Practice - Algebra 1

7.2.5 Practice

7.2.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

Here are two patterns of dots.

Pattern A

Four figures, labeled step 0 through 3. Step 0, no dots. Step 1, row of 4 dots. Step 2, 2 rows of 4 dots each. Step 3, 3 rows of 4 dots each.

Pattern B

Four figures, step 0 through 3. Step 0, 2 dots. Step 1 row of 1 dot above a row of 2 dots. Step 2, 2 rows of 2 dots each, above a row of 2 dots. Step 3, 3 rows of 3 dots each, above row of 2 dots.

How many dots will there be in Step 4 of Pattern A?

How many dots will there be in Step 4 of Pattern B?

Which pattern shows a quadratic relationship between the step number and the number of dots?

Pattern A
Pattern B

Each expression represents the total number of dots in a pattern where $n$ represents the step number.

Select two expressions that represent a quadratic relationship between the step number and the total number of dots. (If you get stuck, consider sketching the first few steps of each pattern as described by the expression.)

$n^2$
$2n$
$n \cdot n$
$n+n$
$n+2$
$n \div 2$

Use the pattern below to answer the questions.

How many blocks are in Step 4?

How many blocks are in Step 5?

How many blocks are in Step $n$ ?

$(n+2)^2$
$(n+2)^2-n$
$n+6$
$n^2-2$