Standard 1: Number and Operation

01. Understand and use numbers

Compare magnitudes and relative magnitudes of rational numbers, including integers, fractions, and decimals.

Understand and use real numbers (integers, fractions, decimals, and absolute values) to solve problems.

Solve problems requiring the conversion between simple decimals, fractions, ratios, and percents (including: unit cost, discount & sale price, percent one number is of another, number from a percent, and proportions).

Locate the position of rational numbers on a number line (including ordering and comparing real numbers from least to greatest and using <,>,=).

Model and write numerical fractions.

Rewrite multiple factors using exponents.

Explore scientific notation and its uses.

Apply the number theory concepts of primes, composites, and prime factorization and find the Least Common Multiple (LCM) and the Greatest Common Factor (GCF).

Recognize pertinent information for problem solving.

Describe the use of integers in real-world situations.

Use appropriate vocabulary.

02. Performs computations accurately

Recall the common equivalent fractions, decimals, and percents of halves, fourths, and tenths.

Add, subtract, multiply, and divide whole numbers, integers, fractions and decimals (including: developing computational fluency with division facts, mental math with multiples of 10, subtracting temperatures, and computing and counting change greater than $20.00.

Evaluate whole numbers in exponential form.

Expand the use of exponents (including finding products by applying rules for exponents, writing equivalent forms of numbers using exponents & scientific notation, identifying equivalent roots & radicals, computing 2^nd & 3^rd degree exponents, and estimating square roots using perfect squares.

Evaluate numerical expressions using the order of operations with whole numbers, integers, and decimals.

Accurately use divisibility rules & factorization.

Explore basic operations with integers (includes: order of operations and calculating % and % of change.

Select and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three.

Understand the purpose and capabilities of appropriate technology.

Use computer applications to display and manipulate data (includes making a sketch to aid in organizing and visualizing data).

Use a variety of strategies including common mathematical formulas to compute problems drawn from real life situations (strategies include: draw a picture, make a model, guess and test, make a list, make a table, find a pattern, work backwards, solve a simpler problem, draw a diagram, or write an equation).

Use appropriate vocabulary and notations.

Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to communicate mathematical information.

03. Estimates & judges reasonableness of results.

Estimate to predict computation results.

Recognize and explain when estimation is appropriate and describe the usefulness of an estimate as opposed to an exact answer.

Identify whether a given estimate is an overestimate or underestimate.

Estimate using decimals and fractions (including rounding to a given place value).

Use estimation to determine if solutions to word problems are reasonable.

Use a four-function calculator to solve complex grade-level problems.

Apply solutions and strategies to new problem situations.

Formulate conjectures and discuss why they must be or seem to be true

Use appropriate vocabulary and notations.

01. Understand and use U.S. customary and metric measurements.

Select and use appropriate units and tools to make formal measurements in both systems. (segments and angles)

Apply estimation of measurement to real-world and content problems using standard measuring devices.

Recognize and explain the differences between measures of length, perimeter, area, and volume (capacity) and their measures within both systems.

Find the perimeter, circumference, or area of triangles, circles, and quadrilaterals.

Convert units of measurement within each system to solve a problem.

Convert between systems of measurement.

Solve problems involving length, perimeter, area, volume (capacity), angle measure, weight, mass, time, money, and temperature (including: estimating measures, calculating change back, making accurate measurements, etc.

Solve problems involving perimeter and area of rectangles and triangles.

Know the formulas for perimeter, area, and circumference.

Use appropriate vocabulary and notations.

02. Apply concepts of rates, ratios, and proportions.

Explain rates and their relationships to ratios, and use proportions to solve problems represented with a diagram.

Reduce rates to unit rates.

Develop the use of rates to make indirect measurements.

Develop the use of proportions, ratios, and scales.

03. Apply dimensional analysis.

Identify properly constructed dimensional analysis conversions.

