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SCHOOLING CORE REFERENCE • MATHS • SCIENCE • ENGLISH • LAND NAVIGATION

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Core Learning Surface

Schooling Core Reference

Basic maths, science, English, and land navigation in one study page with quick rules, worked examples, review tables, and a simple practice cycle you can repeat every day.

Maths Land Nav Science English
Maths Basics Numbers, arithmetic, fractions, algebra, geometry, and data reading.
Science Basics Scientific method, matter, motion, life science, Earth systems, and safety.
English Basics Grammar, sentence building, punctuation, reading response, and paragraph writing.
Land Navigation Map orientation, grid coordinates, compass bearings, pace count, and route control.
Maths

Basic Maths

Start with number sense and arithmetic, then move through fractions, algebra, geometry, and graphs. Keep every step written clearly so you can check where a mistake happened.

Maths Workstation

100 addition and subtraction problems, one at a time

Progress saves in this browser. This first maths bank stays on addition and subtraction only. Submit each answer to refresh to the next problem, then reshuffle after all 100 are answered.

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Maths Workstation

100 multiplication and division problems, one at a time

Progress saves in this browser. This second maths bank stays on multiplication and division. Submit each answer to refresh to the next problem, then reshuffle after all 100 are answered.

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Maths Workstation

100 distance conversion problems, one at a time

Progress saves in this browser. This third maths bank stays on distance conversions. Submit each answer to refresh to the next problem, then reshuffle after all 100 are answered.

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Problem 1 of 100
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Operations Breakdown

Use these four quick maths sections when you want to isolate one operation at a time before mixing them together again.

Addition Drills

Addition combines parts into one total.

  • Line up place values when numbers have more than one digit.
  • Regroup when a column adds to 10 or more.
  • Check your sum by subtracting one addend from the total.
Worked example

248 + 137 = 385.

Subtraction Drills

Subtraction finds how much is left or how far apart two values are.

  • Rewrite the larger number on top before subtracting.
  • Borrow from the next place value when the top digit is too small.
  • Check your answer by adding the difference back to the smaller number.
Worked example

503 - 186 = 317.

Multiplication Drills

Multiplication is fast repeated addition and helps with equal groups, area, and scaling.

  • Memorize small facts first so larger problems move faster.
  • Break harder products into easier chunks such as 7 x 12 = 7 x 10 + 7 x 2.
  • Check a product by dividing it by one factor.
Worked example

8 x 14 = 8 x 10 + 8 x 4 = 80 + 32 = 112.

Division Drills

Division splits a total into equal groups or tells how many groups fit.

  • Think of the matching multiplication fact before dividing.
  • Check whether there is a remainder when the total does not split evenly.
  • Verify by multiplying the quotient by the divisor.
Worked example

96 / 8 = 12 because 12 x 8 = 96.

Distance Conversion Drills

Work these conversions when you need to swap between metric and imperial distance units quickly and keep a good field estimate.

Meters to Feet

Use meters to feet when you need to move from metric distance into a more common U.S. length reference.

  • Multiply meters by about 3.28 to estimate feet.
  • Round to the nearest tenth when you want a clean quick answer.
  • Double-check by asking whether the feet value is a little more than three times the meters value.
Worked example

10 meters is about 32.8 feet.

Miles to Kilometers

Use miles to kilometers when you need to convert road or map distance into metric form.

  • Multiply miles by about 1.61 to estimate kilometers.
  • Use one decimal place for fast travel and map checks.
  • If the kilometer result is not larger than the miles value, recheck the multiplication.
Worked example

5 miles is about 8.1 kilometers.

Inches to Centimeters

Use inches to centimeters when you need to convert a smaller imperial length into metric form.

  • Multiply inches by 2.54 to convert to centimeters.
  • Keep one decimal place when you want a clean quick answer.
  • If the centimeters result is not more than double the inches value, recheck the calculation.
Worked example

12 inches is 30.5 centimeters.

Yards to Meters

Use yards to meters when you need to swap a field or map distance into metric form.

  • Multiply yards by about 0.91 to estimate meters.
  • Round to the nearest tenth for fast comparisons.
  • If the meter answer is larger than the yards value, check the work again.
Worked example

10 yards is about 9.1 meters.

Number Sense & Order of Operations

Know how big a number is, what each digit means, and what order to solve parts of an expression.

