Lesson Sixteen - Adding & Subtracting Integers
The study of integers begins here. First the rationale for negative numbers is discussed. This includes examples using signed (or directed) numbers in practical situations.
The rules for adding integers are discovered using examples of travel on a north/south highway. Using the graphic representation of subtraction developed in Lesson 1, the rule for subtracting integers is developed. The order of operations is then applied to addition and subtraction of integers.
You Will Learn
- To compare integers.
- To add integers.
- To subtract integers.
- To apply the rules for order of operations to problems involving the addition and subtraction of integers.
30 Minutes. Teaching guide and worksheet enclosed.
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Lesson Seventeen - Multiplication & Division of Integers
This lesson is in two parts. Rather than simply applying a rule for multiplication and division of integers, a logical approach uses what we know to develop a method for these computations. The PEMDAS process is applied to integer problems involving all four operations. The second part of this lesson introduces the square root. Various patterns involving square roots are investigated, leading to a method of finding the square root of any square number between zero and ten thousand.
You Will Learn
- The meaning of multiplication by a negative number.
- To multiply integers and divide integers.
- To apply the rules of order of operations to various integer problems.
- To verify if a given number between 0 and 10,000 is a square number and, if it is, to find the square root.
30 Minutes. Teaching guide and worksheet enclosed.
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Lesson Eighteen - Negative & Fractional Powers
This lesson deals with negative and fractional powers. Through a discovery process, the meaning of the negative power as a reciprocal is developed. The order of operations for problems with negative exponents is discussed.
Utilizing what we know about exponents, the meaning of fractional powers is discovered. Negative fractional powers are explained based on what has already been learned in this lesson. Finally, powers of negative numbers are investigated to bring to a close the exploration of powers and roots.
You Will Learn
- To explain the meaning of a negative exponent.
- To explain the meaning of a fractional exponent.
- To explain the meaning of a negative fractional power.
- To simplify a negative base that is raised to a power.
30 Minutes. Teaching guide and worksheet enclosed
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Lesson Nineteen - Geometry 1
This program discusses the meaning of geometry and its usefulness. Basic geometric shapes are defined and the various dimensions are discussed. The subject of angles is investigated, with a look at the different types of angles and how to measure them.
Quadrilaterals are discussed, including the square, the rhombus, the parallelogram, the rectangle and the trapezoid. This leads to a discussion of area-what it measures and how we find the area of various quadrilaterals. Finally, volume is introduced and discussed.
You Will Learn
- To define point, line, plane, space, segment, ray, angle, and polygon.
- To measure an angle using a protractor.
- To classify a given quadrilateral as a square, rhombus, parallelogram, rectangle, or trapezoid.
- To compute the areas of a square, rectangle, and parallelogram.
- To compute the volumes of a cube and a rectangular prism.
30 Minutes. Teaching guide and worksheet enclosed.
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Lesson Twenty - Geometry 2
In this program, perimeter is defined and methods of computing the perimeter are discussed. Triangles are thoroughly investigated. Triangles are defined by angles and by sides. The formula for the area of a triangle is explained.
The circle is defined and the various parts of a circle are introduced. The circumference (or perimeter of the circle) is studied along with the circle's area. Common three-dimensional shapes such as the cube, the prism, the cylinder, the pyramid and the cone are examined.
You Will Learn
- To compute the perimeter of a figure given the length of its sides.
- To classify a triangle by type.
- To compute the area of a triangle given its base and height.
- Given the radius or diameter of a circle, you will compute its circumference and area.
- To classify a three-dimensional shape as a cube, prism, cylinder, pyramid, or cone.
30 Minutes. Teaching guide and worksheet enclosed. |
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