Sample Lesson

This lesson sampler includes eight lessons from Introduction to Algebra. Collectively, they are intended to give
the reader snapshots of lesson content, structure, and composition. Each lesson includes Teacher Pages (TP), Student Pages (SP), and Reproducibles Pages (R). Assessments (A) and overhead transparency masters (OH)
are not included here.

These particular lessons were selected because they are relatively simple to implement without professional development (expected for new users) or extra support. Permission is granted to teachers to use these lessons
for program field-testing.

 

Lesson 1.1

Whole Numbers: Using an Area Model to Explain Multiplication
This lesson (Week 1, Lesson 1) begins with strategies to assist students in deriving multiplication facts and progresses to a visual method for recording multidigit multiplication based on area of rectangles. The lesson also introduces the commutative, associative, and distributive properties in the context of multiplication concepts and procedures. An area model is used as an alternative multiplication strategy for struggling students and as a vehicle for understanding the traditional multiplication algorithm.

Some Important features on the planning information page (TP2):

  • Manipulatives help students understand the concept of the area of rectangles prior to generalizing the model.
  • Group work establishes a spirit of classroom collaboration from the beginning of the school year.
  • Making concepts meaningful prior to formalizing definitions and procedures is fundamental to the program.

Lesson 12.1

Brief Explanation


Lesson 12.2

Fractions: Multiplication 1
This lesson extends the concepts and procedures for multiplication of whole numbers to fraction multiplication; namely, that multiplication can be represented as repeated addition or with an area model. Connecting to students’ prior knowledge makes fraction multiplication meaningful, its procedures plausible, and helps to ensure better retention.

Previous fractions lessons included the use of manipulatives, pictures, and sense-making strategies to address fraction concepts (the meaning of parts and wholes; fraction equivalence and comparisons; and fraction, decimal, and percent conversions), and addition and subtraction rules. Later lessons will explore fraction division and decimal multiplication and division. Many opportunities for practice with rational numbers concepts and procedures are provided throughout a 15-week period.

Math Background 1 (TP11) connects previous models to current work. Other math backgrounds provide adult justifications for fraction multiplication procedures.


Lesson 13.1

Brief Explanation


Lesson 17.2

Understanding Percents
This lesson falls near the beginning of a cluster of lessons that deals with proportional reasoning concepts, including ratio, rate, proportion, and percent. This lesson stresses visuals, familiar contexts, and mental math to promote sense-making strategies to find percents of numbers. In earlier lessons, students linked percents to fractions and decimals. In future lessons, students learn routines for these computations.
Important features of the lesson:


  • Visuals (SP6): students estimate the fullness of the containers, relying on benchmark percents, such as 50%, 25% and 10%.
  • Familiar context (SP6-9): students find simple percents of a dollar and of a meter. Later, students use mental strategies to find more difficult percents of amounts, based on benchmarks.
  • Multiple strategies are recommended and illustrated in the Math Background (TP10).


Lesson 21.1

Brief Explanation


Lesson 25.1

Using Algebra to Prove Conjectures 1
In this lesson, students experience the power of algebra as they prove number tricks using algebraic expressions. Earlier lessons in the cluster focused on variables, writing and simplifying expressions, and solving equations. In later lessons, students simplify more difficult expressions, solve more complex equations, and use algebra to solve a variety of problems.