Subject Verb Agreement

Mini Lesson: Subject-Verb Agreement

Subject: English Language Arts

Grade Level: 6th-8th

Objective: Students explore subject–verb agreement using real-life examples and then talk about the difference between formal and informal language and how to use this important grammatical rule.

Common Core Standards:
•CCSS.ELA-Literacy W.6.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
•CCSS ELA-Literacy W.6.5: With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

Time: 15 Minutes

Materials: Internet Access to watch video clips
Student Handouts Mini Lesson (Attached)

Rationale: After reviewing subject-verb agreement, middle school students will explore newspaper and song lyrics to identify both correct and incorrect subject-verb agreement. The emphasis on the lesson is on asking students to discover how this important grammatical rule is used (or deliberately ignored) in a variety of settings.

Assessment: Students comprehension of Subject-Verb agreement will be conduct during class/small group collaborative discussion and written work to be handed in.

Launch:
Students will watch the following clip: http://www.schooltube.com/video/b7de4895bc086b3b83f7/

Explore: After the brief review is given regarding subject/verb agreement, students will he given a worksheet with song lyrics to discuss in small working groups.
I will play the song for the class to hear the music as it sounds:

Upon completion, volunteers will be asked to share their corrections with classmates.

Summarize:
Hand out the “Making Subjects and Verbs Agree” to students for their Daybook. Class discussion will include the following questions:
• What is a subject? What is a singular subject? What is a plural subject?
• What is a verb? What is a singular verb? What is a plural verb?
• What is a pronoun?
• What does it mean to have subject-verb agreement?
• Can you think of any examples of songs, headlines, or quotes that lack subject-verb agreement?
• What sounds better – a sentence with or without subject-verb agreement?
• Does anyone know another language? If so, how does subject-verb agreement work in Spanish, Italian, etc?
• When you are grammatically correct in your writing and speech, what kind of impression do you give? Likewise, when you are grammatically incorrect, what kind of impression do you give?

Extension Assignments: Challenge students to find examples in media (music, newspaper articles, ads, etc) where subject verb agreement is not present. Students can complete the assignment found here for more practice.
http://www.englishwsheets.com/subject-verb-agreement-1.html

Resources:
Celce-Murcia, M., & Larsen-Freeman, D. (1999). The copula and subject–verb agreement. In The grammar book: An ESL/EFL teacher’s course, (2nd ed., pp. 53-78). Boston: Heinle & Heinle.

Paiz, Joshua M. and Chris Berry. (2013) Making Subject and Verbs Agree. http://owl.english.purdue.edu

Mini Lesson

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EXTRA – FORM ANY SHAPE ON A GEOBOARD; FIND ITS AREA BY MAGIC

Bibliographic Information:
Lobsco, Michael L. “Form Any Shape On This GeoBoard, and Find Its Area By Magic.” Mental Math Workbook, Scholastic Inc, 1998. Pages 75-77. (ISBN # 0-439-14863-4)

Mathematical Concept:
Using a Geoboard, Calculating Area

Grade Levels: 6th – 8th

NCTM Standards and Principles of School Mathematics:• Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Use geometric models to represent and explain numerical and algebraic relationships.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Materials:
Geoboard Pattern
Piece of Wood 10 in x 10 in (25 cm x 25 cm) x ¼ inch (1.9 cm) thick
Small Nails
Hammer
Rubber Bands
Linseed oil, Shellac, or paint (optional)

Detailed Description:
With this common grid of nails, you can do more than form many geometric shapes and symmetrical designs. You can perform the spectacular feat of finding the area of regular or jagged intricate shapes using the magical formula learned in this activity. With this secret formula you can actually do what appears to be impossible. Have a friend make the most complicated shape on the board with a rubber band. You can relay how large it is in less than a minute!

Construction Procedure:
1. Photocopy the pattern attached and place it on top of the square board. Be sure you enlarge the photocopy to 300%.
2. Tape the corners of the sheet onto the board to keep it in place.
3. Nail nails on the dots into the board so that each protrudes ½ in (1.3 cm) above the surface. Remove the paper.
4. Sand the board and finish with shellac, oil, or paint. Dry completely.

