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The Basics Of Tenth Grade Math On One Page

Don’t know what’s going on with your kid’s math homework? Let’s make this easy on you. Here’s a resource for parents who want to teach their tenth grade kid some math over the summer, or whenever. It covers the key stuff in your local grade 10 curriculum. Read through the sections and download the workbooks. Try to have as much fun with it as you can because the key to learning is feedback. Make some rules, offer rewards, and make it a game. If you can make practice fun and challenging, your child will thrive!

Mastered tenth-grade math? Check out our Grade 11 Math Curriculum resource page (coming soon).

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    Introduction To Math Education

    Like building a house, there are no shortcuts to learning math. All new math is build on top of an existing math foundation. Sir Isaac Newton, the inventor of calculus once wrote: “If I have seen further, it is by standing on the shoulders of giants.”. We discover new things by building on previous things. It is important that our the foundation is strong. This makes learning advanced math easier. Knowing the prerequisite knowledge unlocks paths and makes learning the new stuff easier. Without a strong foundation anyone will find it difficult to follow the new material. This causes stress and confusion in later years. Like building a house, we should aim to have the most complete foundation we can. Get the cracks fixed and you will build a beautiful house.

    Think of educational learning as a pyramid. The foundation is Elementary School Math and the Pinnacle being a pHD. A knowledge gap at he base affects your ability to learn at the top.
    Think of educational learning as a pyramid. The foundation is Elementary School Math and the Pinnacle being a pHD. A knowledge gap at the base affects your ability to learn at the top.
    Grade 10 Math Curriculum 1-Pager
    Grade 10 Math Curriculum 1-Pager

    Grade 10 Math Curriculum

     

    It is very important for parents to be aware of what their child is learning in school.

    Your school gets its direction from a governing body. The school board issues a curriculum (or math standards) for schools to follow. The curriculum varies across the world. For example, in Saudi Arabia, algebra starts in Grade 1, while in Ontario it starts in Grade 8. That means your school’s curriculum differs from what you may find online. In this article, we cover an estimation of what you can expect from your school’s curriculum.

    • Solving Linear Systems (Graphing, Substitution Method, Elimination Method)
    • Factoring Quadractics, Completing The Square, Applications
    • Graphing Geometry: Trigonometric Identities, Special Triangles, Area Problems, Volume And Surface Area. 
    • Probability & Statistics: Basic Probability, Probability Models, Sample Spaces, Comparing Spaces

    Find an online math tutor today!

    Grade 10 Math Curriculum Examples

    Recall the cartesian plane from grade 9. There is an x-axis and a y-axis. We now will learn how to analyze systems of linear equations. That’s just a fancy way of saying we will analyze lines on graphs.

    Introduction To Lines

    Line Formula breakdown

    In Grade 10 you will learn how to analyze systems of linear equations. That means you will look at multiple lines and find the intersection (solution).

    All lines has a slope (m) which is the “m” in the formula of the line which is y=mx+b. Y is the positions on the y-axis, m is slope of the line. The slope is the formula  Δy/Δx = (y2-y1)/(x2-x1). 

    What Is The Slope Of A Line

    Do you see how a line goes up or down? That’s called a slope. The first thing you gotta know about lines is that each one has got a slope. A line has the formula y = mx+b.  “m” is the slope of the line and “x” is the “knob” that is changing. The slope (m) is the proportion of rise over run. What is “rise over run”? It is the change of the y values (called “Delta y or Δy”) of two points divided by the change of the x value (called “Delta x” or Δx”) of two points. 


    For example, If m=1 that mean it “rises” 1 and “runs” 1. If m=2 that means it rises 2 and runs 1. If m = -1 that means it drops 1 and runs 1. Do you see how that works? What patterns in the graph do you see between the change of slope (m) and the rise/run?
     
     

    Since lines are straight, the slope is constant anywhere on the line. If you have a line graphed, you can determine the slope by taking any two point and dividing the rise over the run. That means the rise is the change in the y-values (delta  delta y

     

    ) . The run is the change in x values (called “delta”

    Δ

    x). So m = (y2-y1)/(x2-x1). .

    This video shows that the slope of a line is. It is the rise over run of the line over time. It is the proportion of the change in output (y) over the change in input (x).

    What does “Rise over Run” mean?

    This diagram explains what the slope of a line is.

