## Essential Arithmetic Skills

- Counting by twos, fives, tens, twelves, fifteens and twenties
- Adding and subtracting numbers up to 1000 without using a calculator or writing instruments
- Rounding numbers to the nearest ones, fives, tens, hundreds and thousands
- Solving basic story problems
- Using a calculator
- Using a ruler and drawing compass
- Calculating map distances
- Converting units of measurement
- Memorizing the 0-12 multiplication table
- Adding, subtracting, multiplying and dividing fractions
- Adding, subtracting, multiplying and dividing decimals
- Adding, subtracting, multiplying and dividing negative numbers

## Essential **Algebra Skills**

- Using algebraic symbols
- Solving simple equations with variables
- Calculating exponential growth
- Finding prime numbers and square roots
- Solving inequalities
- Understanding sequences
- Using absolute value
- Working with polynomials
- Working with factorization
- Working with quadratic equations
- Working with rational and irrational numbers
- Working with radicals
- Comparing functions

## Essential Geometry Skills

- Measuring angles
- Calculating area
- Calculating surface area
- Calculating diameter
- Calculating square footage
- Calculating perimeter
- Calculating volume
- Calculating scale
- Calculating arc length
- Calculating area of circles
- Graphing lines and slopes
- Working with coordinate planes
- Proving simple geometric theorems
- Making geometric constructions based on a given set of numbers
- Working with the Pythagorean theorem
- Calculating linear equations
- Understanding congruence
- Understanding similarity

## Essential Statistics Skills

- Finding averages
- Finding means and medians
- Converting whole numbers to percentages and vice versa
- Calculating ratios, rates, percentages and proportions
- Deciphering information on line graphs, bar graphs, circle graphs and tables
- Deciphering information on a Vinn diagram
- Deciphering the reliability of a research study based on statistical information provided

## Essential Science and History Skills

- Reading and following a map
- Creating a historical timeline
- Interpreting the Periodic Table of the Elements
- Drawing a simple diagram of an atom
- Drawing simple diagrams of molecules
- Using a telescope
- Using a microscope
- Calculating time zone differences
- Making and testing a hypothesis and using the scientific method
- Identifying local plants and animals (daisy, bluebell, iris, crocus, pansy, lilac, rose, marigold, tulip, daffodil, buttercup, lavendar, juniper, oak tree, maple tree, ivy, blueberry bush, apple tree, pear tree, palm tree, raspberry bush, blackberry bush, cedar, pine)
- Classifying animals into major taxonomic groups (mammals, birds, reptiles, amphibians, fish, arthropods, vertebrates, invertebrates, those having live births and those which lay eggs)

## Science Projects

- Building science-related structures and models with mixed media
- Building science-related structures and models with Lego (such as solar system models, lifelike animal and vehicle replicas, etc.)
- Block building
- Train set building
- Playing with magnets
- Breaking open and identifying rocks
- Building circuits
- Taking nighttime walks
- Watching astronomical events (like a lunar eclipse, shooting stars or the Aurora Borealis)
- Making homemade environmentally friendly house cleaners (using borax, lemon juice, baking soda, vinegar and more)
- Learning computer programming basics
- Growing crystals
- Making a model of our solar system
- Making a balloon rocket
- Making a volcano using baking soda and vinegar
- Making a bottle submarine
- Making invisible ink
- Hunting for fossils
- Making a rainbow
- Making a bat house
- Making a birdhouse
- Making a birdbath
- Making a bee house for honeybees
- Making a foam-and-cardboard planetarium
- Growing coral
- Comparing rates of decomposition
- Going on tidepooling and nature collecting excursions
- Watching sunsets and sunrises

**History Discussion Questions**

- What are some of the important similarities between various historical cultures? What are some of the important differences?
- Were there any good civilizations in history? Were there any bad ones?
- What part did ethnocentrism play in various historical cultures? What part did racism play?
- What are the main reasons nations and states waged war? Why did smaller tribes and peoples wage war?
- How was history influenced by various technological discoveries, including metalwork, gunpowder, the printing press, the train and many more?
- What are some examples of religious wars? To what extent were they motivated by the spread of religious ideas and the quashing of other religious ideas and to what extent were they motivated by other desires or needs?
- What are some possible reasons towns and civilizations spring up independently in so many different parts of the world within a few hundred years of each other?
- Why did safe, prosperous nations, like Rome, continuously try to grow larger? Was this a wise strategy?
- What are some of the historical reasons for poverty?