Maths Review Lessons
Click the title to go to the video or downloadable pdf file. Some lessons also have worksheets for downloading. Worksheets can also be generated at the website at www.Math-Aids.com. Accelerate Christian Home Schooling has no affiliation with Math-Aids.
Basic Arithmetic | |
 | Add with Carry |
 | Subtract with Borrow |
 | Long Division |
 | Long Multiplication |
Add with Carry
Adding rows of numbers from right to left. If the sum of a column is more than 9, make the "overflow" part of the next column.
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Practice and Assessment
- Go to www.Math-Aids.com/Addition/Addition_Worksheets_MV.html
- After some practice, do the following Assessment under test conditions;
- Choose 3 Digits or 4 Digits;
- Do one sheet of 12 problems with 2 Addends, one sheet with 3 Addends and one sheet with 4 Addends;
- Send marked tests back to Accelerate Christian Home Schooling (by post or emailed scans).
Subtract with Borrow
Also called Subtract with Regrouping. When we "borrow" from the next column, we are really regrouping our amounts. 24, for example is 20 + 4. We can regroup this to become 10 + 14, allowing us to subtract more easily.
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Practice and Assessment
- Go to www.Math-Aids.com/Subtraction/Subtraction_Worksheets_MV.html
- After some practice, do the following Assessment under test conditions;
- Choose 4 Digits;
- Do one sheet of 20 problems where Problems May Require Some Regrouping and May Subtract Across Zero;
- Send marked tests back to Accelerate Christian Home Schooling (by post or emailed scans).
Long Division
How many times does a number go into a bigger number? We use "short division" for simpler examples, but set it out carefully as "long division" for harder examples.
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Practice and Assessment
- Go to www.Math-Aids.com/Division/Long_Division.html
- After some practice, do the following Assessment under test conditions;
- Choose 2 Digits in Divisor; 2 Digits in Quotient; Mixed problems with and without remainders;
- Do one sheet of 12 problems;
- Send marked tests back to Accelerate Christian Home Schooling (by post or emailed scans).
Long Multiplication
Neat, careful setting out is important with long multiplication. If we want to multiply by, say, 453, then we carefully multiply first by 3, then by 50 and finally by 400. Keep those columns lined up!
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Practice and Assessment
- Go to www.Math-Aids.com/Multiplication/Multiplication_Worksheets_MDV.html
- After some practice, do the following Assessment under test conditions;
- Choose 3 Digits in the Multiplicand; Choose 2 Digits in the Multiplier; Do one sheet of 12 Problems;
- Choose 4 Digits in the Multiplicand; Choose 3 Digits in the Multiplier; Do one sheet of 12 problems;
- Send marked tests back to Accelerate Christian Home Schooling (by post or emailed scans).
The Equation Triangle
The best way to work with equations is to use good old algebra. If this is still new to you, or if you struggle with algebra, the Equation Triangle is a useful tool to change the subject of many simple equations.
What is an Equation?
An equation equates. It shows that two sides are equal, and uses the "equal sign" (=). So, whatever you do to one side, you have to do the same to the other side.
Inverse Operations
Give, take... Double, halve... Take apart, put together... In maths, operations are what we do to a number. Inverse operations are when we do the opposite.
"Fixing" an Equation
Well, the equation might not be broken... but it might be written in a way that is inconvenient or confusing. If we want to fix it so it reads better, we have to undo what's wrong with it, and to undo something we need to do the opposite - the inverse.
Changing the Subject (of an Equation)
It's all very nice to say that y = 2x + 7, but what if I want to know what x is? If we want to know what x equals, we have to change the equation to read x = something. Here we use our skills of "fixing" an equation to make this possible.
Equivalent Fractions
"Eight out of ten people say that maths is fun." That's because I asked thirty students in my maths class, and twenty-four wanted to avoid detention. 8 out of 10 and 24 out of 30 are equivalent fractions, because on a pie chart (or pizza chart) they tell of exactly the same part of the whole. What's more, they can both be reduced to the smallest numbers 4 out of 5.
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Adding and Subtracting Fractions
Adding and subtracting fractions is pretty straightforward, as long as they have the same denominators. Pizzas help to show how!
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Lowest Common Multiples and Adding and Subtracting Fractions
Adding or subtracting fractions is not so easy if they have different denominators. We have to find the Lowest Common Denominator (LCD), by finding the Least or Lowest Common Multiple (LCM). We do this by first finding the Highest Common Factor (HCF)! Sound confusing? We hope this video makes it simpler than it seems at first.
