Welcome to the Seventh Grade Math homepage! In seventh grade, students embark on a journey of deepening advanced mathematical concepts, building on their foundation from previous years. They delve into algebraic thinking, mastering equations, inequalities, and functions. Through systematic practice, they refine their skills in multi-step problem-solving, preparing for more complex mathematical challenges ahead. A significant focus of the year is on proportional relationships and percentages, where students explore real-world applications and mathematical modeling. They develop fluency in operations with rational numbers, including decimals, fractions, and integers, and deepen their understanding of ratios and proportions. Seventh graders also explore geometry and measurement, investigating concepts such as area, volume, and scale drawings. They apply their knowledge to solve geometric problems and analyze shapes using precise mathematical language. Throughout the year, students are encouraged to think critically and communicate their mathematical reasoning effectively.

- Math
- 7th Grade

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In this unit, seventh graders will explore spatial relationships and dimensions. They’ll differentiate between scaled and non-scaled figures, calculate scale factors, and draw scaled replicas. Students will analyze how different scale factors affect size and use reciprocal scaling. They’ll apply scale drawings to calculate distances, dimensions, and area representations, mastering scales with or without units. By the end of the unit, students will have a solid grasp of scaled drawings, enhancing their geometric understanding and spatial reasoning skills.

- Unit 1.1: Differentiate between scaled and non-scaled copies of a figure
- Unit 1.2: Identify corresponding parts and determine the scale factor between two figures
- Unit 1.3: Draw a scaled copy of a given figure using a given scale factor
- Unit 1.4: Use corresponding sides, corresponding distances and corresponding angles to tell whether one figure is a scaled copy of another
- Unit 1.5: Describe how scale factors of 1, less than 1, and greater than 1 affect the size of a scaled copy, and explain how scaling can be reversed using reciprocal scale factors
- Unit 1.6: Use a scale drawing and its scale to calculate actual distances
- Unit 1.7: Determine the scale and the dimensions of a scale drawing when given the actual dimensions of an object
- Unit 1.8: Reproduce a scale drawing at a different scale and determine how much actual area is represented by one square unit in a scale drawing
- Unit 1.9: Explain how to use scales without units to determine scaled or actual distances.
- Unit 1.10: Use different scales, with or without units, to describe the same drawings.

In this unit, seventh graders will explore ratios and equations. They’ll compare ratios in contexts like recipes and scaled copies, and use tables to describe and calculate constants of proportionality. Students will write equations for proportional relationships, recognizing how different equations can express the same relationship. They’ll interpret and solve problems using tables, graphs, and equations, understanding that proportional relationships are characterized by y=kx. By the end of the unit, students will represent and compare proportional relationships across various mathematical forms, enhancing their skills in mathematical reasoning and problem-solving.

- Unit 2.1: Compare and create representations to compare ratios in the context of recipes or scaled copies.
- Unit 2.2: Use a table to describe a proportional relationship, calculate the constant of proportionality, and find missing values.
- Unit 2.3: Find the constant of proportionality from information given on a table and use the constant of proportionality to fill information on a table.
- Unit 2.4: Write equations to represent a proportional relationship described in a table.
- Unit 2.5: Write two equations that represent the same proportional relationship.
- Unit 2.6: Use tables and equations to solve problems involving proportional relationships.
- Unit 2.7: Use a table of values to determine if a relationship is proportional.
- Unit 2.8: Recognize that proportional relationships are characterized by equations in the form y = kx.
- Unit 2.9: Write an equation to represent a proportional relationship and solve problems about proportional relationships.
- Unit 2.10: Generalize that the graph of a proportional relationship lies on a line through the origin.
- Unit 2.11: Interpret points on the graph of a proportional relationship, and identify the constant of proportionality from the graph of a proportional relationship.
- Unit 2.12: Interpret and compare two related proportional relationships on the same graph.
- Unit 2.13: Interpret and compare the same proportional relationship using two different sets of tables, graphs, and equations.
- Unit 2.14: Represent a proportional relationship in four different ways.
- Unit 2.15: Interpret and compare the same proportional relationship using two different sets of tables, graphs, and equations.

In this unit, seventh graders will calculate percentages of rectangular areas and understand why these percentages remain consistent in scaled copies. Students will solve problems involving equivalent ratios with fractions, calculate scale factors and constants of proportionality, and use fractions and decimals to describe increases and decreases. They’ll apply their skills to real-world scenarios like percent increases and decreases in taxes, tips, discounts, and measurement errors represented as percent error. By the end of the unit, students will master using percentages to solve diverse mathematical problems, strengthening their practical and theoretical understanding of proportional reasoning.

- Unit 3.1: Calculate the percentage of a rectangular area that is covered by another region, and explain why the percentage is the same in scaled copies of the same figure.
- Unit 3.2: Solve problems involving equivalent ratios with fractional quantities.
- Unit 3.3: Calculate and interpret the scale factor and constant of proportionality for a proportional relationship.
- Unit 3.4: Use fractions to describe increases and decreases.
- Unit 3.5: Use decimals to describe increases and decreases Lesson 6 Find percent increases and decreases when given an original amount.
- Unit 3.6: Use double number lines to solve problems about percent increases and decreases.
- Unit 3.7: Use equations to represent percent increases and decreases.
- Unit 3.8: Find percentages of quantities that are not whole numbers.
- Unit 3.9: Understand and solve problems about sales tax.
- Unit 3.10: Understand and solve problems about commission, markups, and discounts.
- Unit 3.11: Understand and solve problems involving percentage increase and percentage decrease using real world contexts such as tax, tip, and discount.
- Unit 3.12: Understand problems about measurement error and use percentages to represent measurement error as percent error.
- Unit 3.13: Solve and interpret problems that involve percent error by finding the correct amount, erroneous amount, or percent error.
- Unit 3.14: Generate values that fall within the acceptable range for a measurement, given a maximum percent error and the correct value.
- Unit 3.15: Solve problems about real-world situations that involve percent increase and decrease.

