Unit 1: Day 3

Day 3: Surface Area of prisms, pyramids, cylinders, cones, and spheres

 Prism: To find the SA of a prism, combine the area of the 2 bases and the area of the sides. 

Pyramid:To find the SA of a pyramid, take the base area, and add 1/2 x base perimeter x slant height.

Cylinder: To find the SA of a cylinder, take the area of the bases and add 2πrh (radius and height).

Cone: To find the SA of a cone, take the area of the base and add πrL (radius and slant height).

Sphere: To find the SA of a sphere, use the equation 4πr².

Youtube! This video should add some further understanding and enjoyment of the narrator's awesome accent.

 

Quiz Time!

1. What is the surface area of this prism?

 

2.  What is the SA of this sphere?

 

3. What kind of accent did the narrator have? 

Key

1. The SA is 108 in²

2. The SA is 113 cm²

3. The narrator is from India

Unit 1: Day 2

Day 2: Introducing the concept of scale

This lesson will build on day one. Once you know how to find the area of one shape, you can then figure out the area of a larger or smaller similar shape.

The basic concept is that of dilations and ratios. Take this picture for example:

We have the 2 side lengths of the bigger triangle. To find out x, we set up a proportion that looks like this:                                    4  =  2 We'll solve this using the fish method, or cross multiplying. 2x9= 18, then we divide it by
9      x.  4, giving us 4.5cm as x.


You can use this method with any set of 2 numbers. They don't have to be side lengths. You could use area and a side length, area and perimeter, or perimeter and a side length.

Video!! 

This should help with the above if you're still confused.

Quiz Time!

1. What is the area of the bigger shape?

2. Can you only scale using side lengths?

3. What would the dimensions of the rectangle be if you used a dilation factor of 3?

Key

1. The area of the larger triangle is 18 cm². We cross multiplied 6 and 12, and divided by 4. 

2. No, you can scale an object accurately using any 2 measurements.

3. The length would be 15 units and the height would be 9 units. 

Unit 5: Day 6

Day 6: State and Define the Objective 

Students will be able to write the equation of a line given data points. 

This objective is referring to the equation, Y=MX+B. When given two points, it is possible to apply them to the equation so that you are able to find the equation of a line. 

Day 6: Pictures and Graphs that Represent Objective 

This is the equation used to find the y intercept. Y+_MX+B, B representing the Y intercept in the equation. 

This graph represents the equation of a line, given two points. As you can see, the line intercepts three points, although only two are necessary to find the line of best fit. You can also see the equation for the line of best fit at the top of the graph. You can find this equation using the slope intercept form.

The only ultimate difference between a point and a data point is that data points are real life situations. In most situations, the y- intercept is how much packaging costs, without any of the merchandise in it.

Quiz Time!

1. A tall Chai Tea from Starbucks costs $2.70 and has 12 ounces of tea, while a venti costs $3.35 with 20 ounces. Write the equation of the line.

2. At Yankee Candle, a candle that burns for 150 hours costs $27.99, while a candle that lasts 45 hours costs $17.99. Find the equation of the line.

3. At Dick's Sporting Goods, a 15 lbs kettlebell costs $39.99, while a 45 lbs kettlebell costs $89.99. Find the equation of the line. 

Key 

1.

2.

3.

Unit 1: Day1 video

 

 

This video will teach you how to find the area and perimeter of basic shapes, supplementing the lesson on Day 1.

Unit 1 Day 1

Day 1: Finding the area of basic shapes

 

Square: To find the area of a square, multiple base x height.  For example, a square with a height of 5 feet would have 25 feet squared of area.

Rectangle: To find the area of a rectangle, you also multiply length x width. For example if the base was 10 and the height was 2, the area would be 20 feet squared.

Triangle: To find the area of a triangle, you use the equation base x height divided by 2. For example, if the base was 5 and the height 6, the area would be 15 feet squared. 

Trapezoids: To find the area of a trapezoid, you take the sum of the 2 bases, multiply it by the height, and divide by 2. For example, if base 1= 5in and base 2= 10in, and the height= 5in, the area would be 37.5 inches squared. 

Parallelograms: Parallelograms may look complicated, but you just have to use the same equation as for a square: base x height. 

Circles: To find the area of a circle, you use the equation πr², with r meaning radius.

Polygons: A polygon is a shape with at least 3 sides and angles. For our purposes, it'll be pentagons and octagons, but this can be applied to almost any shape. For its area, you take the apothem (the distance from the center to an outside edge), the length of a side, and the number of sides. Then you use the equation 1/2nsr (number of sides, side length, apothem).For example, if the apothem were 5, it was a pentagon, and the length of each side was 5, you would get 62.5².

Definitions:

Point: The definite position on a graph to indicate position or direction.

Line: A long thin mark made on the surface

Plane: a flat or level surface

Line Segment: The finite section of a line

Ray: a line outward from the center

Angle: The space between converging lines or surfaces

Median: The middle number or point

Altitude: The height of a thing above the reference point

Perpendicular:Meeting a given line at right angles

 

 

Quiz Time!

 

1. What is the area of this  circle given the diameter is 12 inches?

 

2. What is the formula for area of a polygon?

 

3. What is the area of this trapezoid?

 

 

 

 

 

 

 

 

 

Key

 

1. The area of the circle is 113.04 inches². To get this I multiplied pi by the square of 6, which is 36.

 

2. The formula for the area of a polygon is (1/2)nsr.

 

3. The area of this trapezoid is 18 meters², which I got by adding 3 and 6 (9), multiplying it by 4 (36) and dividing it in half.

 

Unit 5: Day 5

Day 5:  State and Define the Objective 

Students will graph linear inequalities. 

This objective is referring to the equations and inequalities which determine which points are plotted on the X and Y intercepts. 

Day 5: Pictures and Graphs Relating to Objective 

This graph represents the linear inequalities by illustrating the greater or lesser values, which are shaded. 

This graph illustrates the dotted line separating the greater or lesser then values of the inequality. 

This shows the inequality itself. Inequalities must first be organized into the format of an equation so that you can solve for the X and Y intercepts. 

Quiz Time!

1. Graph the equation y<1x+2

2. Graph the equation y> 2x +1

3. Graph the equation y>4x-1

Key:

1.

The graph has a dotted line and is shaded below because it's not inclusive of the line and is less than.

 

2.

The graph has a solid line and is shaded above because it's inclusive of the line and is greater than.

 

3.

The graph has a dotted line, because it is not inclusive of the line, and is shaded above for greater than.

Day 5 Youtube Video: Students will Graph Linear Inequalities

This represents how to graph linear inequalities, and it also demonstrates how to shade the linear inequality.