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Assessment
- Go to this link; Print out the test (2 pages) and score key (2 pages). Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Subtracting Fractions with Borrow
If we don't have enough pieces of pizza, we'll just have to cut up another whole one!
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Multiplying Fractions
This is one of the easiest thing to do, once you know how. That doesn't mean you don't have to be careful, though.
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Multiplying Fractions with Cancelling
When multiplying fractions, it's not uncommon to get an answer that can be reduced to a simpler fractions. All that work, and then you have to simplify! Cancelling first means you can save a lot of effort later, and maybe even save multiplying big numbers! Definitely worth it.
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Dividing Fractions
Can you divide fractions the same way that you multiply them? Well, yes... but dividing numbers can lead to fractions or decimals that complicate things. So, keeping in mind that dividing is the INVERSE of multiplying, why not just INVERT the fraction and then simply multiply?
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Fractions and Decimals
Decimals are simply fractions over ten, a hundred, a thousand, and so on; so it's not surprising that changing decimals to fractions is quite simple, when done carefully!
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Mixed Numbers and Decimals
Mixed numbers are just numbers with a whole part and a fraction part; so are decimals. Provided we are careful, changing decimals to mixed numbers is a simple exercise.
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Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Changing Fractions to Decimals
Fractions can easily be changed to decimals if they are over ten, a hundred or a thousand (and so on). What if they're not? What if the fraction is over five, or eight, or seven? A few simple tricks, or a little bit of skill, or a good cheap calculator will do the trick.
Back to index at the top of the page
Assessment
- Go to this link; Print out the test and score key. Do not give the student the score key, but you should use it to mark the test.
- The test should be done under test conditions. You should then mark the test, showing all corrections;
- Send tests back to Accelerate Christian Home Schooling (by post or emailed scans);
- Contact us if necessary.
Fractions, Decimals and Percentages
PerCENTages are just fractions over a CENTury - over a hundred. Percentages and decimals can be simply turned into fractions over a hundred, and reduced if necessary.
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There is no assessment or worksheet for this video yet.
Triangle Geometry
This video introduces the triangle, and shows how to prove the angle sum of triangles (and quadrilaterals). It also shows that an exterior angle of a triangle is equal to the sum of the opposite interior angles. Yay!
The Right-Angle Triangle
The Right-Angle Triangle (also known as the Right-Triangle) is really pretty special. It's hard not to get excited about it. It really deserves to be named "Shape of the Year." It's just soooooooo special!
Pythagoras' Theorem
Pythagoras was a Greek philosopher and mathematician. He lived around five hundred years before Jesus was born, and did not worship the God of the Jews; however, his theorem about the sides of a right-angle triangle was pretty neat.
Pythagoras' Theorem - Proof
You can prove this using a piece of squared paper, but that's a lot of work and is only approximate. Here is just one method using algebra to prove that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Trigonometry 1: Introduction
Trigonometry (as the name implies; tri-gono-metry = three angled measure) is all about triangles - specifically, right-angled triangles. To understand trigonometry, however, we will start with a circle (because it has a tangent), and a folded sheet.
Trigonometry 2: Trigonometric Ratios
The values of Sine, Cosine and Tangent - what they mean and how to remember them.
Trigonometry 3: Worked Examples
Worked examples of calculations using the trigonometric ratios.
Trigonometry 4: Getting a Tan
You'll love getting a tan once you learn how this important ratio helps us to work out distances and heights.
Trigonometry 5: Inverse Trig Functions
Inverse trigonometric functions answer the question: "What angle gives me that trig value?" It's working backwards, undoing the trig function, hence "inverse".
Trigonometry 6: Degrees, Minutes and Seconds.
Degrees have smaller divisions, just like hours, and they're called the same: minutes and seconds. This video is just a few minutes, and with a decent calculator you'll be calculating trigonometry in seconds!
Trigonometry 7: Bearings
I used to love watching the movie and TV series, "12 o'clock High." You may have heard people talking about watching "your six". These clock terms, along with compass points, are used to describe directions and angles. That makes them useful in trigonometry. ... and "bearings" aren't those steel balls that make motors and wheels turn smoothly. When we get our bearings, we work out our directions, then we can use trigonometry to work out the rest!
Scientific Notation
This worksheet introduces Scientific Notation and shows how to covert to and from Standard Notation.
It is assumed that the student knows basic index notation.
