# Syllabus for Arithmetic

1. Foundations

• Sets
- what is a set: notation, extension property
- subsets, unions, intersections, complements

• Logic
- informal logic: parsing propositional statements
- formal logic: and, or, not, if-then
- truth tables and deduction

• Operations (see Whole Numbers: Properties of Operations , below)

2. Whole Numbers and their Properties

• Counting
- one to one correspondence
- inclusion-exclusion
- cartesian products

• Factors
- prime numbers
- unique prime factorization
- counting factors
- LCM: how to obtain it; properties of the LCM
- GCD: how to obtain it; properties of the GCD

• Negative Numbers
- interpretation of negative numbers
- rules for manipulation of negative numbers

• Properties of Operations
- abstract operations: commutativity, associativity, identities, inverses
- properties of addition, multiplication, subtraction, division
- consequences of these properties
- distributivity
- mental math consequences

• Place Value
- how our numeration system works
- other bases
- algebraic representation of numbers in terms of their digits
- negative place value and decimals (see Decimals: place value, below)

Common Algorithms
- justification of addition, subtraction and multiplication algorithms
- understanding alternative algorithms

3. Division and Fractions

• Division
- inverse of multiplication
- repeated subtraction
- division algorithms
- division of fractions (see: Fractions: multiplication and division, below)

Ratio and Proportion
- proportionality word problems
- recognizing when given data is in terms of proportion
- cross-multiplication and its justification

• Fractions
- models of fractions: number line /measurement, ratio, quotient, operator
- equivalent fractions and cross-multiplication
- mixed versus improper fractions
- multiplication and division: models, procedures

• Decimals
- place value
- terminating decimals to fractions
- classification of fractions as terminating or repeating decimals

• Scientific Notation
- definition and conversion into and out of
- estimatio of physical quantities
- approximate computation in scientific notation
- logarithmic scales : brief intro

• Percentages
- representation as a fraction or decimal
- percentage increase and decrease

4. General Skills and Attitudes

• Problem Solving Strategies
- trial and error
- reducing the problem
- harnessing physical intuition

• Generalization and Abstraction
- observing patterns
- using variables to express and justify observations

• Word Problems
- unambiguous usage of variables
- units
- writing equations for a problem

- NCTM Standards for active learning, justification/proof, verbalizing
- articulate and grammatical mathematical expression
- argumentation

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of February 24th you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!