Fractions
Similarity
Probability
Area and Perimeter
Tiling the Plane
100
1/2 + 3/4 =
5/4 or 1 1/4
100
How are the perimeters of two similar figures related? Give an example.
The perimeter of the larger is the scale factor times the perimeter of the smaller figure.
100
What is the theoretical probability of choosing a yellow ballon?
3/25
100
A square has a side length of 6 units. Find the area and the perimeter.
The area is 36 square units, and the perimeter is 24 units.
100
What is another word for tilings?
tessallations
200
2 - 2/5 = ?
8/5 or 1 3/5
200
How are the areas of two similar figures related? Give an example.
The area of the larger figure is the square of the scale factor times the area of the smaller figure.
200
What is the probability of not choosing a red balloon?
10/25
200
A juice can is about 2.25 inches in diameter. What is the circumference?
Approximately 7.07 in.
200
Which of these shapes work as tiles and which do not? Why? hexagon rectangle equilateral triangle
All rectangles and triangles can be used as a tile. A regular hexagon can tile the plane, but not all hexagons can.
300
3/8 x 6/7 =
18/56 or 9/28
300
Rectangle A measures 3 inches by 5 inches. Find the measures of two similar rectangles.
similar rectangles 6x10, 9x15, 12x20, etc.
300
What is the theoretical probability of getting a yellow or an orange balloon?
10/25
300
Draw two shapes with perimeters of 18 units but different areas. Give the area of each shape.
A 2x7 rectangle has a perimeter of 18 units and an area of 14 square units. A 4x5 rectangle has a perimeter of 18 units and an area of 20square units. Any rectangle whose length and width add to 9 units will work.
300
Find the dimensions of two possible rectangles that can be made with 36 square tiles.
1x36, 2x18, 3x12, 4x9 or 6x6
400
1 2/3 - 5/6 =
5/6
400
A figure is put in a copier using a copier size factor of 125 %. What scale factor and ratio of similarity relate the copy to the original figure?
5/4
400
The number of balloons of each color is doubles. What happens to the probability of choosing a red ballooon?
15/25 = 30/50 so the probability is the same.
400
Draw two shapes with areas of 25 square units but different perimeters. Give the perimeter of each shape.
A 5x5 square has an area of 25 sqaure units and a perimeter of 20 units. A 1x25 rectangle has an area of 25 square units, but a perimeter of 52 units.
400
A regular polygon has an angle sum of 1,080 degrees. How many sides does it have?
8
500
5/7 divided by 2 1/3 = ?
15/ 49
500
What is the minimum number of side and/or angle measurements needed to check the similarity of two triangles?
If two corresponding angles have the same measure, the third angles will have the same measure and the triangles will be similar. If all three pairs of corresponding sides have the same ratio, the triangles are similar.
500
How many balloons of each color would you need to add to the original bag to make the probability of drawing a red balloon 1/2 ?
Some possibilities: Add 1 yellow and 4 oranges, or 2yellows and 3 oranges, or 3 yellows and 2 oranges, or 4 yellows and 1 orange, or 5 yellows, or 5 oranges.
500
Find the rectangle with an area of 36 square units and whole-number side lengths that has the smallest perimeter possible.
6x6
500
Use the parallelogram on the board. Find two ways that copies of it can be used to tile a surface.
Using the idea of translations, you can tile the plane with strips of parallelograms arranged so that the top of the parallelogram exactly matches the bottom of a parallelogram in the next strip. You can also offset the strips so that the top of a parallelogram matches the midpoint of the top of a parallelogram in the next strip.
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