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| Number Sense - Grade 7 | |
| 1. Students use real numbers expressed in a variety of forms and translate among these representations. | |
| 1.1 Students read, write, compute and approximate numbers in scientific notation | Note: Positive and negative powers of 10 will be used |
| 1.2 Students translate among fraction, decimal, and percentage forms of rational numbers, including terminating and repeating decimals, as needed to solve problems | |
| 1.3 Students describe and give examples of the use of the square root symbol and determine the two integers between which a particular square root lies | |
| 1.4 Students interpret the absolute value of a real number as its distance from zero on a number line and determine the absolute value of real numbers | |
| 2. Students increase facility with the algebraic operations on rational numbers. | |
| 2.1 Students utilize the four basic operations of arithmetic with any combination of integers, fractions, and decimals, correctly implementing order of operations and parenthetical notation | Note: including positive and negative values |
| 2.2 Students simplify numerical expressions by applying properties of real numbers (identity, inverse, distributive, associative, commutative), and justify the process used. | |
| 2.3 Students explain and use the inverse relationship between exponentiation and root extraction | |
| 3. Students use proportions, ratios and rates to solve problems. | |
| 3.1 Students use proportions to solve problems involving a change of scale or a comparison of quantities | Scale changes in applications related to drawings, models, maps, and recipes |
| 3.2 Students identify and interpret situations involving direct variation and represent these situations on a coordinate graph | |
| 3.3 Students use rates and other derived units to solve problems | Notes: rates such as speed and density, derived units such as kilowatts per household per day or person-hours |
| 3.4 Students use percentages and quantities when calculating increases and decreases and interest | solve consumer-application problems that involve discount, markup, commission, profit and simple compound-interest |
| 3.5 Students show how cross-multiplication can be used to solve problems involving proportion. | |
| Symbols and Algebra - Grade 7 | |
| 1. Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities, and their graphs. | |
| 1.1 Students use variables and appropriate operations to write an expression, equation, inequality, or system of equations or inequalities which represent a verbal description | The difference between a number and four times the number is 163, what
is the number? How many quarters do you have if you have 6 more quarters than dimes and together the coins are worth $30.00? |
| 1.2 Students simplify algebraic expressions in one or more variables by combining like terms or canceling | m3p + mpm2 + 3pmp2 = 2m3p
+ 3mp3
a2bc / ab3 = ac / b2 |
| 1.3 Students evaluate algebraic expressions given replacement values for the variables | Note: These should include polynomial expressions and those with more than one variable |
| 1.4 Students use algebraic terminology correctly | Example terms: variable, constant, coefficient, expression, equation, inequality |
| 1.5 Students identify and give examples of the use of variables in expressions, equations, formulas, and properties | Expression (2w + 2l) Equation (y = x2 + 6) Formula ( F = 9/5 C + 32) Property ( a + b = b + a) for all real numbers a and b. |
| 1.6 Students represent quantitative relationships graphically on the coordinate plane and describe key features of the graph | |
| 2. Students interpret and evaluate expressions involving integer powers and roots of monomials | |
| 2.1 Students interpret whole number powers as repeated multiplication, negative integer powers as reciprocals, and simplify and evaluate expressions that include exponents and know how to combine exponents | |
| 2.2 Students simplify square roots of perfect square monomials | |
| Functions - Grade 7 | |
| 1. Students identify, describe, represent, extend, and create linear and non-linear number patterns. | |
| 1.1 Students write the equation for the next term in number patterns involving multiples, squares, cubes, and reciprocals | |
| 1.2 Students identify direct and inverse variation in situations and represent that variation graphically, and by an equation | |
| 2. Students solve simple linear equations and inequalities over the rational numbers. | |
| 2.1 Students graph a linear function on the coordinate plane given its equation, given its slope and y-intercept, or given both its x- and its y-intercepts | |
| 2.2 Students solve two-step linear equations and inequalities in one variable over the rational numbers and judge the reasonableness of the results | |
| 2.3 Students solve multi-step problems involving rate, average speed, distance and time, or direct variation | |
| Measurement and Geometry - Grade 7 | |
| 1. Students select, use, and justify methods for finding perimeter, circumference, area, and volume of common geometric objects and use these to derive methods for finding or estimating measures of less common objects. | |
| 1.1 Students estimate and find the area of complex 2-dimensional figures by subdividing them into rectangles, triangles and circles and adding or subtracting areas | |
| 1.2 Students find the perimeter, area, volume, or surface area of irregular geometric figures that are formed from standards geometric objects by using formulas for the standard objects and adding or subtracting as needed. | |
| 1.3 Students use proportions to find measures and ratios for areas and volumes of similar figures | |
| 2. Students construct elements of geometric figures and identify and use their properties | |
| 2.1 Students identify and construct basic elements of geometric figures | Note: Include altitudes, midpoints, angle bisectors, perpendicular bisectors; and central angles, radii, diameters, and chords of circles |
| 2.2 Students recall the Pythagorean Theorem and state it in their own terms, giving examples of when and how it is used, and use it to find or approximate the length of the missing side of a right triangle and check the reasonableness of answers | |
| 2.3 Students determine the measures of central, interior, and exterior angles of regular polygons | |
| Statistics, Data Analysis, and Probability - Grade 7 | |
| 1. Students organize data in more than one variable, generate descriptive summary statistics, and describe potential relationships among variables | |
| 1.1 Students describe and use measures of central tendencies (mean and median), frequency (mode), and distribution (range, inter-quartile range) appropriately | |
| 1.2 Students 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 | |
| 1.3 Students represent two nominal (categorical) variables in a contingency table, and describe similarity or differences in proportions in rows or columns | |
| 1.4 Students provide reasonable estimates of the accuracy of measurements and of rounding errors in calculations | |
| 2 Students use probability to answer questions about the likelihood of an event. | |
| 2.1 Students represent probability of events ratios, decimals, and percents | |
| 2.2 Students give samples to illustrate that the sum of the probabilities of all possible events is 1, and use this fact in finding the probability of an event not occurring | The batting average of a baseball player (which is a probability based on that batter's record) is .285; what is the probability the player will not make a hit when she comes up to bat? |
| 2.3 Students identify the number of possible arrangements of several objects using a diagram | |
| Mathematical Reasoning - Grade 7 | |
| 1. Students relate geometric figures to geometric properties as simple examples of deductive reasoning | |
| 1.1 Students classify triangles and quadrilaterals by relating them to the definitions and properties of these types of figures | |
| 1.2 Students determine when two triangles or two quadrilaterals are not similar or are not congruent and state the reason for this conclusion in terms of conditions not satisfied | |
| 2. Students formulate, justify, and verify their solutions appropriately. | |
| 2.1 Students frame the symbolic representation of problems appropriately and recognize the assumptions made | |
| 2.2 Students provide accurate explanations to justify each step of solutions of equations | |
| 2.3 Students verify that solutions are reasonable by giving examples and using estimation |