Question

1. draw the next three figures in this pattern. figures of squares what do you observe about this pattern? how many squares will be in the 9th figure of this pattern? ______ 6. sam is building a wall with legos. the 1st row is made of red legos, the 2nd row is made of blue legos, the 3rd row is made of red legos, and the 4th row is made of blue legos. is this a repeating pattern or a growing pattern? explain. 7. sydney is making a bracelet using different shaped beads. she uses a repeating pattern of o o ♥ o ★. if her bracelet includes 20 beads, how many heart beads will sydney use for her bracelet?

Explanation:

Problem 5 (Figure Pattern and 9th Figure Squares)

Step 1: Identify the Pattern for Squares

Looking at the first three figures (squares):

• 1st figure: \(1\times1 = 1\) square (since \(1^2 = 1\))
• 2nd figure: \(2\times2 = 4\) squares (since \(2^2 = 4\))
• 3rd figure: \(3\times3 = 9\) squares (since \(3^2 = 9\))

So the pattern is that the \(n\)-th figure has \(n^2\) squares.

Step 2: Calculate the 9th Figure

For the 9th figure, \(n = 9\). Using the pattern \(n^2\), we calculate \(9^2\).

\(9^2=9\times9 = 81\)

Problem 6 (Lego Wall Pattern)

A repeating pattern has a cycle that repeats, while a growing pattern increases in quantity/complexity. Here, the Lego rows alternate colors (red, blue, red, blue...). The row content (color) repeats every 2 rows, and there's no growth in the number of Legos per row (or other growing aspect) mentioned. So it's a repeating pattern because the color cycle (red, blue) repeats without any growth in elements like number of Legos per row.

Problem 7 (Bracelet Beads)

Step 1: Identify the Pattern Cycle

The repeating pattern is \( \bigcirc\bigcirc\heartsuit\bigcirc\bigstar \), which has 5 beads per cycle.

Step 2: Find Number of Cycles in 20 Beads

Total beads = 20. Number of cycles = \( \frac{20}{5}=4 \) cycles.

Step 3: Count Heart Beads per Cycle and Total

In each cycle, there is 1 heart bead (\(\heartsuit\)). For 4 cycles, total heart beads = \(1\times4 = 4\).

Answer:

s:

1. Number of squares in 9th figure: \(\boldsymbol{81}\)
2. It is a repeating pattern (explanation as above).
3. Number of heart beads: \(\boldsymbol{4}\)