NMCT Online Exercises
National Standards and Benchmarks - Mathematics
Provided below are exercises on math benchmarks
National Standards and Benchmarks EXERCISES
Math Exercises by Grade Level
Math 4th Grade
Mth.1.4.1 Understand base-ten by identifying the place value of whole numbers up to 1,000 and decimal numbers down to 100ths.
Mth.1.4.2 Demonstrate the ability to read, write and compare simple fractions and decimals in English and the local counting system.
Mth.1.4.3 Represent whole numbers, fractions and decimals and operations involving them, in a variety of ways using physical models, diagrams and number expressions.
Mth.1.4.4 Perform the basic operations to add, subtract, multiply and divide whole numbers and decimals and add and subtract fractions with like denominators.
Mth.1.4.5 Use a variety of methods and ways to round and estimate whole numbers, decimals and fractions.
Mth.1.4.6 Use a variety of strategies including the understanding of decimals and fractions to solve problems and explain the reasoning used to reach the solution.
Mth.2.4.1 Identify and classify two- and three-dimensional shapes.
Mth.2.4.2 Describe similarities and differences between one, two- and three-dimensional geometric figures.
Mth.2.4.3 Demonstrate understanding of common units in the English and metric systems by choosing appropriate units to measure common objects and quantities.
Mth.2.4.4 Use standard and non-standard units to determine length, volume and weight and describe the characteristics of each type of measurement.
Mth.2.4.5 Use the understanding of geometry, measurement and transformation to solve problems and explain the reasoning used to reach the solution.
Mth.3.4.1 Use patterns and functions to represent and solve real world situations and explain the reasoning used to reach the solution.
Mth.4.4.1 Collect, organize, display and describe data systematically.
Mth.4.4.2 Read and interpret data using pictographs, tables or charts.
Math 6th Grade
Mth.1.6.1 Compare, order, round and group natural numbers.
Mth.1.6.2 Demonstrate fluency in the basic operations of adding, subtracting, multiplying and dividing whole numbers, fractions and decimals.
Mth.1.6.3 Identify the characteristics of prime numbers and composite numbers and decompose composite numbers into factor pairs and prime factors using exponents.
Mth.1.6.4 Use models and pictures to represent ratio and proportions and solve problems.
Mth.2.6.1 Add and subtract customary units of length, mass, capacity and time.
Mth.2.6.2 Perform slides, flips, turns and rotations and indicate the motion, position and direction applied.
Mth.2.6.3 Use formulas to compute the perimeter and area of polygons.
Mth.2.6.4 Describe, compare and classify geometrical figures using mathematical terminology. (For example, students will be able to use terms such as number of edges and faces, number and size of angles and number of vertices.)
Mth.3.6.1 Represent patterns in a variety of ways, (For example, students will be able to represent patterns in numeric, algebraic, pictorial, oral and graphic form.)
Mth.3.6.2 Model and solve real world problems using various representations such as graphs and tables.
Mth.3.6.3 Locate whole numbers, fractions and decimals on a number line.
Mth.3.6.4 Solve simple algebraic expressions.
Mth.4.6.1 Analyze and interpret data, including range, median, mode, mean and frequency and present information to an audience.
Mth.4.6.2 Make predictions that are based on experimental or theoretical probabilities and determine their reasonableness.
Mth.4.6.3 Formulate and solve problems that involve collecting and analyzing data to reach conclusions and make generalizations.
Math 8th Grade
Mth.1.8.1 Represent, compare, order and use numbers in a variety of forms, including integer, fraction, decimal, percentage and exponents, in mathematical problem-solving situations.
Mth.1.8.2 Demonstrate fluency in computing with rational numbers, fractions, decimals, percentages and integers.
Mth.1.8.3 Square whole numbers, rational numbers and integers and find square roots of perfect squares. (For example, students will be able to find the square root of 1, 2, 4, 9, etc.)
Mth.1.8.4 Use ratio, proportion, and percentage in problem solving.
Mth.2.8.1 Use a compass, protractor and straight edge to draw two-dimensional figures and do constructions (For example, students will be able to bisect an angle or line segment, create a right angle or draw a circle.)
Mth.2.8.2 Identify similar and congruent figures including lines of symmetry and diagonals.
