Chapter 1 – Algebraic Notation

# Note to Students:

Students should be aware that these worksheets are not ‘fill in the blank’ worksheets. We have intentionally given you no space to write answers on the worksheets. You should have a notebook for your work, perhaps even beginning by sketching ideas on a white board or scratch paper until you have sufficient organization to put a coherent explanation in your notebook. Note also that the expectation is to write ‘explanations’ and not ‘answers’. These activities are not designed to teach computational skills, but instead are designed to introduce mathematical concepts. The process used to solve problems is the focus, not the end result.

# Activity 1a – Multiplication via the FOIL Method

This first activity reviews multiplication, starting with the algorithm for multiplying two digit numbers. Students may bring a variety of techniques to the discussion, and it is important to see multiple representations. One important aspect of learning mathematics is to be able to make connections between different approaches that solve the same problem. The insights from multiplying two digit numbers should lead to insights on the FOIL process.

Part II of this activity is for more advanced students. It leads toward the Binomial Theorem and the connection to the theory of probability

Multiplication via the FOIL Method

# Activity 1b – Factoring

This activity builds the fundamentals of the factoring process. The `Box Method’ is used to demonstrate certain principles, though students may have a variety of methods that work. Again, the goal here is to share ideas, approach the problem from multiple perspectives, and understand the connections between various approaches.

Factoring

# Activity 1c – Reducing Fractions

This activity reviews the basics of reducing fractions by factoring. The topic begins with numerators and denominators which are integers before progressing to polynomials. It is important that students understand the factoring process and why terms that are added can’t be cancelled.

Reducing Fractions

# Activity 1d – Multiplying and Dividing Fractions

This activity reviews the basics of multiplying and dividing fractions. It relies on students’ ability to reduce fractions.

Multiplying and Dividing Fractions

# Activity 1e – Adding and Subtracting Fractions

This activity reviews the basics of adding and subtracting fractions. The activity begins with numerators and denominators which are integers before progressing to polynomials. It is important that students be able to describe the process for finding a common denominator, including the factoring process on the early questions before tackling the harder questions.