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List of important numeracy skills and vocabulary for Pilots:

1. Basic Arithmetic: There are several types of math that pilots use in their career and throughout their training including basic arithmetic, algebra, geometry, mental math and more. Basic arithmetic are the basics: addition, subtraction, multiplication, and division. A typical example of this for a pilot may be magnetic compass deviation and variation. So adjusting a compass for deviation may be as simple as adding 7 degrees to a heading of 172. 172 + 7 = 179.

2. Multiplication: Other typical calculations may be simple multiplication. For example, aviation gas weighs 6lbs per gallon. If you have a fuel tank of 15 gallons, when full how much weight are you carrying? 6 x 15 = 90lbs.

3. Algebra: This is when you need to solve for some unknown variable “x” based on other relationships and factors that you already know and have. For a pilot, this might be a simple formula like if you are travelling at 60 miles per hour, and your destination is 90 miles away, how long will it take you to get there? It would take 1hr 30min to your destination.

4. Mental Math:

Being able to do basic quick mental math in your heard is a great skill to have as a pilot. An example of this would be listing the three basic steps needed to plan your descent. Count down to yourself or co-pilot the steps needed.

Three basic steps to follow when planning your descent:

Step 1)

Step 2)

Step 3)

5. Geometry:

Pilots must use geometry to calculate angles for taking off and landing. Planes have recommended angles for takeoff and landing. If a pilot descends or climbs at an angle that is too steep, it can lead to a tail strike, resulting in the plane’s tail hitting the runway. Speed, altitude and distance from the destination are factors pilots use when determining the angle of descent and the angle of climb.

6. Division:

How many gallons of fuel to order:

Begin by determining how many pounds of fuel are needed.

-omit last 0, divide by 1/2,

-add both to get gallons needed.

Example:  you need 3000 lbs = 3000, omit last 0 = 300, add 1/2 of
that = 300+150 = 450 gallons needed.

7. Weight Calculations:

Weight calculations use the basic arithmetic skills of addition and subtraction. For an airplane to fly, it cannot weigh more than the amount of lift it generates.

Example:  2,810 pound takeoff weight – 1,650 empty weight = 1,160 pounds useful load.  Useful load is the weight of people, baggage, useable fuel and drainable fuel on a flight. If the useful load is miscalculated it can cause problems for take off and cause poor performance of the airplane.

8. Fuel Calculations:

Fuel calculations also use basic addition and subtraction skills. In this case, 13 gallons per hour x 2 hours = 26 gallons. This shows that the pilot would need 26 gallons for an in-flight of two hours.

9. Crosswind component calculations:
When you are landing or taking off, if there is a wind which is perpendicular to the runway, this is referred to as a crosswind. Too strong a crosswind can be dangerous, so it is important to calculate the crosswind and determine if it is safe to takeoff or land under the conditions.

Crosswind component = Wind speed x cosine of angle between the wind and runway

10. Interpolation
Interpolation is the mathematical term for making an educated estimation based on surrounding data. This technique uses basic arithmetic skills as well as algebraic skills since the unknown variable you are solving for, “x,” must be determined based on its relationship to the data you do have.

Example: A straight line passes through two points of known value 9 and 10. You can estimate the point of unknown value because it appears to be midway between the other two points. The interpolated value of the middle point could be 9.5.

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Numeracy Skills needed for a chef by Sydney Campbell

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Numeracy Skills needed for a chef by Sydney Campbell

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ADJUSTING PORTION SIZE TO MEASUREMENTS OF A RECIPE- A chef uses measurements when trying out a new recipe or creating one of their own. If they need to adjust the portion size of the recipe, then they must know how to manipulate fractions.

For example: Chef Amber needs to cook enough mac-n-cheese for four people. Her recipe for mac-n-cheese has a portion size of eight people and calls for 1 ⅓ cup of cheddar. In order to cut the recipe in half, she must half the measurements:

1 ⅓ cup => ⅔ cup

2. CONVERSION- Working with the same recipe, Chef Amber must be familiar with conversions, such as how many tablespoons go into a cup so that she can half the 1 ¾ milk required for the recipe.

