Download Geometers

GEOMETER’S
SKETCHPAD
by
Cora Tenza
California Standards addressed:
Grade 3
Measurement and Geometry
1.3 Find the perimeter of a polygon with integer sides.
2.1 Identify, describe, and classify polygons (including pentagons,
hexagons, and octagons)
2.2 Identify attributes of quadrilaterals (e.g., two equal sides for
the isosceles triangle, three equal sides for the equilateral
triangle, right angle for the right triangle).
2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the
parallelogram, right angles for the rectangle, equal sides and
right angles for the square).
2.4 Identify right angles in geometric figures or in appropriate
objects and determine whether other angles are greater of less
than a right angle.
California Standards..
Grade 4:
Measurement and Geometry:
1.0 Students understand perimeter and area:
1.1 Measure the area of rectangular shapes by using appropriate
units, such as square centimeter, square meter, square
kilometer, square inch, square yard, or square mile.
1.4 Understand and use formulas to solve problems involving
perimeters and areas of rectangles and squares. Use those
formulas to find the areas of more complex figures by
dividing the figures into basic shapes.
California Standards..
2.0 Students use two dimensional coordinate grids to represent points
and graph lines and simple figures:
2.1 Draw the points corresponding to linear relationships on
graph paper (e.g., draw 10 points on the graph of the
equation y = 3x and connect them by using a straight line).
2.2 Understand that the length of a horizontal line segment
equals the difference of the x-coordinates.
2.3 Understand that the length of a vertical line segment equals
the difference of the y-coordinates.
California Standards..
3.0 Students demonstrate an understanding
of plane and solid geometric objects and
use this knowledge to show relationships
and solve problems:
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3.1 Identify lines that are parallel and perpendicular.
3.2 Identify the radius and diameter of a circle.
3.3 Identify congruent figures.
3.5 Know the definitions of a right angle, an acute
angle, and an obtuse angle.
California Standards..
Measurement and Geometry (Grade 5)
1.0 Students understand and compute the volumes and
areas of simple objects:
1.1 Derive and use the formula for the area of a triangle and
of a parallelogram by comparing it with the formula for the
area of a rectangle (i.e., two of the same triangles
make a
parallelogram with twice the area; a
parallelogram is
compared with a rectangle of the same
area by cutting
and pasting a right triangle on the
parallelogram).
1.4 Differentiate between, and use appropriate units of
measures
for, two- and three-dimensional objects (i.e.,
California Standards..
3.7 Know the definitions of different triangles (e.g.,
equilateral, isosceles, scalene) and identify
their attributes.
3.8 Know the definition of different quadrilaterals
(e.g., rhombus, square, rectangle, parallelogram,
trapezoid).
Drawing tools:
 Selection arrow – selects and deselects objects
 Point tool – draws points
 Compass tool – draws circles
 Straightedge tool - draws:
 Segment
 Ray
 Line
 Text tool -creates labels and captions
 Object Information tool – displays information
about an object
The Selection Arrow Tools:
• Translate: selects objects and moves selections without
• Rotate:
• Dilate:
changing size or orientation
rotates objects from center of rotation
selects and shrinks or enlarges
SELECT AND DESELECT:
• Use point
• Hold down shift key
• Drag down a selection marquee – rectangle surrounds the object
To deselect:
• click an empty place
• click on the selected object
Shortcut buttons
F4 = selection arrow
F5 = point tool
F6 = Compass tool
F7 = Straightedge tools
F8 = Text tool
FREQUENTLY ASKED QUESTIONS:
Q. How would you select all of the points on the screen at
once?
A. Choose the Point tool, then choose Select All Points from the
Edit menu
Q. If all the points on the screen are selected, how can you
deselect only one of them and leave the others selected?
A. Hold down Shift and click the point you want to deselect.
Q. How would you change the shape of a triangle?
A. Use the Selection Arrow tool to drag a vertex or edge.
Q. How do you clear the screen?
A: - choose New Sketch from File menu
- hold down Shift key while choosing the Undo command from Edit menu
- hold down Ctrl, Shift, and Z at the same time
Q. How do you switch to the Selection Arrow tool temporarily while using any
drawing tool?
A. hold down the Ctrl key.
Q. What is the difference between Segment tool and Segment command?
A. The Segment tool creates new endpoints if they don’t exist, whereas the
command requires that the endpoints exist and be selected.
Q. What do you do if the command in the Construct menu is dimmed or
unavailable?
