Grade 7 math

Converting Fractions, Decimals & Percentages (Mixed Review)

Convert between fractions, decimals, and percentages.

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Fractions to Terminating & Repeating Decimals

Use long division to write fractions as terminating or repeating decimals.

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Percent Problems (Mixed Review)

Find a percent of a number, or what percent one number is of another.

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Percent Applications (Mixed Review)

Solve percent problems involving discount and simple interest.

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Multiplying & Dividing Decimals by 10, 100, and 1,000 (Mixed Review)

Multiply and divide decimals by 10, 100, and 1,000.

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Discount and Sale Price

Find the sale price after a percent discount, only: 10% and 50% off first, then 25% off, 5% steps, prices with cents, any percent, and a second discount on top of the first.

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Markup, Sales Tax, Tips & Commission

Use percents to find selling prices after markup, totals with sales tax and tips, commissions, and percent markup.

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Percent Increase, Decrease & Error

Find the percent of increase or decrease, a new amount after a percent change, and percent error.

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Profit & Loss: Percent Profit

Find profit or loss, percent profit or loss, and the selling price after a percent gain or loss.

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Simple & Compound Interest

Use I = Prt to find the total owed or earned, the interest rate, the time and the principal, then find balances with interest compounded each year.

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Simple Interest

Find simple interest with I = Prt, only: one year at a whole-number rate first, then several years, decimal rates like 3.5%, time in months, and larger amounts.

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Proportional Relationships

Solve proportions for a missing value.

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Scale Drawings & Scale Factor

Find actual or scale lengths using a given scale factor.

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Unit Rates & Complex Fractions

Find unit rates, including with fractional quantities.

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Formulas: Distance, Rate & Time

Use the formula d = rt to solve for distance, rate, or time, and rearrange formulas to solve for a variable.

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Constant of Proportionality

Find the constant of proportionality k from tables, graphs, equations, and word problems.

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Identifying Proportional Relationships

Decide whether a table, graph, or equation shows a proportional relationship.

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Proportional Relationships: Tables, Graphs & Equations

Show one proportional situation three ways: complete the table, graph the points and write the equation y = kx.

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Scaled Copies: Scale Factor, Angles & Area

Decide whether a figure is a scaled copy, find scale factors, see that angles stay the same, find how area changes, and use map scales with and without units.

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Integer Operations (Mixed Review)

Add, subtract, multiply, and divide positive and negative integers.

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Operations with Rational Numbers (Mixed Review)

Add, subtract, multiply, and divide signed fractions and decimals.

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Adding Rational Numbers

Addition of positive and negative decimals, fractions and mixed numbers only: negative tenths first, then like and unlike denominators, hundredths, mixed numbers and three addends.

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Dividing Integers

Division of positive and negative integers only: (-15) ÷ 3 first, then 24 ÷ (-6) and (-36) ÷ (-4), larger dividends, two-digit divisors and two divisions in a row.

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Dividing Rational Numbers

Division of positive and negative decimals, fractions and mixed numbers only: a decimal or fraction divided by a whole number first, then fraction ÷ fraction, dividing by a decimal, and mixed numbers.

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Multiplying Integers

Multiplication of positive and negative integers only: (-4) × 3 first, then two negatives, two-digit factors, and three or four factors.

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Multiplying Rational Numbers

Multiplication of positive and negative decimals, fractions and mixed numbers only: a decimal or fraction times a whole number first, then fraction × fraction, decimal × decimal, cancelling, and mixed numbers.

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Order of Operations with Negative Numbers

Evaluate expressions with positive and negative integers using the order of operations: parentheses and brackets, exponents, multiplication and division, then addition and subtraction.

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Subtracting Rational Numbers

Subtraction of positive and negative decimals, fractions and mixed numbers only, including subtracting a negative: tenths first, then like and unlike denominators, hundredths, mixed numbers and three numbers.

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One-Variable Equations

Solve one-step equations.

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Two-Step Equations & Inequalities

Solve two-step equations and inequalities for x.

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Adding & Subtracting Linear Expressions

Add and subtract linear expressions in parentheses, such as (3x + 4) − (x − 7), including a number in front of the parentheses and two variables.

