CA CCSSM Standards:
7.NS.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on horizontal and vertical number line diagrams. Includes: opposite quantities combining to make 0 (7.NS.1a); p + q as the number located |q| from p (7.NS.1b); subtraction as adding the additive inverse, with the distance between two numbers as the absolute value of their difference (7.NS.1c); and applying properties of operations (7.NS.1d).
7.NS.2 — Apply and extend previous understandings of multiplication and division to multiply and divide rational numbers, including the sign rules for products and quotients (7.NS.2a–c) and converting rational numbers to decimals that terminate or eventually repeat (7.NS.2d).
7.NS.3 — Solve real-world and mathematical problems involving the four operations with rational numbers.

Learning goal: Students complete their arithmetic foundation by extending all four operations to the full set of rational numbers — positive and negative fractions, decimals, and integers. The number line is the anchoring model: sums are movements, differences are distances, and the sign rules for multiplication emerge from patterns rather than decree. This fluency underpins everything in Grade 7 algebra and beyond.

Students will be able to:

• Represent addition and subtraction of rational numbers as movements and distances on horizontal and vertical number lines.
• Explain why a number and its opposite sum to zero, and use additive inverses to rewrite subtraction as addition.
• Add, subtract, multiply, and divide any combination of positive and negative integers, fractions, and decimals.
• Explain the sign rules for products and quotients (e.g., why a negative times a negative is positive) using patterns or properties of operations.
• Convert a fraction to a decimal by division and identify whether the decimal terminates or repeats.
• Solve multi-step real-world problems (temperature change, elevation, account balances, gains and losses) using rational number operations.

CA CCSSM Standards:
7.RP.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units (e.g., walking ½ mile in ¼ hour is a rate of 2 miles per hour).
7.RP.2 — Recognize and represent proportional relationships between quantities: decide whether two quantities are proportional by testing for equivalent ratios in a table or graphing on a coordinate plane (7.RP.2a); identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions (7.RP.2b); represent proportional relationships by equations y = kx (7.RP.2c); and explain what a point (x, y) on the graph means in context, with special attention to (0, 0) and (1, r) (7.RP.2d).
7.RP.3 — Use proportional relationships to solve multistep ratio and percent problems, including simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

Learning goal: Proportional reasoning is the centerpiece of Grade 7 and the direct on-ramp to slope and linear functions in Grade 8. Students learn to recognize proportionality wherever it appears — recipes, prices, speeds, graphs — to capture it in the equation y = kx, and to wield percents confidently in the financial situations they will meet in real life.

Students will be able to:

• Compute unit rates from ratios of fractions, including complex rates like ½ mile per ¼ hour.
• Test whether a table or graph represents a proportional relationship, and justify (equivalent ratios; a straight line through the origin).
• Identify the constant of proportionality k from a table, graph, equation, or verbal description, and write the equation y = kx.
• Interpret any point (x, y) on a proportional graph in context, including (0, 0) and the unit-rate point (1, r).
• Solve multistep percent problems — sales tax, tips, discounts, markups, commission, simple interest, percent increase/decrease, and percent error — and check answers for reasonableness.

CA CCSSM Standards:
7.EE.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Learning goal: Students learn that algebraic expressions are flexible objects: the same quantity can be written many ways, and choosing the right form reveals structure. Expanding, factoring, and combining like terms are practiced not as symbol-pushing but as meaning-preserving rewrites, verified with substitution and area models.

Students will be able to:

• Combine like terms in linear expressions with integer, fraction, and decimal coefficients.
• Expand expressions using the distributive property, including with negative and fractional factors, e.g., −2(x − ¾).
• Factor a common factor out of a linear expression, e.g., rewrite 6x + 9 as 3(2x + 3).
• Verify that two expressions are equivalent using substitution and explain equivalence with an area/tile model.
• Interpret equivalent forms in context — for instance, explain why a + 0.05a = 1.05a means a 5% increase is a single multiplication.

CA CCSSM Standards:
7.EE.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically; apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
7.EE.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r fluently, comparing the algebraic solution to an arithmetic one (7.EE.4a); solve word problems leading to inequalities of the form px + q > r or px + q < r, graph the solution set, and interpret it in context (7.EE.4b).

