Lesson Twenty One - Graphing in the Coordinate Plane
This program combines arithmetic and geometry to provide knowledge essential for success in algebra. The coordinate plane is introduced using the example of latitude and longitude. Identification of points as ordered pairs is examined, as is construction of a line though given points in the plane. Equations of the type y = ax + b are associated with lines, and the significance of the signs of "a" and "b" is discovered. This is the basis for understanding slope and y-intercept in algebra. The usefulness of this lesson is demonstrated by using a "fit" line to model data.
You Will Learn
- To plot the point associated with an ordered pair.
- Correctly identify the ordered pair for a point on the plane.
- To plot points and draw the line that is the graph of an equation of the form y = ax + b.
- To explain the effect of positive and negative values of "a" and "b" in
y = ax + b.
30 Minutes. Teaching guide and worksheet enclosed.
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Lesson Twenty Two - Number Theory
This program, entitled "Number Theory", investigates concepts in arithmetic that are of importance in algebra. The counting numbers are separated into prime numbers and composites. A simple method for finding the unique product of primes that produces a specific composite number is developed.
Prime factoring is used to find the GCF (greatest common factor) and LCM (least common multiple) of any set of numbers. The concept of relatively prime number is discussed.
You Will Learn
- To find the prime factorization of a composite number.
- The difference between a prime and a composite number.
- To compute the GCF of two or more numbers.
- To compute the LCM of two or more numbers.
30 Minutes. Teaching guide and worksheet enclosed.
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Lesson Twenty Three - Number Patterns 1
Studying number patterns is important for two reasons. First, they help one better understand the concepts of arithmetic and provide a basis for understanding the concepts of more complex mathematics (algebra, trigonometry, calculus). Second, pattern recognition is a useful problem-solving skill, both in mathematics and in real-world situations.
Patterns involving odd and even numbers are investigated. Patterns in multiples of certain numbers lead to an understanding of divisibility rules. Sequences are introduced to heighten sensitivity to patterns and the concept of function is introduced using patterns of number pairs.
You Will Learn
- To determine whether an addition problem will have an odd or even answer.
- To determine whether a multiplication problem has an odd or even answer.
- To state the divisibility rules for two, three, five, and nine.
- To find the next term in an arithmetic or geometric sequence, given the first three terms.
30 Minutes. Teaching guide and worksheet enclosed
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Lesson Twenty Four - Number Patterns 2
The basic operations of addition, subtraction, and cubing (raising to the third power) as well as three types of patterns involving whole numbers are introduced. The unexpected patterns found should amaze you and lead you to a sense of an underlying pattern to mathematics. Ultimately, mathematics can be seen as the study of patterns.
Addition is used to find palindromes. Subtraction is used to find "black holes". The addition of the cubes of the digits of a number lead to the discovery that there are only a few numbers which are the termination of the sequences of these sums.
You Will Learn
- To determine if a number is a palindrome.
- To use subtraction to find a "black hole".
- To add the cubes of the digits of a number.
- To use the "sum of the cubes of the digits" process to find a "lock".
30 Minutes. Teaching guide and worksheet enclosed.
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Lesson Twenty Five - Statistics
In this lesson we introduce the graphing calculator which has made possible the study of statistics earlier in a student's academic career. Statistics allows the student to see the usefulness of mathematics. Here, statistics is introduced using sets of data.
The data is analyzed to measure tendency and variation. The concept of outlier is introduced. The box plot, a graphic display of data, is used to compare sets of data. Qualitative analysis of data is discussed.
You Will Learn
- To find the mean of a set of numbers.
- To find the median of a set of numbers.
- Why the median is a better measure of tendency when the data contain extreme values.
- To compute the range of a set of data.
30 Minutes. Teaching guide and worksheet enclosed. |
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