Download Sample syllabus 2

Geometry and Spatial Sense
CTY Course Syllabus
Day
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Day 1:
Monday
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Day 2:
Tuesday
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Do Now (patterns)
Introductions and Icebreakers
Classroom Rules and Procedures
- Three rules: Be Nice, Be Safe, and Be Your Best
- Students in three groups, each group assigned a rule. Groups discuss and take
notes on the following questions: “What does this rule look like at CTY?” and
“What does this rule NOT look like at CTY?”
- Gallery walk with groups adding to the lists
- Class discussion of rules. Instructor and PA add anything that they think is
important that the students missed
CTY Honor Code
- Students read the Honor Code and highlight what they think is important.
- Students put into groups of three and given roles: talker, recorder and
questioner. Talker states something they think is important in the Honor Code,
questioner asks as question of the talker, recorder takes notes. Everyone
switches roles twice so everyone is each role once.
Pre-Assessment
Measuring with a ruler (review)
Scale Drawings
- An 8.5” x 11” coloring book picture is cut into 2.125” x 2.75” rectangles. The
instructor labels the back of each piece of the picture.
- Scholars are shown how to use a ruler correctly.
- Scholars are given the small grid picture and asked to enlarge the image onto a
full sized sheet of paper, using their ruler as a guide. When scholars finish their
enlargement the tape their section onto a premade grid on the wall creating an
enlarged version of the original picture when everyone’s piece is completed
- Scholars discuss scale, scale factors and similarity.
Do now (trick questions)
Continue discussion of scale factor, check for understanding (white boards)
Review Vocabulary and Notation (point, line, plane, etc.).
- Start Geometry Glossary
- Use Agile Minds software to present vocabulary
- Practice (Agile Minds and white boards)
Classify Angles (Acute, Obtuse, Right and Straight)
- Explore the different types of angles making posters with pipe cleaner angles
- Copy definitions into Geometry Glossary
- Check for understanding using white boards
Review how to use a protractor. Practice using a protractor.
Origami
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Activity
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Day 3:
Wednesday
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Do now (measuring angles and classifying them)
Classify Triangles (by angle and by sides)
- Instructor gives students several examples of different triangles cut out of
colored paper. Students work in pairs to sort the triangles into different
groups. Students paste/tape the groups on easel paper and then post the easel
paper to the walls
- Students do a gallery walk, examining the different groups and writing notes on
the posters to explain the reasoning for the various groupings.
- Instructor facilitates a large group discussion of the various groupings, then,
using the groupings as examples, defines Equilateral, Isosceles, Scalene,
Equiangular, Acute, Obtuse and Right Triangles. Students copy definitions into
their Geometry Glossaries.
Define Congruent
- Copy into Geometry Glossary
- Working in groups, students use rulers, protractors and paddy paper to check if
various line segments, angles, and polygons are congruent.
Define Vertical Angles and Linear Pairs
- Copy into Geometry Glossary
- Use post-it notes to mark as many vertical angles and linear pairs they can find in
the room in a certain amount of time. After time is up, the class discusses if the
Vertical Angle Theorem and Linear Pair’s are supplementary
- Students choose to investigate either vertical angles or linear pairs for their special
properties. Instructor encourages students to create many different examples of
vertical angles (or linear pairs) on a piece of paper using a ruler and then using
paddy paper to trace the angles. Instructor and TA go from group to group to
encourage and offer suggestions/hint.
- Students present their findings to the class.
- Practice problems and check for understanding
White Board problems on vertical angles and linear pairs
Triangle Angle Sum Theorem
- Students cut out a variety of triangles from construction paper.
- Students tear off the corners of their triangles and rearrange the angles to
make a straight line. Students compare their angles to other students in the
class.
- Class completes a Think, Pair Share.
- Students copy the Triangle Angle Sum Theorem into their notes.
Exterior Angles of a Triangle
- Students cut out a variety of triangles from construction paper and trace them
onto white paper. They then use a ruler to draw exterior angles on the
tracings. Students number their triangles’ angles (both on the triangles and the
tracings).
