8th Grade Chapter 6: Statistics - Patterns of Association in Bivariate Data - Mathematical Foundation
8th Grade Chapter 6: Statistics - Patterns of Association in Bivariate Data - Student Workbook
8th Grade Chapter 7: Rational and Irrational Numbers - Mathematical Foundation
8th Grade Chapter 7: Rational and Irrational Numbers - Student Workbook
8th Grade Chapter 8: Integer Exponents, 3D Measurement Problems - Mathematical Foundation
8th Grade Chapter 8: Integer Exponents, 3D Measurement Problems - Parent Workbook
8th Grade Chapter 8: Integer Exponents, 3D Measurement Problems - Student Workbook
8th Grade Chapter 8: Integer Exponents, 3D Measurement Problems - Teacher Workbook
8th Grade Chapter 9: Geometry I - Transformations, Congruence, Similarity - Mathematical Foundation
8th Grade Chapter 9: Geometry I - Transformations, Congruence, Similarity - Parent Workbook
8th Grade Chapter 9: Geometry I - Transformations, Congruence, Similarity - Student Workbook
8th Grade Chapter 9: Geometry I - Transformations, Congruence, Similarity - Student Workbook - Editable
Middle School Math: 8th Grade Textbook - Complete Student Workbook
This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.
This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles. The solution provided (among other possibilities) uses the SAS trial congruence theorem, and the fact that opposite sides of parallelograms are congruent.
The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.
This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.
The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.
In "Adding and Subtracting Algebraic Expressions" students will learn to: identify the terms in algebraic expressions, identify like terms in algebraic expression, identify the special types of polynomials called monomials, binomials and trinomials and add and subtract any type of polynomials.
In "Exponents" students will learn to: identify expressions in simplified standard form, use the rules for exponents to simplify expression and use the rules of exponents to divide a polynomial by a monomial.