STANDARD 4.2: Mathematics

Mathematics

Mission: Through mathematics, students communicate, make connections, reason, and represent the world quantitatively in order to pose and solve problems.

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.

Big Idea Geometry: Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena. Big Idea Measurement: Measurement is a tool to quantify a variety of phenomena.
4.2 A. Geometric Properties
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.
Essential Questions	Enduring Understandings
- How can spatial relationships be described by careful use of geometric language? - How do geometric relationships help in solving problems and/or make sense of phenomena?	- Geometric properties can be used to construct geometric figures. (4.5D1; 4.5D2; 4.5E3) - Geometric relationships provide a means to make sense of a variety of phenomena.
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Identify and describe spatial relationships of two or more objects in space. · Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?) · Relative shapes and sizes
2. Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. · Vertex, edge, face, side, angle · 3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid · 2D figures – square, rectangle, circle, triangle, pentagon, hexagon, octagon
3. Identify and describe relationships among two-dimensional shapes. · Same size, same shape · Lines of symmetry
4. Understand and apply concepts involving lines, angles, and circles. · Line, line segment, endpoint
5. Recognize, describe, extend, and create space-filling patterns.
4.2 B. Transforming Shapes
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.
Essential Questions	Enduring Understandings
- What situations can be analyzed using transformations and symmetries? (4.5E1; 4.5E2; 4.5E3)	- Shape and area can be conserved during mathematical transformations..
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Describe and use geometric transformations (slide, flip, turn).
2. Investigate the occurrence of geometry in nature and art.	Instructional/Assessment Focus: • This CPI is largely an instructional CPI. Assessment of this CPI is generally within the context of one or more of the other content CPIs.
4.2 C. Coordinate Geometry
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.
Essential Questions	Enduring Understandings
- 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) - Coordinate geometry can be used to represent and verify geometric/algebraic relationships.
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Locate and name points in the first quadrant on a coordinate grid.
4.2 D. Units Of Measurement
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.
Essential Questions	Enduring Understandings
- 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) - Measurements can be used to describe, compare, and make sense of phenomena.
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.
2. Select and use appropriate standard units of measure and measurement tools to solve real-life problems. · Length – fractions of an inch (1/4, 1/2), mile, decimeter, kilometer · Area – square inch, square centimeter · Weight – ounce · Capacity – fluid ounce, cup, gallon, milliliter
3. Incorporate estimation in measurement activities (e.g., estimate before measuring).

4.2 E. Measuring Geometric Objects
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.
Essential Questions	Enduring Understandings
- 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)** - Measurements can be used to describe, compare, and make sense of phenomena.
Areas of Focus/Cumulative Progress Indicators	Comments and Examples
By the end of Grade 3:
1. Determine the area of simple two-dimensional shapes on a square grid.
2. Determine the perimeter of simple shapes by measuring all of the sides
3. Measure and compare the volume of three–dimensional objects using materials such as rice or cubes.	Instructional/Assessment Focus: • Students are expected to solve problems (4.5A2)** involving this recognition. • The emphasis in grade 3 would be on the “measure,” rather than the “compare.”

Link to Standard 4.2 Grade K-2

Link to Standard 4.2 Grade 4

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