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Combining Like Terms

Simplify expressions by combining like terms with integer and decimal coefficients.

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Expanding & Factoring Linear Expressions

Use the distributive property to expand linear expressions and to factor out the greatest common factor.

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Hanger Diagrams & Balanced Equations

Solve equations of the form px + q = r and p(x + q) = r using balanced hanger diagrams and tape diagrams, then with rational numbers.

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Solving & Graphing Two-Step Inequalities

Solve two-step inequalities (including flipping the sign when dividing by a negative), graph the solutions, and write inequalities from graphs and word problems.

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Circles: Area & Circumference

Find the area or circumference of a circle using π ≈ 3.14.

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Surface Area & Volume of Prisms (Mixed Review)

Find the surface area or volume of rectangular and triangular prisms.

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Classifying Angles & Triangles

Classify angles as acute, right, obtuse, or straight, and classify triangles by their sides and angles.

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Circles: Circumference Given – Find Area

Given a circle's circumference, find the diameter, radius, and area using π ≈ 3.14.

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Circles: Diameter Given – Find Area & Circumference

Given a circle's diameter, find the circumference and area using π ≈ 3.14.

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Hour & Minute Hand Angles

Find the angle between the hour and minute hands of a clock at any time, including reflex angles and working backwards from an angle to the time.

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Complementary & Supplementary Angles

Use the facts that complementary angles add to 90° and supplementary angles add to 180° to find unknown angles and solve for x.

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Area of Composite Figures

Find the area of figures made from rectangles, triangles, and semicircles by adding or subtracting simpler areas.

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Cross Sections of 3D Figures

Describe the two-dimensional shapes made by slicing prisms, pyramids, cylinders, cones, and spheres, and find the areas of cross sections.

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Area of Shaded Regions with Circles

Find the area of the shaded part of a figure when circles, semicircles, or squares are cut out: area of the whole shape minus the area of the hole.

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Surface Area of Square Pyramids

Surface area of square pyramids only: the square base plus four triangles (base² + 2 × base × slant height), from small numbers to word problems.

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Surface Area of Triangular Prisms

Surface area of triangular prisms only: two triangle faces plus three rectangle faces, with growing triangles and prism lengths.

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Triangle Angle Sum & Side Lengths

Use the 180° angle sum to find missing angles in triangles, and decide whether three lengths can form a triangle.

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Unique Triangles: One, Many or No Triangle

Decide whether a set of side lengths and angle measures makes exactly one triangle, many different triangles, or no triangle at all.

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Vertical & Adjacent Angles

Identify vertical and adjacent angles formed by two intersecting lines and use them to find unknown angles.

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Volume of Composite Prisms & Pyramids

Find the volume of solids made from rectangular prisms, and the volume of pyramids using V = 1/3 × B × h.

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Temperature: Celsius & Fahrenheit

Convert temperatures between °C and °F with F = 9/5 × C + 32, and find temperature changes above and below zero.

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Probability Basics

Find simple probabilities as a fraction in simplest form.

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Probability of Compound Events

Find the probability of two independent events happening together.

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Comparing Data Sets: Mean & MAD

Find the mean and mean absolute deviation (MAD) of data sets and use them to compare two populations.

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Random Samples & Making Predictions

Decide whether a sample is random or biased, and use data from a random sample to make predictions about a population.

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Sample Spaces: Lists, Tables & Tree Diagrams

Count every possible outcome of a chance experiment with a list, table or tree diagram, then use the sample space to find probabilities.

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Theoretical & Experimental Probability

Find theoretical and experimental probabilities and use them to predict how often an event will happen.

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Word Problems

Integer and proportion word problems.

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Decimal Word Problems with Negatives

Stories with positive and negative decimals: temperature changes, elevations, bank balances, rates of change, signed averages, and sale prices with tax.

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Inequality Word Problems

Write and solve one- and two-step inequalities for real-world situations with "at least", "at most", "more than" and "less than".

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Two-Step Equation Word Problems

Write and solve two-step equations of the form px + q = r to solve real-world problems.

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