  • Place value runs ones, tens, hundreds, thousands, and beyond.
  • Use <, >, and = to compare numbers accurately.
  • Follow parentheses, exponents, multiplication/division, then addition/subtraction.
Worked example

18 - (6 / 2) + 4 = 18 - 3 + 4 = 19.

Addition, Subtraction, Multiplication & Division

These four operations are the base of almost every later maths topic.

  • Add to combine amounts and subtract to find the difference.
  • Multiply for equal groups and divide to split or share equally.
  • Check division with multiplication and subtraction with addition.
Worked example

7 x 6 = 42, so 42 / 6 = 7 and 42 / 7 = 6.

Fractions, Decimals & Percentages

These are three ways to name parts of a whole amount.

  • The denominator shows total equal parts and the numerator shows chosen parts.
  • Decimals are place-value fractions based on tenths, hundredths, and thousandths.
  • Percent means out of 100.
Worked example

3/4 = 0.75 = 75%.

Ratios & Algebra Basics

Algebra uses letters to stand for numbers you do not know yet.

  • A ratio compares two amounts, such as 2:3.
  • An equation balances both sides, so whatever you do to one side must happen to the other.
  • Collect like terms before solving.
Worked example

If x + 5 = 13, subtract 5 from both sides to get x = 8.

Geometry & Measurement

Geometry studies shape, space, length, area, and volume.

  • Perimeter is the distance around a shape.
  • Area is the amount of surface inside a flat shape.
  • Volume measures space inside a 3D object.
Worked example

A rectangle 8 cm by 3 cm has perimeter 22 cm and area 24 cm squared.

Data, Graphs & Probability

Read charts carefully and match the graph type to the information shown.

  • Bar graphs compare categories and line graphs show change over time.
  • The mean is the average, the median is the middle, and the mode appears most often.
  • Probability ranges from 0 impossible to 1 certain.
Worked example

Scores 4, 5, 5, 6 give mean 5, median 5, and mode 5.

Perimeter = sum of side lengths Area of rectangle = length x width Percentage = part / whole x 100 Average = total / number of items 1 meter is about 3.28 feet 1 mile is about 1.61 kilometers 1 inch = 2.54 centimeters 1 yard is about 0.91 meters
Signature Tutor Layout

Step-by-Step Maths Examples

This section is the polished walk-through board for every maths focus. Each problem is laid out like a premium study guide so the focus, sample problem, and exact solve order are easy to scan and repeat.

