GRADE 7
All students complete the standards below. In addition, Pre‑Algebra students
study concepts and build skills in more depth, complexity, and breadth as
preparation for Algebra in grade 8.
1. Students know the properties of, and compute with,
rational numbers expressed in a variety of forms:
1.1 Read, write, and compare rational numbers in scientific notation, approximate numbers using scientific notation
1.2 Add, subtract, multiply, and divide rational numbers, integers, fractions, and decimals and take rational numbers to whole number powers
1.3 Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use
1.4 Convert fractions to decimals and percents and use these representations in estimation, computation, and application (i.e. discounts, commission, simple/compound interest)
1.5 Differentiate between rational and irrational numbers
1.6 Know that every fraction is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions
2.
Calculate the percentage of increases and decreases of a quantity
3.
Reason
proportionally to solve problems involving equivalent fractions to equal
ratios.
4. Students use exponents, powers, and roots and use
exponents in working with fractions:
4.1 Understand the meaning of the absolute value of a number, interpret it as the distance of the number from zero on a number line and determine the absolute value of real numbers
Algebra and Functions
1. Students express quantitative relationships by using
algebraic terminology, expressions, equations, inequalities, and graphs:
1.1 Use symbolic algebra to represent situations and to solve problems, especially those that represent linear relationships
1.2 Use variables and appropriate operations to write an expression, equation, or a system of equations which represent a verbal description
1.3 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2
1.4 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative)
1.5 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly
1.6 Represent quantitative relationships graphically and interpret the
meaning of a specific part of a graph in the situation represented by the graph
2. Students
interpret and evaluate expressions involving integer powers and simple roots:
2.1 Interpret
positive whole-number powers as repeated multiplication and negative
whole-number powers as repeated division or multiplication by the
multiplicative inverse. Simplify and evaluate expressions that include
exponents
3. Students
graph and interpret linear and some non-linear functions:
3.1 Graph
linear functions, noting that the vertical change per unit horizontal change is
always the same and know that the ratio is called the slope of the graph
4. Students
solve simple linear equations over the rational numbers:
4.1 Solve two-step linear equations in one variable over the rational numbers, interpret the solutions in terms of the context from which they arose and verify the reasonableness of the results
4.2 Solve
multi-step problems involving rate, average speed, distance, and time, or
direct variation
1. Students
choose appropriate units of measure and use ratios to convert within and
between measurement systems to solve problems:
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters)
1.2 Construct and read drawings and models made to scale
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer
2. Students
compute the perimeter, area, and volume of common geometric objects and use
these to find measures of less common objects; they know how perimeter, area,
and volume are affected under changes of scale:
2.1 Use formulas for finding the perimeter and areas of basic two-dimensional figures and for the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and circular cylinders
2.2 Estimate
and compute the area of more complex or irregular two- and three dimensional
figures by breaking them up into
more basic objects
3. Students
deepen their understanding of plane and solid geometric shapes by constructing
figures that meet given conditions and by identifying attributes of figures:
3.1 Identify basic elements of geometric figures (e.g. altitudes, diagonals, radii, diameters, and chords of circles)
3.2 Demonstrate an understanding of when two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures
3.3 Identify elements of three-dimensional geometric objects and how two or more objects are related in space
Data Analysis and Probability
1. Students
collect, organize, and represent data sets that have one or more variables and
identify relationships among variables within a data set:
1.1 Know various forms of display for data sets, including stem and leaf plot or box and whisker plot; use them to display a single set of data or compare two sets of data
1.2 Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and whether there is an apparent relationship between the two variables
2. Students recognize equally likely outcomes, construct
sample spaces, and determine probabilities of events:
2.1 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one even following another, in independent trials, is the product of the two probabilities
2.2 Understand the difference between independent and dependent events and how this affects the results for specific probability situations
3. Students
make predictions based on experimental or theoretical probability.
Problem Solving and Mathematical Reasoning
1. Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns
1.2 Formulate and justify mathematical conjectures based on a general
description of the mathematical question or problem posed
1.3 Determine when and how to break a problem into simpler parts
2. Students
use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results
2.2 Apply strategies and results from simpler problems to more complex problems
2.3 Make and test conjectures by using both inductive and deductive reasoning
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models to explain mathematical reasoning
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy
2.7 Make
the precise calculations and check validity of the results from the context of
the problem
3. Students determine a solution is complete and move
beyond a particular problem by generalizing to other situations:
3.1 Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tool
3.2 Evaluate the reasonableness of the solution in the context of the original situation
3.3 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems
3.4 Develop
generalizations of the results obtained and apply them in other circumstances
3.5 Use the language of mathematics to express mathematical ideas precisely