Category: 03. A1

Posted on

Algebra I Issue 001: Evaluating Numerical Expressions

Lesson Focus

This issue practices Evaluating Numerical Expressions in Algebra I.

Synopsis

A numerical expression is a mathematical phrase made from numbers and operation symbols but does not contain an equals sign. Evaluating an expression means finding its numerical value by carrying out the indicated operations correctly. Expressions may include addition, subtraction, multiplication, division, exponents, and grouping symbols such as parentheses.

In this issue, you practice evaluating numerical expressions carefully and accurately. You identify the operations that must be performed and work through them in the proper sequence. Developing this skill is essential because algebraic expressions follow the same operational rules; later, numbers will often be replaced by variables whose values must be substituted before an expression is evaluated.

Practice Problems

Problem 1. Evaluate [latex]3 + 4 × 2[/latex].

A. [latex]14[/latex]

B. [latex]11[/latex]

C. [latex]10[/latex]

D. [latex]7[/latex]

E. [latex]24[/latex]

Problem 2. Evaluate [latex]18 ÷ 3 + 5[/latex].

A. [latex]3[/latex]

B. [latex]6[/latex]

C. [latex]11[/latex]

D. [latex]15[/latex]

E. [latex]30[/latex]

Problem 3. Evaluate [latex]2^3 + 4[/latex].

A. [latex]10[/latex]

B. [latex]12[/latex]

C. [latex]14[/latex]

D. [latex]16[/latex]

E. [latex]20[/latex]

Problem 4. Evaluate [latex](6 + 2) × 3[/latex].

A. [latex]14[/latex]

B. [latex]18[/latex]

C. [latex]21[/latex]

D. [latex]24[/latex]

E. [latex]30[/latex]

Problem 5. Evaluate [latex]5(4 – 1)[/latex].

A. [latex]9[/latex]

B. [latex]12[/latex]

C. [latex]15[/latex]

D. [latex]18[/latex]

E. [latex]20[/latex]

Problem 6. Evaluate [latex]7^2 – 9[/latex].

A. [latex]40[/latex]

B. [latex]42[/latex]

C. [latex]49[/latex]

D. [latex]56[/latex]

E. [latex]58[/latex]

Problem 7. Evaluate [latex]30 – 12 ÷ 3[/latex].

A. [latex]6[/latex]

B. [latex]18[/latex]

C. [latex]24[/latex]

D. [latex]26[/latex]

E. [latex]54[/latex]

Google Form

Open Google Form

Answer Key

  1. Problem 1: B
  2. Problem 2: C
  3. Problem 3: B
  4. Problem 4: D
  5. Problem 5: C
  6. Problem 6: A
  7. Problem 7: D
Posted on

Algebra I Issue 002: Order of Operations (PEMDAS)

Lesson Focus

This issue practices Order of Operations (PEMDAS) in Algebra I.

Synopsis

When an expression contains more than one operation, the order of operations provides a consistent set of rules for deciding what to calculate first. A common memory aid is PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, followed by Addition and Subtraction from left to right. Multiplication does not automatically come before division, and addition does not automatically come before subtraction when they appear at the same level.

In this issue, you apply the order of operations to evaluate expressions step by step. You learn to respect grouping symbols, simplify powers, and then perform multiplication, division, addition, and subtraction in the correct order. Accurate use of these rules is fundamental throughout algebra because even a small change in operation order can produce a completely different result.

Practice Problems

Problem 1. Which operation should be done first in [latex]8 + 3 × 5[/latex]?

A. addition

B. multiplication

C. subtraction

D. division

E. comparison

Problem 2. Evaluate [latex]6 + 2^3[/latex].

A. [latex]14[/latex]

B. [latex]16[/latex]

C. [latex]64[/latex]

D. [latex]512[/latex]

E. [latex]10[/latex]

Problem 3. Evaluate [latex](10 – 4)^2[/latex].

