Seventh Grade Standards for Mathematics
Minimum Standards Set
In this document we have listed things students should be able to explain and tasks students should be able to perform. True mathematical literacy includes the capacity to perform simple computations in the mind, more complex computations with traditional algorithms, and computations with large numbers or complex arithmetic with a computing device and have sense of whether or not the result is correct. Students will be expected to give sound mathematics reasons for the decisions they make in computations and in problem solving. The goal is to have the students think above the knowledge and skill level and be able to do higher order or critical thinking. To accomplish this, we urge that teachers be trained in how to let students do critical thinking and not make the mistake of doing it for the students under the assumption that the students cannot do it.
The instruction should require the student to know how to do these things:
- Use mathematics to solve “real life” problems.
- Have a strategy to solve problems that requires the student to select data that is essential to solve the problem, have a plan of attack to find the solution to the problem, perform any necessary calculations or operations to find the solution, determine if the solution is reasonable and correct, and be requires the student to be able to justify the steps taken in the solution process.
- Develop a way to use mathematics to express relationships by using such approaches as symbols, diagrams, graphs, mathematical language, manipulatives, technology, text, or real objects.
- Use the skills learned in number three to justify and defend a solution to a problem.
Number and Operations: The student is expected to—
- Represent and use rational numbers in various forms including integers, common and decimal fractions, mixed numbers, ratios, percent, and scientific notation.
- Perform calculations of addition, subtraction, multiplication and division for any form of rational numbers and use this ability to solve real world problems.
- Know the properties of rational numbers including the identities, the inverses, commutative and associative, and distributive properties and use these to simplify expressions and solve equations.
- Define and illustrate natural number exponents, the zero exponent and negative integer exponents and simplify expressions using the rules of exponents.
Proportionality: The student is expected to—
- Recognize and use constant rates of change seen in real world circumstances including d=rt, C=πd displayed in pictorial, tabular, numeric, graphical, and algebraic representations.
- Be able to determine unit rates and constants of proportionality from information found in mathematical and real-world problems.
- Find solutions to multi-step problems that involve ratios, rates, percents, percent of increase and percent of decrease.
- Use proportions to demonstrate similarity in geometric figures and to solve problems involving similar figures.
- Recognize that probability uses the properties of ratios and proportions and use these to make predictions.
- Represent and simulate simple and compound events using lists, tree diagrams and technology.
- Make predictions and determine solutions using experimental data or theoretical probability for simple and compound events.
- Find the probabilities of a simple event and its complement, and experimental and theoretical probabilities related to simple and compound events using different methods.
Geometry: Student will be able to:
- Identify the parts of both plane and solid figures.
- Use formulas to find the perimeters and areas of plane figures as well as the surface area and volume of solid figures and solve problems involving formulas for the volume and surface area of prisms, pyramids, cylinders, cones and spheres.
- Recognize and explain the relationship between prisms and pyramids as well as cylinders and cones with congruent bases and heights.
- Describe the relationship between lines and transversals and be able to determine how these can be used to determine if lines are parallel.
- Recognize the properties of congruent figures and use these properties to solve problems related to such figures.
- Determine the perimeter and area of composite plane figures composed of combinations of parallelograms, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles.
- Use modeling and investigation to determine formulas for circumference and area of a circle and use the formulas for solving problems related to the circumference and area of a circle.
Functions and equations: The student will be able to:
- Demonstrate whether or not a graph displays a function relationship.
- Describe which element of pair of values is the independent and which is dependent.
- Recognize and explain the difference between direct and inverse variation functions and show examples from geometric formulas where possible.
- Write equations of linear functions in slope intercept form and be able to state which part of the equation describes the slope and which part of the equation describes the y-intercept.
- Write one variable equations and inequalities to represent conditions within problems, solve the sentence, determine if the solution is true and represent the solution(s) on a number line.