One cup is 16 tablespoons, therefore 12 tablespoons equal ¾ of a cup. If 28 tablespoons equal 1 ¾ cups, then half of that would be 14 tablespoons of milk for Chef Amber’s recipe.

We began the problem with cups and solved the problem with tablespoons.

3. ESTIMATION- A really good Chef, roughly estimates how much of an ingredient is needed in a recipe. For them to be able to estimate, they must first maintain the basic knowledge of the measurements they are using.

For example: Chef Amber is recreating a sauce from scratch that she had just thrown together the night before. As she takes a small taste, she realizes it is bitter. She sprinkles in some sugar and estimates that it’s about half a tablespoon. In order to know that, she would have to have the basic knowledge that 3 teaspoons equal 1 tablespoon.

4. BASIC ADDITION FOR MONEY MAKING- When a chef creates their menu, they must take into account how much money it would cost them to create each dish so that they can charge just enough to profit from their food.

For example: If the ingredients to create six dishes of lasagna cost them $30, then they would divide that by 6, which would be $5 so each dish cost them $5 to create. In order to profit off the dish, they choose to sell it for $12 a plate of lasagna.

5. BASIC COUNTING- When a chef is serving a restaurant full of people, they must count how many mouths there are to feed and estimate how many dishes to prepare.

For example: Eight people are seated around a booth. Five of them order the chicken alfredo that creates ten portions per dish. In order to make sure the pasta is made fresh for every guest that orders it, the chef must half the recipe so there is enough for five hungry mouths.

6. TEMPERATURE AND TIME- Being able to tell time and know that sixty seconds equal a minute and sixty minutes equal one hour is necessary for every chef that touches an oven.

For example: The recipe states that it will take an hour for Chef Amber’s brownies to bake at 350 degrees fahrenheit. If she wants to speed up the process a little bit, she could bake the brownies at 375 degrees fahrenheit for only forty-five minutes.

7. NUTRITIONAL DATA- Calculating the nutritional needs of the targeted guests in a restaurant allows for the chef to great a balanced meal, which will appeal to guest that want to indulge without going off the deep end. Nutritional stats are given in percentages, requiring the chef to be familiar with percentages, decimals, and fractions.

8. WEIGHT AND MEASUREMENT- When using fresh ingredients, a chef must calculate the edible portion. First they trim away all the parts that they can’t use and then weigh the edible portion and divide it by AP weight, which will give them a percentage.

For example: Formula (EP weight/AP weight = EP percentage)

Green beans -- 4 lbs. EP/5 lb. AP = 80% EP Yield

9. BASIC MULTIPLICATION AND ADDITION- When a chef is buying ingredients for their dishes, they must add together all of the measurements for each recipe, utilizing multiplication for the recipes that they will need more of.

For example: Chef Amber is preparing to cook at least twenty portions of her most popular dish: ravioli, which requires 2 cups of mozzarella for eight portions. In order to make sure she prepares enough ingredients for twenty portions, she needs (2 x 3 = 6) 6 cups of mozzarella.

10. BUDGETING- When purchasing food to prepare, a chef must calculate the prices of each ingredient and ensure that it does not go over their budget spending for that week.

For example: Chef Amber’s budget for the week was $300 and she spent $250 alone on groceries, which means that she has $50 left for emergency store runs if she runs out of ingredients or forgot one.

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Basic numeracy and math skills are needed to function as a classroom teacher. It is helpful to have a basic knowledge of addition, subtraction, multiplication, division, averaging, working with time constraints, as well as being able to read simple graphs and statistics.

Following are some examples of how the aforementioned skills could be used in a classroom.

1. Basic Counting: This is needed to know how many books, copies, snacks, desks, etc. are needed in a classroom.

28 students + 2 aids = 30 copies, books, etc.

2. Grading: Each assignment handed in needs some sort of assessment. If a student answered 7 out of 10 questions correctly, the teacher needs to be able to divide 7/10 to have a percentage that equates to a letter grade in most U.S. educational institutions.

7/10 = 70% = C-

3. Dividing work over an allotted number of days: A book needs to be read by the end of the unit. The book has 285 pages and the unit needs to be completed in 20 school days.

285 pages/20 school days = Students need to read 14 pages/day.

4. Basic mathematical skills for end of semester grading: Students have accumulated a number of grades throughout the semester. Those grades need to be compiled into an overall average.

