Friday, April 13, 2012

2D and 3D Shapes: Week One

Day 1: Geo Board Challenge

Review basic shapes of circle, square, rectangle, and triangle briefly with students on the white board, but ask more difficult questions. For example, is a square a rectangle? (Yes! It's a special kind of rectangle, but it's still a rectangle.) Introduce parallel, perpendicular, and (if there's time) trapezoid, parallelogram, quadrilateral, pentagon, hexagon, octagon, etc. For the bigger polygons, emphasize that it doesn't have to be a regular polygon (one with all the same length sides and same angles.) Draw some weird pentagons and hexagons and see if the students can still recognize them. (Write terms on the board as you go.)

Pass out geo boards and geo bands. Tell students that you're going to ask some easy questions first, so they need to work quickly! Ask students to make a square on their geo board. (Use your geo board to make a square with all diagonal lines, and ask students if it's still a square.)
Next, ask students to make a rectangle. Again, have students check each other. Show your diagonal square again. Is this a rectangle? (If you covered these vocabulary words earlier, is it a parallelogram? A quadrilateral?) Continue through triangle, perpendicular, parallel, and any other terms you covered.

Now for the challenge questions. Divide students into two teams if desired, and see which team can get all its members to have the correct shape on their geo boards. (Helping is allowed, but emphasize that there's more than one correct way to make all of these shapes.)

Can you make a square from two triangles? A rectangle from two triangles? A rectangle from two squares? A square from two rectangles? A big triangle from two smaller triangles? A pentagon from a square and a triangle? etc.

Day 2: Symmetry

Attention grabber: Tell students that you have a riddle, and whoever solves it will get a
treat. Draw an eight on the board. Ask the students, "What is half of eight?" (Hopefully they will answer four!) Here's the riddle: "I think half of eight is 0. Or 3. How could that be possible?" Show students the lines of symmetry in the number eight that answer this riddle.

Introduce the concept of symmetry (when both sides of an object are the same size and
shape). Demonstrate symmetry of shapes from Day 1 (while reviewing their names) as well as complex 3D shapes (like people, chairs, etc.) Show some examples of shapes that don't have a line of symmetry, like the letter G. Play a quick game of Symmetrical or Not Symmetrical by naming objects and having students show you thumbs up if the object is symmetrical and thumbs down if the object is not symmetrical (or asymmetrical.)

Give students a copy of the symmetry worksheet and ask them to draw the line(s) of symmetry on each shape, then check their answers with a neighbor when they are finished.

Give each student a small piece of paper and ask them to fold it in half. Is this a line of symmetry? Give students scissors and ask them to cut a small shape along the fold. Have students draw what they think their shape will look like when the paper is unfolded on the back of their worksheet, then unfold the paper and see if they were correct. Repeat this activity with more elaborate shapes.

Day 3: Pentominoes and Transformation

Introduce the transformation terms flip (mirror image), slide (translation; moving up,
down, over, etc.), and turn (rotation). Draw a familiar shape, such as a heart or smiley face, on the board. Draw the shape again and ask students whether you did a flip, slide, or turn.
Give each student a copy of the Flip, Slide, Turn worksheet, facedown. Give each student a pentomino. Have them trace their pentomino on the back of their worksheet, then ask them to show you a flip, slide and turn from the traced shape. When the concepts are mastered, have students turn their paper over and complete the worksheet.

If extra time remains, divide the students into small groups or pairs and give each group or pair a full set of 12 pentominoes. Ask them to fit all their pentominoes together to make a rectangle. (This is very difficult!)  Tell students that we'll find a solution to this problem tomorrow.

Day 4: Pentomino Puzzles

Divide students into pairs and give each pair a set of pentominoes.  If desired, teach the students the letter names of the pentominoes.  Give students several challenges, such as those found here.
(For letter names and one large rectangle solution, see this site.)  As a final challenge, ask the students to make one large rectangle using all of their pentominoes.

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