Building the Language of Mathematics for Students

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Building the Language of Mathematics for Students

Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. The terms students should learn to use at each grade level with increasing precision are included in this document.

Mathematics can be thought of as a language that must be meaningful if students are to communicate mathematically and apply mathematic productively. Communication plays an important role in helping children construct links between their formal, intuitive notions and the abstract language and symbolism of mathematics; it also plays a key role in helping children make important connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas.

Curriculum and Evaluation Standards for School Mathematics, the National Council of Teachers of Mathematics (p. 26)
Mathematical vocabulary however should not be taught in isolation where it is meaningless and just becomes memorization. We know from research that meaningless memorization is not retained nor will it help build the deep understanding of the mathematical content. The students must be provided adequate opportunities to develop vocabulary in meaningful ways such as mathematical explorations and experiences. Students should be immersed into the mathematical language as they experience rich high-level tasks. As student communicate their thoughts, ideas, and justify the reasonableness of their solutions the mathematical language will begin to evolve. Student will then build the depth of understanding needed with mathematical vocabulary and content to empower them to be successful in mathematics.

Sixth Grade

Ratios and Proportional Relationships

The Number System

Expressions and Equations


Statistics and


Understand ratio concepts and use ratio reasoning to solve problems.

ratio, equivalent ratios, tape diagram, unit rate, part-to-part, part-to-whole, percent

Apply and extend previous understanding of multiplication and division to divide fractions by fractions.

reciprocal, multiplicative inverses, visual fraction model

Compute fluently with multi-digit numbers and find common factors and multiples.


Compute fluently with multi-digit numbers and find common factors and multiples.

greatest common factor, least common multiple, prime numbers, composite numbers, relatively prime, factors, multiples, distributive property, prime factorization

Apply and extend previous understanding of numbers to the system of rational numbers.

rational numbers, opposites, absolute value, greater than, >, less than, <, greater than or equal to, ≥, less than or equal to, ≤, origin, quadrants, coordinate plane, ordered pairs, x-axis, y-axis, coordinates

Apply and extend previous understanding of arithmetic to algebraic expressions.

exponents, base, numerical expressions, algebraic expressions, evaluate, sum, term, product, factor, quantity, quotient, coefficient, constant, like terms, equivalent expressions, variables

Reason about and solve one-variable equations and inequalities.

inequalities, equations, greater than, >, less than, <, greater than or equal to, ≥, less than or equal to, ≤, profit, exceed

Represent and analyze quantitative relationships between dependent and independent variables.

dependent variables, independent variables, discrete data, continuous


Solve real-world problems involving area, surface area, and volume.

area, surface area, volume, decomposing, edges, dimensions, net, vertices, face, base, height, trapezoid, isosceles, right triangle, quadrilateral, rectangles, squares, parallelograms, trapezoids, rhombi, kites, right rectangular prism, diagonal

Develop understanding of statistical variability.

statistics, data, variability, distribution, dot plot, histograms, box plots, median, mean

Summarize and describe distributions.

this cluster are: box plots, dot plots, histograms, frequency tables, cluster, peak, gap, mean, median, interquartile range, measures of center, measures of variability, data, Mean Absolute Deviation (M.A.D.), quartiles, lower quartile (1st quartile or Q1), upper quartile (3rd quartile or Q3), symmetrical, skewed, summary statistics, outlier

Seventh Grade

Ratios and Proportional Relationships

The Number System

Expressions and Equations


Statistics and Probability

Understand ratio concepts and use ratio reasoning to solve problems.

unit rates, ratios, proportional relationships, proportions, constant of proportionality, complex fractions

Analyze proportional relationships and use them to solve real-world and mathematical problems. : proportion, ratio, proportional relationships, percent, simple interest rate, principal, tax, discount, markup, markdown, gratuity, commissions, fees, percent of error

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

rational numbers, integers, additive inverse

Use properties of operations to generate equivalent expressions.

coefficients, like terms, distributive property, factor

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

numeric expressions, algebraic expressions, maximum, minimum

Draw, construct, and describe geometrical figures and describe the relationships between them. scale drawing, dimensions, scale factor, plane sections, right rectangular prism, right rectangular pyramids, parallel, perpendicular, scalene triangle, obtuse triangle, equilateral tr Solve real-life and mathematical problems involving angle measure, area, surface area, and volume inscribed, circumference, radius, diameter, pi, ∏, supplementary, vertical, adjacent, complementary, pyramids, face, base

Use random sampling to draw inferences about a population.

random sampling, population, representative sample, inferences Draw informal comparative inferences about two populations.

variation/variability distribution, measures of center, measures of variability

Investigate chance processes and develop, use, and evaluate probability models.

sample spaces

Eighth Grade

The Number System

Expressions and Equations



Statistics and Probability

Know that there are numbers that are not rational, and approximate them by rational numbers.

Real Numbers, Irrational numbers, Rational numbers, Integers, Whole numbers, Natural numbers, radical, radicand, square roots, perfect squares, cube roots, terminating decimals, repeating decimals, truncate

Work with radicals and integer exponents.

laws of exponents, power, perfect squares, perfect cubes, root, square root, cube root, scientific notation, standard form of number

Understand the connections betweenp roportional relationships, lines, and linear equations.

unit rate, proportional relationships, slope, vertical, horizontal

Analyze and solve linear equations and pairs of simultaneous linear equations.

intersecting, parallel lines, coefficient, distributive property, like terms, substitution, system of linear equations similar

Define, evaluate, and compare functions.

functions, y-value, x-value, vertical line test, input, output, rate of change, linear function, non-linear function

Use functions to model relationships between quantities.

linear relationship, rate of change, slope, initial value, y-intercept

Understand congruence and similarity using physical models, transparencies, or geometry software.

translations, rotations, reflections, line of reflection, center of rotation, clockwise, counterclockwise, parallel lines,congruence, ≅, reading A’ as “A prime”, similarity, dilations, pre-image, image, rigid transformations, exterior angles, interior angles, alternate interior angles, angle-angle criterion, deductive reasoning, vertical angles, adjacent, supplementary, complementary, corresponding, scale factor, transversal, parallel

Understand and apply the Pythagorean Theorem.

right triangle, hypotenuse, legs, PythagoreanTheorem, Pythagorean triple

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

cones, cylinders, spheres, radius, volume, height, Pi

Investigate patterns of association in bivariate data.

bivariate data, scatter plot, linear model, clustering, linear association, non-linear association, outliers, positive association, negative association, categorical data, two-way table, relative frequency

North Carolina Department of Public Instruction (DRAFT) July 2013

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