Mathematics, Part 11
Question 1: Define exponent and explain its use, particularly for squared and cubed numbers.
Answer 1: An exponent is the superscript number placed next to another number at the top right to indicate how many times the number is multiplied by itself. Exponents provide a shorthand way to write a mathematical problem.If the exponent is 2, then the number is multiplied by itself twice, or squared; that is a² = a * a. For example: 2² = 2 * 2 =4; 3² = 3 * 3 = 9If the exponent is 3, then the number is multiplied by itself three time, or cubed, that is a³ = a * a * a. For example: 2³ = 2 * 2 * 2 = 8; 3³ = 3 * 3 * 3 = 27.The value of a number raised to an exponent is called its power. So, 84 is said to be 8 to the 4th power, or 8 is raised to the power of 4.
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Question 2: List the laws of exponents.
Answer 2: The laws of exponents are…Any number to the power of 1 is equal to itself; that is, a1 = a.The number 1 raised to any power is equal to 1; that is, 1n = 1.Any number raised to the power of 0 is equal to 1; that is a0 = 1.Add exponents to multiply powers of the same base number; that is, an * am = an+m with a as the base number and n and m representing any exponent value.Subtract the exponents to divide powers of the same number; that is an ÷ am = an-m.Multiply the exponent to raise a power to a power; that is (an)m = an*m.Raise each number in the expression to the power to raise a multiplication or division expression to a power; that is, (a * b)n = an * bm and (a/bm) = am /bm.Fractional exponents can be multiplied and divided like other exponents; for example, 5¼ * 5¾ = 5¼ + ¾ = 51 = 5.
Question 3: Describe a teaching strategy that can help build number sense among students.
Answer 3: It is important to think flexibly to develop number sense. Therefore, it is imperative to impress upon students that there is more than one right way to solve a problem. Otherwise, students will try to learn only one method of computation, rather than think about what makes sense or contemplate the possibility of an easier way. Some strategies for helping students develop number sense include the following:Frequently asking students to make their calculations mentally and rely on their reasoning ability. Answers can be checked manually afterwards, if needed. Having a class discussion about solutions the students found using their minds only and comparing the different approaches to solving the problem. Have the students explain their reasoning in their own words.Modeling the different ideas by tracking them on the board as the discussion progresses. Presenting problems to the students that can have more than one answer.
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