Grades of assignments: 70+80+82+94 = 326
326/4 = 81.5%

5. With the example above another numeracy skill is highlighted, that of rounding. We often don't give percentages in the tenths and hundredths. Hence, teachers need to be able to round to the nearest whole number.

81.5% = 82% = B-

6. Costs for a fieldtrip: The class needs to absorb the cost of a day trip to a museum. The teacher needs to calculate how much each student attending needs to contribute in order to attend.

Transportation: $250/day (250/28 = $8.93)
Entry Ticket: $10
Lunch Provided: $8
Tour Cost $12
Each student: $38.93 for field trip

7. Calculating time needed for students to test: Teachers like to have a test completed within the allotted class time. Thus, it's helpful to calculate how long it may take a student to complete different segments of the test.

10 multiple choice questions: 10 questions x 1 minute = 10 minutes
5 short answer questions: 5 short answer x 5 minutes = 25 minutes
1 three paragraph essay: 1 essay x 20 minutes = 20 minutes
55 minutes to complete test.

8. Setting up stations for students:

28 students/4 stations = 7 students per station.

If you'd like your students to experience each station then each group has roughly 15 minutes per station in a 60 minute class.

9. Basic numeracy with a clock: Dividing up class time based on actual clock time.

A 55 minute class that runs from 12:08-1:03 might be divided up as follows:
12:08-12:13. Introduction, attendance, announcements
12:13-12:18. Review of previous day's content
12:18-12:28. Introduction of today's topic
12:28-12:58. Interaction with new content
12:58-1:03.   Homework explanation

10. Lastly, timelines, bar graphs, and statistics are often found in Language Arts (English, History, Social Studies) textbooks. A teacher will need to understand grouping, y and x axis layouts, and how timelines are marked by years (decades, centuries, etc.)

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Aline Wisse How does a market seller use math and numbers?

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Aline Wisse How does a market seller use math and numbers?

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·       Calculating weight and prices of goods

When you have the cost of an item and its weight in pounds, you're ready to calculate its cost per pound. All you have to do is divide the total cost of the item by the number of pounds it weighs. So if your big bag of candy weighs 5 pounds and costs $13, you'd divide the cost by the weight in pounds: Calculating markup based on cost or selling price.

Markup is the difference between a product's selling price and cost as a percentage of the cost. For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.

·       Calculating retail sales, gross margin and break-even points.

- Calculating retail sales:

1.    Calculate your cost price.

2.    Calculate your wholesale price, by adding up cost and profit margin.

3.    Calculate your RRP (Recommended Retail Price), by multiplying your wholesale price by 2 or 2.5

- To calculate gross margin subtract Cost of Goods Sold (COGS) from total revenue and dividing that number by total revenue (Gross Margin = (Total Revenue – Cost of Goods Sold)/Total Revenue). The formula to calculate gross margin as a percentage is Gross Margin = (Total Revenue – Cost of Goods Sold)/Total Revenue x 100.

- The components gross margin dollars, gross margin percent, and fixed costs are needed to calculate a break-even situation. In this example, we take ($18,750 − $10,000 = $8,750) / $20,000 = . 4375 or 43.8%. In this example, a retailer would have to generate $57,143 in product sales to break-even.

·       Planning and controlling price/stock reductions (markdowns).

For most companies 80% of their revenue comes from 20% of their stock. While these stats will vary to some degree, this is the theory behind ABC inventory analysis – a model that can be usedReduce inventory with stock classification to categorize your stock. Using ABC analysis, you can classify your inventory items into three groups based on their value to the business. A items are the most important in terms of the value they bring to your company, while C items are the least valuable. You can then prioritize the stock you carry, focusing on your A items to ensure better availability, rather than B and C. This could include reviewing their demand forecasts more frequently or interacting more regularly with suppliers to improve lead times.

·       Developing seasonal budgets.

- Create a baseline of basic expenses.

- Plan a year in advance.

- Don't get derailed from your budget during busy season.

- Track, track, track as much as you can.

- Take advantage of your slow season.

- Build more than one budget.

- Consider an alternative fiscal year.

·       Developing inventory plans (determining stock needs in proportion to forecasted sales).

