Maths Video Lessons
Click the title to go to the video. Some lessons have worksheets for downloading. Other worksheets can be generated at the website at www.Math-Aids.com. Accelerate Christian Home Schooling has no affiliation with Math-Aids.
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.
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.
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!
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.
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.
“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.
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 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.
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.
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?
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!
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.
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.
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.
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 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 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!