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**Expressions and Equations**

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Getting Started… Jenna knows that she wants to build square animal pens for her rabbits. If the pen she builds has a side length of 4 meters, what is the area of the pen? Show the equation and the answer with the correct units.

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**More Examples: Side Length Pen Picture Equation Area with units**

5 meters 6 meters

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What About Volume? If the pen is enclosed, what is the volume if the length of one side is 4 meters? Write the equation and the answer in the correct units.

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Vocabulary Exponent: the number of times that the _________ is being ________ by itself Base: the number that is being ___________ by itself repeatedly 25 is the same as saying __________ raised to the _________ power. 25 can be written as ___________________. 25 is equal to _______.

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Vocabulary Exponent: the number of times that the base is being multiplied by itself Base: the number that is being multiplied by itself repeatedly 25 is the same as saying two raised to the fifth power. 25 can be written as 2 x 2 x 2 x 2 x 2 25 is equal to 32.

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**Warm Up Complete the following table:**

Expression Expanded Form Standard Form 35 3x3x3x3x3 243 34 3 x 3 x 3 3 x 3 3

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Exponents or Factor

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Exponents, cont… The exponent of a number says how many times to use the number in a multiplication. In 82, the "2" says to use 8 twice in a multiplication problem, so 82 = 8 × 8 = 64 (8 is a factor of 64) Exponents are also called Powers or Indices. In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared."

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**Examples, cont… Example: 53 = 5 × 5 × 5 = 125**

53 = 5 × 5 × 5 = 125 In words: 53 could be called "5 to the third power,” "5 to the power 3" or simply "5 cubed." 24 = 2 × 2 × 2 × 2 = 16 In words: 24 could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th."

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**What if the Exponent is 1 or 0?**

If the exponent is 1, then you just have the number itself (example 91 = 9) If the exponent is 0, then you get 1 (example 90 = 1) But what about 00? It could be either 1 or 0, and so people say it is "indeterminate".

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Assignment Task: Certain biological cells quadruple (multiply by 4) each hour. Start with one cell at 2:00 and find out how many cells there will be by 5:00. Create a diagram or table to represent the cell growth. Include an equation using exponential notation.

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Challenge Every positive integer can be expressed as the sum of four or fewer squared numbers (Note: You can use the same integer more than once.) Examples: 5 = 101 = 170 = Write 83 as the sum of three square numbers.

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The Djinni’s Offer After opening an ancient bottle you find on the beach, a Djinni appears. In payment for his freedom, he gives you a choice of either 50,000 gold coins or one magical gold coin. The magic coin will turn into two gold coins on the first day. The two coins will turn into four coins total at the end of two days. By the end or the third day there will be eight gold coins total. The Djinni explains that the magic coins will continue this pattern of doubling each day for one moon cycle, 28 days. Which prize do you choose? When you have made your choice, answer these questions: The number of coins on the third day will be 2×2×2. Can you write another expression using exponents for the number of coins there will be on the third day? Write an expression for the number of coins there will be on the 28th day. Is this more or less than a million coins?

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The Offer Day Exp Notation # of Coins 1 2 3 4 5 6 15 20 28

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Warm Up: Evaluate 33 + (3-2) – 10 = [ – (5-2)] / 22 =

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Around the World Visit any station (no more than 2 people to a station) and solve the problem. Come to Ms. Willging to have your answer checked and get a stamp on your passport. Continue to visit “cities” and collect as many stamps as possible.

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**Warm Up Find the value of each: 32 – 22 = 24 ÷ 110 = 16/22 + 8 x 3 =**

32 – 22 = 24 ÷ 110 = 16/ x 3 = 5 x 32 – 72 ÷ 8 = Insert one set of parenthesis to make the statement true: 30 ÷ 21 – 6 x 4 = 8

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Warm Up If a paramecium (a single-celled organism) separates into two each day. How many paramecium would there be on day 6 (if you have just one on day 1)? Write an equation using exponents for this answer. Solve the following: y = 52 – /4 =

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