in common with another square. Groups attempt to find as many different pentomino shapes as possible. During the second students check for congruency, then trace the shapes they found onto TEAMS Mathematics Geometry In My World Program 4 3

4 the 1 grid paper and begin cutting them out. Students check for congruent shapes by rotating and flipping the pieces and comparing them to each other. Students call-in the number of shapes their group found and describe one of these shapes to the Distance Learning Instructor. Allow students time to discuss and share shapes so they can find these on their own. Teacher Notes Pentomino Shapes There are 12 unique pentomino shapes. They are identified by a letter of the alphabet which closely resembles the shape. are the names of shapes created by 5 squares connected together. Dominoes are two squares connected, triominoes are shapes made with three squares and tetrominoes are made with four squares. 1 Tile Monomino 2 Tiles Domino 3 Tiles Triominoes 4 Tiles Tetrominoes TEAMS Mathematics Geometry In My World Program 4 4

5 12 Pentomino Pieces Geometry In My World I P X L U Z V W Y T N F Symmetry If a figure can be reflected over a line in such a way that the resulting image coincides with the original, then the figure has reflectional symmetry. This is also called line symmetry or bilateral symmetry. The line of reflection is called the line of symmetry. I, X, U, V, W, and T have bilateral symmetry. If a figure can be rotated about a point so that it s rotated image coincides with the original figure after turning less that 360 o, the figure has rotational symmetry. Pentomino X and Z have rotational symmetry. Activity #2 Description Materials Advanced Preparation and Students use the paper cutouts from Activity #1 to record the area and perimeter of each pentomino shape. Sets of 12 pentominoes, one for each pair of students Duplicate SAS#4.1, one per student TEAMS Mathematics Geometry In My World Program 4 5

6 Lesson Implementation The Distance Learning Instructor introduces the activity by describing/reviewing area and perimeter. The Classroom Teacher facilitates the activity by walking around the room checking for understanding. Students work with partners and share cutouts from Activity #1, write the area and perimeter on SAS#4.1. Students call-in area and perimeter of a shape (please have them identify the pentomino by its alpha letter). Activity #3 Description Materials Advanced Preparation Lesson Implementation and Rectangles Students create rectangles using varying numbers of pentomino pieces. They record rectangles on centimeter grid paper and fill in SAS#4.2. Pentomino pieces - one set per pair of students Centimeter grid paper Color pencils, markers, crayons SAS#4.2 Duplicate SAS#4.2 - one per pair + transparency Duplicate centimeter grid paper - several per student The Distance Learning Instructor introduces the activity. The Classroom Teacher facilitates the activity by asking students to create ANY rectangle using any number of pentominoes they choose. The Classroom Teacher encourages students to use any strategy to find the answers for the worksheet, SAS#4.2. Remind students that they DO NOT have to find the rectangles in the order listed on SAS#4.2. Have students share solutions and record on transparency of SAS#4.2. TEAMS Mathematics Geometry In My World Program 4 6

7 Students use pentomino pieces to create rectangles. They record their rectangle on centimeter grid paper with colored markers to designate the pentomino pieces they used. They then fill in SAS#4.2 with dimensions and measurements. If students finish early, they can start looking for patterns. Post-viewing Activities Complete Activity #3 Symmetry and Students use the cut out pentomino shapes to look for bilateral and rotational lines of symmetry Pentomino Containers Students determine which pentomines can fold up into an uncovered box. TEAMS Mathematics Geometry In My World Program 4 7

8 SAS#4.1 and of Pentaminoes Use Pentomino pieces from Hands-On #1. Draw the pentomino piece. Then, figure out the area and perimeter of each piece. Draw Pentomino 5 12 Draw Pentomino Draw Pentomino TEAMS Mathematics Geometry In My World Program 4 8

9 SAS#4.2 and Rectangles Study the example and notice how it fits into the table. # of pentominoes 3 Dimensions: 3 X 5 : 15 : 16 Number of Can You Make a Rectangle? Dimensions TEAMS Mathematics Geometry In My World Program 4 9