4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.2. 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. Recognize right triangles as a category, and identify right triangles. 4.G.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Anchor Standard/Mathematical Practice(s)

MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. MP.7.Look for and make use of structure.

Information Technology Standard

Use technology tools and skills to reinforce classrom concepts and activities.

Revised Bloom's Level of thinking

Remembering Understanding Applying

Learning Target/Task Analysis

4.G.1 This standard asks students to draw two-dimensional geometric objects and to also identify them in twodimensional figures. This is the first time that students are exposed to rays, angles, and perpendicular and parallel lines. Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen daily. Students do not easily identify lines and rays because they are more abstract.

right angle acute angle obtuse angle straight angle segment line ray perpendicular lines parallel lines

Example: Draw two different types of quadrilaterals that have two pairs of parallel sides? Is it possible to have an acute right triangle? Justify your reasoning using pictures and words. Example: How many acute, obtuse and right angles are in this shape?

Draw and list the properties of a parallelogram. Draw and list the properties of a rectangle. How are your drawings and lists alike? How are they different? Be ready to share your thinking with the class.

4.G.2 Two-dimensional figures may be classified using different characteristics such as, parallel or perpendicular lines or by angle measurement. Parallel or Perpendicular Lines: Students should become familiar with the concept of parallel and perpendicular lines. Two lines are parallel if they never intersect and are always equidistant. Two lines are perpendicular if they intersect in right angles (90º). Students may use transparencies with lines to arrange two lines in different ways to determine that the 2 lines might intersect in one point or may never intersect. Further investigations may be initiated using geometry software. These types of explorations may lead to a discussion on angles. Parallel and perpendicular lines are shown below:

This standard calls for students to sort objects based on parallelism, perpendicularity and angle types. Example:

Do you agree with the label on each of the circles in the Venn diagram above? Describe why some shapes fall in the overlapping sections of the circles. Example: Draw and name a figure that has two parallel sides and exactly 2 right angles. Example: For each of the following, sketch an example if it is possible. If it is impossible, say so, and explain why or show a counter example. • A parallelogram with exactly one right angle. • An isosceles right triangle. • A rectangle that is not a parallelogram. (impossible) • Every square is a quadrilateral. • Every trapezoid is a parallelogram.

Example: Identify which of these shapes have perpendicular or parallel sides and justify your selection.

A possible justification that students might give is: The square has perpendicular lines because the sides meet at a corner, forming right angles.

Angle Measurement: This expectation is closely connected to 4.MD.5, 4.MD.6, and 4.G.1. Students’ experiences with drawing and identifying right, acute, and obtuse angles support them in classifying two-dimensional figures based on specified angle measurements. They use the benchmark angles of 90°, 180°, and 360° to approximate the measurement of angles. Right triangles can be a category for classification. A right triangle has one right angle. There are different types of right triangles. An isosceles right triangle has two or more congruent sides and a scalene right triangle has no congruent sides. 4.G.3 Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more lines of symmetry. This standard only includes line symmetry not rotational symmetry. Example: For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do you think there would be for regular polygons with 9 and 11 sides. Sketch each figure and check your predictions. Polygons with an odd number of sides have lines of symmetry that go from a midpoint of a side through a vertex.

I can...

I can identify points, lines, line segments, rays, and angles. I can identify parallel and perpendicular lines and distinguish between the two. I can identify points, lines, line segments, rays, and angles in a 2 dimensional shape. I can identify parallel and perpendicular lines in a 2 dimensional shape. I can sort two dimensional shapes based on specific criteria. I can recognize that triangles can be classified based on the lenghts of their sides. I can identify a triangle based on the size of its angles. I can recognize lines of symmetry in 2 dimensional figures.

Essential Vocabulary

acute angle, right angle, obtuse angle, points, lines, line segments, rays, perpendicular, parallel, right triangles, line of symmetry, line symmetrical figures

Sample Assessments

Have students locate examples of each geometric term in the classroom, take pictures of the examples outside, or cut out pictures of examples from a magazine. Create a geometric collage using what students found.

