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Top skills in 7-9

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1 lesson
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Problem solving strategy

When one comes across a prblem that seems like it's too hard to solve, many give up. However, when equipped with the right strategies, there's no problem in this world that is impossible. As the saying goes, an elephant is eaten one little piece at a time and the same goes for probolem solving. Have a look at the steps below that are meant for solving typical school math written problems.

  1. Read the task through carefully TWO TIMES.
  2. What is the QUESTION? Highlight it.
  3. What is known? Circle all pieces of information there are.
  4. Make a drawing of the problem.
  5. How can you solve the problem? 
  6. Write an expression
  7. Calculate
  8. Check whether your answer makes any sense!

Exercices:

A 30m long rope is used to make a rectangle that is 4m wider than its length. Calculate the width and length of the rectangle using a linear equation.

CDs were sold for a discount of 5,40€. Jane calculated that 7 CDs now cost the same as 5 CDs with the normal price. What is the price before the discount?

Jane, Rita and Howard get 51€ for plowing all the snow of their neighbours driveways. They split the money as follows: Rita gets 7€ more than Howard and Jane, who worked the most, gets twice the amount of Rita and Howard combined. How much money do they each get?



0 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Graphing equations

Math is often ambiguous at best, especially when things get more and more complicated. However, this is also true for real life: How do you make sense of team or player statistics in sports, for example? How do the meteorologists figure out where the weather patterns are taking us? The common denominator is graphing. With visualisations we can make complicated things make sense much easier.

Let’s learn the theory:

Credit: Math antics, YouTube

Exercises:

  1. Look at the graph. What is…
    • The largest value of the function?
    • Smallest value of the function?
    • Which value of x gives the the largest value? 
    • What is the value of the finction when x = -3?

 

2. Graph the following equations using intercepts.

  • Graph 2x + 4 = 0
  • Graph 2y - 6 = 0

3. Graph the following three equations on the same set of coordinate axes.

  • y=x+1y=2x+1y=−x+1

4. Graph the following three equations on the same set of coordinate axes.

  • y=2x+1y=2xy=2x−1

 Credit: math.libretexts.org



+4 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Coding

Learning coding nowadays is almost what learning to read and write was to people in the past. If you learn the “language of the machines” you will have a much better understanding of the world of the future and even the world you live in right now!

Here are a few excellent websites that teach you coding. They are sorted by the type of coding they are and what their difficulty level is. You should start from the right one according to your level of experience.

To understand what coding is mostly about, watch this hilarious video! Machines only do what you tell them to do! :D

https://www.scratchjr.org/ (very easy). https://codecombat.com/ (Easy). https://www.codecademy.com/login (Intermediate). Microsoft.com makecode (Intermediate). Khanacademy.org programming (Advanced)



+2 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Statistics: Mean, median and mode

When looking at box scores of your favourite NHL, NBA, Champions League or F1 racing team, it is important to understand what kind of descriptors are used to make sense of the big set of numbers that are collected. For example, it might be important to know how many times a point guard loses the ball in a basketball match or how fast an F1 driver drives around a certain track. But how can we compare different point guards or F1 drivers to know which one is best and gets the contract or a place in the starting five. This is when mean, median and mode come in handy.

Let’s learn the theory:

Exercises:

1. Scores in a math test were 16, 22, 19, 22, 20, 15, 18, 17 and 24.

  • Calculate the mode
  • Calculate the median
  • Calculate the mean

2. Grade in all the math test throughout the academic year for John were 8-, 8+, 7½, 8+, 7, 8½ and 9

  • Calculate the mode
  • Calculate the median
  • Calculate the mean



+3 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

How to calculate to get the probability of getting 11 with two dice

Thanks to Don't Memorise



0 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Geometry

Practical excercices:

1. Go around your home and take pictures of things that represent the following (Google the names first if needed!):

  • Cone
  • Pyramid
  • Rectangular prism
  • Sphere
  • Tetrahedron
  • Cylinder
  • Cuboid

2. Draw a floor plan of your dream house. Use at least the following shapes in your plan and name them in your drawing.

  • Quadrilateral
  • Circle
  • Square
  • Rectangle
  • Parallelogram
  • Trapezoid

3. Practice using the compass by drawing these beautiful mandala shapes.

Let’s learn the theory:

Credit: Math Antics, YouTube

Exercises:

1. Draw a circle and mark the following parts in it:

  • Diameter
  • Radius
  • Chord
  • Circumference

2. Try to find as many objects around you that are shaped like a circle. Take some thread and measure their circumference and diameter. Plot the results in a graph (example below). What do you notice?

