 | | | | | MINNESOTA GRADE 8 STANDARDS
These standards and benchmarks are to be used as a source document for
identifying what all students should know and be able to do to
demonstrate mathematical proficiency. To determine grade level
placement of specific standards and benchmarks, judgment by experienced
teachers was used to determine at what grade level 80% of children
would master the specific material. The current document
identifies the grade at which mastery of each concept is expected but
does not identify when those concepts are introduced and reinforced.
Schools must determine where in their curriculum these concepts would
be introduced and reinforced so that they may be assessed at the
indicated grade level.
Teachers must develop and enrich students’ knowledge of mathematics
beyond what is outlined in this document. It is critical for teachers
to recognize the entire progression of standards and benchmarks before
and after their grade level.
I. MATHEMATICAL REASONING
Standard: Apply skills of mathematical representation, communication
and reasoning throughout the remaining four content strands.
Note about assessment of this standard: The Mathematical Reasoning
standards will primarily be assessed within the context of the
standards in the remaining four content strands. The depth of
mathematical reasoning will increase as the skill level in the four
other strands increases.
The student will:
1. 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.
2. Appropriately use examples and counterexamples to make and test conjectures, justify solutions and explain results.
3. 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.
4. Support mathematical results by explaining why the steps in a
solution are valid and why a particular solution method is appropriate.
5. Determine whether or not relevant information is missing from a problem.
6. Use accurately common logical words and phrases such as “and,” “or,” “if … then …,” “unique,” “only if.”
II. NUMBER SENSE, COMPUTATION AND OPERATIONS
A. 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.
The student will:
1. Represent and compare rational and irrational numbers symbolically and on a number line.
2. Use rational and irrational numbers to solve real-world and mathematical problems.
3. Use scientific notation with positive and negative powers of 10,
with appropriate treatment of significant digits, to solve real-world
and mathematical problems.
4. Classify numbers as rational or irrational.
B. 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 nth roots, and how the operations relate to one
another. Appropriately use calculators and other technologies to solve
problems.
The student will:
1. Use calculator approximations of irrational and rational numbers in multi-step real world and mathematical problems.
2. Find integer approximations of square roots of positive integers without a calculator.
3. Multiply and divide expressions involving exponents with a common base.
4. Use the inverse relationship between nth roots and nth powers of
rational numbers to solve real-world and mathematical problems.
5. Apply the correct order of operations and grouping symbols when using calculators and other technologies.
6. Know, use and translate calculator notational conventions to mathematical notation.
7. Understand that use of a calculator requires appropriate
mathematical reasoning and does not replace the need for mental
computation.
III. PATTERNS, FUNCTIONS AND ALGEBRA
A. Patterns and Functions
Standard: Understand and describe progressions. Use graphs and tables to solve real world and mathematical problems.
The student will:
1. Recognize when a list of numbers forms an arithmetic or geometric
progression and be able to determine subsequent terms in the
progression.
2. Represent quantitative relationships graphically and use the graphs to solve realworld and mathematical problems.
3. Generate a table of values from a formula and graph the resulting ordered pairs on a grid.
B. Algebra (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.
The student will:
1. Multiply and divide expressions of the form axn.
2. Use simple formulas with more than one variable to solve real-world and mathematical problems.
3. Use proportions and percents with one unknown quantity to solve real-world and mathematical problems.
4. Apply the correct order of operations including addition,
subtraction, multiplication, division, grouping symbols and powers, to
simplify and evaluate algebraic expressions.
IV. DATA ANALYSIS, STATISTICS, AND PROBABILITY
A. Data and Statistics
Standard: Represent data and use various measures associated with data to draw conclusions and identify trends.
The student will:
1. Construct and analyze histograms, circle graphs, stem-and-leaf plots and box-and-whisker plots.
2. Compute the quartiles of a data set.
B. Probability
Standard: Calculate and express probabilities numerically and apply
probability concepts to solve real-world and mathematical problems.
The student will:
1. Understand that if p is the probability of an event occurring,
then 1 - p is the probability of the event not occurring.
2. Convert between odds and probabilities.
3. Use a variety of experiments to explore the relationship between
experimental and theoretical probabilities and the effect of sample
size on this relationship.
V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT
A. Spatial Sense
Standard: Recognize the relationship between different representations
of two- and three-dimensional shapes. Understand the effect of various
transformations.
The student will:
1. Use models and visualization to understand and create various two-dimensional diagrams of three-dimensional shapes.
2. Predict the position and orientation of simple three-dimensional
geometric shapes under transformations such as reflections, rotations
and translations.
B. Geometry
Standard: Use basic geometric principles and proportional reasoning to solve real-world and mathematical problems.
The student will:
1. Apply the relationship between changes in one or more linear distances in a planar figure and the change in area.
2. Use the concept of similarity in simple two-dimensional figures to
solve real-world and mathematical problems involving proportionality.
3. Know how to find the volumes of cubes, prisms, spheres and cylinders.
4. Know how to find the surface areas of cubes, prisms and cylinders.
5. 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.
C. Measurement
Standard: Make calculations of time, length, area and volume within and
between standard measuring systems using good judgment in choice of
units.
The student will:
1. Find approximate equivalent measures of length, temperature and
weight for common units in U.S. customary and metric measuring systems.
2. 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.
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