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Jar of Pi
Standard Met: CCSS.Math.Content.7.G.B.4
What You Need: Jar lids, tacks, string, centimeter rulers, pencils, calculators (optional)
What To Do: Pi is the ratio of the circumference of a circle to its diameter. You can tell students that or you can help them discover it.
To start your discovery, in the week leading up to Pi Day (March 14), have students collect clean lids from jars and bottles. Working in pairs, they choose three lids from the collection and trace them onto a piece of paper to create circles of different sizes. Next, give each pair a piece of string at least 12 inches long. Have one partner use a ruler to find the center of the first circle, hold the string at the center with a tack, and then measure the diameter and record this length. The second partner wraps the string around the circumference of the matching lid and records this length. Have students record these two numbers for each of their three lids.
Finally, ask students if they can find a relationship or determine a ratio between the numbers. With enough shared data and discussion, kids will discover pi!
Who Am I?
Standard Met: CCSS.Math.Content.7.G.A.1
What You Need: Paper, pencils
What To Do: Golf is not the only game where a low score wins. This simple geometry game is based on an old standby, 20 Questions, and is a great way to practice geometry vocabulary. First, pair students and assign each pair a figure (such as an acute triangle) or term (such as parallel lines). Partners brainstorm and write down a list of clues describing the figure or term. The more clues the better. Then, invite groups, one by one, to the front of the class and ask them to reveal one clue. For example, if the group’s figure is a rectangle, the first might be, “I am a quadrilateral” or “I have two sets of parallel lines.” The class makes a guess, and continues to guess until arriving at the correct answer or all clues have been used up. For each clue given and corresponding guess made, the class gets one point. The object of the game is to guess correctly using the least number of clues and scoring the lowest number of points.
Standard Met: CCSS.Math.Content.7.G.A.2
What You Need: Graph paper, pencils
What To Do: Have partners sit back-to-back in chairs with desks in front of them. Whisper the name of a figure or other geometry term to one partner, who will be the leader for this round. Give the other partner a piece of graph paper and a pencil. The lead partner describes the figure or term while their partner tries to draw it.
The leader can use as many geometry terms, attributes, and directional words as needed, but may never say the name or any part of the name of the figure or term. When their partner believes they have completed their drawing accurately according to the verbal directions, the leader checks. If the drawing is accurate, they switch roles. If it is not, have them try again. The drawings should be similar, but they don’t have to be congruent (another opportunity to talk about those geometry terms!).
Standard Met: CCSS.Math.Content.6.G.A.1
What You Need: Centimeter graph paper, index cards, centimeter ruler, pencils
What To Do: Using a ruler, partners draw the polygon of their choice on a piece of graph paper, calculate its area, and then cut out the shape and glue it onto an index card. The figure does not have to be a regular polygon: It can be of any design, as long as the partners can accurately calculate its area. On a matching index card, have students write the area of the figure they designed. Have them complete at least eight cards like this (corresponding to four figures) to make a set. When all cards are complete, the partner duos team up to first shuffle and then spread out all 16 of their cards facedown on a desk or table.
Partners takes turns flipping over two cards at a time and trying to find a match of figure and area. They may take their time to calculate the area of the polygons they turn up, using a ruler, if necessary. If it’s a match, the players keep the cards and continue flipping pairs. If not, they return the cards to their original spots and the other two players take a turn. The duo with the most matches wins. As an added challenge, assign specific areas (for example, 20 square centimeters) for students to use in creating their polygons.
What To Do: CCSS.Math.Content.6.G.A.3
What You Need: Graph paper, rulers, pencils
What To Do: A perennial board-game favorite is Battleship. Why not create your own? Begin by having each student draw a coordinate plane on a piece of graph paper and number the axes from 1 to 12. Ask students to draw a polygon in the planes, place a dot at each vertex, and then record the coordinates of each of the vertices.
Partner students and have them face each other across a desk or table with a divider (such as a binder) between them. Give them a new piece of graph paper. Choose one partner to be the leader, and ask her to begin by telling her partner the coordinates of the first vertex on her drawing. The partner should mark this point on graph paper. Students will swap roles until all coordinates have been shared. Then, using a ruler, they connect the vertices on their papers and complete the polygon. Compare drawings to the originals for accuracy. Finally, see if students can name the polygons they have created according to the number of sides. (Get stuck? Visit Drexel University's Math Forum to find a name for your polygon—no matter how many sides it has. For example, students will learn that the 13-sided polygon they drew is a triskaidecagon!)
Photo: Philippe Lissac/Godong/Corbis
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