Mth.2.8.3 Use formulas to find areas of quadrilaterals, triangles and circles, and the surface area and volume of cylinders and prisms using appropriate units of measure.
Mth.2.8.4 Use the Pythagorean Theorem to find lengths of sides of right triangles.
Mth.2.8.5 Solve simple problems involving rates and derived measures. (For example, students will be able to solve problems involving miles per hour or cost per yard.)
Mth.2.8.6 Use proportional reasoning and indirect measurements to draw inferences, such as measuring the thickness of a book and dividing by the number of pages to estimate the thickness of one page.
Mth.3.8.1 Write and solve two-step linear equations and one-step inequalities.
Mth.3.8.2 Graph linear functions in two variables using a table of ordered pairs.
Mth.3.8.3 Use symbolic algebra and additional techniques, such as tables, guess and check and diagrams, to represent situations and to solve problems, especially those that involve linear relationships.
Mth.3.8.4 Model and solve real-world problems using various representations, such as graphs and tables and understand the purpose and utility of each representation.
Mth.4.8.1 Find, describe, and interpret mean, median, mode and range and determine which measure is best to use in a particular situation.
Mth.4.8.2 Read and interpret tables, charts and graphs and make inferences based on the data.
Mth.4.8.3 Use sampling and other data collection tools to gather and analyze data and make conclusions and predictions.
Mth.4.8.4 Compute simple probabilities using appropriate methods such as lists and tree diagrams or through experimental or simulation activities.
Math 10th Grade
Mth.1.hs.1 Demonstrate the inverse relationship between square numbers and square roots.
Mth.1.hs.2 Compare and order rational numbers and square roots using a number line.
Mth.1.hs.3 Solve problems with squares and square roots, limited to square roots of square numbers.
Mth.1.hs.4 Represent numbers in a variety of forms including factors, multiples, exponents, primes, composites, fractions, decimals and percentages and change from one form to another.
Mth.1.hs.5 Apply an understanding of addition, subtraction, multiplication, division and the order of operations when calculating with rational numbers.
Mth.1.hs.6 Use ratios, proportions and percent to represent the relationship between two quantities and solve problems.
Mth.1.hs.7 Add, subtract, multiply, and divide numbers with positive and negative exponents.
Mth.1.hs.8 Estimate a reasonable solution to a problem.
Mth.1.hs.9 Use rounding and estimation to solve real-world situations and recognize the limitation
Mth.2.hs.1 Apply an understanding of the English and metric systems of measurement to solve problems.
Mth.2.hs.2 Use formulas, including appropriate units of measure, to determine the surface area and volume of selected prisms, cylinders and pyramids.
Mth.2.hs.3 Apply the Pythagorean Theorem to solve problems involving right triangles.
Mth.2.hs.4 Perform transformations including reflection, rotation and translation and describe the size, position and orientation of the resulting shapes.
Mth.3.hs.1 Represent a variety of patterns, including recursive patterns, with tables, graphs, words and symbolic rules.
Mth.3.hs.2 Represent mathematical situations as algebraic expressions and equations and describe algebraic expressions using words.
Mth.3.hs.3 Solve single-variable equations and inequalities using rational numbers.
Mth.3.hs.4 Use tables and graphs to represent linear relationships involving equalities and inequalities with two variables and solve problems.
Mth.3.hs.5 Justify the steps used in simplifying expressions and solving equations and inequalities.
Mth.3.hs.6 Identify functions as linear or nonlinear and contrast their properties from tables, graphs or equations.
Mth.3.hs.7 Represent data involving linear relationships from tables as graphs and equations and vice versa.
Mth.3.hs.8 Solve linear equations and inequalities with two variables using algebraic methods, manipulatives or models.
Mth.3.hs.9 Determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line.
Mth.3hs.10 Select and use a variety of strategies including concrete modeling, pictorial representation, and algebraic manipulation to add, subtract, multiply, divide and factor first and second-degree binomials and trinomials in one variable.
Mth.4.hs.1 Analyze and interpret data using mean, median, mode, range and frequency.
Mth.4.hs.2 Design a study, collect data, and select the appropriate representation to make conclusions and generalizations.
Mth.4.hs.3 Judge the validity of reported data, conclusions and generalizations.
Mth.4.hs.4 Calculate probabilities for simple events under different relationships, including independent, dependent, with replacement and without replacement.