- Students tear off the corners of their triangles and, moving the corners around
on the tracings, examine how the interior angles relate to the exterior angles
- Class completes a Think, Pair Share.
White board problems on Triangle Angle Sum Theorem and Exterior Angles of a Triangle
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Activity
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Day 4:
Thursday
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Do now (classify triangles by angles and sides)
Convex vs. Concave Polygons
- In or Out of the group game: Instructor tells the students that there is an “in
group” and an “out group”, but that the instructor will not be telling them what
the groups are. The instructor shows the picture. The students have to guess if
the picture is in the in group or the out group by holding up a card (or, if they
don’t know a “?”). The instructor then tells the students what group the
picture is in.
- Instructor plays the In or Out game with the students using Convex as the In
group and Convex as the out group.
- Official definitions of Polygon, Convex Polygon and Concave Polygon are
written in the Geometry Glossary
- White board problems to check for understanding
Interior Angle Sum Theorem
- Students record the number of sides of all of their toothpick polygons and then
measure all of the angles using a protractor. Students are asked if they notice a
connection between the number of sides and the sum of the interior angles
(they should see that the sum of the angles are the same for any polygon with
the same number of sides). Think, Pair, Share.
- Students are given a sheet with polygons from 3 to 10 sides. Students are
asked to find the number of triangles in each and the sum of the interior angles.
- Students look for a pattern in the
- Instructor formalizes the Interior Angle Sum Theorem
- Students practice (white boards)
Regular Polygons
• Students are asked to find the formula for calculating the measure of an
individual angle in a regular polygon
• Student Practice (white boards)
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Activity
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Day 5:
Friday
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Day 6:
Monday
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Check in Quiz – covering all topics learned so far.
Using a Compass
- Students free practice with tips from teacher. For artistic effect, draw 10
intersecting circles of differing radii on construction paper and color the
resulting sections
Define Perpendicular, Angle Bisector, Segment Bisector and Perpendicular Bisector
(white board problems as a check for understanding)
Basic Constructions
- Teacher and TA lead students through Angle Bisector and Perpendicular
Bisector construction.
Triangle Inequality Theorem
- Students are given sets of pipe cleaners cut to various sizes and color coded.
Students measure the pipe cleaners and try to arrange them into triangles.
Students try to figure out why some sets of sides make triangles while others
do not. Think, pair, share.
- Practice problems (white boards)
- Students are given sets of straws cut to various sizes and color coded. Students
measure the straws and try to arrange them into triangles. Students try to
figure out why some sets of sides make triangles while others do not. Think,
pair, share.
- Practice problems (white boards)
Around the World (review game)
Quiz Corrections – Students are given a quiz that Alan (a fictional student) “took” and
are asked to correct Alan’s mistakes. Many of Alan’s “mistakes” are mistakes that
students actually made during the Check in Quiz on Friday. The entire class discusses
the quiz corrections once everyone is done.
Compass and Straight Edge Constructions
- Students are each assigned a construction to learn how to do by viewing a
website.
- Students practice their construction until they can do it without instructions
- Students teach each other the constructions they learned from the website.
Largest angle across from longest side (etc.)
- Students are given a sheet with many triangles already drawn on it. Students
use a ruler and protractor to measure the sides and angles of the triangle
- Students copy the measurements into a table and are asked to look for a
relationship between the side lengths and the angle measures of the triangles.
Think. Pair. Share.
- Practice problems
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Activity
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Day 7:
Tuesday
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Day 8:
Wednesday
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Do Now (Triangle Inequality Theorem and relative size of angles and sides in a triangle)
Introduction to the Coordinate Grid
- Students are given a brief introduction to the how the coordinate grid works
(the axes, ordered pairs, etc.)
- Class moves outside where teacher has used sidewalk chalk to create two giant
coordinate grid (use painters tape inside the classroom or other indoor space if
bad weather). Instructor and TA divide the class into two groups and run
activities for each group
- Students are each given different ordered pairs to find on the coordinate grid.