Object

Circum-
ference

Diameter

Circum-
ference
/Diameter

3. Calculate the circumference of a circle when the radius is:

  • 5,6 cm
  • 12,6 m
  • 1,0 km
  • 0 m

4. The circumference of a circle is 74,2 m. Calculate:

  • The diameter
  • The radius



+1 vote
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Number Sequences

 

Patterns are everywhere in the world. Maybe the most famous pattern that appears everywhere in the world from nature to fine arts is the Fibonacci sequence. Have a look at the following video to learn more. What kind of repeating patterns can you find at home?

Let’s learn the theory:

Credit: Math Antics, YouTube

 

Exercises:

1. Continue the string of letters two letters so that the string makes sense.

  • A, D, G, J, ___, ___
  • V, R, N, J, ___, ___
  • A, E, I, O, U, ___, ___

 

2. How many sticks will there be in the fourth figure?

 

3. Continue the string of numbers with 3 more numbers.

  • 17, 15, 11, …
  • 56, 53, 50, 47, …
  • 10, 7, 4, 1, …

 

4. Write the first for numbers of the sequence according to the following rules:

  • First number is 2 and the following number is always 7 bigger than the previous one
  • First number is 1 and the following numbers are always three times bigger than the previous
  • 3 – the place of the number in the sequence + 40

 

5. What is the missing number?

  • 2, 3, ---, 5, 6, …
  • 5, 2, -1, ___, -7…
  • 500, ___, 20, 4, …



+2 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Linear equation

Quite often in life, we know some variables, but we must figure out an unknown. For example, we may want to save money for a moped, but to know how long it is going to take, we must be able to calculate it according to our weekly allowance, price of the moped and perhaps other things we are going to end up buying with the money.

Practical example:

How long would it take for you to come up with the money if your weekly allowance was 10€, the price of the moped 1550€ and you would buy sweets with 2€ every week? What kind of calculations do you need to make to get the answer?

Equations are a way of writing expressions with unknown variables that can be figured out using math.

Let’s learn the theory:

Credit: Math Antics, YouTube

Excercises:

1. Figure out the X

  • x/9 = 1/3
  • 20/x = 5/1
  • x/12 = 2/3
  • 6/16 = 3/x
  • x/4 = 5/20
  • 3/8 = x/24

2. A runner’s step is such that on a 100m distance he takes 83 of them. How many steps must he take to run 1,7km? Come up with the equation and solve the X.

3. Solve the equation by dividing both sides with the same number.

  • 3x = 60
  • 10x = -30
  • -2x = 24
  • -5x = -30

4. Solve the equation by multiplying both sides with the same number.

  • x/3 = 4
  • x/3 = -7
  • x/-9 = 4

5. Solve the equation.

  • x/3 = 500
  • x + 9 = 13
  • 12x = 11x + 3



+2 votes
2 lessons
In 7-9 by Juhani Katajamäki Guru (6.1k)  

Functions

Have you ever come across the problem of understanding how warm or cold it is when the temperature is given in Fahrenheit or vice versa, if you live in the US, in Celsius? Wouldn’t it be convenient if you could have a machine that would do the conversion for you? This is what functions do: You input something, and it is given as output as something else according to a rule.

Let’s learn the theory:

Credit: Math Antics, YouTube

Excercises:

1. A function subtracts 9 from a number. What is the output of the function when input is 15? 45? 9? 5?

2. Calculate ƒ(x) = 5x + 1 when x = 7
x = 10
x = -1
x = -7

3. Calculate ƒ(x) = -3x + 10 when
x = 2
x = 12
x = 0
x = -6

3. For ƒ(x) = x – 6, which value of x gives the output of
5
0
-4
-12



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