Learning goal: Students make the leap from arithmetic to algebra as a problem-solving method: a situation becomes an equation, legal moves preserve balance, and the solution answers the original question. Inequalities extend the same reasoning to situations with ranges of answers, and estimation keeps every answer honest.

Students will be able to:

• Translate real-world situations into equations of the form px + q = r and p(x + q) = r, and solve them fluently.
• Compare an algebraic solution to an arithmetic solution of the same problem and explain how the steps correspond.
• Solve multi-step problems mixing fractions, decimals, and percents, converting between forms strategically.
• Estimate to judge whether an exact answer is reasonable, and catch errors by estimation.
• Write and solve inequalities of the form px + q > r or px + q < r, graph the solution set on a number line, and interpret it in context (including why the inequality reverses when multiplying or dividing by a negative).

CA CCSSM Standards:
7.G.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions; focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
7.G.3 — Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Learning goal: Students develop spatial and proportional reasoning together: scale drawings apply proportionality to geometry (lengths scale by k, areas by k²), triangle construction builds intuition for what conditions determine a shape (foreshadowing congruence criteria), and slicing solids connects 2D and 3D thinking.

Students will be able to:

• Compute actual lengths and areas from a scale drawing using the scale factor, and explain why area scales by the square of the factor.
• Reproduce a scale drawing at a different scale.
• Attempt triangle constructions from three given measures and classify the conditions as producing a unique triangle, more than one triangle, or no triangle, connecting the “no triangle” case to the triangle inequality.
• Predict and describe the 2D cross-sections produced by slicing right rectangular prisms and pyramids with planes at various angles.

CA CCSSM Standards:
7.G.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
7.G.6 — Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Learning goal: Students come to own the circle formulas by deriving them — unrolling circumferences to discover π and rearranging wedges to see A = πr² — and use angle relationships as their first taste of geometric deduction, writing equations from diagrams. Measurement culminates in applied design problems with composite areas, surface areas, and prism volumes.

Students will be able to:

• Apply C = πd and A = πr² to solve problems, and give an informal derivation of each (and of the relationship between them).
• Identify supplementary, complementary, vertical, and adjacent angle pairs in a figure.
• Write and solve equations for unknown angles in multi-step figures using angle relationships.
• Compute areas of composite 2D figures built from triangles, quadrilaterals, and polygons.
• Compute surface area and volume of cubes, right prisms, and composite solids, and apply them to design problems (e.g., minimize material for a required volume).

CA CCSSM Standards:
7.SP.1 — Understand that statistics can be used to gain information about a population by examining a sample; generalizations are valid only if the sample is representative, and random sampling tends to produce representative samples.
7.SP.2 — Use data from a random sample to draw inferences about a population with an unknown characteristic of interest; generate multiple samples of the same size to gauge the variation in estimates or predictions.
7.SP.3 — Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers as a multiple of a measure of variability.
7.SP.4 — Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
7.SP.5 — Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
7.SP.6 — Approximate the probability of a chance event by collecting data and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
7.SP.7 — Develop a probability model (uniform and non-uniform) and use it to find probabilities of events; compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy (7.SP.7a–b).
7.SP.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation (7.SP.8a–c).

Learning goal: Students learn to reason under uncertainty: a random sample can tell you about a whole population (and a biased one can mislead you), two groups can be compared honestly using center and spread, and chance can be modeled, predicted, and tested. This is the foundation of statistical literacy for citizenship as much as for mathematics.

Students will be able to:

• Explain why random sampling supports valid generalization and identify sources of bias in non-random sampling methods.
• Draw an inference about a population from a random sample, and use repeated samples to describe the variability of estimates.
• Compare two data distributions using their centers and spreads, expressing the gap between centers as a multiple of a measure of variability (e.g., MAD).
• Express probabilities as numbers from 0 to 1 and interpret values near 0, ½, and 1 as unlikely, neither, and likely.
• Approximate a probability from long-run relative frequency, and predict frequencies from a known probability.
• Build uniform and non-uniform probability models, use them to compute event probabilities, and explain discrepancies between predicted and observed results.
• Find probabilities of compound events using organized lists, tables, tree diagrams, and designed simulations.