- Students plot points and draw a picture using the coordinate grid
Pythagorean Theorem
- Define Hypotenuse and Legs of a right triangle
- Students draw a right triangle and then “square” each side.
- Using patty paper, students trace and cut out the area of the square for each
leg of right triangle. They then compare that area to the area of the square for
the hypotenuse (Think. Pair. Share).
- Formalize the Pythagorean Theorem.
- White Board Practice.
Origami
Do now (Pythagorean Theorem)
Intro to Quadrilaterals
- Instructor defines quadrilateral, scholars copy definition into their Geometry
Glossary
- Students are given a variety of quadrilaterals cut out of construction
paper/tagboard. Students work in pairs to create groupings for the different
quadrilaterals. Students then paste/tape their groupings (without labels) onto
chart paper and hang around the room.
- Students conduct a gallery walk around the room. The pairs try to figure out
what reasoning the other groups used when creating the groupings.
- Class discussion about the groupings and the various properties they used to
group the different quadrilaterals
Quadrilateral Properties
- Students investigate properties of quadrilaterals (angles, sides and diagonals)
using paper folding, paddy paper and measuring (Think. Pair. Share.).
- Practice problems
Catch a Quad
- Students are given a set of “ crime mysteries.” Each mystery can be solved by
applying knowledge of the properties of quadrilaterals to three clues which
gradually eliminate all of the “innocent” quadrilaterals
Create a Quadrilateral Crime
- Student pick a quadrilateral and write their own mystery, including three clues
that will gradually reveal the chosen quadrilateral.
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Day
Activity
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Day 9:
Friday
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Day 10:
Monday
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Day 11:
Tuesday
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Investigate Properties of Circles
Define circle vocabulary (radius, diameter, chord, arc, circumference, tangent line,
interior angles) and copy into Geometry Glossary
Use paper folding (of paper plates) to investigate properties of circles
Practice problems (white boards)
Discovering Pi
- Students measure the diameter (ruler) and circumference (string/pipe
cleaners/wire and a ruler) of a bunch of pre-drawn circles and objects from
home (cans, lids, coins, etc.).
- Students then are instructed to divide their circumference measurements by
their diameter measurements and keep track of the results. Students should
look for a pattern in the results. Think. Pair. Share.
- Instructor clarifies the concept of Pi and shows students the first 100 decimal
places.
- Students find circumference using pi.
Between the Folds – students watch PBS documentary on origami artists. Class
discussion
Origami
Quiz Corrections – students correct a fictional student’s “mistakes”
Create a Quadrilateral Crime (continued)
- Students type their mysteries
- Students exchange their mysteries with other students in the class and solve. If
a mystery has any issues with it, the students work together to fix the mystery.
Nets
- Students are given nets and make predictions about what shapes they will
make
- Students use nets to create models of polyhedrons.
- Students label the models, making notes of similar characteristics amongst the
different shapes
Students are challenged to create as many nets as possible that will create a cube
(differentiation: advanced students are given more difficult polyhedrons to create).
Compare the cube nets that the students created.
Area and Volume
- Students are given a formula sheet with area and volume formulas.
- Students are shown examples using the different formulas.
- Students work together and on their own to find area, surface area and volume
of different figures
Create a Candy Container
- Students are challenged to design a new candy container for Starbursts.
- Minimize surface area
- Hold at least 16 Starburst but prefer it hold as many as 24 (don’t care after 24)
- Be useable for consumers
- Have a unique design so it stand out on the shelves.
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Activity
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Create a Candy Container (all day)
Prepare Presentations for Candy Container
- Includes net, brag sheet (why should they use this container), surface area
calculations and volume calculations.
Day 13:
Thursday
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Prepare Presentations for Candy Container (continued)
Student Evaluations
Post Assessment
Origami
Day 14:
Friday
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Origami
Candy Container Presentations
Goodbyes
Day 12:
Wednesday
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