Download V.A. Activity -quadrilateralsB

Project for EDUC521: Create a geometry activity that is an example of vertical
acceleration.
Context: You have been hired to teach grade 7 and/or grade 8 mathematics. You
realize that the previous geometry experiences of your students are minimal in
some areas. You will create a task that will take 1 (or 2) one-hour classes to
complete, is interactive and requires students to participate, answer questions,
explain their thinking, make connections etc. (all things a good teacher does) and
addresses the content sufficiently so you can move forward and teach that topic in
the junior high geometry .
- Make it hands on
- Include Facilitator’s notes
- Indicate what materials and in what quantities are needed.
- Include an assessment task and the directions for how it should be administered.
Including a scoring rubric would be nice but is optional as we did not discuss that in
our intial discussion.
- Include a minimum of five statements that ask students to decide if they are
always true, sometimes true, or never true for your topic.
- Where appropriate, identify literacy strategies that may be useful and explain
how or give a math example where appropriate (for example – a Frayer Model to
explain a word or concept)
- Be cognizant of the Van Hiele Model of development as you develop your activity
- Include the elementary outcomes you feel that your activity is including.
If you have any questions, please ask. It is better to do a smaller well-developed
task, than to try to include too much. I realize this is likely the first time you have
done this and you can always improve on it.
You will have approximately ½ hour to explain your activity to the class. You will not
be expected to do the entire activity as we don’t have the time.
A Vertically Accelerated Lesson:
Purpose of activity: To review types of quadrilaterals, their properties and
related geometry language.
Facilitator’s Notes
Purpose of activity: To review types of quadrilaterals, their properties and
related geometry language.
This activity can be used at the end of grade 6 geometry to review work on
quadrilaterals or before starting the work on polygons or constructions and
minimum sufficient conditions in grade 7.
The intent of the activity is that students write down what they think the
properties are before they discuss with a partner or the class. Then they should
modify their list during the class discussion.
The classroom teachers should have his/her own quadrilaterals built ahead of
time so they can be easily used to confirm properties, etc.
Materials: Pre-packaged Geo-Strips
Pattern Blocks
In this activity Geo-Strips will be used to review 5 types of quadrilaterals(square,
rhombus, kite, rectangle, parallelogram), some of their properties (sides, angles,
diagonals, reflective symmetry, and rotational symmetry), and the related language
of geometry. Geo-Strips can be used to construct models of quadrilaterals, to
assist students in building strong visual images of the types of quadrilaterals,
reviewing their properties and the relationships among the different quadrilaterals.
(A).
For the first Geo-Strip activity students can work in groups of four. One set of
Geo-Strips is to be shared between two groups of four. Put some of the equilateral
triangles. Squares, blue rhombus and hexagons from the Pattern blocks out for
each student to use with the Geo-Strips.
$Tell the class that each student is to take the Geo-Strips that they need to build
one square (using only one Geo-Strip for each side and connecting the sides at the
ends).
$Now, build your square.
$The squares built should all be different in some way. (colour does not count)
$Put your squares flat on the table.
$How do you know that this is a square? Convince me.
$How do you know that you have a right angle in your square? Let’s be sure.
$How can we use a Pattern Block to be sure? (Some students will take one Pattern
Block square to put in one angle of their Geo-Strip square. Others may take four
squares and put one in each angle of the square.
$How are all the squares you build alike?
$What are the properties of squares? You will get many answers and then say let’s
look at the sides, angles, diagonals and symmetry.
$Write as many ways as possible that these squares and all the squares all over
Nova Scotia, the Atlantic Provinces and the world are alike. Try to use good
geometry language in your writing.
$How can squares be different? Write a list of ways that squares can be different.
Each of you make your list.
$Then you can discuss your list with someone at your table who has completed
her/his list.
$Class discussion should bring out all the ways that squares can be different .
$This is a good time to bring out the property that all squares are similar. The use
of the overhead, a Pattern Block square, and several of the students’ Geo-Strip
squares makes it easy to enlarge the image of the Pattern Block square to be
congruent with any Geo-strip square which is held on the overhead screen.
$Ask students to take all the Pattern Block squares out of their Geo-Strip square.
$Leave it flat on the table.