Students use the angle finder created in class. Teacher calls out angles formed by parts of the circle—½, ¼, 3/4—and students create the angles with their finders. Teacher could extend the activity by showing other angles and asking students to form a similar degree angle with the finders. Problem Task: Students will use their angle finder to locate and identify angles in real-life settings (i.e., classroom, playground, home). Students will trace the measurement of the angle finder to represent the measurement of the angle. Students will label the representation with rays, vertex, and interior arc. Working with partners, students draw several angles and have partners measure them, and vice versa. Measure the angles of a regular polygon—students understand that angles are equal. Students will locate angles in the classroom or outside. After writing down the angle measurement and item, the students will draw each of the angles found using a protractor. Ruby is standing on first base. Jasmine is standing on second base. What is the angle of measure from home plate between the two girls? What is the angle between third base and second base? Answer: 45° Bella and Edward’s teacher told them that the two outside rays in this drawing are perpendicular. She asked them to find the missing measure. What is it? Answer: 45° (again!)

Give students several pictures of various two-dimensional figures. Practice finding figures by giving students criteria for classifications (i.e., parallel lines, perpendicular lines, acute angles, obtuse angles, and right angles). Finally, have the students identify the right triangles and classify these into a separate group. Create an art project using all of the new geometric classification terms. Give students different two-dimensional figures and have them classify them and justify their classification.

Have students use grid to draw parallel, perpendicular, & intersecting lines and plot coordinates for each. They can also find the coordinates for the missing sides of various polygons. They could also draw lines parallel or perpendicular to a line you assign them to plot.

Using previous knowledge of angle measure, students will be able to view the diagrams at the right, and determine the missing angles.

Using protractors, students will draw angles with missing measure and trade drawings with a partner. The partner will then solve for the missing angle.

## Common Core Standards

4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.4.G.2. 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. Recognize right triangles as a category, and identify right triangles.

4.G.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

## Anchor Standard/Mathematical Practice(s)

MP.4. Model with mathematics.MP.5. Use appropriate tools strategically.

MP.6. Attend to precision.

MP.7.Look for and make use of structure.

## Information Technology Standard

Use technology tools and skills to reinforce classrom concepts and activities.## Revised Bloom's Level of thinking

RememberingUnderstanding

Applying

## Learning Target/Task Analysis

4.G.1This standard asks students to draw two-dimensional geometric objects and to also identify them in twodimensional

figures. This is the first time that students are exposed to rays, angles, and perpendicular and parallel

lines.

Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen daily.

Students do not easily identify lines and rays because they are more abstract.

right angle acute angle obtuse angle

straight angle segment line

ray perpendicular lines parallel lines

Example:

Draw two different types of quadrilaterals that have two pairs of parallel sides?

Is it possible to have an acute right triangle? Justify your reasoning using pictures and words.

Example:

How many acute, obtuse and right angles are in this shape?

Draw and list the properties of a parallelogram. Draw and list the properties of a rectangle. How are your

drawings and lists alike? How are they different? Be ready to share your thinking with the class.

4.G.2

Two-dimensional figures may be classified using different characteristics such as, parallel or perpendicular lines

or by angle measurement.

Parallel or Perpendicular Lines:

Students should become familiar with the concept of parallel and perpendicular lines. Two lines are parallel if

they never intersect and are always equidistant. Two lines are perpendicular if they intersect in right angles (90º).

Students may use transparencies with lines to arrange two lines in different ways to determine that the 2 lines

might intersect in one point or may never intersect. Further investigations may be initiated using geometry

software. These types of explorations may lead to a discussion on angles.

Parallel and perpendicular lines are shown below:

This standard calls for students to sort objects based on parallelism, perpendicularity and angle types.

Example:

Do you agree with the label on each of the circles in the Venn diagram above? Describe why some shapes fall in

the overlapping sections of the circles.

Example:

Draw and name a figure that has two parallel sides and exactly 2 right angles.

Example:

For each of the following, sketch an example if it is possible. If it is impossible, say so, and explain why or show

a counter example.

• A parallelogram with exactly one right angle.

• An isosceles right triangle.

• A rectangle that is not a parallelogram. (impossible)

• Every square is a quadrilateral.

• Every trapezoid is a parallelogram.

Example:

Identify which of these shapes have perpendicular or parallel sides and justify your selection.

A possible justification that students might give is:

The square has perpendicular lines because the sides meet at a corner, forming right angles.

Angle Measurement:

This expectation is closely connected to 4.MD.5, 4.MD.6, and 4.G.1. Students’ experiences with drawing and

identifying right, acute, and obtuse angles support them in classifying two-dimensional figures based on specified

angle measurements. They use the benchmark angles of 90°, 180°, and 360° to approximate the measurement of

angles.

