How to make a How to make a greeting card greeting card origami box…origami box…

Start with a recycled greeting Start with a recycled greeting card.card.

QuestionsQuestions

What shape is a greeting card?What shape is a greeting card?

How do you know?How do you know?

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

QuestionsQuestionsWhat geometric term describes What geometric term describes the relationship between the the relationship between the two halves of the greeting two halves of the greeting card?card?

What geometric term describes What geometric term describes the fold line of the greeting the fold line of the greeting card?card?

Step 2: Now we must cut both Step 2: Now we must cut both halves to make squares.halves to make squares.

By rotating one By rotating one of the halves 90° of the halves 90° to the right, we to the right, we

can trim the can trim the excess from excess from both pieces.both pieces.

QuestionQuestion

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

Now both halves are squares. Now both halves are squares. Step 3: Trim the second half ¼ Step 3: Trim the second half ¼ inch on two adjacent sides. Theinch on two adjacent sides. The

larger square will make the box lid.larger square will make the box lid.

QuestionsQuestionsWhat geometric term describes What geometric term describes the two squares?the two squares?

Why should we trim two Why should we trim two adjacent sides of one of the adjacent sides of one of the squares and not two opposite squares and not two opposite sides?sides?

Step 4: Mark the diagonals on Step 4: Mark the diagonals on both of the squares. Be sure to both of the squares. Be sure to

use a straight edge or ruler.use a straight edge or ruler.

QuestionsQuestionsWhat is a diagonal?What is a diagonal?

How many diagonals does a How many diagonals does a square have? a pentagon?square have? a pentagon?

What is one special What is one special characteristic of the diagonals characteristic of the diagonals of a square?of a square?

Step 5: Fold one of the vertices of Step 5: Fold one of the vertices of the square until it touches the the square until it touches the intersection of the diagonals. intersection of the diagonals.

(Fold point A to point B)(Fold point A to point B)

A

B

QuestionsQuestions

What is a vertex?What is a vertex?

How many vertices does a How many vertices does a square have? a pentagon?square have? a pentagon?

If two lines intersect, what is If two lines intersect, what is their intersection?their intersection?

Now we have a pentagon. Step 6: Now we have a pentagon. Step 6: Take the folded side of the Take the folded side of the pentagon and fold it to the pentagon and fold it to the diagonal it is parallel to. diagonal it is parallel to.

(Fold CD to EF)(Fold CD to EF)

C

D

F

E

QuestionsQuestions

What are parallel lines?What are parallel lines?

How many sides does a How many sides does a pentagon have?pentagon have?

Step 7: Unfold the square and Step 7: Unfold the square and then repeat the last two folds then repeat the last two folds

starting at each of the 3 starting at each of the 3 remaining vertices. remaining vertices.

QuestionsQuestions

What is the area of the square?What is the area of the square?

How do you know?How do you know?

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

QuestionsQuestions

What kind of triangles are What kind of triangles are shaded on the square?shaded on the square?

What relationship do the line What relationship do the line segments marked have to each segments marked have to each of the diagonals?of the diagonals?

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

QuestionsQuestions

What shape do we have now?What shape do we have now?

Is it concave or convex?Is it concave or convex?

What is its area?What is its area?

Step 10: Fold the tips of the wide Step 10: Fold the tips of the wide flaps to the intersection of the flaps to the intersection of the

diagonals. (Fold points X and Y to diagonals. (Fold points X and Y to point B) point B)

B

X

Y

QuestionsQuestions

What shape do we have now?What shape do we have now?

What is its area?What is its area?

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

box. box.

QuestionQuestion

How many dimensions does the How many dimensions does the object have now?object have now?

Step 12: Fold the remaining Step 12: Fold the remaining smaller flaps over the sides and smaller flaps over the sides and

press flat into the base. press flat into the base.

You have now completed half of You have now completed half of the box. the box.

QuestionsQuestions

What shape is the object now?What shape is the object now?

What is its surface area?What is its surface area?

What is its volume?What is its volume?

Repeat step 5-12 to make theRepeat step 5-12 to make thebox lid. box lid.

If done If done correctly, correctly,

your box lid your box lid should fit on should fit on the base with the base with

just a little just a little coaxing.coaxing.

QuestionsQuestions

What geometric term is used to What geometric term is used to describe the box lid and describe the box lid and bottom?bottom?

What is the surface area and What is the surface area and volume of the box lid?volume of the box lid?

QuestionsQuestionsAre the surface areas and Are the surface areas and volumes of the box lid and volumes of the box lid and bottom actually equal? Why or bottom actually equal? Why or why not?why not?

What step did we take earlier What step did we take earlier to make sure the box lid would to make sure the box lid would fit onto the bottom?fit onto the bottom?