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Standard 4.2 Geometry and Measurement All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.
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Big Idea Geometry: Spatial sense
and geometric relationships are a means to solve problems and make
sense of a variety of phenomena. |
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4.2.6 A. Geometric Properties |
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Descriptive Statement: This includes identifying, describing and classifying standard geometric object, describing and comparing properties of geometric objects, making conjectures concerning them, and using reasoning and proof to verify or refute conjectures and theorems. Also included here are such concepts as symmetry, congruence, and similarity. |
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Essential Questions |
Enduring Understandings |
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- How can spatial relationships be described by
careful use of geometric language? |
- Geometric properties can be used to construct
geometric figures. (4.5D1; 4.5D2; 4.5E3) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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1. Understand and apply concepts involving lines and angles. · Notation for line, ray, angle, line segment · Properties of parallel, perpendicular, and intersecting lines · Sum of the measures of the interior angles of a triangle is 180° |
"Understand and apply" here means "define, recognize, and apply." It is assumed at grade 6 that students will be familiar with and be able to use the notation for "parallel" and "perpendicular." |
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2. Identify, describe, compare, and classify polygons and circles. · Triangles by angles and sides · Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi · Polygons by number of sides. |
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| 3. Identify similar figures. | This is an area of focus in grade 5 and may be assessed at a higher level of understanding in grade 6. |
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4. Understand and apply the concepts of congruence and symmetry (line and rotational).
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This is an area of focus in grade 5 and may be assessed at a higher level of understanding in grade 6. |
| 5. Compare properties of cylinders, prisms, cones, pyramids, and spheres. |
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| 6. Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives. | |
| 7. Identify a three-dimensional shape with given projections (top, front and side views). | "Identify" here means to recognize and differentiate from other shapes. |
| 8. Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape). |
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4.2.6 B. Transforming Shapes |
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Descriptive Statement: This includes identifying, describing and classifying standard geometric object, describing and comparing properties of geometric objects, making conjectures concerning them, and using reasoning and proof to verify or refute conjectures and theorems. Also included here are such concepts as symmetry, congruence, and similarity. |
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Essential Questions |
Enduring Understandings |
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- What situations can be analyzed using transformations and symmetries? (4.5E1; 4.5E2; 4.5E3) |
- Shape and area can be conserved during mathematical transformations.. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
| 1. Use a translation, a reflection, or a rotation to map one figure onto another congruent figure. | |
| 2. Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings. | This is an area of focus in grade 5 and may be assessed at a higher level of understanding in grade 6. |
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4.2.6 C. Coordinate Geometry |
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Descriptive Statement: Coordinate geometry provides an important connection between geometry and algebra. It facilitates the visualization of algebraic relationships, as well as an analytical understanding of geometry. |
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Essential Questions |
Enduring Understandings |
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- How can geometric/algebraic relationships best be represented and verified? (4.5C2; 4.5D2; 4.5E1; 4.5E2; 4.5F5) |
- Reasoning and/or proof can be used to verify or
refute conjectures or theorems in geometry (4.5D1; 4.5D3; 4.5D4;
4.5D5; 4.5F5) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
| 1. Create geometric shapes with specified properties in the first quadrant on a coordinate grid. | |
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4.2.6 D. Units Of Measurement |
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Descriptive Statement: Measurement helps describe our world using numbers. An understanding of how we attach numbers to real-world phenomena, familiarity with common measurement units (e.g., inches, liters, and miles per hour), and a practical knowledge of measurement tools and techniques are critical for students' understanding of the world around them. |
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Essential Questions |
Enduring Understandings |
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- How can measurements be used to solve problems? (4.5A6) |
- Everyday objects have a variety of attributes,
each of which can be measured in many ways.
-What we measure affects how we measure it.
(4.5A4; 4.5A6) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
| 1. Select and use appropriate units to measure angles, area, surface area, and volume. | Sample SCR Item: What units would you use to measure the volume of air in a room? (Answer: cubic feet or cubic meters, among other possibilities) |
| 2. Use a scale to find a distance on a map or a length on a scale drawing. | |
| 3. Convert measurement units within a system (e.g., 3 feet = ___ inches). | This is an area of focus in grade 5 and may be assessed at a higher level of understanding in grade 6. |
| 4. Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). | This is an area of focus in grade 5 and may be assessed at a higher level of understanding in grade 6. |
| 5. Use measurements and estimates to describe and compare phenomena. | Sample SCR Item: Ten inches of snow is equivalent to one inch of rain. If the forecast is for 3 inches of rain in the next 24 hours, how much snow will accumulate if the temperature drops below freezing, and it snows instead of raining? (Answer: 30 in. or 2 ½ ft) |
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4.2.6 E. Measuring Geometric Objects |
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Descriptive Statement: This area focuses on applying the knowledge and understandings of units of measurement in order to actually perform measurement. While students will eventually apply formulas, it is important they develop and apply strategies that derive from their understanding of the attributes. In addition to measuring objects directly, students apply indirect measurement skills, using, for example, similar triangles and trigonometry. |
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Essential Questions |
Enduring Understandings |
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- How can measurements be used to solve problems? (4.5A6) |
- Everyday objects have a variety of attributes,
each of which can be measured in many ways. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
| 1. Use a protractor to measure angles. | This is an area of focus in grade 5 and may be assessed at a higher level of understanding in grade 6. |
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2. Develop and apply strategies and formulas for finding perimeter and area. |
Sample SCR Item: A fountain is built in the shape of a circle. The fountain is 10 feet across at the widest part. What is the area of the floor of the fountain? (Answer: Approximately 78 1/2 square feet) |
| 3. Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders. |
Sample MC Item:
The area of the base of a cereal box is 12 square inches. The box is 10
inches high. What is its volume? b. 60 cu. in. c. 40 cu. in. d. 22 cu. in. |
| 4. Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa. |
Instructional/Assessment Focus: • Students are expected to solve problems (4.5A2)** involving this recognition • Assessment of this CPI is generally within the context of CPI 4.2.6E2. |
| 5. Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one’s foot). | |
