## Exploring Patterns Homework 1 Answer Key BEST

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How to Solve Exploring Patterns Homework 1

Exploring patterns is a topic that involves observing, analyzing, and predicting different types of patterns in mathematics. In this article, we will show you how to solve some of the problems from Exploring Patterns Homework 1, which you can find here.

Problem 1: Observing Patterns

In this problem, you are given four patterns of shapes and you have to draw the next three terms for each pattern. You also have to explain how you found the next terms. Here are some possible solutions:

Pattern 1: To find the next term, you have to add one more circle to the right of the previous term. So, the next three terms are:

Pattern 2: To find the next term, you have to add one more square to the bottom of the previous term. So, the next three terms are:

Pattern 3: To find the next term, you have to rotate the previous term by 90 degrees clockwise. So, the next three terms are:

Pattern 4: To find the next term, you have to flip the previous term horizontally. So, the next three terms are:

Problem 2: Analyzing Patterns

In this problem, you are given three patterns of tiles and you have to answer some questions about them. You also have to explain your reasoning. Here are some possible solutions:

How many white tiles will be in Design 5 of the pattern Explain your reasoning.

Answer: There will be 9 white tiles in Design 5 of the pattern. To find the number of white tiles in each design, you can use the formula n^2 - n + 1, where n is the design number. For example, in Design 3, there are 3^2 - 3 + 1 = 7 white tiles. So, in Design 5, there will be 5^2 - 5 + 1 = 9 white tiles.

How many shaded tiles will be in Design 5 of the pattern Explain your reasoning.

Answer: There will be 16 shaded tiles in Design 5 of the pattern. To find the number of shaded tiles in each design, you can use the formula n^2 - (n^2 - n + 1), where n is the design number and (n^2 - n + 1) is the number of white tiles from the previous question. For example, in Design 3, there are 3^2 - (3^2 - 3 + 1) = 9 shaded tiles. So, in Design 5, there will be 5^2 - (5^2 - 5 + 1) = 16 shaded tiles.

Problem 3: Predicting Patterns

In this problem, you are given some scenarios that involve patterns and you have to predict what will happen next. You also have to show your work. Here are some possible solutions:

Gregory has a vegetable garden. This year, he gives two tomato plants to friends. Next year, those two friends each give away two tomato plants. The following year, those four friends give away two tomato plants. How many tomato plants have been given away Show your work.

Answer: A total of 30 tomato plants have been given away. To find the number of tomato plants given away each year, you can use the formula

2^(n-1) * 2, where n is the year number. For example, in year 1, Gregory gives 9160f4acd4

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