# Ch 2: SBA Math - Grade 6: Logic & Mathematical Reasoning

### About This Chapter

## SBA Math - Grade 6: Logic & Mathematical Reasoning - Chapter Summary

The short video lessons in this chapter can be viewed from any internet device to make studying accessible, easy and fun. This chapter reviews the logic and mathematical reasoning concepts likely to appear on the SBA, including:

- Functions of critical thinking and logic in math
- Conditional statements, propositions, and truth values
- Logical equivalence and reasoning
- Problem-solving mathematical principles
- Processes for solving word problems

Video transcripts highlight key ideas and lesson quizzes allow students to practice using the information they've covered. Reach out to our instructors if your middle schooler needs additional study help.

### 1. Critical Thinking and Logic in Mathematics

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

### 2. Propositions, Truth Values and Truth Tables

Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.

### 3. Logical Math Connectors: Conjunctions and Disjunctions

Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.

### 4. Conditional Statements in Math

Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.

### 5. Logic Laws: Converse, Inverse, Contrapositive & Counterexample

Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.

### 6. Reasoning in Mathematics: Inductive and Deductive Reasoning

Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.

### 7. Reasoning in Mathematics: Connective Reasoning

Connective reasoning is reasoning that has an operation, or a way to connect two phrases. The five main logic connectives will be reviewed in this lesson.

### 8. Polya's Four-Step Problem-Solving Process

Problem solving can be a problem. Any problem is solved easier with an action plan. Polya's 4-Step Problem-Solving Process is discussed in this lesson to help students develop an action plan for addressing problems.

### 9. Mathematical Principles for Problem Solving

Solving problems is not just a simple, straightforward process. There are a few principles that can help you as you approach any problem solving scenarios. This lesson covers those principles with examples.

### 10. The Three-Way Principle of Mathematics

What methods are there to solve and understand mathematical problems? This lesson will review three methods to understand mathematical problems (verbal, graphical, and by example). Each will be illustrated with examples.

### 11. Solving Mathematical Problems Using Estimation

Estimating is a method of calculating a result that is close to, but not exactly, the correct answer to a math problem. Why would you ever need to do this? This lesson reviews estimating and answers the question as to why you would do it.

### 12. Using Mathematical Models to Solve Problems

Mathematical modeling simply refers to the creation of mathematical formulas to represent a real world problem in mathematical terms. This lesson reviews the creation and pitfalls of mathematical models.

### 13. Solving Word Problems: Steps & Examples

Watch this video lesson to learn how you can solve word problems by following this 3-step process. Learn how to visualize your problem so you fully understand it. Then learn how to write and solve your equations.

### 14. Solving Word Problems with Multiple Steps

Not all word problems are so straightforward that they only require you to do one operation and you're done. Some are more complicated, requiring several steps. Watch this video lesson to learn how to solve these kinds of problems.

### 15. Restating Word Problems Using Words or Images

Watch this video lesson to learn how you can use sketches and notes to help you visualize a problem. Watch how easy it becomes to solve your problem once you have visualized it.

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### Other Chapters

Other chapters within the Smarter Balanced Assessments - Math Grade 6: Test Prep & Practice course

- SBA Math - Grade 6: Basic Arithmetic Operations
- SBA Math - Grade 6: Number Theory
- SBA Math - Grade 6: Introduction to Fractions
- SBA Math - Grade 6: Operations with Fractions
- SBA Math - Grade 6: Ratios, Rates & Proportions
- SBA Math - Grade 6: Percents
- SBA Math - Grade 6: Introduction to Decimals
- SBA Math - Grade 6: Operations with Decimals
- SBA Math - Grade 6: The Coordinate Graph
- SBA Math - Grade 6: Inequalities
- SBA Math - Grade 6: Factoring
- SBA Math - Grade 6: Rational Numbers
- SBA Math - Grade 6: Basic Algebraic Expressions
- SBA Math - Grade 6: Writing Algebraic Expressions
- SBA Math - Grade 6: Algebraic Distribution
- SBA Math - Grade 6: One-Step Equations
- SBA Math - Grade 6: Perimeter & Area
- SBA Math - Grade 6: Surface Area & Volume of Geometric Solids
- SBA Math - Grade 6: Data & Graphs
- SBA Math - Grade 6: Statistics
- Smarter Balanced Assessments - Math Grade 6 Flashcards