Hello, Guest!

Instructional Focus Document
Grade 4 Mathematics
TITLE : Unit 09: Geometry – Points, Lines, and Angles SUGGESTED DURATION : 11 days

Unit Overview

Introduction
This unit bundles student expectations that address identifying basic elements of geometry, lines of symmetry, and the classification of two-dimensional figures based on properties and attributes. According to the Texas Education Agency, mathematical process standards including application, tools, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Grade 3, students used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories. Students also classified and sorted two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language. In Grade 4 Unit 08, students identified parallel and perpendicular lines and used these attributes to develop the formulas for perimeter and area of rectangles and squares.

During this Unit
Students examine the foundations of geometry by identifying points, lines, line segments, rays, angles, and perpendicular and parallel lines. These concepts are essential for the ability to classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Although students have recognized examples of quadrilaterals in previous grade levels, students are expected to use formal geometric language such as parallel, perpendicular, acute, obtuse, and right angle to classify two-dimensional figures. Additionally, students apply knowledge of right angles to identify acute, right, and obtuse triangles. Symmetry is explored within two-dimensional figures as students identify and draw one or more lines of symmetry, if they exist, for two-dimensional figures.

After this Unit
In Unit 10, students will closely examine angles as they measure angles in degrees using a protractor and draw angles of a given measure. They will also determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures. In Grade 5, students will classify two-dimensional figures based on their attributes and properties in a hierarchy of sets and subsets using graphic organizers.

Additional Notes
In Grade 4, identifying points, lines, line segments, rays, angles, and perpendicular and parallel lines as well as identifying and drawing one or more lines of symmetry, if they exist, for a two-dimensional figure are STAAR Supporting Standards 4.6A and 4.6B. These standards are part of the Grade 4 Texas Response to Curriculum Focal Points (TxRCFP): Grade Level Connections. Applying knowledge of right angles to identify acute, right, and obtuse triangles is STAAR Supporting Standard 4.6C, while classifying two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size is STAAR Readiness Standard 4.6D. Both of these standards, along with STAAR Supporting Standard 4.6A are part of the Grade 4 Focal Point: Measuring Angles (TxRCFP). All of the standards in this unit are included in Grade 4 STAAR Reporting Category 3: Geometry and Measurement. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): IIIA. Geometric Reasoning-Figures and their Properties and IX. Communication and Representation.

Research
According to Van de Walle and Lovin (2006), “Children need experiences with a rich variety of both two- and three-dimensional shapes. It is useful for students to be able to identify common shapes, notice likenesses and differences among shapes, become aware of the properties that different shapes have, and eventually use these properties to further define and understand their geometric world. As students find out more about shapes over time, they can begin to appreciate how definitions of special shapes come to be” (p. 212). The National Council of Teachers of Mathematics (2000) concludes that the development of geometric concepts should take “a broader view of the power of geometry by calling on students to analyze characteristics of geometric shapes and make mathematical arguments about the geometric relationship, as well as to use visualization, spatial reasoning, and geometric modeling to solve problems. Geometry is a natural area of mathematics for the development of students’ reasoning and justification skills” (p. 3).

 

National Council of Teachers of Mathematics. (2000). Executive summary: Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades 3 – 5. Boston, MA: Pearson Education, Inc.


  • Geometric, spatial, and measurement reasoning are foundational to visualizing, analyzing, and applying relationships within and between scale, shapes, quantities, and spatial relations in everyday life.
    • Why is developing geometric, spatial, and measurement reasoning essential?
    • How does geometric, spatial, and measurement reasoning affect how one sees and works in the world?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Illustrating and analyzing geometric relationships in models and diagrams aid in representing the attributes of geometric figures with quantifiable measures in order to generalize geometric relationships and solve problem situations.
    • What attributes and properties exist in two-dimensional figures?
    • How can illustrations and/or symbols aid in identifying …
      • points?
      • lines?
      • line segments?
      • rays?
      • angles?
      • parallel lines?
      • perpendicular lines?
    • How are angles classified?
    • What relationships …
      • exist
      • do not exist
      … within and between points, lines, line segments, rays, angles, parallel lines, and perpendicular lines?
    • What strategies can be used to …
      • identify
      • draw
      … one or more lines of symmetry for a two-dimensional figure?
    • What common characteristics exist in two-dimensional figures that have …
      • one
      • more than one
      • no
      … line(s) of symmetry?
    • Where are lines of symmetry found in the real-world?
    • What relationships exist between right angles and …
      • right triangles?
      • acute triangles?
      • obtuse triangles?
    • How is the presence or absence of …
      • parallel lines
      • perpendicular lines
      • angles of a specified size
      … used to classify two-dimensional figures?
    • How can a two-dimensional figure be classified in more than one way?
  • Geometry
    • Geometric Attributes and Properties
      • Classification
    • Geometric Representations
      • One-dimensional representations
      • Two-dimensional figures
    • Symmetry
  • Measurement
    • Geometric Relationships
      • Angles
  • Associated Mathematical Processes
    • Application
    • Problem Solving Model
    • Tools and Techniques
    • Communication
    • Representations
    • Relationships
    • Justification
Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Students may confuse the notation for lines, line segments, and rays.
  • Students might use the terms parallel and perpendicular interchangeably rather than making a connection between the terms and the attributes they represent.
  • Students may misunderstand that notations for points, lines, and rays are only representations of abstract ideas and are not actual objects.
  • Students may refer to a square or rhombus as a diamond.
  • Some students may not associate the line of symmetry as the line of reflection.

