Bedford School District

Curriculum Map Last Updated On 5/22/2024

Grade 7

MATHEMATICS:  Pre-Algebra 7

This course is the natural progression from grade 6 mathematicsPre-Algebra 7 aims to build a strong foundation in mathematical concepts and skills, preparing students for more advanced algebraic thinking. By the end of the course, students should be able to confidently apply mathematical operations to integers, expressions, equations, ratios, proportions, percentages, and more. They should also develop problem-solving skills and the ability to think critically about mathematical concepts.

Course Standards

By the end of the year, students will demonstrate proficiency in solving problems in the following units/topics:

Ratios and Proportional Relationships

• Analyze proportional relationships

• Identify and compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
• Recognize and represent proportional relationships between quantities.
• Use proportional relationships to solve multistep ratio and percent problems, such as simple interest, tax, markups and markdowns, gratuities and commissions, and fees. 

The Number System

• Perform rational number operations

• Apply and extend previous understandings of addition, subtraction, multiplication, and division to add, subtract, multiply, and divide rational numbers, including integers, fractions, and decimals.
• Convert a rational number to a decimal using long division and understand that the decimal form of a rational number terminates in 0s or eventually repeats.
• Solve real-world and mathematical problems involving the four operations with rational numbers.

Expressions and Equations

• Generate equivalent expressions

• Apply properties of operations to generate equivalent expressions (e.g., the distributive property, combining like terms).
• Understand that rewriting an expression in different forms can shed light on the problem and how the quantities in it are related

• Solve problems using linear equations and inequalities

• Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
• 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

Geometry

• Understand geometric relationships

• Draw, construct, and describe geometrical figures and describe the relationships between them.
• Understand and use scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

• Solve problems involving angles

• 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.
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Statistics and Probability

• Analyze and compare populations

• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.

• Find probabilities of events

• Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
• Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency.
• Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

MATHEMATICS:  Pre-Algebra 7/8

Pre-Algebra 7/8 Accelerated is designed to provide an intensive study of key mathematical concepts from both 7th and 8th-grade Pre-Algebra courses, preparing students for success in high school algebra. The course aims to deepen students' understanding of foundational topics while introducing more advanced algebraic concepts. By the end of the course, students will demonstrate proficiency in operations with rational numbers, linear equations, functions, geometric concepts, and statistical reasoning. They will also develop problem-solving skills and the ability to communicate mathematical ideas effectively.

Course Standards

By the end of the year students should demonstrate proficiency in solving problems in the following topics….

• Integer Operations

• Addition, subtraction, multiplication, and division of integers.
• Understanding and applying the properties of integers.

• Expressions and Equations

• Simplifying algebraic expressions.
• Solving one-step and multi-step equations and inequalities.
• Understanding and applying the properties of equality and inequality.

• Ratios, Proportions, and Percentages

• Solving problems involving ratios and proportions.
• Calculating percentages and solving percentage problems.

• Geometry: Area and Volume

• Calculating the area of various geometric shapes.
• Determining the volume of three-dimensional figures.

• Probability and Statistics

• Understanding and calculating simple probabilities.
• Collecting, organizing, and interpreting data.
• Using measures of central tendency (mean, median, mode) and variability (range, interquartile range, mean absolute deviation).

• Linear Equations and Inequalities

• Solving and graphing linear equations and inequalities.
• Understanding and interpreting the slope and y-intercept of a linear equation.

• Systems of Equations

• Solving systems of linear equations using various methods (graphing, substitution, elimination).

• Functions

• Understanding the concept of a function and using function notation.
• Evaluating and interpreting linear functions.

• Quadratic Equations

• Solving quadratic equations by factoring, using the quadratic formula, and completing the square.
• Graphing quadratic functions and understanding their properties.

• Exponents and Radicals

• Applying the laws of exponents.
• Simplifying and operating with radical expressions.

• Polynomials and Rational Expressions

• Adding, subtracting, multiplying, and factoring polynomials.
• Simplifying and performing operations with rational expressions.

• Transformations

• Understanding and applying translations, rotations, reflections, and dilations.
• Using coordinate geometry to describe transformations.

• Coordinate Geometry

• Graphing points, lines, and shapes on the coordinate plane.

• Problem-Solving and Communication

• Applying mathematical concepts to solve real-world problems.
• Using critical thinking and logical reasoning to approach complex problems.
• Explaining mathematical reasoning and solutions clearly and effectively.
• Using appropriate mathematical vocabulary and notation.

MATHEMATICS:  Algebra I

Successful completion of Algebra I in grade 7 qualifies a student for enrollment in grade 8 Geometry.

Course Standards

By the end of the year students should demonstrate proficiency in solving problems in the following topics….

Number and Quantity

• Use rational exponents
• Perform real number operations

Algebra

• Solve linear and quadratic equations
• Solve inequalities and systems of equations

Functions

• Define, evaluate, and compare functions
• Write sequences
• Model relationships

Geometry

• Apply the Pythagorean Theorem

Statistics and Analysis

• Represent and interpret data
• Analyze bivariate data