Clean Solve Order Worked Start To Finish Quick Check Ready
Addition Worked Example
Sample Problem 248 + 137
How To Work It Out Step By Step
  1. 1. Add ones: 8 + 7 = 15, write 5 and carry 1.
  2. 2. Add tens: 4 + 3 + 1 = 8.
  3. 3. Add hundreds: 2 + 1 = 3. Answer: 385.
Subtraction Worked Example
Sample Problem 503 - 186
How To Work It Out Step By Step
  1. 1. Borrow from the tens because 3 is smaller than 6, so 13 - 6 = 7.
  2. 2. Borrow from the hundreds because 0 is smaller than 8, so 9 - 8 = 1.
  3. 3. Subtract hundreds: 4 - 1 = 3. Answer: 317.
Multiplication Worked Example
Sample Problem 8 x 14
How To Work It Out Step By Step
  1. 1. Break 14 into 10 and 4.
  2. 2. Multiply 8 x 10 = 80.
  3. 3. Multiply 8 x 4 = 32.
  4. 4. Add 80 + 32 = 112. Answer: 112.
Division Worked Example
Sample Problem 96 / 8
How To Work It Out Step By Step
  1. 1. Ask what number times 8 gives 96.
  2. 2. 12 x 8 = 96.
  3. 3. So 96 / 8 = 12. Answer: 12.
Meters to Feet Worked Example
Sample Problem 10 meters to feet
How To Work It Out Step By Step
  1. 1. Multiply meters by 3.28.
  2. 2. 10 x 3.28 = 32.8.
  3. 3. Label the answer in feet. Answer: about 32.8 feet.
Miles to Kilometers Worked Example
Sample Problem 5 miles to kilometers
How To Work It Out Step By Step
  1. 1. Multiply miles by 1.61.
  2. 2. 5 x 1.61 = 8.05.
  3. 3. Round to one decimal place for a quick field answer. Answer: about 8.1 kilometers.
Inches to Centimeters Worked Example
Sample Problem 12 inches to centimeters
How To Work It Out Step By Step
  1. 1. Multiply inches by 2.54.
  2. 2. 12 x 2.54 = 30.48.
  3. 3. Round if needed. Answer: about 30.5 centimeters.
Yards to Meters Worked Example
Sample Problem 10 yards to meters
How To Work It Out Step By Step
  1. 1. Multiply yards by 0.91.
  2. 2. 10 x 0.91 = 9.1.
  3. 3. Keep the answer in meters. Answer: about 9.1 meters.
Order of Operations Worked Example
Sample Problem 18 - (6 / 2) + 4
How To Work It Out Step By Step
  1. 1. Solve inside the parentheses first: 6 / 2 = 3.
  2. 2. Subtract next: 18 - 3 = 15.
  3. 3. Add last: 15 + 4 = 19. Answer: 19.
Fractions, Decimals, and Percent Worked Example
Sample Problem 3/4
How To Work It Out Step By Step
  1. 1. Divide numerator by denominator: 3 / 4 = 0.75.
  2. 2. Multiply the decimal by 100 to get percent: 0.75 x 100 = 75.
  3. 3. Write the percent sign. Answer: 3/4 = 0.75 = 75%.
Ratios and Algebra Worked Example
Sample Problem x + 5 = 13
How To Work It Out Step By Step
  1. 1. Subtract 5 from the left side.
  2. 2. Subtract 5 from the right side too so the equation stays balanced.
  3. 3. x = 8.
  4. 4. Check: 8 + 5 = 13. Answer: x = 8.
Geometry and Measurement Worked Example
Sample Problem Rectangle 8 cm by 3 cm
How To Work It Out Step By Step
  1. 1. Add all four sides for perimeter: 8 + 3 + 8 + 3 = 22 cm.
  2. 2. Multiply length by width for area: 8 x 3 = 24.
  3. 3. Label area in square units. Answer: perimeter 22 cm and area 24 square cm.
Data and Graphs Worked Example
Sample Problem Scores 4, 5, 5, 6
How To Work It Out Step By Step
  1. 1. Add the scores: 4 + 5 + 5 + 6 = 20.
  2. 2. Divide by 4 to get the mean: 20 / 4 = 5.
  3. 3. Put the numbers in order to find the median: 4, 5, 5, 6, so the middle is 5.
  4. 4. The mode is the number used most often: 5. Answer: mean 5, median 5, mode 5.
Operation Check Worked Example
Sample Problem 42 / 6
How To Work It Out Step By Step
  1. 1. Think of the matching multiplication fact.
  2. 2. 7 x 6 = 42.
  3. 3. So 42 / 6 = 7.
  4. 4. Check by multiplying back: 7 x 6 = 42. Answer: 7.

Solve StandardUse the same pattern every time: read the problem carefully, do one step at a time in order, and check the answer with the opposite operation or a quick estimate.

Quick Fraction Reference

Fraction Decimal Percent How To Work It Out
1/2 0.5 50% 1 ÷ 2 = 0.5, then 0.5 × 100 = 50%.
1/4 0.25 25% 1 ÷ 4 = 0.25, then 0.25 × 100 = 25%.
3/4 0.75 75% 3 ÷ 4 = 0.75, then 0.75 × 100 = 75%.
1/5 0.2 20% 1 ÷ 5 = 0.2, then 0.2 × 100 = 20%.

When a fraction does not convert quickly in your head, divide the numerator by the denominator first, then multiply by 100 for percent.

Field Skills

Land Navigation Basics

Land navigation combines map reading, compass work, terrain association, and disciplined note taking. Learn how to orient the map, plot the route, walk the leg, and relocate if the ground stops matching the plan.

Map Orientation & Terrain Association

Start by making the map and the ground agree before you move.

  • Set north on the map to match north on the ground before reading the route.
  • Match big terrain shapes such as ridges, valleys, roads, streams, and hilltops first.
  • Use handrails like roads, trails, ridgelines, or rivers to keep movement simple.
Worked example

If the creek should stay on your left and the hill mass should rise ahead, the terrain picture should match that map picture as you move.

Grid Coordinates & Plotting

Read grid references the same way every time so points are plotted accurately.

  • Read right first for the easting, then up for the northing.
  • A 4-digit grid gives a square, a 6-digit grid narrows to 100 meters, and an 8-digit grid narrows to 10 meters.
  • Use a protractor or grid tool to measure the tenths inside the square instead of guessing.
Worked example

Grid 123456 means go to easting 12, then northing 34, then measure 0.3 across and 0.6 up inside that square.

