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Comprehensive Grade 6 Mathematics: Transformations and Tessellations

Explore Grade 6 math concepts including tessellations, and geometric transformations: reflection, translation, and rotation with examples, assessments, and extended exercises.

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MATHEMATICS 6 TERM 1 WEEK 2 DAY 1
@ @ P R E - L E S S O N A. Directions: Tell if each polygon can be tessellated. Write YES if it can, NO of it cannot.
@ @ P R E - L E S S O N
@ @ P R E - L E S S O N B. Directions: The teacher will show a triangle and demonstrate translation, reflection, and rotation. Observe the movement carefully and answer the questions below.
@ @ P R E - L E S S O N 1. What transformation is shown when the triangle slides to another position without turning? Answer: Translation
@ @ P R E - L E S S O N 2. What transformation is shown when the triangle is flipped to form a mirror image? Answer: Reflection
@ @ P R E - L E S S O N 3. What transformation is shown when the triangle turns around a fixed point? Answer: Rotation
REFLECTION
@ @ D I S C U S S I O N Reflection can also be called flip. Reflection is done when the figure is flipped and produces its mirror-image which is being flipped or reflected across a line called the mirror line.
@ @ D I S C U S S I O N Example 1. (Reflection) The figure reflected across a vertical line of symmetry.
@ @ D I S C U S S I O N Example 2. (Reflection) The figure reflected across a horizontal line of symmetry
@ @ D I S C U S S I O N Example 3. Draw the missing figures so each is a reflection of the other across the vertical and horizontal lines of symmetries.
@ @ D I S C U S S I O N Solution:
@ @ D I S C U S S I O N Example 3. (Glide Reflection) Step 1. Move the object by sliding.
@ @ D I S C U S S I O N Step 2. After sliding, draw the mirror image (reflection) with respect to the line of symmetry.
@ @ A S S E S S M E N T Directions: Check the boxes that show reflections.
@ @ A S S E S S M E N T
@ @ A S S E S S M E N T
Directions: Draw reflections of the following shapes. @ @ E X T E N D E D
@ @ E X T E N D E D 1.
@ @ E X T E N D E D 2.
@ @ E X T E N D E D 3.
@ @ E X T E N D E D 4.
@ @ E X T E N D E D 5.
@ @ E X T E N D E D 6.
MATHEMATICS 6 TERM 1 WEEK 2 DAY 2
@ @ P R E - L E S S O N Directions: Draw reflections of the following shapes.
@ @ P R E - L E S S O N 1.
@ @ P R E - L E S S O N 2.
@ @ P R E - L E S S O N 3.
@ @ P R E - L E S S O N 4.
@ @ P R E - L E S S O N 5.
@ @ P R E - L E S S O N 6.
@ @ P R E - L E S S O N 7.
@ @ P R E - L E S S O N 8.
TRANSLATION
@ @ D I S C U S S I O N Translation can also be called slide. Translation is done when the figure slides or moves from one place to another. The resulting figure/shape must be of the same size but there is change in the direction.
@ @ D I S C U S S I O N Translation can also be called slide. Translation is done when the figure slides or moves from one place to another. The resulting figure/shape must be of the same size but there is change in the direction.
@ @ D I S C U S S I O N Example 1. (Translation) Figure translated to the right (slide to the right)
@ @ D I S C U S S I O N Example 2. (Translation) Figure translated vertically downward (slide down)
@ @ D I S C U S S I O N Example 3. (Translation) Figure translated to the right and downward (slide to the right and down)
@ @ D I S C U S S I O N Example 4. (Translation): Slide the figure 2 units to the right and 3 units upward.
@ @ D I S C U S S I O N Step 1. Plot the vertices of the new triangle by sliding them 2 units to the right and 3 units upward. Step 2. Connect the points to form the figure.
@ @ D I S C U S S I O N
@ @ A S S E S S M E N T A. Directions: Draw the resulting figure following the direction of the movement.
@ @ A S S E S S M E N T 1. Translate the figure 2 units to the left
@ @ A S S E S S M E N T 2. Translate the figure 3 units to the right.
@ @ A S S E S S M E N T 3. Translate the figure 2 units to the right and 3 units upward.
@ @ A S S E S S M E N T 4. Translate the figure 3 units to the right and 3 units downward.