Underdeveloped Concepts:

  • Students may understand that many shapes fall under the classification of quadrilaterals, but may not know how the name of each quadrilateral depends on its attributes.
  • Some students may think that two-dimensional figures are only polygons.

Unit Vocabulary

  • Acute angle – an angle that measures less than 90°
  • Acute triangle – a triangle in which each of the three angles is acute (less than 90°)
  • Adjacent angles – two non-overlapping angles that share a common vertex and exactly one ray
  • Angle – two rays with a common endpoint (the vertex)
  • Angle congruency marks – angle marks indicating angles of the same measure
  • Classify – applying an attribute to categorize a sorted group
  • Congruent – of equal measure, having exactly the same size and same shape
  • Degree – the measure of an angle where each degree represents 1 over 360.png of a circle
  • Equiangular – all angles in a polygon are congruent in measure
  • Equilateral – all side lengths of a polygon are congruent in measure
  • Intersecting lines – lines that meet or cross at a point
  • Irregular figure – a polygon with sides and/or angles that are not all congruent
  • Line – a set of points that form a straight path that goes in opposite directions without ending
  • Line of symmetry – line dividing an image into two congruent parts that are mirror images of each other
  • Line segment – part of a line between two points on the line, called endpoints of the segment
  • Obtuse angle – an angle that measures greater than 90° but less than 180°
  • Obtuse triangle – a triangle that has one obtuse angle (greater than 90°) and two acute angles
  • Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart
  • Perpendicular lines – lines that intersect at right angles to each other to form square corners
  • Point – a specific location in space
  • Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
  • Ray – part of a line that begins at one endpoint and continues without end in one direction
  • Regular figure – a polygon with all sides and angles congruent
  • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
  • Right triangle – a triangle with one right angle (exactly 90°) and two acute angles
  • Side congruency marks – side marks indicating side lengths of the same measure
  • Straight angle – an angle that measures 180° (a straight line)
  • Triangle – a polygon with three sides and three vertices
  • Two-dimensional figure – a figure with two basic units of measure, usually length and width

Related Vocabulary:

  • 7-gon (heptagon)
  • 9-gon (nonagon)
  • 11-gon (hendecagon)
  • 12-gon (dodecagon)
  • Circle
  • Decagon
  • Diagonal
  • Equilateral triangle
  • Hexagon
  • Horizontal
  • Isosceles trapezoid
  • Isosceles triangle
  • Label
  • Line of reflection
  • Octagon
  • Parallelogram
  • Pentagon
  • Quadrilateral
  • Rectangle
  • Rhombus
  • Right trapezoid
  • Scalene triangle
  • Side
  • Square
  • Trapezoid
  • Unit
  • Vertex
  • Vertical
Unit Assessment Items System Resources Other Resources

Show this message:

Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Creator if your district has granted access to that tool.

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

 

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

 

Texas Education Agency – Mathematics Curriculum

 

Texas Education Agency – STAAR Mathematics Resources

 

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

 

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

 

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

 

Texas Education Agency Texas Gateway – Resources Aligned to Grade 4 Mathematics TEKS


TEKS# SE# Unit Level Taught Directly TEKS Unit Level Specificity
 

Legend:

  • Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
  • Student Expectations (TEKS) identified by TEA are in bolded, black text.
  • Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
  • Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Legend:

  • Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
  • Unit-specific clarifications are in italicized, blue text.
  • Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
  • A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
4.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE

Including, but not limited to:

  • Mathematical problem situations within and between disciplines
    • Everyday life
    • Society
    • Workplace

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • X. Connections
4.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
Process Standard

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

  • Problem-solving model
    • Analyze given information
    • Formulate a plan or strategy
    • Determine a solution
    • Justify the solution
    • Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
4.1C

Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.


