Standards

Common Core State Standards, Grade 8 Mathematics:

Shown with checks, the following chart shows in which chapters the grade 8 mathematics standards are first addressed.

Due to the nature of this course, the shaded portion following a check, represents the chapters which either include further development of that standard, or are directly or indirectly a result of that standard appearing previously.

Descriptions of the CCSS can be found at http://www.maine.gov/education/lres/math/standards.html#ccss .

Note, chapter 13 and the appendix, are both still under construction.

Below are the chapters in which the following High School Common Core State Standards are first addressed.

Additional geometry standards, which were embedded in the 2016-17 school year, are currently not shown here.

Common Core State Standards

For Mathematical Practices:

Due to the nature of this book, there will be plenty of opportunities to connect the standards for mathematical practices with the content.

1 Make sense of problems and persevere in solving them.

For example, in chapter 2, learners will be challenged to create a ghost made solely out of parabolas, where they will have to “analyze givens, constraints, relationships, and goals”, “make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt”, “try special cases and simpler forms of the original problem in order to gain insight into its solution”, and “monitor and evaluate their progress and change course if necessary.”

2 Reason abstractly and quantitatively.

For example, in chapter 1, learners will be challenged to discover what it means to add and multiply polynomials by each other, where they will have to “bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize - to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to the referents - and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved”, and create a “coherent representation of the problem at hand”, “attending to the meaning of quantities”, and use “different properties of operations and objects.”

3 Construct viable arguments and critique the reasoning of others.

For example, in chapter 3, collaborating learners will be challenged to discover how many solutions a polynomial equation can have, where they will have to “understand and use stated assumptions, definitions, and previously established results in constructing arguments”, “make conjectures and build a logical progression of statements to explore the truth of their conjectures”, “recognize and use counterexamples”, “justify their conclusions”, and “respond to the arguments of others.”

4 Model with mathematics.

For example, in chapter 7, learners will be challenged to solve a civil engineering problem, where they will have to “apply the mathematics they know to solve problems”, “identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas”, “interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.”

5 Use appropriate tools strategically.

For example, in chapter 8, learners will be challenged to discover the three possible outcomes for the solution of a system of two linear equations, where they will have to “analyze graphs of functions and solutions”, “visualize the results of varying assumptions, explore consequences, and compare predictions with data”, and “use technological tools to explore and deepen their understanding of concepts.”

6 Attend to precision.

For example, in chapter 6, collaborating learners will be challenged to write a proof for the Pythagorean Theorem, where they will have to “communicate precisely to others”, “use clear definitions in discussion with others and in their own reasoning”, “state the meaning of the symbols they choose”, and “examine claims and make explicit use of definitions.”

7 Look for and make use of structure.

For example, in chapter 4, learners will be challenged to derive a method for determining the roots of any quadratic equation, where they will have to “look closely to discern a pattern or structure”, “step back for an overview and shift perspective”, and “see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.”

8 Look for and express regularity in repeated reasoning.

For example, in chapter 9, learners will be challenged to convert square roots to continued fractions, where they will have to “notice if calculations are repeated, and look for general methods and for shortcuts”, “maintain oversight of the process, while attending to the details”, and “continually evaluate the reasonableness of their intermediate results.”