    “Rise” means how much a line changes in the y-axis between two points. “Run” means how much a line changes in the x-axis between two points. Rise over run is the way that you calculate slope(m).

    What Is The Y-Intercept Of A Line

    The Y-Intercept is the y value at which a line crosses the y-axis. You can find the y-intercept by reading the graph of a line. Determine the y-value at the point where the line crosses the y-axis. That’s it! You can also find the y-intercept by reading the the “b” on the line formula y = mx + b. 

    If you have two points of a line graphed, then you can extend the line. The point where it crosses the y-axis is the y-intercept. You can then tell what the “b” is in the line formula.

    This video shows what the Y-Intercept of a line is. It is the point at which the line crosses the y-intercept. It is also the "b" in the line formula y=mx+b.

    How to Solve A Linear System With The Graphing Method

    In this video we show how to solve a system of linear equations using the graphing method. The first step is to graph the two lines. If you have the formula, determine the y-intercept and put a mark on that value. Then using the slope, plot a point at x=1 or any other point. Now connect the y-intercept with that point and you have graphed the line. The point at which the two lines intersect is called the solution of the system of linear equations.

    If you have a system of linear equations and you want to know the solution to both of them graph them out. The intersection (if there is any) will be the solution to both of them.

    There’s three things you need to know to do this:

    1). How to read a line formula y=mx+b (What’s the slope (m)? What’s the Y-intercept (b))

    2). How to plot the Y-intercept on graph.

    3). How to extent the line from the slope (m)

    When you plotted both lines, the point where the two lines meet has coordinates (x, y). If you “Plug” those coordinates into your line equations, they will have the same y-value. 

    Elimination Method Of Solving Systems Of Linear Equations

    Before we get to the elimination method, you have to understand what we are going to be working with. We are always going to work with 2 linear equations, which are straight lines. This is called a system of linear equations. Now that we know a system of linear equations has 2 lines, what are we going to do with them? For every system, there will be a solution (where the lines cross). Now this is when the elimination method comes into play. What do you think of when you hear the word elimination? Erase? Not quite. We actually eliminate one of the equations to help us find the solution. The first step we are going to take is to actually add the equations together. What is that eliminating? Well, we are going to combine these equations to find the solutions. When you are adding these equations, be careful to not only add the unknown terms but the ones that we know as well. Notice how you are left with one equation because one of the terms cancels out? Now, using your algebra skills you can find the value of the unknown. (Even though we are solving for the x/y value, your teachers can give one or the other first, so make sure to keep that in mind! With this value, you can substitute it in the first equation to find the other unknown. (since we found the x/y value first, now we are going to find the x/y value). With these 2 values, you can put them both in the second equation to see if they are correct. If they are, that’s awesome! You are on your way to mastering the elimination method. If not, that’s alright, try going back and see which step went wrong.

    In this video we explain how to get the midpoint using the midpoint formula which is a function of two points.
    This is a gif explaining how math substitution method for solving linear equations

    Substitution Method Of Solving Systems Of Linear Equations

    The substitution method substitutes one of the equations into the other in order to find a missing variable(x or y).
    Notice how one equation has an x/y alone on one side? We are going to take the value on the other side of the x/y and substitute it into the corresponding value in the other equation. Now we have eliminated one unknown variable, so we can use our algebra skills to find out one part of the solution.
    With this number, let’s take it back to our first equation. Substitute the number we got with its corresponding variable, and we will find out what the other part is.

    How To Find The Midpoint Between Two Points

    Recall the coordinate plane we learned in grade 9, there are points on the plane. This system allows us to graph certain points. Now, we will look at multiple points and find out the distance between them as well as the midpoints.

    What do you think of when you hear the word “midpoint”? The middle between 2 points? Actually, that is exactly what it is. Although it is not just the middle on the horizontal axis, but the vertical one as well. So we use the equation:

    In this video we explain how to get the midpoint using the midpoint formula which is a function of two points.

    Tenth Grade Math Problem Worksheets

    Are you looking for something you can hand to your kid to start learning? Check out our free 10th grade math worksheets. You can download or try out our math problem generator to learn online.  You can make a copy, download, and print these problems. Make it an exciting game and start learning Grade 10 math today! If you don’t have a printer, open it with the iPad/Tablet. 

    We also love to write blogs about learning. check out our blog on 6 free back to school math activities to get to the next level.

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