Curriculum Benchmarks

Grade 7 – Math

In Mathematics students will learn to:

Work flexibly and fluently with fractions, decimals, and percents to solve problems
Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line
Develop meaning for percents greater than 100 and less than 1
Represent numbers in scientific notation (positive powers only) and use that notation in problems
Understand and use ratios and proportions to solve unit rate, scale and map problems
Use factors, multiples, prime factorization, and relatively prime numbers to solve problems
Develop meaning for integers and represent and compare quantities with them
Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers
Use the properties of numbers to simplify computations with integers, fractions, and decimals
Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems
Select appropriate methods and tools for computing with rational numbers from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods

Represent, model, analyze, and generalize a variety of patterns and problems with tables, graphs, words, diagrams and equations and compare the different representations
Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations
Evaluate simple algebraic expressions for given variable values
Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships
Compare positive rate of change to a negative rate of change
Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations, with particular attention to proportional relationships

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects and between the number of sides and the sum of the interior angles of a polygon
Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling
Identify attributes of three-dimensional figures
Graph points and identify coordinates of points in all four quadrants
Use ruler, protractor, and compass to draw polygons and circles
Demonstrate an understanding of the relationships of angles formed by intersecting lines

Understand both metric and customary systems of measurement
Convert from one unit to another both within the same system and between systems using formulas
Select and apply techniques, formulas, units and tools to accurately find length, area, volume, and angle measures
Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles
Find the area of more-complex shapes
Determine the surface area and volume of selected prisms, pyramids, and cylinders
Solve problems involving rates and scale factors

Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population
Use Venn diagrams, stem-and-leaf plots, tables and charts to describe and analyze data
Use measures of central tendency (M/M/M) and spread (range) to compare data
Use tree diagrams, tables, organized lists and area models to compute simple compound probabilities