My students asked to have the time before the test to practice, instead of the book group I wanted to do. (110 min class and a 1 hour exam.) Very reasonable. But that meant that I had to come up with practice problems! I'll post those now, then the test when all students have taken it.
Photo by scrappy annie @ Flickr
322 Midterm Practice
The StandardsA. Analysis of characteristics and properties of
2-D geometric objects: number of edges; side length; angle size; parallel; perpendicular; convexity, etc.
1. concept: definition and recognition
2. application: use to sort and characterize, build or draw
3. combination: consider multiple properties in a single object
4. familiarity with examples: triangles, quadrilaterals, polygons
D. Distance, area, angle
1. concept: definition and key properties
2. formulas: use and derivation
3. connections among formulas
Try your choice of the following problems. Look for problems that allow you to problem solve and share your thinking.
Which standards could you demonstrate on which problems?
1) Connect each side property to an angle property and draw a different polygon to match each pair.
|(at least) 3 congruent sides||no adjacent congruent angles|
|pair of perpendicular sides||(at least) 1 angle > 180 degrees|
|3 parallel sides||pair of adjacent congruent angles|
2) Sometimes quadrilaterals are defined by their diagonals rather than by sides and angles. Determine which quadrilateral goes with which definition below, and make your argument. If no quadrilateral goes with a definition, state why.
a. Diagonals both bisect each other.
b. At least one diagonal bisects the other.
c. Diagonals are equal length.
d. Diagonals are perpendicular.
e. Diagonals do not intersect.
f. Diagonals are perpendicular bisectors.
3) On our Area on a Grid class workshop, find the areas of the shapes using formulas.
4) On graph paper, divide a square up into exactly 7 triangles with as many different triangle types as possible. Can you get all 7 types?
a) Make an area formula for a trapezoid, or prove the one you know, using the formulas for rectangles and triangles.
b) Make an area formula for a kite.
c) Make an area formula for a chevron, using the diagonal lengths.
6) On graph paper, find squares with areas listed or argue why you can’t: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
a. Note: 5 is possible.
b. Find the edge length for each square you found using the Pythagorean Theorem. What do you notice?
7) Draw a 2 circle Venn diagram with the labels only in your mind (eg. a line of symmetry and at least one pair of parallel sides). Write in the quadrilateral types where they go, and give to a tablemate to figure out the labels.