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Course Description
In this course, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two and threedimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. Students engage with relevant mathematical contexts to make math meaningful. As students encounter challenging problems, and practice asking for help and a willingness to learn from others, they build the social emotional learning competencies of selfmanagement, self awareness, relationship skills, and social awareness.
Grade Level(s): Seventh Grade
Related Priority Standards (State &/or National): K12 Mathematics Missouri Learning Standards
Essential Questions
 What do effective problem solvers do, and what do they do when they get stuck?
 How can I effectively explain my mathematical thinking and reasoning to others?
 What does it mean for two things to be proportionally related? How can you tell?
 How are percentages used to represent change?
 Which representations best help you make sense of certain mathematical scenarios?
 How can rational numbers be used to represent real world situations?
 Our world is really complexhow can we simulate parts of it to make better predictions?
 When is a sample not representative of a population?
Enduring Understandings/Big Ideas
 Any proportional relationship can be represented by an equation.
 A proportional relationship is a collection of equivalent ratios.
 Addition, subtraction, multiplication, and division can be extended to rational numbers.
 Circumference of a circle is proportional to its diameter.
 We can estimate probabilities of outcomes of chance experiments.
CourseLevel Scope & Sequence (Units &/or Skills)
Unit 1: Scale Drawing
 Students will solve problems including scale drawings of real objects and geometric figures including actual lengths and areas from a scale drawing and reproducing the drawing at a different scale.
 Students will use visual models to build conceptual understanding of scale factor by examining the relationships among corresponding pints, sides, and angles of scaled copies.
 Students will measure precisely using rulers or informal measuring tools.
 Students will draw scaled copies, ensuring that angle measures are unchanged and side lengths are changed by a common factor.
Unit 2: Proportional Relationships
 Students will represent proportional relationships using equations.
 Students will write equations for the two ways a proportional relationship can be considered.
 Students will compare proportional and nonproportional relationships, focusing on the structure of the equation for each.
 Students will determine that proportional relationships are straight lines passing through the origin and categorize graphs as proportional or nonproportional.
 Students will interpret graphs of proportional relationships and reason that graphs can be used to compare constants of proportionality.
 Students will compute unit rates with complex fractions and with like or different units.
 Students will determine when two quantities are in a proportional relationship.
 Students will identify and or compute the constant of proportionality (unit rate).
 Students will explain what a point on the graph of a proportional relationship means in terms of the situation.
 Students will interpret the unit rate as the slope of the graph.
 Students will derive and write the equations y=mx + b (yintercept, slope).
Unit 3: Measuring Circles
 Students will develop a formal definition of a circle and describe and measure a circle using the radius and diameter.
 Students will apply understanding of scaled figures and proportional relationships to explore the relationship between a square’s perimeter and diagonal length.
 Students will determine the perimeter of shapes composed of circular parts and solve for unknown lengths.
 Students will develop a formula for the area of a circle.
 Students will apply the area of a circle formula to solve problems involving the area of shapes composed by circular parts and polygons.
Unit 4: Proportional Relationships and Percentages
 Students will compute unit rates with complex fractions and with like or different units.
 Students will determine when two quantities are in a proportional relationship.
 Students will identify and or compute the constant of proportionality (unit rate).
 Students will explain what a point on the graph of a proportional relationship means in terms of the situation.
 Students will recognize that the graph of any proportional relationship will pass through the origin.
 Students will interpret the unit rate as the slope of the graph.
 Students will compare two different proportional relationships.
 Students will write the equations y=mx + b (yintercept, slope).
 Students will understand that percentages are not whole numbers.
 Students will model problems involving percent increase and decrease with tape diagrams and write expressions to represent the scenarios.
 Students will use tape diagrams to make sense of problems involving percent increase and decrease to determine percent of change.
 Students will connect proportional relationships and percent change scenarios in order to write equations.
 Students will represent percent increase and decrease problems with equations, and use them to solve for various unknown values.
 Students will apply percent reasoning to contexts involving money  specifically sales tax, tips, and simple interest.
 Students will interpret and solve problems about real world situations involving proportional relationships and percent change.
 Students will determine missing measurements in proportional relationships involving fractional quantities or percentages.
Unit 5: Rational Number Arithmetic
 Students will add, subtract, multiply, and divide rational numbers.