A. [latex]12[/latex]

B. [latex]24[/latex]

C. [latex]30[/latex]

D. [latex]36[/latex]

E. [latex]96[/latex]

Problem 4. Evaluate [latex]20 ÷ 5 × 2[/latex].

A. [latex]2[/latex]

B. [latex]4[/latex]

C. [latex]8[/latex]

D. [latex]10[/latex]

E. [latex]20[/latex]

Problem 5. Evaluate [latex]3 + 18 ÷ (2 + 4)[/latex].

A. [latex]6[/latex]

B. [latex]9[/latex]

C. [latex]12[/latex]

D. [latex]21[/latex]

E. [latex]24[/latex]

Problem 6. Evaluate [latex]4 × 3^2[/latex].

A. [latex]24[/latex]

B. [latex]36[/latex]

C. [latex]64[/latex]

D. [latex]144[/latex]

E. [latex]48[/latex]

Problem 7. Evaluate [latex]7 + 5(6 – 2)[/latex].

A. [latex]27[/latex]

B. [latex]48[/latex]

C. [latex]75[/latex]

D. [latex]19[/latex]

E. [latex]35[/latex]

Google Form

Open Google Form

Answer Key

  1. Problem 1: B
  2. Problem 2: A
  3. Problem 3: D
  4. Problem 4: C
  5. Problem 5: A
  6. Problem 6: B
  7. Problem 7: A
Posted on

Algebra I Issue 003: Properties of Real Numbers

Lesson Focus

This issue practices Properties of Real Numbers in Algebra I.

Synopsis

The real number system follows several properties that allow expressions to be rewritten without changing their value. The commutative properties allow the order of addition or multiplication to change, while the associative properties allow numbers to be regrouped. The distributive property connects multiplication with addition or subtraction. Identity and inverse properties describe special relationships involving 0, 1, opposites, and reciprocals.

In this issue, you practice recognizing and applying these properties to numerical and algebraic expressions. Rather than memorizing names alone, focus on what each property permits you to do. These rules provide the logical foundation for simplifying expressions, combining like terms, factoring, solving equations, and explaining why algebraic transformations are valid.

Practice Problems

Problem 1. Which shows the commutative property of addition?

A. [latex]a + b = b + a[/latex]

B. [latex]a(b + c) = ab + ac[/latex]

C. [latex]a + 0 = a[/latex]

D. [latex]a × 1 = a[/latex]

E. [latex]a + (b + c) = (a + b) + c[/latex]

Problem 2. Which shows the distributive property?

A. [latex]a + b = b + a[/latex]

B. [latex]a(b + c) = ab + ac[/latex]

C. [latex]a + 0 = a[/latex]

D. [latex]a × 1 = a[/latex]

E. [latex]ab = ba[/latex]

Problem 3. What is the additive identity?

A. 0

B. 1

C. -1

D. a

E. 10

Problem 4. What is the multiplicative identity?

A. 0

B. 1

C. -1

D. a

E. 10

Problem 5. Simplify using the distributive property: [latex]3(x + 4)[/latex].

A. [latex]3x + 4[/latex]

B. [latex]x + 12[/latex]

C. [latex]3x + 12[/latex]

D. [latex]7x[/latex]

E. [latex]12x[/latex]

Problem 6. Which property is shown by [latex](2 + 3) + 4 = 2 + (3 + 4)[/latex]?

A. commutative

B. associative

C. distributive

D. identity

E. inverse

Problem 7. Which is always true for real numbers [latex]a[/latex] and [latex]b[/latex]?

A. [latex]a – b = b – a[/latex]

B. [latex]a ÷ b = b ÷ a[/latex]

C. [latex]a + b = b + a[/latex]

D. [latex]a + b = ab[/latex]

E. [latex]a^2 = a[/latex]

Google Form

Open Google Form

Answer Key

  1. Problem 1: A
  2. Problem 2: B
  3. Problem 3: A
  4. Problem 4: B
  5. Problem 5: C
  6. Problem 6: B
  7. Problem 7: C