Process Standard

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE TO SOLVE PROBLEMS

Including, but not limited to:

  • Appropriate selection of tool(s) to apply in order to solve problems
    • Tools
      • Real objects
      • Manipulatives
      • Paper and pencil
      • Technology

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
4.1D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.


Process Standard

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

  • Mathematical ideas, reasoning, and their implications
    • Multiple representations, as appropriate
      • Symbols
      • Diagrams
      • Language

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

  • Representations of mathematical ideas
    • Organize
    • Record
    • Communicate
  • Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
  • Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

  • Mathematical relationships
    • Connect and communicate mathematical ideas
      • Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
      • Current knowledge to new learning

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • X. Connections
4.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

  • Mathematical ideas and arguments
    • Validation of conclusions
      • Displays to make work visible to others
        • Diagrams, visual aids, written work, etc.
      • Explanations and justifications
        • Precise mathematical language in written or oral communication

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.6 Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:
4.6A Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.
Supporting Standard

Identify

POINTS, LINES, LINE SEGMENTS, RAYS, ANGLES, AND PERPENDICULAR AND PARALLEL LINES

Including, but not limited to:

  • Point – a specific location in space
    • Has no dimension and is usually represented by a small dot
  • Line – a set of points that form a straight path that goes in opposite directions without ending
    • Line labels
      • Lines named according to two points on a line
      • Lines named by one lower case cursive letter
    • Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart
      • Various orientations including vertical, horizontal, diagonal, and parallel lines of even, uneven, or off-set lengths
      • Notation may be given using chevrons or arrows to represent parallel lines.
        • If more than one set of parallel lines are present, the number of chevrons or arrows distinguishes the sets of parallel lines.
    • Intersecting lines – lines that meet or cross at a point
      • Various orientations including vertical, horizontal, diagonal, and intersecting lines of even, uneven, or off-set lengths
    • Perpendicular lines – lines that intersect at right angles to each other to form square corners
      • Various orientations including vertical, horizontal, diagonal, and perpendicular lines of even, uneven, or off-set lengths
      • Notation is given as a box in the angle corner to represent a 90° angle.
    • Lines in pictorial models and polygons
    • Extending lines beyond pictorial models
  • Line segment – part of a line between two points on the line, called endpoints of the segment
  • Ray – part of a line that begins at one endpoint and continues without end in one direction
    • Relationships between line segments, rays, and lines
      • A line segment is part of a ray and part of a line
      • A ray is part of a line
  • Degree – the measure of an angle where each degree represents  of a circle
    • Unit measure labels as “degrees” or with symbol for degrees (°)
  • Angle – two rays with a common endpoint (the vertex)
    • Angle labels for a single angle
      • Angle with one letter, the letter of the vertex
      • Angle label with three letters, where the middle letter is the vertex of the angle
      • Angle label with a number or letter designated within the angle
      • Angle symbol with one letter, the letter of the vertex
      • Angle symbol with three letters, where the middle letter is the vertex of the angle
      • Angle symbol with a number or letter designated within the angle
    • Angle labels for adjacent angles
      • Adjacent angles – two non-overlapping angles that share a common vertex and exactly one ray
    • Various angle types/names
      • Right angle, 90°, used as a benchmark to identify and name angles
        • Acute angle – an angle that measures less than 90°
        • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
          • Notation is given as a box in the angle corner to represent a 90° angle.
        • Obtuse angle – an angle that measures greater than 90° but less than 180°
        • Straight angle – an angle that measures 180° (a straight line)
    • Angles in pictorial models and polygons

Note(s):

  • Grade Level(s):
    • Grade 3 used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
    • Grade Level Connections (reinforces previous learning and/or provides development for future learning)
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • IX. Communication and Representation
4.6B Identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure.
Supporting Standard

Identify, Draw

ONE OR MORE LINES OF SYMMETRY, IF THEY EXIST, FOR A TWO-DIMENSIONAL FIGURE

Including, but not limited to:

  • Line of symmetry – line dividing an image into two congruent parts that are mirror images of each other
  • Two-dimensional figure – a figure with two basic units of measure, usually length and width
  • Two-dimensional figures and real-world figures
  • Shapes with more than one line of symmetry
  • Shapes with no lines of symmetry
  • Shapes on which lines of symmetry have not been drawn
  • Across a vertical line, across a horizontal line, or across a diagonal line of symmetry
  • A line of reflection exists for a figure if for every point on one side of the line of reflection, there is a corresponding point the same distance from the line.