1.    Demand forecast: using historical sales data, KPIs and variables like seasonality, promotions and market predicts to make data-driven forecasts.

2.    Control costs: considering things like choosing the right suppliers, automating purchase order process, reducing cash tied up in slow-moving products etc.  –

3.    Store efficiently: storing the right amount of products in the right place to optimize your order fulfillment routes if you have multiple inventory locations

·       How to Interpret Your Profit and Loss Statement •

- Revenue. Revenue is often referred to as the “top line,” because it's the very first line you'll see on your profit and loss statement. ...

- Earnings Before Interest and Tax (EBIT) EBIT reflects the company's productive efficiency, before taking into consideration the tax burden or how the company is financed. ...

- Net Earnings.

·       Evaluating balance sheets (composed of assets, liabilities and equity).

- The balance sheet displays the company's total assets, and how these assets are financed, through either debt or equity. It can also be referred to as a statement of net worth, or a statement of financial position. The balance sheet is based on the fundamental equation: Assets = Liabilities + Equity.

·       Performing ratio analysis. (Comparing items on the balance sheet or income statement with other items on these statements. Reviewing the past year's ratios will pinpoint trends, which can be used to forecast the future.)

- Ratio analysis compares line-item data from a company's financial statements to reveal insights regarding profitability, liquidity, operational efficiency, and solvency. Ratio analysis can mark how a company is performing over time, while comparing a company to another within the same industry or sector. Quick Ratio: In order to calculate the quick ratio, take the Total Current Ratio for 2010 and subtract out Inventory. Divide the result by Total Current Liabilities. You will have: Quick Ratio = 642-393/543 = 0.46X. For 2011, the answer is 0.52X.

·       Forecasting cash flow budgets. (Projecting cash receipts and cash expenses for a period of time into the future, usually done on a monthly basis.)

- Subtract total cash outflows from total cash inflows to determine the net cash flow for each period. Add the net cash flows for each period to check that they equal the total net cash flow for the year.

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The coffee industry is booming and becoming a barista could be a great career path. There is so much more to being a barista than just pouring coffee.

1. You must know how many grams of coffee beans to use for certain drinks. For example, when making a pour over, the correct amount of grounds to water ratio is crucial in order to extract the full flavor of the beans. 21 grams of grounds to about 275 grams of hot water is a good starting point. However, with a lighter roasted, fruity notes, coffee you should use less grounds.
2. How many degrees should the water be? Your water for a pour over should be around 202 degrees F or, for my metric friends out there, around 94 degrees Celsius.
3. You need to know how to use a scale. A barista should know how to read a coffee scale. These measurments are normally in grams. A specialty coffee shop will use a coffee scale for almost all of there drinks.
4. Making espresso is a very sensitive process and knowing the numeracy involved is crucial to a good shot. Espresso is more concentrated then a pour over so less grams of beans is preferred. 19 grams of fine grounds is a good starting point.
5. Espresso continued: The amount of time it takes to pull your shot of espresso is also important. A good barista can count efficiently, use a timer, or have a good machine that is dialed in to the right settings. A good shot runs 23-28 seconds long.
6. making lattes requires exact measurements. A good barista should know how to use measuring cups. As you become more experienced you will be able to eye ball some of the measurements.
7. If you work at a roastery, you may have to bag some of the coffee beans. Putting beans into bags requires measurements normally in ounces. Coffee is normally sold in 12oz bags. Knowing abbreviations is good too such as oz and gr.
8. The cash register. At the cash register, simple addition and subtraction skills are key. You must give the correct amount of change to a customer and charge them the correct amount. Becoming familiar with that nations currency will be crucial.
9.Clock in and out. You may be required to log your hours or use a time clock. If your coffee shop uses a machine to clock in and out it is pretty easy but if you are required to write it down you should understand the 12 hour clock.
10. Check your paycheck. You always want to make sure you are getting paid for your time. Always match your paycheck to the amount of hours you worked to ensure you are being treated fairlly.

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How Do Veterinarians use math and specific vocabulary in their Jobs?

