Foundations of Algebra

In this unit, students will learn to describe mathematical relationships and patterns using pictures, words, and algebraic language. Students will use logical reasoning and prior knowledge to develop solutions.

In this unit, students will locate positive and negative numbers on a number line and use this representation to model addition, subtraction, and algebraic relationships.

In this unit, students will zoom into smaller subdivisions of the number line to examine the structure of decimals and fractions and deepen their understanding of number line concepts introduced in Unit 2.

In this unit, students will apply the definition of area using two-dimensional shapes, describe area using units of measure, and create area models to support multiplication with larger numbers and algebraic expressions.

In this unit, students will use mobile diagrams to understand balance, apply that same logic to manipulate and describe algebraic expressions, and use layers of instructions to explain the steps of an equation.

In this unit, students will understand horizontal and vertical axes, use input and output values to place points in two-dimensional space, and plot points on the coordinate plane.

In this unit, students will determine where to begin when solving a problem, identify what can be figured out from each part of a question, and apply previously learned skills to try different problem-solving approaches.

In this unit, students will connect ideas about fractions, algebra, the number line, and area models, with a focus on understanding and using operations with fractions.

In this unit, students will connect patterns and relationships, use graphs to identify patterns, and use equations to describe those patterns.

In this unit, students will use factors to make a product, reverse the multiplication process to find factors, identify factors that multiply to create a number or expression, and use area models to represent expressions.

In this unit, students will understand and apply the basic rule that exponents involve multiplication, use exponents to simplify expressions with very large or very small numbers, and apply powers of 10 to simplify expressions and equations.

In this unit, students will use the knowledge, skills, and habits mathematicians rely on when approaching problems. Students will revisit strategies for reasoning through unfamiliar problems, including puzzling and persevering, seeking and using structure, using tools strategically, describing repeated reasoning, and communicating with precision.