Grade 7

Formulate statistical questions that anticipate variability, distinguish categorical from numerical data and discrete from continuous data, and select appropriate data-collection methods, including a census, representative sample survey, observational study, or experiment. Calculate and interpret the mean, median, mode, and range for ungrouped data, select an appropriate measure of centre based on distribution and extreme values, and recognize biased survey wording and answer choices. Construct and interpret circle graphs using category frequencies, fractions, percentages, and central angles totaling $360^\circ$, and identify misleading scales, intervals, labels, units, boundaries, category choices, or visual dimensions in data displays.

Interpret equations as statements that two expressions are equal, using balance models and equivalent operations on both sides to represent one-variable relationships with integers and rational numbers. Represent one-variable inequalities on number lines with open or closed endpoints and shading for the full solution range, including positive and negative fractions and decimals, and reverse the inequality symbol when multiplying or dividing by a negative. Write and solve one-step and straightforward two-step linear equations and inequalities from contexts using inverse operations, then verify equation solutions by substitution and interpret results in context.

Add and subtract positive and signed fractions with unlike denominators by finding common denominators, simplifying results, and expressing answers as fractions or mixed numbers; multiply fractions and mixed numbers, and divide whole numbers by positive proper fractions or mixed numbers using models and reciprocals. Convert among fractions, terminating decimals, repeating decimals, and percents by preserving equivalence, including decimals through thousandths and percents less than, equal to, or greater than 100%; express terminating decimals as simplified fractions with denominators of tenths, hundredths, or thousandths. Compare and order positive rational numbers represented as fractions, decimals, or percents using benchmarks, number lines, place value, or common representations, while reasoning about magnitude and proportional relationships.

Classify triangles by angle measures and side-length relationships, use the $180^\circ$ triangle angle sum to determine unknown angles, and construct triangles from given side or angle measurements using the triangle inequality and angle-sum constraints. Identify complementary and supplementary angles, and determine unknown angles formed by intersecting lines using vertical-angle equality and linear-pair sums of $180^\circ$, including simple numerical or algebraic equations. Classify quadrilaterals by properties such as parallel or perpendicular sides, equal side lengths, and angle relationships, recognizing inclusive categories among parallelograms, rectangles, rhombi, squares, kites, and trapezoids.

Students represent, locate, compare, and order positive and negative integers and zero on a number line, interpret their signs in real-world contexts, and determine absolute values as distances from zero. Students add and subtract integers using number lines, counters, and symbolic rules, including zero pairs, additive inverses, opposite signs, and negative results. Students evaluate numerical expressions involving integers by applying grouping symbols, whole-number exponents, multiplication and division, and addition and subtraction in the correct order.

Students identify independent and dependent variables and represent linear relationships with tables, graphs, and equations such as $y=kx$ and $y=mx+b$. They recognize constant first differences and constant rates of change, determine rate of change from tables or graphs as $\Delta y/\Delta x$, and distinguish linear relationships from nonlinear ones. Students plot ordered pairs, interpret points and scales in context, and distinguish proportional relationships that pass through the origin from nonproportional linear relationships with an initial value.

Calculate the areas of triangles, parallelograms, trapezoids, and composite figures using perpendicular heights, decomposition, and addition or subtraction, and calculate composite perimeters by summing all exterior boundaries while excluding shared interior edges. Calculate the surface area and volume of rectangular prisms using $2lw+2lh+2wh$ and $lwh$, respectively, and convert among common metric units of length, area, and volume, including millimeters, centimeters, meters, kilometers, milliliters, and liters, using scale factors and their squares or cubes. Relate radius and diameter with $d=2r$ and $r=d/2$, and explore circumference as proportional to diameter using $C=\pi d$, with $\pi$ approximated by $3.14$ or $\frac{22}{7}$.

Students extend numerical patterns involving addition, subtraction, multiplication, division, integers, fractions, and decimals, represent them in tables and simple one-variable algebraic expressions, and describe their rules precisely in words using whole-number term positions. Students identify variables, coefficients, constants, terms, and like terms; translate between verbal phrases and algebraic expressions while preserving operation order, grouping, and meaning. Students combine like terms using whole-number coefficients and evaluate expressions by substituting integers, fractions, or decimals, applying parentheses, operations, and simple whole-number exponents in the correct order.

Apply divisibility tests for 2, 3, 4, 5, 6, 8, 9, and 10; determine prime factorizations, greatest common factors, and least common multiples of positive whole numbers using factorization or lists. Interpret and write repeated multiplication in exponent notation and evaluate powers with whole-number bases and exponents, including powers of 10, the convention $a^0=1$ for nonzero bases, and the sign effects of even and odd exponents on negative bases while distinguishing $(-a)^n$ from $-a^n$. Recognize perfect squares from 0 through 144 and determine their principal whole-number square roots, while understanding that equations such as $x^2=49$ have both positive and negative integer solutions.

Students represent finite sample spaces with organized lists and tree diagrams, determine theoretical probabilities from equally likely outcomes and experimental probabilities from relative frequencies, and express, compare, and interpret probabilities as fractions, decimals, and percents, including complements and expected variation across repeated trials. They calculate sale prices by applying a discount percentage, calculate taxes and tips as percentage increases to a stated base or recover an original amount when appropriate, and compare values using unit prices with equivalent units and monetary amounts rounded to cents. They create and evaluate simple budgets by organizing income, savings, and fixed or variable expenses, calculating spending percentages, and determining whether allocations produce a surplus or deficit without using compound interest, credit charges, taxes, or investment decisions.

Students interpret ratios in context, distinguish part-to-part from part-to-whole comparisons, write them in words, colon, and fraction forms, and generate, simplify, and compare equivalent ratios by scaling both terms consistently. They interpret rates as multiplicative comparisons between quantities, calculate and compare unit rates involving positive whole numbers, decimals, and fractions, and distinguish rates from total amounts in contexts, tables, equations, and graphs. They recognize proportional relationships through constant ratios or unit rates, tables of equivalent ratios, equations of the form $y=kx$, and graphs that pass through the origin, and use scale factors or unit rates to solve missing-value problems.

Students plot and identify points in all four quadrants and on the axes using ordered pairs, and determine horizontal or vertical distances by comparing the relevant coordinates. Students translate figures using integer-coordinate shifts, reflect them across the coordinate axes, and rotate them about the origin by $90^\circ$, $180^\circ$, or $270^\circ$, applying coordinate rules to locate images. Students perform ordered sequences of these transformations, recognize that changing the order can change the image, and identify congruent figures by matching corresponding vertices, side lengths, and angle measures.