Mathematics can be used to describe patterns. in the world

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Presentation transcript:

Mathematics can be used to describe patterns. in the world Mathematics can be used to describe patterns in the world. Scientists use math to describe various aspects of life, including how cells multiply, how objects move through space, and how chemicals react. Often, when scientists try to describe these patterns, they need to describe something that changes or varies. Scientists call the quantities that change variables, and they represent them using letters and symbols.

In this course, you will spend time learning In this course, you will spend time learning about variables, what they can represent, and how they serve different purposes. To start, you will use variables to describe the dimensions and areas of different shapes. You will begin to organize the descriptions into algebraic expressions. As you work with your teammates, use these questions to help focus your team’s discussion: How can you organize groups of things? What is the area? Which lengths can vary?

4-71. When a collection of algebra tiles is described with mathematical symbols, it is called an algebraic expression. Take out the tiles shown in the picture. Then work with your team to do the following tasks. Use mathematical symbols (numbers, variables, and operations) to record the area of this collection of tiles. Write at least three different algebraic expressions that represent the area of this tile collection.

4-72. The expressions that you have written to represent area and perimeter are made up of terms that are separated by addition and subtraction. a. b. c.

4-74. The expressions that you have written to represent area and perimeter are made up of terms that are separated by addition and subtraction. a. Write an expression for the perimeter of the figure below: b. How many x lengths are represented in the expression in part (a)? How many unit lengths? c. Combining like terms (like terms contain the same variable raised to the same power) is a way of simplifying an expression. Rewriting the perimeter of the shape above as P = 4x + 6 combines the separate x‑terms as 4x and combines the units in the term 6.

Practice/Exit Ticket 4.3.1 2x2 + 6x + 10 4. 8x2 + 3 + 4x2 + 2x + 3 + 4x2 + 5x + 4 4x2 – 7x + 3 5. 2a2 + 3a3 - 4a2+ 6a + 12- 4a + 2 + 2x2 – 2x – 5 5x + 6 + 5x2 + 6x – 2