How to make a greeting card origami box…

Start with a recycled greeting card.

Questions What shape is a greeting card? How do you know?

Step 1: Cut the card in half, cutting along the fold.

Questions What geometric term describes the relationship between the two halves of the greeting card? What geometric term describes the fold line of the greeting card?

Step 2: Now we must cut both halves to make squares. By rotating one of the halves 90° to the right, we can trim the excess from both pieces.

Question Why did rotating one of the greeting card halves and trimming the excess give us squares?

Now both halves are squares Now both halves are squares. Step 3: Trim the second half ¼ inch on two adjacent sides. The larger square will make the box lid.

Questions What geometric term describes the two squares? Why should we trim two adjacent sides of one of the squares and not two opposite sides?

Step 4: Mark the diagonals on both of the squares Step 4: Mark the diagonals on both of the squares. Be sure to use a straight edge or ruler.

Questions What is a diagonal? How many diagonals does a square have? a pentagon? What is one special characteristic of the diagonals of a square?

Step 5: Fold one of the vertices of the square until it touches the intersection of the diagonals. (Fold point A to point B) B A

Questions What is a vertex? How many vertices does a square have? a pentagon? If two lines intersect, what is their intersection?

Now we have a pentagon. Step 6: Take the folded side of the pentagon and fold it to the diagonal it is parallel to. (Fold CD to EF) F D E C

Questions What are parallel lines? How many sides does a pentagon have?

Step 7: Unfold the square and then repeat the last two folds starting at each of the 3 remaining vertices.

Questions What is the area of the square? How do you know?

Step 8: Unfold the square and mark it as shown below.

Questions What kind of triangles are shaded on the square? What relationship do the line segments marked have to each of the diagonals?

Step 9: Cut along the lines marked, and cut off the right triangles shaded in step 8.

Questions What shape do we have now? Is it concave or convex? What is its area?

Step 10: Fold the tips of the wide flaps to the intersection of the diagonals. (Fold points X and Y to point B) Y B X

Questions What shape do we have now? What is its area?

Step 11: Fold up the sides of the large flaps, and tuck in the small segments to form the base of the box.

Question How many dimensions does the object have now?

Step 12: Fold the remaining smaller flaps over the sides and press flat into the base.

You have now completed half of the box.

Questions What shape is the object now? What is its surface area? What is its volume?

Repeat step 5-12 to make the box lid. If done correctly, your box lid should fit on the base with just a little coaxing.

Questions What geometric term is used to describe the box lid and bottom? What is the surface area and volume of the box lid?

Questions Are the surface areas and volumes of the box lid and bottom actually equal? Why or why not? What step did we take earlier to make sure the box lid would fit onto the bottom?