From arithmetic to algebra: variables, expressions, and the distributive property
Build a friendly algebra foundation by plugging numbers into expressions, distributing multiplication, handling negative signs, and combining like terms.
Common CoreA-SSE.A.1
6 lessons22 short videos5 key concepts, out loud
1.1
Meet variables and plug in numbers.
Meet variables, replace them with numbers, and calculate
A-SSE.A.1
Key idea
A variable can stand for a number. To evaluate an expression, replace each variable with its given value using parentheses, then follow the order of operations.
Learn what variables mean, plug in given numbers, and calculate the value of algebraic expressions.
Key concept · Lesson 1.1
Substitute with parentheses
Listen0:00 / 0:18
Transcript. When you replace a variable with a negative number, put the value in parentheses first. The parentheses keep the negative sign attached, especially when an exponent is involved. After substituting, follow the normal order of operations and calculate carefully.
1.2
The Distributive Property (Area Models)
Multiply a number by a sum using area models
A-SSE.A.1
Key idea
The distributive property allows you to multiply a single term by each term inside parentheses, which can be visualized as finding the total area of a split rectangle.
Learn how to multiply a number by a sum using visual area models to see why the distributive property works.
Key concept · Lesson 1.2
Distribute to every term
Listen0:00 / 0:19
Transcript. The number outside parentheses multiplies every term inside. Draw or imagine one arrow to each term, then multiply while keeping each sign attached. For example, three times the quantity x plus four becomes three x plus twelve.
1.3
Distributing Negatives
Multiply grouped terms by a negative number without sign errors
A-SSE.A.1
Key idea
Distributing a negative sign changes the sign of every term inside the parentheses because you are multiplying each term by -1.
Master the art of distributing negative signs and subtraction across parentheses without making common sign errors.
Key concept · Lesson 1.3
Distribute the negative
Listen0:00 / 0:15
Transcript. A minus in front of parentheses means negative one is multiplying the whole group. Distribute that negative to every term. A negative times a positive stays negative, while a negative times a negative becomes positive.
1.4
Combining Like Terms & Simplifying
Group and combine similar parts of an expression
A-SSE.A.1
Key idea
Combine terms with the exact same variables and exponents by adding or subtracting their coefficients, keeping the variable part unchanged.
Learn to identify terms with matching variables and exponents, then combine them to simplify algebraic expressions.
Key concept · Lesson 1.4
Combine only like terms
Listen0:00 / 0:19
Transcript. Terms combine only when their variable parts match exactly, including the exponent. Add or subtract the coefficients and keep the variable part unchanged. If the letters or powers differ, leave those terms separate in the simplified expression.
1.5
Patterns to Expressions
Turn a growing pattern into a rule you can use for any step
A-SSE.A.1
Key idea
A growing pattern has a part that stays the same and a part that grows with the step number. Naming the step number n and describing the picture in terms of n produces an expression that computes any step directly, without stepping through every one before it.
Study a growing tile pattern, write an expression in n that matches its structure, and use it to jump straight to any step.
Key concept · Lesson 1.5
Build the rule from two parts
Listen0:00 / 0:18
Transcript. A growing pattern has a changing part and often a fixed part. The amount added each step becomes the coefficient of n. Then adjust the constant so the rule matches step one, and use it to jump directly to any step.
1.6
Review & Assessment
Practice and test your skills with expressions and the distributive property
Review, practice, quiz and test
Key idea
Review substitution, distribution, negative signs, and combining like terms with targeted practice and a chapter assessment.
Consolidate your understanding of evaluating and simplifying expressions before taking the chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