A. Every command on the Construct menu requires that one or more objects be
selected before using the command. Construction commands are available
according to the types of objects selected. Selecting too many, too few, or the
wrong kind of object will prevent you from using these commands. However, if
you think that you have the correct prerequisites, yet the command is still
unavailable, press F1 while highlighting the menu command and the Help
window will appear. You can check for further errors by pressing the mouse
button on the Object Information tool. This will display a menu of currently
selected objects. If you think about what you need mathematically to construct
the objects in this menu, the prerequisites will become obvious.
Q. How do we show labels of points and straight objects, set units for distances
and angles, and give precise measurements to inches and centimeters?
A. Click Preferences on Display menu.
Labels, Captions and Measurements
ACTIVITIES:
•
•
•
•
•
•
Display the label for a segment
Move and change the label
Create a caption for a drawing
Display the length of a segment
Change the text style for the caption
Change the length of a segment
NOTES:
• Holding down the Shift key while drawing assists you in making segments
that are horizontal, vertical, or at 15 degree angle interval
• Every object has a label whether it is visible or not
• Labels for segments are lower-case and point labels are upper-case.
• Point labels can also be reformatted by double-clicking the label (not the
object) with the Text tool or by using commands in the Text
• Font and Text Style submenus when the points are selected.
QUESTIONS:
Q. What tool or command do you use to display, move, and change
object labels?
A. Use the Text tool:
• Click an object to display or hide its label
• Click and drag a label to move it
• Double-click a label to edit it.
Q. What’s the difference between a caption and a label?
A. A label is created automatically with the object. You have to create a
caption explicitly. When a label is shown, it appears near the
object and cannot be moved far away from it. A caption can be
created in any blank space in the sketch and can be moved
anywhere in the sketch.
Q. With which tool can you create a caption?
A. Drag the Text tool in a sketch to create a caption.
Q. Describe how to reformat an object label without using the Text
tool
A. Select the object and use a text formatting submenu (Text Style or
Text Font) in the Display menu.
Q. How can you find the length of a segment?
A. Select the segment, then choose Length from the Measure menu.
Q. How do you get a displayed length of a segment to change?
A. Drag either endpoint of the segment, and the displayed length
updates as you change the segment’s length.
MEASUREMENTS, CALCULATIONS and
POLYGONS INTERIORS
ACTIVITY:
1.
2.
3.
4.
5.
6.
7.
Construct a line parallel to a horizontal line through an opposite
point.
Use the text tool to label the vertices and the sides of the triangle.
Using the formula: A = base x height / 2, find the area of the triangle.
Using each side as the base, find the area of the triangle and compare.
Construct the interior of the triangle and measure the area.
Find the perimeter from the measure menu and compare the result
when you add the 3 sides.
Measure all three internal angles of your triangle and add them
together. Then move parts of the triangle around to see that no matter
what the shape or size of the triangle, its angles total 180 degrees.
QUESTIONS:
Q. What steps do you use to create a polygon interior?
A. In order, select all the vertices of the polygon, then
choose Polygon Interior from the Construct menu.
Q. How do you find the area of a polygon interior?
A. Select the polygon interior, then choose Area from the
Measure menu.
MEASURING CIRCLES, ANGLES and ARCS
ACTIVITIES:
1.
2.
3.
4.
5.
6.
7.
8.
Measure the circumference and radius of the circle and calculate their ratio
Construct an arc on a circle and measure its arc angle and arc length.
Measure and compare central and inscribed angles
Construct a sector and compare its area to the area of the circle
Move all the parts of the circle around, noticing which measures change
and which don’t. Figure out why.
Calculate a value for pi using Calculate and some of the measures you
already have, without using the pi value
Place 3 points in your sketch, select them, and use the Arc Through 3
points command to construct an arc. Investigate some of the properties of
this arc.
Make a pretty design using circles, arcs, sectors and arc segments.
QUESTIONS:
Q. How do you measure the number of degrees of an angle?
A. Select the 3 points that define the angle (with the vertex of the
angle as the second point), then choose Angle from the
Measure Menu.
Q. How do you find the distance along the circumference between two
points on the circumference of a circle.
A. Select the center of the circle followed by the two points and
choose Arc on Circle in construct menu. Then choose Arc
Length from the Measure menu.
Q. What are the ways to add entry to a table.
A. - Select the table and choose Add entry in the Measure menu
- Ctrl-E is the shortcut for Add Entry.
- Double click the table with the Selection Arrow tool