Compass Bearings & Back Azimuths

An azimuth gives direction, and a back azimuth tells you how to return or verify the reverse line.

  • Hold the compass level, read the direction of travel arrow, and keep the bezel or dial steady.
  • To get a back azimuth, add 180 degrees if the azimuth is under 180, or subtract 180 if it is 180 or more.
  • Always note whether you are using magnetic north or grid north before sharing a bearing.
Worked example

If your azimuth is 70 degrees, your back azimuth is 250 degrees. If your azimuth is 240 degrees, your back azimuth is 60 degrees.

Pace Count & Distance Control

Distance discipline keeps you from drifting too far past or too short of the point.

  • Know how many paces you take over 100 meters on flat ground before you need the number in the field.
  • Heavy load, darkness, slope, mud, and vegetation all change pace count and walking speed.
  • Break long legs into shorter checkpoints so you can confirm progress before the final point.
Worked example

If your pace count is 62 paces per 100 meters, then about 310 paces is about 500 meters.

Route Planning, Attack Points & Catching Features

Good routes are controlled by recognizable features, not just by one long straight line.

  • Use checkpoints along the way so each leg has a clear start, line of travel, and end.
  • Pick an attack point near the final location so the last movement is short and precise.
  • Choose a catching feature beyond the objective so you know when you have gone too far.
Worked example

Move road to creek bend to saddle, then use the saddle as the attack point and the ridgeline beyond the objective as the catching feature.

Relocation & Resection

If you lose confidence in your location, stop, confirm, and relocate before moving farther.

  • Look for two or three known terrain features that you can identify on the map and on the ground.
  • Take bearings to those features and draw back azimuths to estimate your position.
  • When visibility is poor, relocate from the last point you knew for sure instead of chasing guesses.
Worked example

If two back azimuth lines cross near the bridge symbol on the map, that crossing gives your best relocation estimate.

Read right, then up 6-digit grid = 100 m precision 8-digit grid = 10 m precision Back azimuth = azimuth ± 180 Distance = paces / pace-count-per-100 m x 100 Handrails • attack points • catching features

Land Navigation Quick Reference

Task Rule Quick Example
Grid reading Read right first, then up. Easting 12, then northing 34 becomes grid 1234.
Back azimuth Add 180 below 180 degrees; subtract 180 at 180 degrees or above. 65 degrees becomes 245 degrees. 240 degrees becomes 60 degrees.
Pace count Know your paces for 100 meters before the route begins. 62 paces x 5 legs is about 500 meters.
Route control Use handrails, checkpoints, attack points, and catching features. Road to creek bend to hilltop is easier to verify than one long blind leg.
Relocation Stop and resection from known points instead of guessing forward. Use two hilltops or towers to draw back azimuths and find the intersection.

Good land navigation is controlled movement: orient first, confirm often, and only speed up after the map, compass, and terrain all agree.

Science

Basic Science

Science asks questions, gathers evidence, tests ideas, and explains how the natural world works. Write down observations carefully and separate what you saw from what you guessed.

Science Workstation

100 science problems, one at a time

Progress saves in this browser. Submit each answer to refresh the workstation to the next science problem. After all 100 are answered, the bank reshuffles and starts a new cycle.

Cycle 1
Answered 0 / 100
Correct 0 / 100
Problem 1 of 100
Loading first problem...
Select an answer and submit to refresh the workstation. Answer explanation appears here after each response.

Scientific Method

A simple science cycle keeps investigations clear and repeatable.

  • Ask a question based on something you notice.
  • Build a hypothesis that can be tested.
  • Run an experiment, collect results, and compare them with the hypothesis.
Worked example

Question: Do plants grow faster in sunlight? Test equal plants with different light levels and measure growth each day.

Matter, Forces & Life Science

Science basics connect what things are made of, how they move, and how living things survive.

  • Matter has mass and takes up space; it can be solid, liquid, or gas.
  • Forces such as push, pull, friction, and gravity change motion.
  • Living things need energy, respond to their environment, and reproduce.
Worked example

A ball slows on grass because friction acts against its motion.

Atoms, Elements & Compounds

Atoms are tiny building blocks, elements use one kind of atom, and compounds join different atoms together.

