Name
Master 8.26
Date
Extra Practice 1
Lesson 8.1: Sketching Views of Objects
1. Sketch the top, front, and side views of each object.
a)
b)
c)
2. Sketch the top, front, and side views of each object drawn on isometric dot paper.
a)
b)
c)
3.
Use linking cubes.
Make the letter E.
Sketch the front, top, and side views of your model.
4.
Sketch the top, front, and side views of each object at home or in the classroom.
a) a tissue box
b) a CD case
c) a cereal box
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Name
Master 8.27
Date
Extra Practice 2
Lesson 8.2: Drawing Views of Rotated Objects
1.
Build this object.
Rotate the object as describe below,
then match each view to the front, top,
and side views of the rotated object.
A lettered view can be used more than once.
a)
a horizontal rotation of 90° clockwise about
the vertical axis shown
b) a horizontal rotation of 180° clockwise about the vertical axis shown
c) a vertical rotation of 90° away from you about the horizontal axis shown
2.
Suppose the object in question 1 was rotated horizontally 180° counterclockwise about the
vertical axis shown. How would the views of the object after the rotation compare to those in
question 1b? Justify your answer.
3. Here is an isometric drawing of an object.
The object is rotated horizontally 270° clockwise about the axis shown.
a) Draw the front, top, and side views of the object after the rotation.
b) Describe a different rotation that will have the same views as the ones you drew in part a.
4. Use the object in question 3.
Suppose the object is rotated 270° counterclockwise.
Will the new views of the object be the same as those drawn in question 3a?
If your answer is yes, explain how you know.
If your answer is no, draw the new views.
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Name
Master 8.28
Date
Extra Practice 3
Lesson 8.3: Building Objects from Their Views
1. Use linking cubes to build an object for each set of views below.
a)
b)
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Name
Master 8.29
Date
Extra Practice 4
Lesson 8.4: Identifying Transformations
1. Start with the shaded shape.
Use transformations to describe how to create Shapes A, B, C, and D.
2. Use this design.
Match each transformation to a transformation image.
a)
b)
c)
d)
3.
Rotate Shape A 180° about point P.
Translate Shape C 2 units left.
Rotate Shape D 180° about point Q.
Translate Shape G 4 units right.
Use the design to the right.
Identify each transformation.
a) Shape D is the image of Shape C.
b) Shape E is the image of Shape G.
c) Shape C is the image of Shape E.
d) Shape F is the image of Shape C.
e) Shape A is the image of Shape B.
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Name
Master 8.30
Date
Extra Practice 5
Lesson 8.5: Constructing Tessellations
1.
Use dot paper.
Draw a non-symmetrical quadrilateral on dot paper.
Show how it can be used to tessellate.
2.
Copy each shape on grid paper.
Show one way each shape can be used to tessellate.
3.
a) Use dot paper.
Draw a hexagon that will tessellate.
Show part of the tessellation.
Explain how it tessellates.
b) Draw a hexagon that will not tessellate.
Show how it does not tessellate.
Explain why the hexagon does not tessellate.
Which shapes will fill the gaps?
4.
Use the hexagon you drew in question 3b.
Find one or more polygons that you can combine with the hexagon
to create a composite shape that tessellates.
Create the tessellation.
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Name
Master 8.31
Date
Extra Practice 6
Lesson 8.6: Identifying Transformations in Tessellations
1. Here are three patterns.
Describe the transformations that can be used to create each pattern.
Start with the shaded shape.
a)
b)
c)
2. Use this shape and transformations to create a tessellation on square dot paper.
Describe the tessellation in terms of transformations and conservation of area.
3.
Here is a tessellation of a composite shape.
Describe the composite shape.
Describe the tessellation in terms of transformations and
conservation of area.
Describe the tessellation in as many ways as you can.
