MINNESOTA GRADE 7 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 positive and negative rational numbers, represented in a
variety of ways, to quantify information and to solve real-world and
mathematical problems.
The student will:
1. Represent rational numbers as fractions, mixed numbers, decimals or percents and convert among various forms as appropriate.
2. Use scientific notation with positive powers of 10, with appropriate
treatment of significant digits, to solve real-world and mathematical
problems.
3. Locate and compare positive and negative rational numbers on a number line.
B. Computation and Operation
Standard: Compute fluently and make reasonable estimates with rational
numbers in real-world and mathematical problems. Understand the
meanings of the basic operations, including the use of integer
exponents and square roots, and how the operations relate to one
another. Appropriately use calculators and other technologies to solve
problems.
The student will:
1. Add, subtract, multiply and divide fractions and mixed numbers.
2. Use the inverse relationship between extracting square roots and
squaring positive integers to solve real-world and mathematical
problems.
3. Calculate the percentage of increase and decrease of a quantity in real-world and mathematical problems.
4. Convert among fractions, decimals and percents and use these
representations for estimations and computations in real-world and
mathematical problems.
5. Understand and compute positive integer powers of nonnegative
integers and express examples as repeated multiplication such as 3^4 =
3 x 3 x 3 x 3 = 81.
6. Apply the correct order of operations and grouping symbols when using calculators and other technologies.
7. Know, use and translate calculator notational conventions to mathematical notation.
8. 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: Demonstrate an understanding of rate of change graphically and numerically.
The student will:
1. Demonstrate, numerically and graphically, an understanding that rate
is a measure of change of one quantity per unit change of another
quantity in real-world and mathematical problems.
2. Plot points on the graph of a linear function and identify the slope or rate of change.
B. Algebra (Algebraic Thinking)
Standard: Apply arithmetic operations in the correct order to generate
equivalent algebraic expressions and to solve simple formulas in
real-world and mathematical problems.
The student will:
1. Apply the correct order of operations including addition,
subtraction, multiplication, division and grouping symbols to generate
equivalent algebraic expressions.
2. Use the facts that the sum of a number and its opposite is zero and
the product of a number and its reciprocal is one to generate
equivalent algebraic expressions.
3. Solve simple formulas with up to three variables, when the values of two of the variables are given.
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 simple scatter plots.
2. Understand the meaning of, and be able to compute minimum, maximum, range, median, mean and mode 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. Express probabilities as percentages, fractions, proportions and decimals.
2. Use a variety of experiments to explore the relationship between experimental and theoretical probabilities.
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. Recognize a view of a three-dimensional shape, given a view from a different orientation.
2. Use visual representations of transformations such as reflections,
rotations, translations and change of scale in one and two dimensions
to solve real-world and mathematical problems.
B. Geometry
Standard: Use basic geometric principles and proportional reasoning to solve real-world and mathematical problems.
The student will:
1. Calculate the radius, diameter, circumference and area of a circle given any one of these.
2. Calculate the area and perimeter of a sector of a circle given its angle and radius.
3. Use ratios and proportions to interpret map scales and scale drawings.
4. Classify quadrilaterals as squares, rectangles, rhombi, parallelograms, kites, trapezoids or none of these.
C. Measurement
Standard: Make calculations of time, length, area and volume within
standard measuring systems using good judgment in choice of units.
The student will:
1. Choose appropriate units to calculate, measure, and record length,
weight, area and volume in both U.S. customary and metric systems.
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