Right triangles can be a category for classification. A right triangle has one right angle. There are different types

of right triangles. An isosceles right triangle has two or more congruent sides and a scalene right triangle has no

congruent sides.

4.G.3

Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular

and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more

lines of symmetry.

This standard only includes line symmetry not rotational symmetry.

Example:

For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do

you think there would be for regular polygons with 9 and 11 sides. Sketch each figure and check your

predictions.

Polygons with an odd number of sides have lines of symmetry that go from a midpoint of a side through a vertex.

## I can...

I can identify points, lines, line segments, rays, and angles.I can identify parallel and perpendicular lines and distinguish between the two.

I can identify points, lines, line segments, rays, and angles in a 2 dimensional shape.

I can identify parallel and perpendicular lines in a 2 dimensional shape.

I can sort two dimensional shapes based on specific criteria.

I can recognize that triangles can be classified based on the lenghts of their sides.

I can identify a triangle based on the size of its angles.

I can recognize lines of symmetry in 2 dimensional figures.

## Essential Vocabulary

## acute angle, right angle, obtuse angle, points, lines, line segments, rays, perpendicular, parallel, right triangles, line of symmetry, line symmetrical figures

## Sample Assessments

Have students locate examples of each geometric term in the classroom, take pictures of the examples outside, or cut out pictures of examples from a magazine. Create a geometric collage using what students found.Students use the angle finder created in class. Teacher calls out angles formed by parts of the circle—½, ¼,

3/4—and students create the angles with their finders. Teacher could extend the activity by showing other angles and asking students to form a similar degree angle with the finders.

Problem Task:

Students will use their angle finder to locate and identify angles in real-life settings (i.e., classroom, playground, home). Students will trace the measurement of the angle finder to represent the measurement of the angle. Students will label the representation with rays, vertex, and interior arc.

Working with partners, students draw several angles and have partners measure them, and vice versa.

Measure the angles of a regular polygon—students understand that angles are equal.

Students will locate angles in the classroom or outside. After writing down the angle measurement and item, the students will draw each of the angles found using a protractor.

Ruby is standing on first base. Jasmine is standing on second base. What is the angle of measure from home plate between the two girls? What is the angle between third base and second base?

Answer: 45°

Bella and Edward’s teacher told them that the two outside rays in this drawing are perpendicular. She asked them to find the missing measure. What is it?

Answer: 45° (again!)

Give students several pictures of various two-dimensional figures. Practice finding figures by giving students criteria for classifications (i.e., parallel lines, perpendicular lines, acute angles, obtuse angles, and right angles). Finally, have the students identify the right triangles and classify these into a separate group.

Create an art project using all of the new geometric classification terms.

Give students different two-dimensional figures and have them classify them and justify their classification.

## Differentiation

## Intervention:

http://daretodifferentiate.wikispaces.com/Choice+Boardshttp://www.ixl.com/math/grade-4/parallel-perpendicular-intersecting

Read Straight Lines, Parallel Lines, Perpendicular Lines

Read The Dot and the Lineby Juster.

## Enrichment:

http://www.teachertube.com/viewVideo.php?title=angles_in_a_circle&video_id=231281

Math quiz using angles and degrees:

http://www.ixl.com/math/grade/4

Finding degrees of angles:

http://www.mathisfun.com/angles.html

Have students use grid to draw parallel, perpendicular, & intersecting lines and plot coordinates for each. They can also find the coordinates for the missing sides of various polygons. They could also draw lines parallel or perpendicular

to a line you assign them to plot.

## Instructional Resources

http://www.uen.org/Lessonplan/preview.cgi?LPid=11235http://illuminations.nctm.org/LessonDetail.aspx?ID=L270

Using previous knowledge of angle measure, students will be able to view the diagrams at the right, and determine the missing angles.

Using protractors, students will draw angles with missing measure and trade drawings with a partner. The partner will then solve for the missing angle.

http://www.mathsisfun.com/geometry/complementary-angles.html

http://www.mathsisfun.com/geometry/supplementary-angles.html

http://www.khanacademy.org/video/complementary-and-supplementary-angles?playlist=Geometry

Book:

Sir Cumference and the Great Knight of Angleland, by Cindy Neuschwander

## Notes and Additional Information