7th Grade Math

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.

Click here to download a PDF version of Unit 1: Scale 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: Use the unit rate to decide if ratios are proportional.
• Unit 2.2: Generate proportions to find the constant of proportionality.
• Unit 2.3: Use the constant of proportionality to fill information on a table.
• Unit 2.4: Write two equations to represent a proportional relationship in a table.
• Unit 2.5: Use a table and equation to solve problems that involve proportional relationships.
• Unit 2.6: Use a table and equation to solve problems that are not always proportional.
• Unit 2.7: Recognize that proportional relationships are characterized by equations in the form y = kx.
• Unit 2.8: Use an equation to solve problems that involve proportional relationships.
• Unit 2.9: Write an equation for story problems and determine if it is a proportion.
• Unit 2.10: Represent a proportion table or equations with a graph.
• Unit 2.11: Represent a story with a table, equation and graph.
• Unit 2.12: Make a generalization about graphs of proportional relationships.
• Unit 2.13: Interpret points on the graph with the context of a story.
• Unit 2.14: Use the constant of proportionality for more complicated proportion problems.
• Unit 2.15: Find and compare rates.

Click here to download a PDF version of Unit 2:Introducing Proportional Relationships

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: Convert between a fraction, decimal and percent then draw a picture.
• Unit 3.2: Relate percents to proportions to find a fraction of a given amount.
• Unit 3.3: Find the part, the total or the percent in story problems.
• Unit 3.4: Use percents to compare quantities.
• Unit 3.5: Find percent increase and decrease.
• Unit 3.6: Find the new amount given the percent increase or decrease.
• Unit 3.7: Find the original amount given the percent increase or decrease.
• Unit 3.8: Solve markup and markdown problems.
• Unit 3.9: Solve percent error problems.
• Unit 3.10: Solve a variety of problems for review.
• Unit 3.11: Solve simple interest problems.
• Unit 3.12: Solve problems about commissions, taxes, and fees.
• Unit 3.13: Use mental math to solve percent problems.
• Unit 3.14: Work with percentages that are not whole numbers.
• Unit 3.15: Solve multi-step percent problems.

Click here to download a PDF version of Unit 3: Proportional Relationships and Percentages

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.

Click here to download a PDF version of Unit 4: Rational Number Arithmetic

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.

Click here to download a PDF version of Unit 5: Expressions, Equations, and Inequalities