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Name
Master 8.32
Date
Extra Practice Sample Answers
c)
Extra Practice 1 – Master 8.26
Lesson 8.1
1. Answers may vary depending on the orientation
chosen.
a)
3.
b)
4. a)
c)
b)
c)
2. a)
b)
Extra Practice 2 – Master 8.27
Lesson 8.2
1. a) Front: G; Top: A;
Left side: F; Right side: E
b) Front: E; Top: B;
Left side: G; Right side: C
c) Front: D; Top: F;
Left side: H; Right side: J
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2. The views would be the same because a rotation of
180° clockwise is the same as a rotation of 180°
counterclockwise.
3. a)
b) A horizontal rotation of 90° counterclockwise
about the axis shown
4. No
Date
Extra Practice 4 – Master 8.29
Lesson 8.4
1. Rotate the shaded shape 90° counterclockwise about
the vertex shared by the shaded shape and Shape B to
get Shape A.
Rotate the shaded shape 180° about the vertex shared
by the shaded shape and Shape B to get Shape B.
Rotate the shaded shape 90° counterclockwise about the
upper right vertex of the shaded shape to get Shape C.
Translate the shaded shape 6 units right to get Shape D.
2. a) Shape B
b) Shape G
c) Shape F
d) Shape F
3. a) Shape C is reflected in the vertical line that passes
through the side shared by Shapes A and B.
b) Shape G is translated 3 units left.
c) Shape E is rotated 180° about the midpoint of the
side shared by Shapes C and E.
d) Shape C is translated 2 units right and 2 units down.
e) Shape B is reflected in the side shared by Shapes A
and B.
Extra Practice 5 – Master 8.30
Extra Practice 3 – Master 8.28
Lesson 8.5
1.
Lesson 8.3
1. a)
2. a)
b)
b)
c)
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3. a)
Date
shaded triangle and Triangle A to get Triangle A.
Triangle A is rotated 180° about the midpoint of the side
shared by Triangles A and B to get Triangle B.
Triangle B is rotated 180° about the midpoint of the side
shared by Triangles B and C to get Triangle C. Triangle
C is rotated 180° about the midpoint of the side shared
by Triangles C and D to get Triangle D. The row of
triangles is reflected in a horizontal line that passes
through the base of Triangles A and C to complete the
pattern.
c) The shaded shape is rotated 90°, 180°, and 270°
clockwise about the upper right vertex of the shaded
shape to complete the pattern.
The hexagon tessellates
because it covers the page
and leaves no gaps. At any
point where vertices meet,
the angles add to 360.
b) The hexagon does not cover the page. It leaves gaps
that are rhombuses. There are points where vertices
meet and the sum of the angles is less than 360.
So, the hexagon does not tessellate.
2.
4. I combined 2 right triangles with the hexagon to make a
rectangle. I know rectangles tessellate.
Extra Practice 6 – Master 8.31
Lesson 8.6
1. a) For example, label the rectangles to the right of the
shaded rectangle from A to G.
The shaded rectangle is translated 1 unit right to get
Rectangle A. Rectangle A is rotated 90°
counterclockwise about the upper right vertex of
Rectangle A to get Rectangle B. Rectangle B is
reflected in the side shared by rectangles B and C to get
Rectangle C. Rectangle C is rotated 90° clockwise about
the lower right vertex of Rectangle C to get Rectangle D.
Rectangle D is translated 1 unit right to get Rectangle E.
Use similar transformations to complete the pattern.
b) Label the triangle to the right of the shaded triangle with
the letter A, then continue to label with letters, moving in
a clockwise direction. For example, the shaded triangle is
rotated 180° about the midpoint of the side shared by the
Shape A is rotated 90° counterclockwise about the vertex
shared by Shapes A, B, C, and D to get Shape D. Shape D
is reflected in a vertical line passing through the vertex
shared by Shapes A, B, C, and D, then translated 3 units up
to get Shape B. Shape A is reflected in a vertical line
passing through the vertex shared by Shapes A, B, C, and
D, then translated 3 units down to get Shape C.
Under a transformation, a shape and its image are
congruent. So, area is conserved.
3. The composite shape is a regular octagon and a square put
together.
Answers may vary.
For example, students may use translations to describe the
entire tessellation. However, there are many other
transformations and combinations of transformations that
can be used.
Under a transformation, a shape and its image are
congruent. So, area is conserved.
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