In this unit, seventh graders will interpret signed numbers in contexts like temperature, elevation, and financial transactions. Using number lines, they’ll master adding, subtracting, multiplying, and dividing positive and negative numbers, applying these operations to solve real-world problems. By understanding the relationships between these operations, students will confidently solve equations and interpret directed changes in diverse scenarios involving rational numbers.

- Unit 4.1: Interpret signed numbers in the context of temperature and elevation.
- Unit 4.2: Use a number line to add positive and negative numbers, generalize how to add positive and negative numbers
- Unit 4.3: Understand what positive and negative numbers mean in a situation involving money and calculate an account balance after a deposit or withdrawal.
- Unit 4.4: Use a number line to subtract positive and negative numbers.
- Unit 4.5: Solve subtraction expressions that have the same numbers in the opposite order, and explain the relationship between their differences.
- Unit 4.6: Add and subtract signed numbers to represent gains and losses in different contexts.
- Unit 4.7: Understand that the product of a negative number and positive number is negative and explain how signed numbers can be used to represent position and speed.
- Unit 4.8: Interpret signed numbers when used to represent time in situations about speed and direction as well as understand that the product of two negative numbers is positive.
- Unit 4.9: Use the relationship between multiplication and division to develop the rules for dividing rational numbers.
- Unit 4.10: Multiply and divide rational numbers to solve problems involving constant rates.
- Unit 4.11: Use the relationship between addition and subtraction, and the relationship between multiplication and division, to evaluate expressions with all four operations on the rational numbers.
- Unit 4.12: Interpret situations involving rational numbers, including positive and negative values, and use rational numbers to represent and solve problems.
- Unit 4.13: Solve equations that involve negative numbers.
- Unit 4.14: Write and solve equations to represent situations that involve negative numbers.
- Unit 4.15: Use positive and negative numbers to represent directed change.

In this unit, seventh graders will analyze proportional and non-proportional relationships using tape diagrams and equations to find unknown values. Students will match and coordinate different equation forms with verbal descriptions and tape diagrams, solving word problems involving percent changes. They’ll also explore inequalities, writing and solving them to represent real-world scenarios and interpreting their solutions. Throughout, students will expand their understanding of expressions with negative coefficients, applying properties of operations to simplify and manipulate equivalent expressions effectively.

- Unit 5.1: Find unknown values in relationships, and interpret them as proportional and not proportional.
- Unit 5.2: Interpret tape diagrams that represent word problems, and use them to find unknown values.
- Unit 5.3: Write and match equations and tape diagrams that represent the same situation.
- Unit 5.4: Coordinate tape diagrams, equations of the form px + q = r, and verbal descriptions of the situations, and reason about and interpret a solution.
- Unit 5.5: Coordinate tape diagrams, equations of the form p(x + q) = r, and verbal descriptions of the situations, and reason about and interpret a solution.
- Unit 5.6: Write and categorize equations of the forms px + q = r and p(x + q) = r from situations and tape diagrams.
- Unit 5.7: Use a balanced hanger diagram to reason about writing and solving equations in the form px + q = r.
- Unit 5.8: Solve equations of the form px + q = r and p(x + q) = r that involve negative numbers.
- Unit 5.9: Decide between and use two common approaches for solving an equation of the form p(x + q) = r (expanding using the distributive property, or dividing each side by p)
- Unit 5.10: Use tape diagrams to translate verbal descriptions for situations into an equation of the form px + q = r or p(x + q) = r, and solve the resulting equation to determine an unknown quantity in the situation.
- Unit 5.11: Solve word problems about percent increase or decrease by drawing and reasoning about a tape diagram or by writing and solving an equation.
- Unit 5.12: Write inequality statements to represent inequality situations, and use substitution to determine whether a given value for a variable makes an inequality true.
- Unit 5.13: Write inequalities that represent situations, and use substitution or reasoning about the context to find the solution.
- Unit 5.14: Solve inequalities using the associated equation and testing values to determine the direction of the inequality in the solution.
- Unit 5.15: Match an inequality to a situation it represents, explain what the parts of the inequality mean, solve it, and then interpret what the solution means in the situation.
- Unit 5.16: Write and solve an inequality to solve real-world problems and critique the solution to an inequality.
- Unit 5.17: Extend the distributive property to expressions with negative coefficients.
- Unit 5.18: Use the distributive property to find equivalent expressions by expanding or factoring.
- Unit 5.19: Given an expression, write an equivalent expression with fewer terms using properties of operations, and explain why the expressions are equivalent.
- Unit 5.20: Write expressions with fewer terms that are equivalent to a given expression that includes negative coefficients and parentheses.
- Unit 5.21: Write equivalent expressions with fewer terms by combining like terms.

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