Activity Procedure:
1. Work through Activities One and Two in class.
2. Once activities are completed, divide class into working partners.
3. Have each partner form an intricate figure on the geoboard.
4. The other partner should us Pick’s Formula to Solve the Area.

Attachment: Worksheet/Activity Student Page
• Geoboard Pattern to be Enlarged by 300%
Activity One
Activity Two
Answer Key for Activity One and Two

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TRANSLATION: ACTING OUT TRANSLATED FIGURES

Bibliographic Information:
Killian, Elaine. Acting Out Translated Figures.

Mathematical Concept: Translation

Grade Levels: 7th – 8th

NCTM Standards and Principles of School Mathematics:
• Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Use geometric models to represent and explain numerical and algebraic relationships.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Materials:
Masking Taped Grid on the floor of the class
Yarn
Different pre-cut figures written down in (x, y) notation
Copies of Translation Worksheet

Detailed Description:
The following activity will describe translation of figures. By completion of this lesson, students should understand that a translated image is an image that “slides” in a given direction. The original object and its translation have the same shape, size, and face in the same direction. Students will “Act Out” a figure in the exercise given below. Students will participate by being the original figure and a translated figure.

Procedure:
1. Before class, the teacher will create an x and y axis grid on the floor using masking tape.
2. Divide the class into small working groups.
3. Students will come up to the table groups and choose a figure to represent.
4. The figure will be written down in (x, y) ordered notation form.
5. Each student will represent a point on the polygon. The polygon will be completed using yarn to connect the points (students)
6. The next group will come up and perform the given translation.
7. Each group should get a chance to be the original figure and the translated figure.
8. To follow up student comprehension, students will be given the attached “Translation” worksheet for homework.

Attachment: Worksheet/Activity Student Page
Translation – Handout

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ROTATION

Bibliographic Information:
Harrington, Carla. Alexander County Public Schools, Teacher.

Mathematical Concept: Rotation

Grade Levels: 7th – 8th

NCTM Standards and Principles of School Mathematics:
• Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Use geometric models to represent and explain numerical and algebraic relationships.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Materials:
Pencils
Computer with access to Smartboard
Copies of “Rotational Symmetry in the Alphabet” and “Rotational Symmetry in Road Signs” Handouts
Rotation of Shapes Handout

Detailed Description:
These activities are designed to introduce students to Rotational symmetry. Upon completion of these activities, students will know that an image is said to have rotational symmetry if it looks exactly the same when rotated. To illustrate examples of Rotational Symmetry, I will be using the SmartBoards application for Rotation sent to me by Mrs. Carla Harrington. Using this interactive tool, an image may be selected. After covering with virtual “tracing paper” the image is outlined. Then, you may click on Rotate to see how the “traced image” would appear if the original was rotated at 90°, 180°, 270° and 360°. It can be found at the following website:
http://www.teacherled.com/2008/01/28/rotational-symmetry/

Activity Procedure:
1. Give out the sheets titled “Rotational Symmetry in the Alphabet” and “Rotational Symmetry in Road Signs”
2. Have students tell below each letter/sign if it has rotational symmetry.
3. If a letter/sign does have rotational symmetry, have the students to mark the centre of rotation
4. Once students have completed the sheets, discuss the results with the class.
5. Assign Rotation of Shapes Handout for Homework.

Attachment: Worksheet/Activity Student Page
Rotation Handout

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REFLECTION: PRACTICE USING MIRA’S

Bibliographic Information:
Woodward, Ernest and Hamel, Thomas. Geometric Constructions and
Investigations with a Mira. Maine: J. Weston Walch, 1992.

Mathematical Concept: Reflection and using Mira’s

Grade Levels: 6th – 8th

NCTM Standards and Principles of School Mathematics• Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Use geometric models to represent and explain numerical and algebraic relationships.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Materials:
Graphing Paper
Colored Pencils
Sharp Writing Pencils
Mira’s
Copies of pages 3 and 5 from Geometric Constructions and Investigations

Detailed Description:
Completion of the following activities will allow students to learn the language associated with reflections and draw a reflected image of a figure over a line of reflection. Students will also be able to perform two-dimensional reflections while using a Mira, as well as recognize when a figure is not symmetrical. By the end of this lesson, students should realize that if the reflective figure looks reversed from its original, it is not symmetrical.