Measurements
Vets use math to track measurements related to animal care. For example, an increased heart size of a certain percentage can be an indication of heart disease, and tracking the measurement of a tumor's growth can help determine how quickly a cancer is progressing. Vets also measure waste and fluid output to assess various conditions. Using mathematical formulas, vets can accurately assess a wide range of health-related issues.

Medication
Appropriate medication dosing requires a keen attention to mathematical formulas. For example, the amount of pain medication or antibiotic given to a horse would be much greater than the dosage given to a kitten or a small dog. Ensuring that all numerical factors are taken into consideration is critical to ensuring that animals receive the appropriate method of care.

Statistics
Many people consider pets to be members of their family, and as such, they want to ensure their pets are happy, healthy, cared for and pain free. Vets may use numbers to help pet owners make the sometimes difficult decisions about medical care. This might involve explaining specific treatment outcomes in terms of percentages, so that pet owners can make informed decisions about treatment options.

Surgery
When an animal must be put under anesthesia for surgery, vets use math to assess the pre-op blood work and to determine the appropriate amount of anesthesia required to keep the animal sedated. Math may also be used to assess approaches to take in treating different medical conditions. For example, if a vet is repairing a torn ligament in a dog's leg, he needs to assess the dog's weight against the strength of various surgical materials so that he can determine the best approach to follow.

Weight Gain or Loss

Vets use math from the moment their patients enter their practice and are weighed. It’s important for a vet to track an animal's weight, as atypical weight gain or loss between examinations can indicate illness. Vets use weight to help track growth and development, as well as to determine body mass index. Changes in weight can also signal concern to general health such as malnourishment, obesity, swelling from infection or weight loss due to dehydration.

Billing
Many vets play an active role in running the business side of the veterinary practice. This can include using math for duties such as internal accounting, paying vendors, handling payroll, office bookkeeping, accounts payable and receivable -- and even tax preparation. As such, a knowledge of and understanding basic math can be an asset to ensuring smooth, accurate business operations.

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Occupation: Gardener

From: Luis

To: Felipe

Topic: Garden planning

Hi Felipe!

I will answer your question one by one:

1) So, how big should my vegetable garden size be?

The garden size should be approximately 100 square feet per person you’re trying to feed. Some variables may change this size for your specific situation, but as a general rule, the vegetable garden size should be 100 square feet per person you intend to feed.

Individual 100 square feet
Couple 200 square feet
Average Family 300-500 square feet
Large Family (5+) 600-800 square feet
Religious Family (8+) 1000+ square feet

I hope no one takes offense to the “Religious Family” category…my wife and I both come from large families of 8+.

This isn’t a number to live and die by. Of course, there could be reasons to have a smaller garden, and there could definitely be reasons to go bigger. The number one reason that 100 square feet is a good rule of thumb is simply that it’s a manageable garden size for an individual and a garden this size will have decent production.

If you have a small yard though, you may want to go smaller, or even just have a few potted plants that you can bring inside if need be. If you’ve got a larger yard and plenty of space, and you’re not concerned with having too much yield, then by all means go for it and create a larger garden.

My garden size is currently 20×20 (400 square feet). After purchasing our home my wife and I built a 15×15 garden (225 square feet) for ourselves and our two young children. After two years we had grown out of that garden and I began expanding it because our family has grown…a lot! We’ve added 4 more children, which means we’re now a household of 8 instead of a household of 4. So, I think it’s time to expand the garden size again, but my wife is worried about production and time commitment because we haven’t grown anything in a while.

The garden size should really depend on your personal needs and wants. What are you trying to accomplish with this garden and can you give the garden the time needed to accomplish your gardening goals?

2) Question about time commitment

Every garden needs to be cared for and the environment you live in will be a huge factor in how much time your garden needs YOU. Keep in mind that for every square foot of garden you’ll need to be sure to prep the soil, plant, space plants out, weed, water, monitor soil, and protect from adverse weather (extreme heat or extreme cold), etc.

There is a lot of time that goes into your garden. I’m not sure how much time other people spend on their garden, but my wife and I used to spend about 20 minutes a day tending to the garden….that was when it was a 15×15 space. So, a little over 1 minute per 10 square feet of garden. If you’re regularly maintaining the garden it won’t get out of hand. However, if you don’t tend to the garden daily you may find that you spend more time in the garden each time you do get out to tend to it.

