# EMPower Product Sampler Correlations for Geometry

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1 EMPower Product Sampler Correlations for Geometry EMPower Mathematics Topic Correlation Guide Over, Around, and Within: Geometry and Measurement Book Description: Students explore the features and measures of basic shapes. Perimeter and area of twodimensional shapes and volume of rectangular solids provide the focus. Lesson Number: Lesson Name: Mathematical Concepts/ Topics Covered: Opening the Unit Lesson 1: Geometry Groundwork Sharing Secret Designs Shapes identified and sketched Angles introduced Geometry vocabulary list started Prior Geometry knowledge assessed Two-dimensional shape characteristics identified 12 Basic Geometric Shapes identified and described Lesson 2: Get It Right Angles identified and described with conventional notation Right angles introduced Angle measurements estimated with 90 benchmark and determined precisely with protractors Lesson 3: Get It Straight Straight (180 ) angles explored Sums of angles in triangles and rectangles established Lesson 4: Giant-Size Similar shapes identified and described Length and width dimensions introduced and measured Perimeters determined by adding Interim Assessment 1 Shapes and Angles Attributes of shapes and angle measurements knowledge assessed Lesson 5: Line Up by Size Area and perimeter distinguished Lesson 6: Combining Rectangles Rectangle area calculated in square centimeters Composite shapes areas and perimeters compared EMPower 17

2 Lesson 7: Lesson 8: Lesson 9: Disappearing Gridlines Conversion Experience Squarely in English Formulas for area and perimeter derived Missing dimension values determined Area of a right triangle calculated Standard English Units introduced Linear unit conversions established Square units square inches, feet, and yards constructed and connected with area measure Square unit conversions established Lesson 10: Scale Down Scale drawings made and steps for scaling analyzed Interim Assessment 2 A Fresh Look Area, perimeter, measurement, and scale knowledge applied and assessed Lesson 11: Filling the Room Volume explored as capacity Third dimension height becomes apparent Lesson 12: Cheese Cubes, Anyone? Cubic inch introduced then used to measure volume Volume formula derived Lesson 13: On the Surface Surface area and volume compared Surface area and shape relationship generalized Closing the Unit Design a Box Geometry and measurement knowledge applied and assessed 18 EMPower Product Sampler

3 Over, Around, and Within Geometry and Measurement Also available: STUDENT BOOK TERC Mary Jane Schmitt, Myriam Steinback, Tricia Donovan, and Martha Merson

4 Opening the Unit: Geometry Groundwork Is there geometry in your life? Often when we are making something, ideas associated with the study of geometry arise. Do you see shapes within shapes? How do parts fit together? How does measuring help you figure things out when you are cooking, building, or sewing? In this unit, you will learn about shape, line, and form. You will explore the skills that allow people to work mathematically with shapes in everyday life. EMPower Opening the Unit: Geometry Groundwork 1

5 Activity 1: Making a Mind Map Make a Mind Map using words, numbers, pictures, or ideas that come to mind when you think of geometry and measurement. GEOMETRY MEASUREMENT 2 Over, Around, and Within: Geometry and Measurement EMPower

6 Activity 2: Making an Angle Demonstrator Make your own angle demonstrator with the parts that your teacher will give you. Cut out the two strips of paper and place one on top of the other so the two dots are aligned. Put a fastener through the two dots so the paper strips can open and close like a mouth. Now you have an angle demonstrator. Make another one for home use, if you like. Activity 3: Initial Assessment Your teacher will show you some problems and ask you to check off how you feel about your ability to solve each problem: Can do Don t know how Not sure Have you ever noticed that every new place you work has its own words or specialized vocabulary? This is true of topics in math too. In every lesson you will be introduced to some specialized vocabulary. Do not worry if you see words in the problems that you do not recognize. You can write some words down and look them up later, or learn as you go. Activity 4: Homemade Objects Choose an object from the collection provided, or use a homemade object of your own. Object: 1. Sketch your object. EMPower Opening the Unit: Geometry Groundwork 3

7 Activity 4: Homemade Objects (continued) 2. What shapes make up your object? Make a sketch of each shape you see. Name each shape. Sketch Sheet Sketch of Shapes Observed Name or Description of Shapes 3. When you finish drawing and naming the shapes, trade your object and Sketch Sheet with a classmate. See if you can find any additional shapes in your partner s object. Add them to your partner s Sketch Sheet and name them. 4 Over, Around, and Within: Geometry and Measurement EMPower

8 Practice: Using Geometry Write three paragraphs about how you use geometry and measurement. In your work At home In everyday life in your community EMPower Opening the Unit: Geometry Groundwork 5

9 Practice: Seeing Geometry 1. Sketch an object that has some interesting shapes. 2. What shapes and angles do you see in the object? 3. What measurements could you take of the object? 6 Over, Around, and Within: Geometry and Measurement EMPower

10 Extension: Name the Shapes The following are traditional Japanese patterns. 1. Sketch and name the shapes you see within this pattern. 2. Sketch and name the shapes you see within this pattern. 3. Many countries have traditional designs that include geometric shapes. a. Research a design from your own or another tradition. b. Sketch the design. c. Name the shapes you see within the design. EMPower Opening the Unit: Geometry Groundwork 7

11 Geometry and Measurement Unit Goals Recognize and describe shapes and their characteristics. Find area and perimeter of rectangles and volume of rectangular solids. Make drawings to scale. Use linear, square, and cubic units. Use spatial reasoning to solve problems. Make generalizations about two- and three-dimensional shapes. My Own Goals 8 Over, Around, and Within: Geometry and Measurement EMPower