  • The periodic table organizes elements by their properties.
  • Molecules form when atoms bond.
  • Physical changes alter form, while chemical changes create a new substance.
Worked example

Ice melting is a physical change; iron rusting is a chemical change.

Energy, Heat & Motion

Energy does work and can change form from one type to another.

  • Kinetic energy is energy of motion and potential energy is stored energy.
  • Heat moves from warmer objects to cooler ones.
  • Speed tells how fast something moves over a distance.
Worked example

If a car travels 120 km in 2 hours, its average speed is 60 km/h.

Earth, Weather & Space

Earth science connects land, water, air, climate, and the solar system.

  • Weather describes short-term air conditions and climate describes long-term patterns.
  • Earth rotates once every day and revolves around the sun each year.
  • The moon changes phase as its lit side is viewed from Earth at different angles.
Worked example

Summer and winter happen because Earth is tilted while it travels around the sun.

Observation, Variables & Safety

Good science uses clear observations and safe habits.

  • An independent variable is the one you change; a dependent variable is what you measure.
  • Keep control conditions the same for a fair test.
  • Wear eye protection, read instructions, and never mix unknown chemicals.
Worked example

If you test plant growth, light amount is the independent variable and plant height is the dependent variable.

Speed = distance / time Density = mass / volume Hypothesis = testable prediction Control = conditions kept the same
English

Basic English

English class builds clear reading, speaking, and writing. Focus on sentence structure first, then expand into paragraphs, responses, and vocabulary work.

English Workstation

100 English problems, one at a time

Progress saves in this browser. Submit each answer to refresh the workstation to the next English problem. After all 100 are answered, the bank reshuffles and starts a new cycle.

Cycle 1
Answered 0 / 100
Correct 0 / 100
Problem 1 of 100
Loading first problem...
Select an answer and submit to refresh the workstation. Answer explanation appears here after each response.

Sentence Building & Grammar

A complete sentence needs a subject and a verb and must express a full thought.

  • Nouns name people, places, things, or ideas.
  • Verbs show action or state of being.
  • Adjectives describe nouns and adverbs describe verbs, adjectives, or other adverbs.
Worked example

The student writes neatly every day. Subject: student. Verb: writes.

Punctuation & Capitalization

Punctuation controls clarity, pace, and meaning.

  • Use capitals for sentence openings, names, places, days, and months.
  • Use periods for statements, question marks for questions, and exclamation points sparingly.
  • Use commas to separate items in a list or pause after an opener.
Worked example

After lunch, Maya, David, and Amina finished their project.

Reading Comprehension

Good readers identify the main idea, important details, tone, and evidence.

  • Ask who, what, when, where, why, and how while reading.
  • Highlight topic sentences and repeated ideas.
  • Support every answer with proof from the text.
Worked example

If the text says a storm flooded roads and delayed buses, the main effect is travel disruption caused by the storm.

Paragraph Writing & Reading Response

A strong paragraph stays on one idea and proves it with detail.

  • Start with a topic sentence that states the main point.
  • Add evidence, examples, or explanation in the middle.
  • Close with a sentence that sums up the idea or links to the next point.
Worked example

Topic sentence: Reading every day improves vocabulary. Supporting details explain new words, sentence patterns, and better comprehension.

Vocabulary & Spelling

New words stick better when you say them, write them, define them, and use them in sentences.

  • Break long words into prefixes, roots, and suffixes.
  • Use context clues to infer meaning before checking a dictionary.
  • Review difficult words several times across the week.
Worked example

Preview means to see before. Prefix: pre = before. Root: view = see.

Speaking, Listening & Editing

Strong communication includes listening well, speaking clearly, and revising written work.

  • Read your writing aloud to catch awkward wording.
  • Check spelling, punctuation, grammar, and sentence variety during editing.
  • Answer with complete sentences during discussion when possible.
Worked example

Edit this: he dont like runing. Correct version: He does not like running.

Quick Writing Check

Check Question to Ask Fix if Needed
Subject + Verb Does every sentence say who or what plus the action? Add the missing subject or verb.
Punctuation Did each sentence end correctly? Add a period, question mark, or exclamation point.
Capital Letters Did the sentence and names start with capitals? Capitalize the first word and proper nouns.
Main Idea Does the paragraph stay on one topic? Remove off-topic lines or rewrite the topic sentence.

Before handing in work, reread it once for meaning and a second time just for grammar and punctuation.