Teacher Certification: Praxis Core Math Number Quantity

What Is It?

1. Number & Quantity is a fundamental math topic that deals with understanding and working with numbers, quantities, and mathematical relationships.
2. It is tested, applied, audited, and used in the real world to ensure that students, teachers, and educators can accurately interpret and apply mathematical concepts to solve problems and make informed decisions.

Why Does the Exam Ask This?

The exam asks this topic to measure the candidate's ability to apply mathematical concepts to real-world problems, demonstrate a deep understanding of mathematical relationships, and make informed decisions based on data and analysis.

What Do I Need to Know First?

1. Basic algebraic concepts, such as variables, expressions, and equations.
2. Understanding of mathematical operations, including addition, subtraction, multiplication, and division.
3. Familiarity with mathematical notation and vocabulary.
4. Basic geometry and measurement concepts, such as points, lines, angles, and shapes.

Topic Snapshot

Number & Quantity is a critical topic in Teacher Certification, as it assesses a candidate's ability to understand and apply mathematical concepts to real-world problems. This topic is essential for educators to develop and implement effective math curricula, assess student learning, and make data-driven decisions.

Exam / Job / Audit Weighting

• Frequency: High
• Difficulty Rating: Intermediate
• Question Type or Real-World Task Type: Multiple-choice questions, short-answer questions, and scenario-based questions.

Difficulty Level

intermediate

Must-Know Rules, Formulas, Standards, or Principles

1. The Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
2. The Pythagorean Theorem: a^2 + b^2 = c^2.
3. The concept of equivalent ratios: a/b = c/d.

Misconceptions

1. Believing that all mathematical problems require complex calculations.
2. Assuming that mathematical concepts are only relevant to math classes.
3. Thinking that mathematical notation is only used in math classes.
4. Believing that geometry is only about shapes and measurements.
5. Assuming that mathematical concepts are not relevant to real-world problems.

Common Mistakes

1. Forgetting to follow the Order of Operations.
2. Misapplying mathematical concepts to real-world problems.
3. Failing to check units and dimensions.
4. Making calculation errors.
5. Failing to consider multiple solutions.

The Common Trap

The common trap is to assume that mathematical concepts are only relevant to math classes and that they are not applicable to real-world problems.

Terms to Remember

1. Variable: A symbol that represents a value that can change.
2. Expression: A combination of numbers, variables, and mathematical operations.
3. Equation: A statement that two expressions are equal.
4. Inequality: A statement that two expressions are not equal.
5. Ratio: A comparison of two numbers.

Step-by-Step Process

1. Read the problem carefully and identify the key elements.
2. Determine the type of problem (e.g., algebraic, geometric, measurement).
3. Apply the relevant mathematical concepts and formulas.
4. Check the units and dimensions.
5. Verify the solution.

Exam Answer Builder

1-mark Question

• What it tests: Basic math vocabulary.
• Example Question: What is the value of x in the equation 2x + 5 = 11?
• Key Tip for answering well: Read the question carefully and identify the key elements.

2-mark or 3-mark Question

• What it tests: Basic math operations and algebraic concepts.
• Example Question: Solve the equation 2x + 5 = 11.
• Key Tip for answering well: Follow the Order of Operations and check the units and dimensions.

5-mark or long-answer Question

• What it tests: Application of mathematical concepts to real-world problems.
• Example Question: A school has 250 students, and the ratio of boys to girls is 3:5. How many boys and girls are in the school?
• Key Tip for answering well: Read the problem carefully and identify the key elements, then apply the relevant mathematical concepts and formulas.

Case Study or application-based Question

• What it tests: Ability to apply mathematical concepts to real-world problems.
• Example Question: A teacher is planning a field trip for 30 students. The bus rental company charges $50 per hour, and the students will be traveling for 2 hours. How much will the bus rental cost?
• Key Tip for answering well: Read the problem carefully and identify the key elements, then apply the relevant mathematical concepts and formulas.

This vs That

Number & Quantity is often confused with Algebra. While both topics deal with mathematical concepts, Number & Quantity focuses on understanding and working with numbers, quantities, and mathematical relationships, whereas Algebra focuses on solving equations and manipulating variables.

Time-Saver Hack

To quickly identify the type of problem, read the question carefully and identify the key elements. This will help you determine the relevant mathematical concepts and formulas to apply.

Mini Scenarios

Basic Scenario

A teacher is planning a math lesson for 25 students. The students will be working in pairs, and each pair will need 2 pencils and 1 calculator. How many pencils and calculators will the teacher need in total?

