Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Geometry
Problem
Hint
1) A pinwheel is made of four identical shapes each with a different color arranged counterclockwise in color order red, blue, green, and gold. They are evenly spaced. The wind spins the pinwheel counterclockwise, and when it stops, the red shape is now where the blue shape used to be. If the pinwheel went through two complete rotations before red ended up where blue used to be, how many total degrees did the red shape travel? "counterclockwise" means turning in this direction: ↶.
1. One complete rotation is ____ degrees.
2. Two complete rotations are ____ degrees.
3. Each shape is how many degrees from the one next to it?
    ____ degrees.
4. The red shape and the blue shape are this many degrees apart?
    ______
5. Total rotation = two complte rotations which are ___ degrees
    + ___ red rotation to blue = _____ total degrees.
2) John is trying to make a rectangle on the given coordinate grid. He has already labeled the point A at (-1, 3), the point B at (1, -1), and point C at (-2, 2). Where should he plot point D to complete the rectangle?

 1. To get from point B to A go down ___ and left ___ spaces.
2. Find point D from point C by these same offsets: (___,___)

Problem
Hint
3) Toleen's math teacher makes a model of a solid rectangular prism out of white one centimeter cubes to explore surface area and volume. She paints the entire outside surface red. If the dimensions of the prism are 3 cm by 4 cm by 6 cm, how many of the cubes have exactly two sides painted red? Here is the shape:
OK, the cubes on the inside have no paint.
The cubes on the middle of the sides have 1 side painted.
The corners (8 of them) have 3 sides painted.
The edges that are not the corners have 2 sides painted.
How many cubes are edges that are not corners? ______
4) In Latoya's class they are cutting out snowflakes from square paper folded in half and them in half again to make a folded square. Latoya cuts along the three lines shown in the picture of the folded square and removes the smaller piece. When she unfolds this smaller piece what shape will it be?
So, the shape you see is 1/4 of the total shape (2 folds).
The lower left corner is the middle of the shape.
Take your pencil and draw in the other 3 parts.
It is a ________________
5) In right triangle AMC (see diagram) triangles ANP and PLC are congruent. MNPL is a square and segment LC has length 2 cm. What is the perimeter of the square MNPL?
'congruent' means ANP and PLC are the same triangles.
Since they are congruent and LC is 2 cm, then NP is _______ cm.
It is a square, so the perimeter of the square is _____ cm.