2) What is the best size for raised vegetable garden beds?

The best size for raised vegetable garden beds depends on the space you have and how much you’ve decided you need to grow. I have a very large 20×20 raised vegetable garden bed. Something this big means that I have to walk through the garden itself in order to plant, maintain, and harvest. I’m fairly certain I’ll be building a new raised garden bed about 20×6. This is still a large garden, but it’s much more narrow so I can stand to the side of the garden and do most of what is needed to maintain the garden. It’s also much easier for my children to do their jobs in the garden when it’s this narrow.

3) Length and Width

For many gardeners the raised vegetable garden bed size will depend on the lumber you’re able to secure from your local home improvement store. Lumber typically comes in 8-foot lengths – which is great if you cut them in half and just do a 4×4 raised vegetable garden bed. These smaller vegetable gardens don’t require any less work, but they can be slightly easier to navigate, particularly for children.

I’ve also seen many 8×4 and 8×8 raised vegetable garden beds. Again, this is because of the standard length of lumber from the home improvement store. These smaller and more narrow raised beds also lend themselves to more appealing landscaping because you can create beautiful paths between your raised beds.

4) Depth

As far as depth goes I would suggest a minimum of 6-8 inches or two 2×4’s stacked on their side. My large 20×20 garden has a depth of about 2-3 feet, but the new one I’m building will only be about 8 inches deep so my children have easier access to it. I have seen numerous raised gardens with 16-24 inch depths. These heights make it easier to plant, weed, and harvest because you won’t need to bend over as much.

5) How many hours of full sun does a vegetable garden need?

Your vegetable garden will need 4-8 hours of full sunlight. Of course, each plant has slightly different needs, but as a general rule of thumb 4-8 hours of direct sunlight is great for a healthy garden. Every plant is different. Most leafy vegetables need the least amount of sunlight (about 4 hours will do), and your root vegetables like carrots and beets will need a good 6 hours. Your vines, melons, fruit veggies like tomatoes, cucumbers, squash, peppers, etc. will need the most sunlight.

Keep in mind that the temperature and soil conditions will also need to be considered. Four to eight hours of full sun here in the 100 degrees Texas heat is different than 4-8 hours of full sun in Canada because the temperature is so different. In hot climates like Texas, 4-8 hours maybe a little too much and may cause the plants to burn.

6) Eyerly Family

The Eyerly Family is a family of 8 that loves gardening. Over the past several years we have been applying what we learn about gardening to our own 16x16 raised back yard garden. Our garden is very prolific and we grow a wide variety of vegetables which we love to eat!

I hope these information helps you and give you some ideas in how you want to make your own garden.

be blessed!,

Luis

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Occupation: Chemist

Name: Joy Bielenberg

List of important numeracy skills and vocabulary for chemists:

1.  Radioactive decay:  Radioactive decay is determined by understanding and using formulas and calculus.  Although I thought of it last, when viewing a picture of Marie Curie, I chose to list radioactive decay first because it is important to all of us, not just to chemists and physicists.  The radioactive decay equation allows scientists to figure out how many radioactive atoms are left in a sample after any amount of time.  The speed of radioactive decay is proportional to the number of radioactive atoms in the sample.  Each type of radioactive atom is also represented by a decay constant representing the likelihood that any individual atom will decay at any given time.  Atoms that decay faster have larger decay constants. Since the decay rate changes as the number of atoms changes, simple multiplication won’t do.  Curie lost her life to the effects of the radiation she studied.  Humanity is also at risk unless proper storage of radioactive materials and waste are taken seriously.

Mathematical formulas, calculus, time, speed, proportion, use of constant, rate

2.  Scale drawing:  Chemists who have the opportunity to design their own laboratory will likely make use of a scale drawing.  This will allow multiple approaches to the efficiency of layout for performance and for safety before any hammer is used.  The hood and exhaust must be placed in an area that allows for accessibility without being in the direct line of foot traffic.  Other safety concerns include how to store flammable, combustible, explosive and potentially hazardous materials.  A scale drawing is a place to start to determine how space can and should be allotted.

