1. Demonstrate an understanding of angles by:
• identifying examples of angles in the environment
• classifying angles according to their measure
• identifying examples of angles in the environment
- One place that knowing your angles is very important is in construction. a 90 degree or right angle is one of the most commonly used as it makes structures much more stable. If a building were built with angles other than 90 degrees it would be more likely to collapse.
• classifying angles according to their measure
- Angles are named according to their measurement. Refer to the picture below.
![Picture](/uploads/1/4/7/1/14718762/351196643.gif)
- estimating the measure of angles, using 45°, 90° and 180° as reference angles
- If you know what 45, 90 and 180 degree angles look like it makes estimation much simpler because it allows you to compare the unknown angle to the three you do know and make a reliable estimation.
- determining angle measures in degrees
- Angles are measured in degrees, this can be done using a protractor.
- Practice using THIS website.
- drawing and labeling angles when the measure is specified.
- Using a protractor practice drawing these angles: 40, 72, 188, 115, 90 and 30 degrees.
2. demonstrate that the sum of interior angles is: • 180° in a triangle 360° in a quadrilateral.
- The 3 angles on the inside of a triangle will always add up to 180°
- The 4 angles on the inside of quadrilateral will always add up to 360°
![Picture](/uploads/1/4/7/1/14718762/109803642.gif)
3. Develop and apply a formula for determining the: • perimeter of polygons• area of rectangles• volume of right rectangular prisms.
- Perimeter
- Square- P=Lx4
- Rectangle P=2L+2W
- Other polygons L+L+L+L+L...
- Area
- Rectangle- A=LxW
- Volume
- Rectangle- A=LxWxH
![Picture](/uploads/1/4/7/1/14718762/856602405.png)
4. Construct and compare triangles, including:
• scalene
• isosceles
• equilateral
• right
• obtuse
• acute
in different orientations.
• scalene
• isosceles
• equilateral
• right
• obtuse
• acute
in different orientations.
- Triangles are named based on the length of their sides and angles. Refer to THIS website for a more detailed description of the triangles listed above.
5. Describe and compare the sides and angles of regular and irregular polygons.
- A Polygon is a shape where all the sides are straight and completely connected making a closed shape. If there are any gaps or curved lines in the shape it is not a polygon.
- A regular polygon will have all the sides equal in length and the the angles equal as well.
- An irregular polygon will have one or more of the sides different lengths, resulting in different angles as well.
- For a more detailed description of polygons refer to THIS website.
6. Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image.
- A transformation is when you take a point on a graph and move it somewhere else on the graph. Often 3 or more points on a graph can create a 2D shape, and when all three points are moved the whole shape moves. In grade 6 we need to know how to do three kinds: translations, rotations and reflections.
- A translation is a slide where the shape of the object keeps the same size, shape and direction but changes location by either sliding up/down or left/right. For instance if the original x,y coordinates were (2, 4) and the translated object's coordinates (2, 8) the object would have been translated 4 units to the right.
![Picture](/uploads/1/4/7/1/14718762/1440531586.png)
2. A rotation is when the shape spins around a fixed point on the graph. The shape will keep the same size and shape, but will change direction.
3. A reflection is when an objected is flipped over a line. It will keep the same size and shape but will be facing the opposite direction (kind of like when you look at yourself in a mirror everything will look backwards).
![Picture](/uploads/1/4/7/1/14718762/661584847.jpg)
7. Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe
the transformations.
8. Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs.
- Practice a series of transformations. On a piece of graphing paper start with an object anywhere on the graph. Start by translating it up 4 units. Then rotate that image 90 degrees around the origin. Finish by reflecting that shape using the x axis as your line of reflection.
8. Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs.
- A Cartesian plane is a type of graph with 4 different quadrants. The first quadrant is located above the x axis and to the right of they y axis (all the points in this quadrant will be positive).
![Picture](/uploads/1/4/7/1/14718762/593779106.gif)
9. Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to
whole number vertices).
- With a partner, practice each type of transformation listed above, while keeping your shape in the first quadrant.