7th Grade Math

Get ConnectED

Patterns

PART A B C

Multi-Part

Lesson 2

SPI 0706.1.2

Generalize a variety of

patterns to a symbolic rule

from tables, graphs, or

words. Also addresses

GLE 0706.1.3, GLE 0706.1.5.

50 Expressions and Patterns

Sequences

Use toothpicks to build the figures below.

Figure 1 Figure 2 Figure 3

Make a table like the one Figure

Number

1

2

3

4

Number of

shown and record the figure Toothpicks

number and number of

toothpicks used in each

figure.

Construct the next figure in

this pattern. Record your results.

Repeat Step 3 until you have found the next four

figures in the pattern.

the Results

1. How many additional toothpicks were used each time to form the
   next figure in the pattern? Where is this pattern found in the table?


2. Based on your answer to Exercise 1, how many toothpicks would
   be in Figure 0 of this pattern?


3. Remove one toothpick from your pattern so that

Figure 1

Figure 1 is made up of just three toothpicks as shown.

Then create a table showing the number of toothpicks

that would be in the first 7 figures by using the same

pattern as above.

4. How many toothpicks would there be in Figure n of this new
   pattern?


5. How could you adapt the expression you wrote in Exercise 4 to
   find the number of toothpicks in Figure n of the original pattern?


6. MAKE A PREDICTION How many toothpicks would there be in
   Figure 10 of the original pattern? Explain. Then check your
   answer by constructing the figure.

Main Idea

Explore patterns in

sequences of

geometric figures.

044_050_C1_L2_895130.indd 50 12/29/09 12:22 PM