Ratios, measurement, fractions

3.   Research Grant Writing:  Many chemists will be involved in research which may require funding through a grant.  Include an itemized list of each anticipated expense.  Think about laboratory space, specialized instruments, reagents, travel expenses and personnel wages.  The more specific you can be about budget items the more credibility.  Use the funding agencies regulations as a guide to what they will and will not cover.

Simple math, budgeting

4.  Use of numerical information in the Periodic Table:  Each box on the table represents one element. Basic information about the element is included on every periodic table, including the following:

1.       The name of the element

2.       The one- or two-letter atomic symbol

3.       The atomic number, which is the number of protons in the atom's nucleus

4.    The atomic mass in atomic mass units (or AMUs, where one AMU is equal to 1/12th​ the mass of a carbon-12 atom, or about 1.66 x 10 to the minus 27 Kg). (Note: The terms atomic mass and atomic weight are often interchanged, but they do have distinct definitions. Atomic weight is calculated based on the atomic masses and relative abundances of all naturally occurring isotopes of an element.)

For a single atom of an element, the atomic weight would be a whole number, adding the number of protons, neutrons, and electrons together for the atom. However, the value given in the periodic table is an average of the mass of all isotopes of a given element. While the number of electrons does not contribute significant mass to an atom, isotopes have differing numbers of neutrons, which do affect mass.

Working with exponents, proportion, average

5.  Making solutions:  The mole is useful in chemistry because it is defined such that the mass of Avogadro's number of particles (atoms or molecules) of a substance (the molar mass) is equal to the sum of the numerical values of the atomic masses of its constituent elements.

Calculate the molecular mass of CuSO4 · 5 H2O hydrated copper sulphate. Solution: Molecular mass of CuSO4 · 5 H2O = 64 + 32 + (16 × 4) + 5 × ((1 × 2) + 16) = 64 + 32 + 64 + 5 × (2 + 16) = 64 + 32 + 64 + 5 × 18 = 64 + 32 + 64 + 90 = 250

The following steps describe the procedure for making a solution of a specific molarity from a pure, solid substance. First, weigh out the correct mass of solute. Dissolve the solute in water, keeping the volume less than the desired total volume of solution. Dilute the solution to the desired total volume of solution.

Order of operations, use of periodic chart, division

6.  Graphing data:  Chemists frequently present the results of experiments.   Plotting data on a graph has the major advantage of making clear trends and patterns that are present, especially to audiences that do not understand mathematical notation.  In experiments there is a control variable that can be changed, and an observed variable that is measured as the control is changed.   All other quantities are kept constant.  When plotting a graph of data, the control variable is plotted along the horizontal (or x) axis and the observed variable along the vertical (or y) axis.  Use of technology can be extremely helpful in producing graphs.

Variables, measurement

7.  Scientific Notation:  Scientific notation enables simpler order-of-magnitude comparisons. A proton's mass is 0.0000000000000000000000000016726 kg.  If written as 1.6726×10−27 kg, it is easier to compare this mass with that of an electron. The order of magnitude of the ratio of the masses can be obtained by comparing the exponents instead of the more error-prone task of counting the leading zeros. In this case, −27 is larger than −31 and therefore the proton is roughly four orders of magnitude more massive.

Exponent, coefficient, integer

8.  pH scale:  The pH scale measures how acidic or basic a substance is. The pH scale ranges from 0 to 14. A pH of 7 is neutral. A pH less than 7 is acidic. A pH greater than 7 is basic.

The pH scale is logarithmic and as a result, each whole pH value below 7 is ten times more acidic than the next higher value. For example, pH 4 is ten times more acidic than pH 5 and 100 times (10 times 10) more acidic than pH 6. The same holds true for pH values above 7, each of which is ten times more alkaline (another way to say basic) than the next lower whole value. For example, pH 10 is ten times more alkaline than pH 9 and 100 times (10 times 10) more alkaline than pH 8.

Logarithmic scale

9. Use of statistics:  Once the study is complete and the observations have been made and recorded the researchers need to analyze the data and draw their conclusions. Typically, data are analyzed using both descriptive and inferential statistics. Descriptive statistics are used to summarize the data and inferential statistics are used to generalize the results from the sample to the population. In turn, inferential statistics are used to make conclusions about whether or not a theory has been supported, refuted, or requires modification.