Procedure:
1. Activity One:
a. Hand out graphing paper to each student.
b. Have the students divide a piece of graph paper into four quadrants by drawing the axis lines.
c. In any one quadrant, create a pattern of polygons from the lines on the paper and diagonals.
d. Have students to copy the patterns into the other three quadrants by reflecting the pattern over the axis lines.

2. Activity Two:
a. Divide the class into working partners.
b. Hand each student a piece of graphing paper.
c. Divide the graph paper into four quadrants by drawing the axis lines.
d. Have each student draw a pattern in any one of the quadrants.
e. Each student should pass their graph paper to their partner.
f. The partner is to reflect the pattern over the axis lines.

3. Activity Three:
a. Pass out copies of page 3 from Geometric Constructions and Investigations
b. Pass out a mira to each student. Direct students to find the beveled edge (the edge that seems to cut inward) and that this beleved edge should be placed down.
c. Allow students to practice using the mira as they complete page 3 from Geometric Constructions and Investigations.
d. Students should use the mira to find the line of reflection which puts the boy on the swing.
e. Have students to trace the line of reflection.
f. Finally, students will trace the boy on the other side of the Mira while looking through it as the teacher monitors the activity and gives assistance as necessary.

4. Activity Four:
a. Pass out copies of page 5 from Geometric Constructions and Investigations
b. Instruct students to complete this activity the same way as Activity 3 was completed. They are to follow the handouts instructions to place the hats on the woman’s head.
c. Remind students to trace the line of reflection onto the handout

Attachment: Worksheet/Activity Student Page
Geometric Constructions and Investigations page 3

Geometric Constructions and Investigations page 5

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SYMMETRY: POLYGONS AND LINES OF SYMMETRY

Bibliographic Information:
Muschla, Judith A. and Gary R. Muschla. “Polygons and Lines of Symmetry.” Geometry Teachers’s Activities Kit: Ready-to-use Lessons & Worksheets for Grades 6-12. West Nyack, New York. © 2000, pages 130. (ISBN 0-13-016777-0)

Mathematical Concept: Symmetry

Grade Levels: 6th – 7th

NC Standard Course of Study:
Competency 3: The learner will understand and use properties and relationships of geometric figures in geometry.
3.01: Using three-dimensional figures:
– Identify, describe, and draw from various views (top, side, front, corner).
– Build from various views.
– Describe cross-sectional views.

3.02: Identify, define, and describe similar and congruent polygons with respect to angle measures, length of sides, and proportionality of sides.

3.03: Use scaling and proportional reasoning to solve problems related to similar and congruent polygons.

Materials:
Pencils
Rulers
Protractors
Unlined Paper (optional)
Handout

Detailed Description:
Students will draw polygons that have a specific number of lines of symmetry. Students should work individually to complete this activity. Because the sides and angles of many kinds of polygons are congruent, they can be used to illustrate symmetry. In this activity, as students draw polygons, they will also consider their lines of symmetry.

Procedure:
1. Introduce this activity by explaining that symmetry is a relationship in which opposite sides of an object or figure are mirror images of each other.
2. Ask students if they can name examples of symmetry in the world/nature? (Human beings have 2 eyes, 2 ears, 2 arms, 2 legs; most animals are symmetrical; many flowers; buildings; butterflies)
3. Handout copies of the worksheet titled “Polygons and Lines of Symmetry.”
4. Review the instructions with the students.
5. Students are to complete the activity independently.
6. Once all students are finished with the assignment, the class will go over the answers.

Extension Assignment:
As an extension to this assignment, the class may be assigned to form a poster of symmetrical images found in magazines. Students should cut out the figure, glue it onto poster board, and draw its line of symmetry.

