Middle School Math (Grade 8)

Student Learnings: What students should know and be able to do

Mathematical Reasoning Standard

• Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands.
• Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of a solution in a given context.
• Appropriately use examples and counterexamples to make and test conjectures, justify solutions and explain results.
• Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.
• Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.
• Determine whether or not relevant information is missing from a problem.
• Use accurately common logical words and phrases such as “and,” “or,” “if … then …,” “unique,” “only if.”

Number Sense Standard

• Use rational and irrational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.
• Use scientific notation with positive and negative powers of 10, with appropriate treatment of significant digits, to solve real-world and mathematical problems.
• Represent and compare rational and irrational numbers symbolically and on a number line.

Computation and Operation Standard

• Compute fluently and make reasonable estimates with rational and irrational numbers in real-world and mathematical problems.
• Understand the meanings of the basic operations, including the use of integer exponents and n^th roots, and how the operations relate to one another.
• Appropriately use calculators and other technologies to solve problems.
• Find integer approximations of square roots of positive integers without a calculator.
• Use the inverse relationship between n^th roots and n^th powers of rational numbers to solve real-world and mathematical problems.
• Multiply and divide expressions involving exponents with a common base.
• Use calculator approximations of irrational and rational numbers in multi-step real-world and mathematical problems.
• Apply the correct order of operations and grouping symbols when using calculators and other technologies.
• Know, use and translate calculator notational conventions to mathematical notation.
• Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.
• Use rational and irrational numbers to solve real-world and mathematical problems.
• Classify numbers as rational or irrational.

Patterns and Functions Standard

• Understand and describe progressions.
• Use graphs and tables to solve real-world and mathematical problems.
• Recognize when a list of numbers forms an arithmetic or geometric progression and be able to determine subsequent terms in the progression.
• Represent quantitative relationships graphically and use the graphs to solve real-world and mathematical problems
• Generate a table of values from a formula and graph the resulting ordered pairs on a grid.
• Use simple formulas with more than one variable to solve real-world and mathematical problems.

Algebraic (Algebraic Thinking) Standard

• Use algebraic operations to generate equivalent expressions, and use proportional reasoning to solve real-world and mathematical problems.
• Demonstrate the ability to manipulate an equation by applying arithmetic operations to both sides to maintain equivalence.
• Multiply and divide expressions of the form axⁿ.
• Apply the correct order of operations including addition, subtraction, multiplication, division, grouping symbols and powers, to simplify and evaluate algebraic expressions.

Measurement Standard

• Make calculations of time, length, area and volume within and between standard measuring systems using good judgment in choice of units.
• Find approximate equivalent measures of length, temperature and weight for common units in U.S. customary and metric measuring systems.
• Use arithmetic to solve simple real-world and mathematical problems involving mixed units such as minutes and hours in elapsed time, degrees and minutes in latitude and longitude and feet and inches in distance.
• Use proportions and percents with one unknown quantity to solve real-world and mathematical problems.

Spatial Sense Standard

• Recognize the relationship between different representations of two- and three-dimensional shapes.
• Understand the effect of various transformations.
• Use models and visualization to understand and create various two-dimensional diagrams of three-dimensional shapes.
• Predict the position and orientation of simple three-dimensional geometric shapes under transformations such as reflections, rotations and translations.
• Apply the relationship between changes in one or more linear distances in a planar figure and the change in area.
• Use the concept of similarity in simple two-dimensional figures to solve real-world and mathematical problems involving proportionality.
• Know how to find the volumes of cubes, prisms, spheres and cylinders.
• Know how to find the surface areas of cubes, prisms and cylinders.
• Calculate perimeter and area of two-dimensional figures obtained by putting together triangles, parallelograms, and sectors of circles to solve real-world and mathematical problems.

Geometry Standard

• Use basic geometric principles and proportional reasoning to solve real-world and mathematical problems.

Data and Statistics Standards

• Represent data and use various measures associated with data to draw conclusions and identify trends
• Compute the quartiles of a data set.
• Construct and analyze histograms, circle graphs, stem-and-leaf plots and box-and-whisker plots.

Probability Standard

• Calculate and express probabilities numerically and apply probability concepts to solve real-world and mathematical problems.
• Understand that if p is the probability of an event occurring, then 1 – p is the probability of the event not occurring.
• Convert between odds and probabilities.
• Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the effect of sample size on this relationship.

Instructional resources used for this curriculum:

Copyright 2004, Holt Rinehart Winston Publishing
Middle School Mathematics, Course 3