Statistical analysis

10.  Conversion of measurements:  Even though, especially in science, the United States has made attempts to convert to the metric system of measurement, many measurements are recorded in the English system.  Scientists must be able to convert from one system to the other.   Conversations are also often needed within a system, say from grams to kilograms.

Decimals, fractions

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Names: Cortnie Brooks, Malcolm McLeod, Ed Pulaski

List of important numeracy skills and vocabulary for firefighters:
1. Air Temperature and Windspeed: Firefighters must take a lot of measurements to keep themselves and their crews safe. When it comes to fighting wildfires in rural ares, measuring the temperature (90°, 100°, 110°) and wind speed (10 mph, 20 mph, 30 mph) in the surrounding area is an important part of fighting those fires safely and effectively. These measurements can determine how quickly a fire can spread and how dangerous they will be for the firefighters. MPH stands for "miles per hour".

2. Humidity and Moisture: Measuring the Relative Humidity (RH) in the air is also an important part of fighting wildfires, because fuels such as grass and pine needles lose moisture quickly with changes in relative humidity, and when the RH drops the fire burns more quickly and becomes more dangerous. RH is measured in percentages (80%, 90%, 100%). When the RH is 100% it means the air is holding as much moisture as it can. Moisture is also measured by looking at the moisture-content of the soil, and also in the different kinds of fuels in an area and how much time they will likely burn when the fire reaches them ("1 hour fuels" are those with less than 1/4" in diameter such as dried plants, "10 hour fuels" are those 3/4" to 1" in diameter, "100 hour fuels" are 1" to 3", and "1000 hour fuels" are 3" to 6").

3. Lightning Activity Level: The Lightning Activity Level (LAL) is a measurement of the cloud-to-ground lightning activity observed (or forecasted to occur) within a 30-mile radius of the observation site. (LAL 1 = no thunderstorm clouds have been observed within a 30-mile radius, LAL 2 = a single or a few clouds, LAL 3 = occasional lightning with an average of 1 to 2 strikes per minute, LAL 4 = frequent lightning with 2 to 3 strikes per minute, LAL 5 = frequent and intense lightning with greater than 3 strikes per minute),

4. Size and Containment of the fire: Firefighters in the United States measure the size of fires in acres (1 acre = 43560 square feet or 4046 square meters). They calculate the total acreage of a fire using local maps of the area, firefighters observing the fire on the ground, and observation planes observing the fire in the air, and they continue to measure this area over time and give regular reports to the public (100 acres, 500 acres, 1000 acres). They also measure how "contained" the fire is (the fire is 5%, 25%, 75% 100% contained) and how many miles it is from nearby towns (3 miles, 5 miles, 10 miles to the southeast).

5. Length of fire hoses: Firefighters must know the length of their hoses (50 feet per hose), and how many hoses it would take to reach a fire that is 300 feet away (6 hoses) from their firetruck or a fire hydrant.

6. Diameters of fire hoses: The diameter of the hose is the most important factor in determining the volume of water delivered to the fire, and they come in different diameters (such as 1 3/4 inches, 2 1/2 inches, 3 inches, 4 inches, 5 inches, and 6 inches).

7. Water pressure: Nozzles on fire hoses need a certain amount of water pressure to work (such as 100 psi, 150 psi, 200 psi). PSI is a measurement of pressure that stands for "pounds per square inch".

8. Water volume: The water pressure and diameter of the hose also determine the volume of water coming out of the hose (50 gpm, 75 gpm, 100 gpm). GPM stands for "gallons per minute".

9. Volume of water in the firetruck: Firetrucks (also called fire engines or simply "engines" for short) measure their water tanks in gallons (500 gallons, 1000 gallons, 1500 gallons). They also know the the capacity of the water pump on their truck (1000 gpm, 1500 gpm, 2000 gpm). GPM stands for "gallons per minute".

10. Time until the firetruck runs out of water: Firefighters know the size of their engine's tank and the capacity of their pump, and therefore they can calculate how many minutes they have until their firetruck runs out of water (30 seconds, 1 minute, 2 minutes).

This was a helpful resource that we used for completing this assignment, with more facts and figures about firefighting: https://www.nps.gov/articles/understanding-fire-danger.htm