About This Chapter
SBA Math - Grade 8: Logic & Mathematical Reasoning - Chapter Summary
If your 8th grader needs to improve his or her logic and reasoning skills used to solve mathematical problems, look no further than this chapter's video lessons. After completing the lessons, students should be ready to do the following on the 8th grade SBA Math assessment:
- Define logic
- Create and interpret truth tables
- Distinguish between conjunctions and disjunctions
- Understand conditional statements
- Identify types of logical fallacies
- Differentiate between the types of mathematical reasoning
- List the steps in Polya's problem solving process
- Explain key math principles used in problem solving
- Solve problems using mathematical models
- Restate and solve word problems
With our lessons, students have access to entertaining videos, transcripts and self-assessment quizzes. Our professional instructors break down math concepts and guide them through each stage of solving sample problems. The videos also contain engaging graphics and realistic examples to boost their understanding of the material.
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 within the Smarter Balanced Assessments - Math Grade 8: Test Prep & Practice course
- SBA Math - Grade 8: Basic Arithmetic Operations
- SBA Math - Grade 8: Number Theory
- SBA Math - Grade 8: Introduction to Fractions
- SBA Math - Grade 8: Operations with Fractions
- SBA Math - Grade 8: Ratios, Rates & Proportions
- SBA Math - Grade 8: Percents
- SBA Math - Grade 8: Introduction to Decimals
- SBA Math - Grade 8: Operations with Decimals
- SBA Math - Grade 8: The Coordinate Graph
- SBA Math - Grade 8: Inequalities
- SBA Math - Grade 8: Factoring
- SBA Math - Grade 8: Rational Numbers
- SBA Math - Grade 8: Roots & Radical Expressions
- SBA Math - Grade 8: Exponents & Exponential Expressions
- SBA Math - Grade 8: Basic Algebraic Expressions
- SBA Math - Grade 8: Writing Algebraic Expressions
- SBA Math - Grade 8: Algebraic Distribution
- SBA Math - Grade 8: Rational Expressions
- SBA Math - Grade 8: Linear Equations
- SBA Math - Grade 8: Systems of Linear Equations
- SBA Math - Grade 8: Properties of Functions
- SBA Math - Grade 8: Graphing Functions
- SBA Math - Grade 8: Symmetry, Similarity & Congruence
- SBA Math - Grade 8: Lines & Angles
- SBA Math - Grade 8: Perimeter & Area
- SBA Math - Grade 8: Surface Area & Volume of Geometric Solids
- SBA Math - Grade 8: Triangles
- SBA Math - Grade 8: Triangle Theorems & Proofs
- SBA Math - Grade 8: Similar Polygons
- SBA Math - Grade 8: The Pythagorean Theorem
- SBA Math - Grade 8: Transformations
- SBA Math - Grade 8: Data & Graphs
- SBA Math - Grade 8: Statistics
- SBA Math - Grade 8: Probability
- SBA Math - Grade 8: Rate of Change
- Smarter Balanced Assessments - Math Grade 8 Flashcards