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Making Connections (Grades 7)

Master Teacher

Linda Brown

Time Allotment

Two 90-minute blocks

Overview

Through the activities presented in this lesson, students will recognize patterns in real-life situations and relate them to math and algebra.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

identify patterns and extend them
use patterns to solve problems

Standards

Algebra—Grade 7

I. Understand patterns, relations, and functions.

A. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

1. Describe, extend, analyze, and create a wide variety of patterns to investigate relationships and to solve problems.

Media Components

Video

Math Vantage: Patterns, Lesson 1: Discovering Patterns

Web Site

Paper Pool Game - Students will learn to analyze numeric and geometric patterns by playing "Paper Pool." Print out a copy of the game worksheet.

Materials

15 cards numbered 1-15 (one set per student)
deck of playing cards
color tiles (40 per group)
graph paper
Paper Pool Game worksheets
Activity Sheet

Prep for Teachers

Prepare a set of cards for each student.
Cue the videotape to the first clip.
On the Internet, go to NCTM Illuminations and preview the lesson on paper pool. Make copies of the recording sheets for the students.
Mark the Web site for the students on your favorites: Paper Pool Tables

Introductory Activity

The following activities will allow your students to begin recognizing and identifying patterns in real life situations.

Step 1

Play "Guess My Rule" with your students. Identify one attribute that several of your students have (i.e., glasses, striped shirt, tennis shoes). Pick one student who fits "your rule" to stand in the rule side of the room and one student who does not fit "your rule" to stand on the other side of the room. Have students suggest other students who might fit "your rule." Have these students stand in the appropriate place in the room. Continue doing this until the students can guess what your rule is.

Step 2

Ask the students if they have ever wondered how a magician did his tricks. Then ask them if they know any magic tricks with cards. Have them share their tricks and see if anyone can guess the secret to solving the trick.

Step 3

Explain that math is made up of all kinds of patterns and that today you will explore how patterns are use to solve problems, create magic, and predict outcomes.

Learning Activities

Step 1

Have the students take their stacks of cards in order from 1-15. Put the first card, number 1 down. Place the next card under the deck and place the next card, number 3, down. Place the next card under the deck and turn the next card up, number 5, and place it down. Continue doing this until the last card is placed down. Ask: What was the last card? What do you think the last card would be if you started with 5 cards? 10 cards? 20 cards? Try this with one card, then two, three, and so on. Record your last card each time. What pattern do you see? Can you use this pattern to predict what the last card would be with 16 cards? How about 20?

Step 2

Focus for Media Interaction: Explain to your students that they will be watching a magician do a magic trick with cards. But that it actually has a mathematical solution. Ask the students to look for the pattern that the magician is using.

Focus for Media Interaction: Tell students to watch the magician closely because you will discuss his "trick" after they view the clip. START the video where the magician is beginning the card trick with three rows of four cards each. This is right after you see the magician flick the deck of cards in a hat and two aces come across the screen. STOP the video after the trick when the girls says, "That's my card. How did you do that?" And the magician says, "It's magic." Discuss the "trick" that the magician used to guess the correct card, and ask the students if they figured out how the magician did this.

Focus for Media Interaction: Tell students to listen to for the secret of the card trick. START the video again and listen to the explanation of how the card trick works. STOP the video when the magician says, "Very good." Compare the reasons the students gave with the one on the video.

Step 3

Divide the class into groups of 3 or 4. Have the students arrange the color tiles into the pattern below.

* * * *

* * *

* * * * *

* * * * * * *

Step 4

Next, have the students create a Sequence Table that shows the term number (the number that tells the position of each term in the sequence) and the term (the number of color tiles used in that sequence).

Example

Term number: 1 2 3 4

Term 1 3 6 10

See if the students can predict how many color tiles will be used in the 5^th position (term number 5) by discovering a pattern.

End of Day One

Step 5 (Beginning of Day Two)

As a whole class if you have one computer, or in small groups if you have several computers, have the students go to Paper Pool Game and play the Paper Pool Game. Make sure they have the recording

sheets to keep a record of what they find out. Use the recording sheets to make predictions about how many hits will occur on different size pool tables.

Culmination Activity/Assessment

Use the "Shaking Hands" (Activity Sheet 1) activity to assess student understanding. Students may wish to work in small groups to act out the first part of the activity.

Click here for the "Shaking Hands" answer key.

Cross-Curricular Extensions

Art: Explore patterns in art. Create pictures using patterns such as tessellations, lines of symmetry, and transformations.

Science: Identify patterns found in nature.

History: Identify patterns in history and how they are used to predict future trends.

Community Connections

Invite an architect, builder, graphic designer, historian, or a meteorologist in to talk about how they use patterns in their job.

Activity Sheets (PDF)

Activity Sheet 1