Note(s):

  • Grade Level(s):
    • Grade 3 used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Grade Level Connections (reinforces previous learning and/or provides development for future learning)
  • TxCCRS:
    • IX. Communication and Representation
4.6C Apply knowledge of right angles to identify acute, right, and obtuse triangles.
Supporting Standard

Apply

KNOWLEDGE OF RIGHT ANGLES TO IDENTIFY ACUTE, RIGHT, AND OBTUSE TRIANGLES

Including, but not limited to:

  • Angle – two rays with a common endpoint (the vertex)
    • Various angle types/names
      • Right angle, 90°, used as a benchmark to identify and name angles
        • Acute angle – an angle that measures less than 90°
        • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
          • Notation is given as a box in the angle corner to represent a 90° angle.
        • Obtuse angle – an angle that measures greater than 90° but less than 180°
  • Triangle – a polygon with three sides and three vertices
    • Triangles are named based on their largest angle.
      • Acute triangle – a triangle in which each of the three angles is acute (less than 90°)
      • Right triangle – a triangle with one right angle (exactly 90°) and two acute angles
      • Obtuse triangle – a triangle that has one obtuse angle (greater than 90°) and two acute angles

Note(s):

  • Grade Level(s):
    • Grade 3 used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories.
    • Grade 4 introduces formal and symbolic geometric language for lines, line segments, rays, and angles.
    • Grade 5 will classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • IX. Communication and Representation
4.6D Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.
Readiness Standard

Classify

TWO-DIMENSIONAL FIGURES BASED ON THE PRESENCE OR ABSENCE OF PARALLEL OR PERPENDICULAR LINES OR THE PRESENCE OR ABSENCE OF ANGLES OF A SPECIFIED SIZE

Including, but not limited to:

  • Two-dimensional figure – a figure with two basic units of measure, usually length and width
  • Regular figure – a polygon with all sides and angles congruent
  • Irregular figure – a polygon with sides and/or angles that are not all congruent
  • Classify – applying an attribute to categorize a sorted group
  • Angle – two rays with a common endpoint (the vertex)
    • Various angle types/names
      • Right angle, 90°, used as a benchmark to identify and name angles
        • Acute angle – an angle that measures less than 90°
        • Right angle – an angle (formed by perpendicular lines) that measures exactly 90°
          • Notation is given as a box in the angle corner to represent a 90° angle.
        • Obtuse angle – an angle that measures greater than 90° but less than 180°
  • Line – a set of points that form a straight path that goes in opposite directions without ending
    • Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart
      •  means  is parallel to .
      • Notation may be given using chevrons or arrows to represent parallel lines.
        • If more than one set of parallel lines are present, the number of chevrons or arrows distinguishes the sets of parallel lines.
    • Perpendicular lines – lines that intersect at right angles to each other to form square corners
      •  means  is perpendicular to .
      • Notation is given as a box in the angle corner to represent a 90° angle.
  • Sides of two-dimensional figures are composed of line segments, the part of a line between two points on the line
  • Congruent – of equal measure, having exactly the same size and same shape
    • Angle congruency marks – angle marks indicating angles of the same measure
      • mAmC means ∠A is congruent to ∠C.
    • Side congruency marks – side marks indicating side lengths of the same measure
      •  means  is congruent to .
  • Equilateral – all side lengths of a polygon are congruent in measure
  • Equiangular – all angles in a polygon are congruent in measure
  • Types of two-dimensional figures
    • Circle
      • A figure formed by a closed curve with all points equal distance from the center
      • No straight sides
      • No vertices
      • No parallel or perpendicular sides
    • Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
      • Types of polygons
        • Triangle
          • 3 sides
          • 3 vertices
          • No parallel sides
          • Types of triangles
            • Triangles are named based on their largest angle.
              • Scalene triangle
                • 3 sides
                • 3 vertices
                • No congruent sides
                • No parallel sides
                • Up to one possible pair of perpendicular sides
                  • Right triangle with two sides that are perpendicular to form a right angle and three different side lengths
                • No congruent angles
                  • Right triangle with one 90° angle and two other angles each of different measures
                  • Obtuse triangle with one angle greater than 90° and two other angles each of different measures
                  • Acute triangle with all angles less than 90° and all angles of different measures
              • Isosceles triangle
                • 3 sides
                • 3 vertices
                • At least 2 congruent sides
                • No parallel sides
                • Up to one possible pair of perpendicular sides
                  • Right triangle with two sides that are perpendicular to form a right angle and are each of the same length
                • At least 2 congruent angles
                  • Right triangle with one 90° angle and two other angles each of the same measure
                  • Obtuse triangle with two angles of the same measure and one angle greater than 90°
                  • Acute triangle with all angles measuring less than 90° and at least two of the angles of the same measure
              • Equilateral triangle/Equiangular triangle (a special type of isosceles triangle)
                • 3 sides
                • 3 vertices
                • All sides congruent
                • No parallel or perpendicular sides
                • All angles congruent
                  • Acute triangle with all angles measuring 60°
        • Quadrilateral
          • 4 sides
          • 4 vertices
          • Types of quadrilaterals
            • Trapezoid
              • 4 sides
              • 4 vertices
              • Exactly one pair of parallel sides
              • Types of trapezoids
                • Isosceles trapezoid
                  • 4 sides
                  • 4 vertices
                  • Exactly one pair of parallel sides
                  • At least 2 congruent sides, where 2 of the sides are opposite each other
                • Right trapezoid
                  • 4 sides
                  • 4 vertices
                  • Exactly one pair of parallel sides
                  • 2 pairs of perpendicular sides
                  • 2 right angles
            • Parallelogram
              • 4 sides
              • 4 vertices
              • Opposite sides congruent
              • 2 pairs of parallel sides
              • Opposite angles congruent
              • Types of parallelograms
                • Rectangle
                  • 4 sides
                  • 4 vertices
                  • Opposite sides congruent
                  • 2 pairs of parallel sides
                  • 4 pairs of perpendicular sides
                  • 4 right angles
                • Rhombus
                  • 4 sides
                  • 4 vertices
                  • All sides congruent
                  • 2 pairs of parallel sides
                  • Opposite angles congruent
                • Square (a special type of rectangle and a special type of rhombus)
                  • 4 sides
                  • 4 vertices
                  • All sides congruent
                  • 2 pairs of parallel sides
                  • 4 pairs of perpendicular sides
                  • 4 right angles
        • Pentagon
          • 5 sides
          • 5 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • Hexagon
          • 6 sides
          • 6 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • 7-gon (heptagon)
          • 7 sides
          • 7 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • Octagon
          • 8 sides
          • 8 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • 9-gon (nonagon)
          • 9 sides
          • 9 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • Decagon
          • 10 sides
          • 10 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • 11-gon (hendecagon)
          • 11 sides
          • 11 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
        • 12-gon (dodecagon)
          • 12 sides
          • 12 vertices
          • Possible parallel and/or perpendicular sides
          • Possible acute, obtuse, and/or right angles
  • Classification of two-dimensional figures based on attributes of sides and angles

Note(s):

  • Grade Level(s):
    • Grade 3 classified and sorted two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language.
    • Grade 5 will classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Measuring angles
  • TxCCRS:
    • III.A. Geometric Reasoning – Figures and their properties
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of each subject in the required curriculum.

School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated commensurate with the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.


School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the ELPS in a manner that is linguistically accommodated to help the student acquire English language proficiency.

http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4 


Choose appropriate ELPS to support instruction.

ELPS# Subsection C: Cross-curricular second language acquisition essential knowledge and skills.
Click here to collapse or expand this section.
ELPS.c.1 The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1B monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1D speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)
ELPS.c.1E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment
ELPS.c.1F use accessible language and learn new and essential language in the process
ELPS.c.1G demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations
ELPS.c.1H develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2 The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.2A distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters
ELPS.c.2C learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment
ELPS.c.2G understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar
ELPS.c.2H understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs.
ELPS.c.3 The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.3A practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible
ELPS.c.3B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E share information in cooperative learning interactions
ELPS.c.3F ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments
ELPS.c.3G express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.3I adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.
ELPS.c.4 The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.4E read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language
ELPS.c.4G demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.4I demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with content area needs
ELPS.c.4J demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs
ELPS.c.4K demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs.
ELPS.c.5 The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5A learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired
ELPS.c.5D edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired
ELPS.c.5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
Last Updated 03/01/2019
Loading
Data is Loading...