 Students will represent addition and subtraction on horizontal and vertical number lines.
 Students will describe situations that have a number and its opposite with a sum of zero.
 Students will understand subtraction of rational numbers as adding the additive inverse.
 Students will determine the distance between two rational numbers on the number line as the absolute value of their difference.
 Students will interpret sums, differences, products, and quotients of rational numbers by describing real world context.
 Students will generate equivalent representations of rational numbers.
 Students will explore adding rational numbers and generalize rules about the sign of the sum.
 Students will subtract rational numbers to compare differences and notice that the order of subtraction changes the sign of the difference.
 Students will formalize that the product of a positive and negative number is negative, by relating multiplication to repeated addition.
 Students will perform all four operations with positive and negative numbers using a variety of strategies.
 Students will reason about variable expressions involving adding, subtracting, multiplying, and dividing signed numbers.
 Students will generalize patterns for the value of variable expressions.
 Students will apply understanding of the distance formula, d = rt, to make observations about the rules for multiplying rational numbers.
 Students will identify and create equivalent expressions involving positive, negative, and zero exponents.
 Students will express and perform operations with very large or very small quantities using powers of ten and scientific notation.
 Students will synthesize understandings of rational number arithmetic and interpret negative quantities such as rates of change.
 Students will solve equations of the form p + x = q and px = q with rational values.
Unit 6: Expressions, Equations, and Inequalities
 Students will find unknown values on balanced hanger diagrams that model twostep equations.
 Students will connect the Distributive Property with solving equations of the form p(x + q) = r, using hanger diagrams to assist.
 Students will practice solving equations of the form p(x + q) = r, focusing on the structure of the equation to determine the most efficient solution method.
 Students will build fluency in algebraic manipulation by solving a variety of equations.
 Students will use tape diagrams and equations of the form px + q = r and p(x + q) = r to describe relationships in realworld scenarios.
 Students will create tape diagrams, write equations, and solve realworld problems, focusing on equations of the form p(x + q) = r.
 Students will decide which type of equation, px + q = r or p(x + q) = r, describes the relationships in a realworld story problem.
 Students will represent percent increase and decrease using tape diagrams and equations.
 Students will solve inequalities of the forms px + q < r and p(x + q) < r by first writing and solving a related equation.
 Students will interpret and solve inequalities that represent realworld situations, while making sense of quantities and their relationships in the problem.
 Students will use the Distributive Property to expand and factor expressions that include subtraction and negative values.
 Students will use the properties of operations to understand how like terms can be combined to write an equivalent expression with fewer terms.
 Students will combine like terms to write equivalent expressions with fewer terms, now including negative coefficients and parentheses.
Unit 7: 2D and 3D Geometry
 Students will compose, decompose, and measure angles.
 Students will find an unknown angle given the measure of a supplementary or complementary angle.
 Students will calculate the surface area and volume of threedimensional figures.
 Students will find the measures of nonadjacent supplementary and complementary angles and draw conclusions about the angle relationships of polygons.
 Students will write and solve equations of the form px + q = r and p(x + q) = r to represent angle relationships shown in diagrams.
 Students will examine and compare sets of triangles that share three common angle measures or side lengths.
 Students will use various tools to draw triangles, noticing that certain conditions determine how many unique triangles can be drawn.
 Students will draw triangles given one angle and two side lengths, or three angles.
 Students will calculate the volume of any right prism by multiplying the area of its base by its height.
 Students will determine fractions and decimal approximations for rational and irrational numbers.
Unit 8: Data, Statistics, and Probability
 Students will use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest.
 Students will analyze different data distributions of statistical measures.
 Students will compare the numerical measures of center, measures of frequency, and measures of variability from two random samples to draw inferences about the population.
 Students will investigate the probability of chance events between zero and one.
 Students will predict outcomes using theoretical probability.
 Students will perform experiments that model theoretical probability.
 Students will compare and explain theoretical and experimental probabilities.
 Students will find probabilities of compound events using organized lists, tables, tree diagrams, and simulations.
 Students will compare and explain differences between data displays.
 Students will calculate percents.
 Students will determine probability of unknown events by comparing the results of repeated experiments and the expected probability.
 Students will explain the purpose of sampling and which methods of obtaining a sample tend to produce representative samples.
Course Resources & Materials: DESMOS
Date Last Revised/Approved: 2022