@ @ A S S E S S M E N T B. Continue the pattern by drawing the resulting figures.
@ @ A S S E S S M E N T 1. 2.
Directions: Draw the resulting figure following the direction of the movement. @ @ E X T E N D E D
1. Translation: 4 right @ @ E X T E N D E D
2. Translation: 3 left @ @ E X T E N D E D
3. Translation: 3 right and 2 down @ @ E X T E N D E D
4. Translation: 4 right and 3 down @ @ E X T E N D E D
MATHEMATICS 6 TERM 1 WEEK 2 DAY 3
@ @ P R E - L E S S O N Directions: Put a check in the box that shows translation.
@ @ P R E - L E S S O N 1. 3. 2. 4.
@ @ P R E - L E S S O N 5. 7. 6. 8.
ROTATION
@ @ D I S C U S S I O N Rotation can also be called turn. Rotation is done by turning or rotating the figure around a fixed point (or center). The rotation can be done either clockwise or counterclockwise.
@ @ D I S C U S S I O N Example 9. (Rotation) Rotate triangle ABC around point A by turn clockwise.
@ @ D I S C U S S I O N Solution. Step 1. Identify the fixed point. - The fixed point is A.
@ @ D I S C U S S I O N Step 2. Draw the axes and direction of the rotation - Draw a horizontal and a vertical line intersecting at the fixed point and draw an arrow about the axes following the direction of the rotation.
@ @ D I S C U S S I O N Step 3. Keep the fixed point in place. Rotate the side of the figure where the fixed point is located according to the intended rotation.
@ @ D I S C U S S I O N Step 4. Draw the rotated figure.
@ @ D I S C U S S I O N Example 10. (Rotation) Rotate triangle ABC around point A by turn clockwise.
@ @ D I S C U S S I O N Solution.
@ @ D I S C U S S I O N Example 11. (Rotation) Rotate triangle ABC around point B by turn counterclockwise.
@ @ D I S C U S S I O N Solution.
@ @ A S S E S S M E N T Directions: Draw the resulting figure following the direction of the rotation.
@ @ A S S E S S M E N T 1. Rotate the figure around point A by turn counterclockwise.
@ @ A S S E S S M E N T 2. Rotate the figure around point A by turn clockwise.
@ @ A S S E S S M E N T 3. Rotate the figure around point C by turn clockwise.
@ @ A S S E S S M E N T 4. Rotate the figure around point C by turn counterclockwise.
@ @ A S S E S S M E N T 5. Rotate the figure around point B by turn counterclockwise.
@ @ A S S E S S M E N T 5. Rotate the figure around point B by turn clockwise.
Directions: Rotate the shaded object about the point marked. @ @ E X T E N D E D
Example @ @ E X T E N D E D 90° counterclockwise
1. @ @ E X T E N D E D 180° clockwise
2. @ @ E X T E N D E D 90° clockwise
3. @ @ E X T E N D E D 180° counterclockwise
4. @ @ E X T E N D E D 90° counterclockwise
5. @ @ E X T E N D E D 180° clockwise
MATHEMATICS 6 TERM 1 WEEK 2 DAY 4
@ @ P R E - L E S S O N Directions: Put a check in the box for the correct answer.
@ @ P R E - L E S S O N 1. Which image shows a reflection?
@ @ P R E - L E S S O N 2. Which image shows a rotation?
@ @ P R E - L E S S O N 3. Which image shows a translation?
TRANSLATION, REFLECTION, AND ROTATION
@ @ D I S C U S S I O N Directions; Write RE if the pattern shows reflection, T if the pattern shows translation, and RO if the pattern shows rotation.
@ @ D I S C U S S I O N 1. ___________ 2. ___________
@ @ D I S C U S S I O N 3. ___________ 4. ___________
@ @ D I S C U S S I O N 5. ___________ 6. ___________
@ @ A S S E S S M E N T Directions: Tell how each figure was moved. Write translation, rotation, or reflection.
@ @ A S S E S S M E N T
@ @ A S S E S S M E N T
@ @ A S S E S S M E N T
Directions: Draw the following shapes and show the indicated transformation. Describe how the shape moves or changes after the transformation. @ @ E X T E N D E D