12 Over, Around, and Within Geometry and Measurement Also available: TEACHER BOOK TERC Mary Jane Schmitt, Myriam Steinback, Tricia Donovan, and Martha Merson

13 Facilitating Opening the Unit: Geometry Groundwork Synopsis This session assesses students familiarity with basic concepts and vocabulary associated with geometry and measurement. The activities establish a baseline by extending a variety of opportunities for students to interact with and comment on aspects of shapes, including dimensions, angle size, perimeter, area, and volume. 1. Students complete a Mind Map, recording their ideas and associations with geometry and measurement. 2. Students complete a self-assessment based on several problems. 3. Students discuss the geometrical shapes in homemade objects. Objectives Is there geometry in your life? Demonstrate prior knowledge of geometry Construct an angle demonstrator and record an angle Keep a record of vocabulary useful to the study of geometry Identify and sketch shapes EMPower Facilitating Opening the Unit: Geometry Groundwork 1

18 Looking Closely Observe whether students are able to Demonstrate prior knowledge of geometry Do students have experience with this area of mathematics? Do they seem curious? Construct an angle demonstrator and record an angle Constructing a measurement tool will help students navigate through the activities of this unit. In addition, it will give you insight into their facility with constructing, aligning, and tracing skills they will call on as they find area, perimeter, and volume, and record angles. Take note of students who seem adept at this activity; later you can assign students to work in pairs in ways that nurture emerging learners and challenge more advanced students. If some students have difficulty constructing the tools, pair these students with those who have succeeded and can offer help. Keep a record of vocabulary useful to the study of geometry Rather than consulting a dictionary, try to piece together definitions based on students prior knowledge. These definitions can be refined over time. Do English language learners know geometric terms in their own languages? Ask them to record these as well. Identify and sketch shapes Can students identify and name the overall shape of objects? Can they identify and name shapes within objects? Direct students to compare the attributes of shapes, such as length and position of sides and the number and shape of angles (e.g., wide-open or pointy). 6 Over, Around, and Within: Geometry and Measurement EMPower

19 WHAT TO LOOK FOR IN OPENING THE UNIT Concept Development Identifies and names overall shapes of objects Identifies and names shapes within objects Compares shapes with other shapes Records angles using angle demonstrator Expressive Capacity Uses appropriate vocabulary when describing and comparing shapes Describes shapes within objects with precision Use of Tools Constructs angle demonstrator Uses angle demonstrator Background Knowledge Is familiar with geometric shapes Has vocabulary for different shapes, angles, and geometric properties, e.g., area, perimeter, and volume WHO STANDS OUT? (LIST STUDENTS INITIALS) STRONG ADEQUATE NEEDS WORK NOTES FOR NEXT STEPS EMPower Facilitating Opening the Unit: Geometry Groundwork 7

20 LESSON COMMENTARY: OPENING THE UNIT Rationale This lesson is an invitation for students at all levels to discuss shapes, measurements, and the ways in which geometry and measurement contribute to our ability to construct and describe objects. Constructing a measurement tool helps students internalize a sense of angle size. EMPower builds on students prior knowledge; therefore, objects of students own making are an ideal starting point. Math Background Recognizing the basic shapes rectangles, squares, circles, and triangles is critical to the study of geometry and measurement. Observing the characteristics of a shape, such as the number of angles or sides, their relative sizes, and the sides relative positions, allows us to tap into the established knowledge base about the shape, for example, how to find the measurement for a missing side or angle, or the formula for area. The world is full of squiggly lines and amorphous, incomplete, or open shapes. Open shapes are problematic when determining area. With no clear boundaries, open shapes lead to questions about infinity. Amorphous shapes present a challenge of a different kind. Finding the area of a shape with curves demands making approximations using rectangles, some of which are tiny, to fill in the shape. In calculus, this is done by finding the area under curve through integrals. However, knowing how to find the area of rectangular, triangular, or hexagonal shapes is the first step toward arriving at an estimate of the area or volume of an amorphous shape. Facilitation To promote the communication central to mathematics, ask students to interview each other about their homemade objects. Post interview questions such as What steps did you take to make the object? What geometric shapes are part of your object? What did you measure? What were the most difficult and enjoyable parts of making the object? In some classes, interviewing can be difficult, given the English-proficiency level of the students. Further simplify the task by giving sentence starters, e.g., I have a ; I made it by. 8 Over, Around, and Within: Geometry and Measurement EMPower

22 continued from previous page I asked students to speculate: What do you think I did to make the cake this shape? What pan(s) do you imagine I used? Student: You used a square pan and cut out a heart. (I made a mental note that she called the rectangle that she drew a square ): Teacher: That s one way, but that s not how I did it. Student: I think you had a big circular pan and cut off pieces. Like this: Teacher: That s another way, but not how I did it. Student: You had a heart-shaped pan. Teacher: No, but I ll give you a hint. I used two pans, a square one and a round one. Here they are. (Silence.) Then: Student: Okay, I see two parts of the circle, and you pushed the square between them. (He gestured over the cake.) Teacher: Yeah, that s exactly what I did. Who s hungry? Mary Jane Schmitt Bridge to Learning and Literacy, Harvard University, MA 10 Over, Around, and Within: Geometry and Measurement EMPower

23 Blackline Master 1: Angle Demonstrators EMPower 2005 Key Curriculum Press Blackline Masters

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