Elementary Math Operations

Study Notes

Number sense:
- Counting numbers up to 1000
- Identifying even and odd numbers
- Comparing numbers using greater than, less than, and equal to
Addition and subtraction:
- Basic facts within 20 (e.g. 2+2, 5-3)
- Adding and subtracting multiples of 10 (e.g. 10+20, 50-30)
- Solving simple word problems using addition and subtraction
Multiplication and division:
- Introducing basic multiplication facts (e.g. 2 x 3, 5 x 2)
- Understanding basic division concepts (e.g. sharing, grouping)

Geometry:
- Identifying and naming basic shapes (e.g. square, rectangle, triangle, circle)
- Recognizing shapes in real-world objects
- Understanding basic shape properties (e.g. number of sides, number of corners)
Measurement:
- Measuring lengths using units (e.g. inches, centimeters)
- Comparing lengths using longer/shorter and equal
- Introducing basic time concepts (e.g. days of the week, months)

Data:
- Collecting and organizing data
- Creating simple bar graphs and picture graphs
- Answering basic questions using data
Patterns:
- Identifying and extending patterns using shapes, colors, and numbers
- Creating simple patterns using everyday objects

Money:
- Identifying and counting coins (e.g. pennies, nickels, dimes)
- Understanding basic money concepts (e.g. value, equivalent amounts)
Time:
- Telling time to the hour and half hour
- Understanding basic time concepts (e.g. AM/PM, morning/afternoon)

A percentage is a way to express a value as a fraction of 100
To convert a fraction to a percentage, multiply by 100
To convert a percentage to a fraction, divide by 100
Percentage can be used to express increase or decrease in value
It can also be used to find a percentage of a quantity
Common applications of percentage include discounts and sales, interest rates, and grades and marks

A ratio is a comparison of two quantities
There are two types of ratios: part-to-part ratio and part-to-whole ratio
Part-to-part ratio compares two parts of a whole
Part-to-whole ratio compares one part to the entire whole
Equivalent ratios have the same value
Example: 2:3 is equivalent to 4:6
Ratios are used in real-life situations such as recipes and cooking, mixing and blending, and scaling and proportions

A fraction is a way to represent a part of a whole
There are three types of fractions: proper, improper, and mixed fractions
Proper fraction has a numerator less than the denominator
Improper fraction has a numerator greater than or equal to the denominator
Mixed fraction is a combination of a whole number and a proper fraction
To add or subtract fractions, they must have the same denominator
To multiply fractions, multiply the numerator and denominator separately
To divide fractions, invert and multiply
Fractions can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD)
Example: 6/8 can be simplified to 3/4