Attachment: Worksheet/Activity Student Page
Symmetry – Polygons and Lines of Symmetry – Handout

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NETWORKS: FROM POINT TO POLYHEDRON

Bibliographic Information:
Thomas, Christine D. and Carmelita Santiago. (2002). “Building Mathematically Powerful Students Through Connections.” Mathematics Teaching in the Middle School, May 2002. Vol. 7, Iss. 9, p. 484-488.

Mathematical Concept: Exploring Networks with Polyhedron

Grade Levels: 6th – 8th

NCTM Principles and Standards for School Mathematics:
• precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
• understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
• create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Materials:
75 colored non-bendable straws
Yarn, twine, dental floss, or string
Scissors
Rulers
Protractors
Bamboo Skewers
Sharp Knife
Instruction Sheet

Student Materials:
Notebook/Portfolio for Research
Calculator
Colored Pencils/Markers

Detailed Description:
This activity is based on parts from the “Building Mathematically Powerful Students through Connections” article. Prior to completing this unit, the instructor is encouraged to design each of the straw polyhedron and display them around the room. The models will be used to investigate concepts such as: point line, line segment, rays, angles, and networks. While engaged in this project, students will view themselves as mathematicians and researchers. As models are developed by the students, they will explore two-dimensional figures through investigations of polygons and their properties. Finally, the teams will delve into three-dimensional polyhedrons. Students will examine their string of triangles in terms of network, which is a figure made up of points (vertices) connected by non-intersecting edges (arcs).

Procedure:
1. Organize students into research teams of 2-4 students
a. Each student’s mission will be to contribute to the team’s development of the model, acquire an understanding of geometry concepts and relationships among the concepts, extend the team’s thinking about mathematics through research, and share and discuss insights with the team.
i. Through investigations, students should be able to find congruent angles: alternate interior angles, alternate exterior angles, corresponding angles, and supplementary angles.
b. The students will maintain a research portfolio in which they will keep:
i. A log of daily investigations, facts, and findings
ii. Charts, diagrams, and classroom notes to support investigations, facts, and findings
iii. Make inferences or speculations based on conclusions from the investigations
iv. A vocabulary list of new terms
v. Written reflections for each day’s activities

2. Students will be assigned to find potential connections to real-life situations through research, exploration, and mathematical discoveries.
a. Each team will have a person to work on the following tasks, or the teacher may divide each group of 4 as one specific team (i.e. Group 1 will be the Research Team, etc.)
i. The research team will investigate how the structures changes from adding new straws and/or vertices, analyze the properties of triangles, parallelograms, and trapezoids, and include the study of parallel lines .
ii. The measurement team will find the following measurements: the length of the straw, angle measures, and the area formulas for the triangle, trapezoid, and parallelogram.
iii. The algebraic team will create a chart and look for patterns to determine the number of straws required for a string of equilateral triangles of any length, as well as determine a formula for finding the number of straws to create a string of n triangles. (2n + 1)
iv. The discrete mathematics team will use the horizontal string of triangles to define and investigate networks. This group will also conduct internet research on mathematician Leonhard Euler, specifically looking for information on his work in graph theory.

3. Network: After gaining some background knowledge of the study of networks, the students will examine their string of triangles in terms of networks.
i. Students will examine the number of edges leading into each vertex and number each vertex accordingly.
ii. Discussion should ensue about finding an Euler path (traversing all edges without using any edge twice)
iii. Students should discover that they must begin at a certain vertex to completely travel the network and pass through every edge once and only once.
iv. Euler’s Theorem: If a network has 2 or fewer odd vertices, then it has at least 1 Euler path.
v. Students should conclude that because the string of connected triangles was a network with 2 odd vertices, they must begin and end at an odd vertex to trace an Euler path.

4. Pass out the instruction sheet titled Straw Polyhedra & Other Nets

5. Pass out copies of Polyhedra outlines as accessed on “Let’s Face It” (from PBS.org Mathline) for students to use as visual guides while constructing the Polyhedron networks. Students can use these handouts as guides for what the polyhedra should look like when it is lying flat.

Attachment: Worksheet/Activity Student Page
• Instructions as taken from the following website:
http://www.math.nmsu.edu/~breakingaway/Lessons/straw/straw.html

Instructions

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