About This Chapter
TACHS: Mathematical Reasoning - Chapter Summary
With its series of short, engaging lesson videos, this chapter will help you improve your mathematical reasoning skills in time for the Test for Admission into Catholic High Schools (TACHS). Our expert instructors will review with you examples of conjecture and different types of reasoning in mathematics. From these lessons, you should gain a better understanding of:
- Conjecture in mathematics
- Connective, inductive and deductive reasoning
- Critical thinking and logic
- Converse, inverse, contrapositive and counterexample: logical equivalence
The videos use graphics and narration to explain these topics. Transcripts and quizzes are included in the chapter. If you have any questions about mathematical reasoning, visit the dashboard and use the 'ask-an-expert' feature to contact a math professional.
TACHS: Mathematical Reasoning Chapter Objectives
Catholic high schools in the Archdiocese of New York and the Diocese of Brooklyn/Queens use the TACHS to measure the academic skills of 8th graders who are applying for admission to their institutions. This entrance exam is composed of four sub-tests: Reading, Language, Mathematics and Ability. The objective of the first section of the math sub-test is to assess candidates' understanding of mathematical relationships and processes, while the second section of the math test measures candidates' ability to perform operations and utilize problem-solving strategies to work out math problems. This chapter will help you prepare for the mathematics subtest by improving your understanding of mathematical reasoning.
1. Conjecture in Math: Definition & Example
This lesson will define the term conjecture, provide examples, and discuss conditions for writing them. We'll also highlight the use of conjectures by professionals and other people in their daily routines.
2. 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.
3. 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.
4. 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.
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.
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Other chapters within the Test for Admission into Catholic High Schools (TACHS): Practice & Study Guide course
- TACHS: Vocabulary Practice
- TACHS: Reading Comprehension
- TACHS: Reading Interpretation & Analysis
- TACHS: Technical & Informational Text
- TACHS: Literary Text
- TACHS: Poetry
- TACHS: Language & Spelling
- TACHS: Sentence Structure & Word Usage
- TACHS: Expressing Ideas in Writing
- TACHS: Number Sense & Operations
- TACHS: Basic Arithmetic Operations
- TACHS: Integers
- TACHS: Irrational & Rational Numbers
- TACHS: Inequality Practice
- TACHS: Estimation in Mathematics
- TACHS: Decimals
- TACHS: Fractions
- TACHS: Percent
- TACHS: Ratios & Proportion
- TACHS: Basic Algebraic Expressions
- TACHS: Algebraic Distribution
- TACHS: Square Roots
- TACHS: Exponents & Exponential Expressions
- TACHS: Scientific Notation
- TACHS: Standard Measurement
- TACHS: Introduction to Geometry
- TACHS: Geometric Measurement
- TACHS: Symmetry, Similarity & Congruence
- TACHS: Properties of Lines
- TACHS: The Coordinate Graph
- TACHS: Transformations in Math
- TACHS: Triangles
- TACHS: Triangle Theorems & Proofs
- TACHS: The Pythagorean Theorem
- TACHS: Graphical Representations of Data
- TACHS: Statistics & Data Analysis
- TACHS: Probability & Permutations
- TACHS: Properties of Functions
- TACHS: Graphing Functions
- TACHS: Factoring
- TACHS: Simplifying & Solving Rational Expressions
- TACHS: Linear Equations
- TACHS: Systems of Linear Equations
- TACHS: Mathematical Patterns
- TACHS: Reasoning Abilities
- TACHS Flashcards