Applied Scenario

A school has 300 students, and the ratio of boys to girls is 3:5. How many boys and girls are in the school?

Tricky Scenario

A teacher is planning a field trip for 30 students. The bus rental company charges $50 per hour, and the students will be traveling for 2 hours. However, the bus will be traveling for 1 hour before reaching the destination. How much will the bus rental cost?

Diagnostic MCQ Bank

Question 1

What is the value of x in the equation 2x + 5 = 11? A) 2 B) 3 C) 4 D) 5

Correct Answer

B) 3

Explanation

To solve the equation, subtract 5 from both sides: 2x = 6, then divide both sides by 2: x = 3.

Why the correct answer is right

The correct answer is 3 because it is the solution to the equation.

Why the trap option is tempting

The trap option is tempting because it is close to the correct answer, but it is not the correct solution.

Question 2

Solve the equation 2x + 5 = 11.
A) x = 2 B) x = 3 C) x = 4 D) x = 5

Correct Answer

B) x = 3

Explanation

To solve the equation, subtract 5 from both sides: 2x = 6, then divide both sides by 2: x = 3.

Why the correct answer is right

The correct answer is 3 because it is the solution to the equation.

Why the trap option is tempting

The trap option is tempting because it is close to the correct answer, but it is not the correct solution.

Question 3

A school has 250 students, and the ratio of boys to girls is 3:5. How many boys and girls are in the school? A) 150 boys and 100 girls B) 180 boys and 70 girls C) 200 boys and 50 girls D) 250 boys and 0 girls

Correct Answer

A) 150 boys and 100 girls

Explanation

To solve the problem, multiply the total number of students by the ratio: 250 x (3/8) = 125 boys, and 250 x (5/8) = 156.25 girls, round down to 150 boys and 100 girls.

Why the correct answer is right

The correct answer is 150 boys and 100 girls because it is the solution to the problem.

Why the trap option is tempting

The trap option is tempting because it is close to the correct answer, but it is not the correct solution.

Question 4

A teacher is planning a field trip for 30 students. The bus rental company charges $50 per hour, and the students will be traveling for 2 hours. However, the bus will be traveling for 1 hour before reaching the destination. How much will the bus rental cost? A) $100 B) $120 C) $150 D) $200

Correct Answer

C) $150

Explanation

To solve the problem, multiply the bus rental cost by the number of hours: $50 x 2 = $100, then add the additional hour: $100 + $50 = $150.

Why the correct answer is right

The correct answer is $150 because it is the solution to the problem.

Why the trap option is tempting

The trap option is tempting because it is close to the correct answer, but it is not the correct solution.

Question 5

A school has 300 students, and the ratio of boys to girls is 3:5. How many boys and girls are in the school? A) 180 boys and 120 girls B) 200 boys and 100 girls C) 220 boys and 80 girls D) 250 boys and 50 girls

Correct Answer

A) 180 boys and 120 girls

Explanation

To solve the problem, multiply the total number of students by the ratio: 300 x (3/8) = 112.5 boys, round down to 112 boys, and 300 x (5/8) = 187.5 girls, round down to 187 girls.

Why the correct answer is right

The correct answer is 180 boys and 120 girls because it is the solution to the problem.

Why the trap option is tempting

The trap option is tempting because it is close to the correct answer, but it is not the correct solution.

Real-World Patterns

Number & Quantity shows up in real-world patterns in the following ways:

1. Budgeting and financial planning: Understanding numbers and quantities is essential for creating and managing budgets, making financial decisions, and analyzing financial data.
2. Data analysis and interpretation: Number & Quantity is critical for analyzing and interpreting data, identifying trends, and making informed decisions.
3. Scientific research and experimentation: Scientists and researchers rely on mathematical concepts, including Number & Quantity, to design experiments, collect and analyze data, and draw conclusions.

30-Second Cheat Sheet

1. The Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
2. The Pythagorean Theorem: a^2 + b^2 = c^2.
3. The concept of equivalent ratios: a/b = c/d.
4. Variables: Symbols that represent values that can change.
5. Expressions: Combinations of numbers, variables, and mathematical operations.

Related Concepts

1. Algebra: Solving equations and manipulating variables.
2. Geometry: Understanding points, lines, angles, and shapes.
3. Measurement: Understanding units and dimensions.

Verified Source List

1. Official Praxis Core Math Study Guide
2. Khan Academy Math Course
3. OpenStax Algebra and Geometry Textbooks
4. National Council of Teachers of Mathematics (NCTM) Standards and Resources
5. American Mathematical Association of Two-Year Colleges (AMATYC) Resources