$Push it over so that the angles in their Geo-Strip square are not right angles.
$What is the name of this quadrilateral?
$Many rhombi can be visualized as pushed over squares, squares that have lost
their right angles.
$Now, put your rhombus flat on the table.
$Take one of the Pattern Blocks (other than the square or hexagon) and fit it into
one angle of your rhombus.
$Discuss with your partner what happened.
$Ask several students to explain to the class their thinking about this.
$How are all of your rhombi alike? Make a list of all of the properties of rhombi.
Make a list of how some rhombi could be different? Work by your self to make
these lists.
$When you are finished your lists, compare your lists with someone at your table
who is finished.
$After all students have had some opportunities to discuss the properties of a
rhombus with another student, some students should be called on to each give one
of the properties of that all rhombi have and other students should be asked to
tell the class how rhombi can be different.
$This is a good time to explore the question, “Are all rhombi similar?” Are some
rhombi similar? What do you need to know about two rhombi to be sure that they
are similar?
(B)
Now, listen carefully to these directions. We are going to make another
quadrilateral from Geo-Strips using part of the rhombus that you have just made.
 Take your rhombus and remove two brads that are opposite each other so that
you now have two pairs of congruent sides.
 Put one pair of connected congruent sides on the table in front of you. That
connected pair of sides are to be used for your next quadrilateral.
 Take the other pair of connected congruent sides to another table and trade
with another student. Look for someone whose connected pair of sides looks
very different from your pair. Look for different size and colour.
 Go back to your seat to make your new quadrilateral by joining your old
connected pair of sides (leave them connected) to the new pair of connected
sides for which you traded. (Wait time) Hold it up by one of the brads
connecting a pair of congruent sides.
 What quadrilateral has each of us made?
 Tell me a property of the sides of a kite. Rectangles also have two pairs of
congruent sides. How are the two pairs of congruent sides in a kite different
from the two pairs of congruent sides in a rectangle?
 One more thing that we want to do is to move the sides of the kite so that we
can make a concave kite.
 Each of you should make a list of all the properties of a kite. How are all kites
alike? How can kites be different?
 Through class discussion bring out all the properties of a kites.
 This activity with the trading of the connected congruent pair of sides helps
students to develop a strong visual image for kites and their properties.
(C.)
$Take apart the kite and use these same Geo-Strips to make a rectangle that is not
a square. Lay them flat on your table.
$How do you know that this is a rectangle? Convince me.
$How do you know that you have a right angle in your rectangle? Let’s be sure.
$You will need Pattern Blocks to be sure that you have right angles in your
rectangle.
$How are all rectangles alike?
$Each of you make a list of all the properties of a rectangle. When you are finished
discuss this with someone at your table and compare your lists.
$A class discussion all the properties of rectangles should then take place.
(D.)
$Take your rectangle and push it over.
$What quadrilateral have you formed?
$How are all parallelograms alike?
$Make a list of all their properties, etc.
$The diagonal properties of rectangles often require more explanation.
$Another task you could do is to help with the diagonal properties is have students
cut out a long skinny rectangle and a larger rectangle using square dot paper. Paper
folding on the diagonals make the properties stand out and help students to
remember these properties.
Determine if each of these statements is always true, sometimes true, never true.
Be prepared to explain your thinking.
1. The diagonals of a kite are perpendicular to each other.
2. Convex quadrilaterals have opposite sides congruent.
3. The angles in a square are acute.
4. Parallelograms have rotational symmetry of order 4
5. A parallelogram will have at least one line of reflective symmetry.
Complete the following table to consolidate the properties of quadrilaterals.
Square
No. of pairs
of
congruent
sides
No. of pairs
of
congruent
angles
Right angles
No. of pairs
of
parallel sides
Diagonals are
congruent
Diagonals
bisect each
other
Diagonals are
perpendicular
Diagonals
bisect angles
of figure
No. of lines
of symmetry
Order of
Rotational
symmetry
Sketch
Rectangle
Parallelogram
Rhombus
Trapezoid
Kite
Primary
Outcomes
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade6
E5
E11
E9
E8
E9
E6
E8
E11
E4
E5
E8
If they are shaded grey, it means the whole outcome was not addressed.