working algebra knowledge for all ages

HOW WE PACKAGE ! OUR WARES

row, column or diagonally X / Y / SLOPE

ANGLES INSIDE SIDES OUTSIDE

two large triangles, two

small triangles, a medium-size

triangle, a square and

a parallelogram

Tangram

the area of the trapezoid with bases and and altitude is given

by the formula .

TRAPEZOIDS & TRIANGLES are polygons

Trapezoid PQRS with PQ parallel to RS.

Things You'll Need TO ! 1 sheet of standard printer paper ! Instructions ! 1Lay the paper on your work surface vertically. Fold it from top to bottom and

crease it well. Keep it folded down with the open edge at the bottom.2 Fold the top right and left corners down to meet in the middle of the folded rectangle.3 Fold the bottom edge up to cover the folded-down corners. Turn the piece over and fold the opposite bottom edge up in the same way.4Fold each of the four bottom corners in, lapping them over each other. You should end up with a triangle shape.5Place your thumbs inside the bottom opening, one in the center of each open edge. Extend your thumbs. Press down on the paper to make a square. Hold the square with the flaps facing down. Fold the bottom point up to meet the top point. Flip the figure over fold the other bottom point up to meet the top point. The model should look like a triangle again.7Place your thumbs inside the bottom opening, one in the center of each open edge. Extend your thumbs and press down to make a square shape as before. Crease firmly.8Pull the outermost triangles apart gently. Your paper boat is ready to float.

FLOAT YOUR TRAPEZOIDAL BOAT

TODAY

Take 14 toothpicks, and arrange 12 of them to form the shape shown HEREIN.

!  Challenges Move two toothpicks in the arrangement and add the two extra toothpicks to make: Two congruent triangles, two congruent parallelograms, and an irregular pentagon. Two congruent triangles, two congruent parallelograms, and a trapezoid. Two congruent triangles, two congruent parallelograms, and two congruent hexagons. Three congruent triangles and two congruent trapezoids. Three congruent triangles and two non-congruent parallelograms. Three congruent triangles, two congruent hexagons, and a trapezoid. Four congruent triangles and an irregular hexagon. Four congruent triangles and two congruent parallelograms. Five congruent triangles and a parallelogram. Exactly six congruent triangles. Six triangles, not all congruent, and two congruent parallelograms. Seven triangles, not all congruent, and a trapezoid. Sketch each solution you discover on the back of this paper. There may be multiple solutions for several of the challenges.

Take 14 toothpicks, and arrange 12 of them to form the shape shown HEREIN.

TRIANGLES & SQUARES ARE POLYGONS

QUADRILATERALS

PRISM (VOLUME) OR PLANE?(FLAT)

THINKING mathematically

! TRAPEZOID, RECTANGLE TRIANGLES are polygons

YOU AND YOUR ALGEBRA

Circle polygons

HEXAGONAL PRISM

6

PENTAGONAL PRISM 5

SQUARE Pyramid          

!

cone

cone

Triangular Prism Cube

3 4

Prism Cube

4

Pentagonal Pyramid flat

5

3

! circle

triangles

A Trapezoid has 2 parallel lines

*Call it (quadril)ateral (four sides Polygon (many sides)

�Rectangular Prism 4 4

Triangular Pyramid         

3

3 Rectangular Pyramid 4

3

Similar POLYGONS

ANGLES ARE INSIDE* SIDES ARE OUTSIDE*

* * * *

Paper Model of a

TRIA

NGUL

AR P

RIS

M

P A N G A E A

First, Sophie painted the paper plate with the glitter paint. But even coloring it with a plain old blue marker will do. While the paint dried, we cut out little fish that I had traced on different colored construction paper. (I folded the paper together so that we cut several fish at once). Then, we put the fish on the plate, covered it with plastic wrap, and drew lines for the net on the plastic wrap with the Sharpie. Here’s how it turned out:

! choose a rectangle that is twice as wide as it is tall. Divide the wide side into six sections. Draw six arc sections that just touch in the middle. Mark an extra edge on one side of the arcs so there will be some overlap to glue. Cut out, remembering to leave the arcs connected as well as the tabs. Even if you don't get the arcs perfect, you will end up with a quite nice ball! This is how paper hot air balloon kits from the 1970s were assembled,

PAPER SPHERE

OBTUSE / ACUTE < >

Oblique Oblique not 90 degrees

OBTUSE / ACUTE < <

CYLINDER