Understand units and their relationship to one another and to real world applications (including: comparing amounts of money to determine or make change and identifying the number of items that could be purchased from a given amount of money.

01. Use algebraic symbolism as a tool to represent mathematical relationships.

Use variables in simple expressions, equations, and inequalities.

Translate simple word statements and story problems into algebraic expressions and equations.

Use “<,” “>,” “=,” “≠,” “≤,” and “≥” to express relationships.

02. Evaluate algebraic expressions.

Evaluate simple numeric and algebraic expressions using commutative, associative, identity, zero, inverse, distributive, and substitution properties.

Understand and use the order of operations in evaluating simple algebraic expressions.

03. Solve algebraic equations and inequalities.

Solve one step equations with whole numbers and decimals using inverse operations. 

Solve simple two step equations.

Interpret expressions or solve problems using models & manipulatives.

Explore solutions of simple one step equations using negative numbers.

Explore graphical representation to show simple linear equations.

04.  Understand the concept of functions.

Extend patterns involving rational numbers and describe the rule that generates the pattern (includes: finding any term in a sequence given an expression or rule for the nth term).

Use functional relationships to explain how a change in one quantity impacts a change in another quantity.

Use appropriate vocabulary and notations.

05.  Represent equations, inequalities and functions in a variety of formats.

Represent a simple set of data in a table, as a graph, and as a mathematical relationship.

06.  Apply functions to a variety of problems.

Use patterns and linear functions to represent and solve simple problems.

01. Apply concepts of size, shape, and spatial relationships.

Classify relationships among types of one- and two-, dimensional geometric figures, using their defining properties.

Draw and measure various angles and shapes using appropriate tools.

Apply fundamental concepts, properties and relationships among points, lines, rays, planes, angles, and shapes (includes: parallel lines, perpendicular lines; symmetry, congruency, similarity; acute, right, obtuse, adjacent, vertical, and corresponding angles; and horizontal, vertical, congruence, symmetry, curve, perpendicular, parallel, & intersection).

Explain and model the effects of reflections, translations, and rotations on various shapes (includes identifying, comparing, & constructing various 2 & 3 dimensional geometric shapes using appropriate tools.

Identify congruence, similarities, and line symmetry of shapes.

Explore and describe the concept of surface area and volume (capacity).

Use appropriate vocabulary and symbols.

Apply formulas for perimeter, circumference and area to triangles, quadrilaterals, and circles.

Apply formulas to measure volume & surface area.

02. Apply the geometry of right triangles.

Explore right triangle geometry.(definition of hypotenuse)

03. Apply graphing in two dimensions.

Identify and plot points on a coordinate plane (includes: creating, graphing, and analyzing ordered pairs).

01. Understand data analysis.

Read and interpret tables, charts, and graphs, including frequency tables, scatter plots, broken line graphs, line plots, line graphs, bar graphs, histograms, circle graphs, and stem-and-leaf plots.

Explain conclusions drawn from tables, charts, and graphs.

Use appropriate vocabulary and notations.

02. Collect, organize, and display data.

Collect, organize, and display discrete and continuous data with appropriate notation in tables, charts, and graphs, including: scatter plots, line graphs, broken line graphs, line plots, bar graphs, circle graphs, and stem-and-leaf plots).

03. Apply simple statistical measurements.

Determine the measures of central tendency – mean, median, and mode – with simple sets of data (includes: solving practical problems involving the mean of a set of numbers).

Explore and discuss distribution of data, including range, frequency, gaps, and clusters.

04. Understand basic concepts of probability.

Predict, perform, and record results of simple probability experiments (includes: expressing probability of a simple event as ratios, fractions, decimals, or percents).

Recognize equally likely outcomes.

Explain that probability ranges from impossible to certain (0% to 100%).

Use the language of probability.

05. Make predictions or decisions based on data.

Make predictions based on simple experimental and theoretical probabilities.

Use appropriate vocabulary and notations.