Download Year 8 Maths Knowledge Map – Spring Term Key Word Definition

Year 8 Maths Knowledge Map – Spring Term
Key Word
Integer
Sum
Product
Ratio
Definition
An integer (from the Latin integer meaning "whole") is a
number that can be written without a fractional
component.
The result of adding two or more numbers.
The answer when two or more numbers are multiplied
together.
A ratio shows the relative sizes of two or more values.
Ratios can be shown in different ways. Using the ":" to
separate example values, or as a single number by dividing
one value by the total.
Equivalent
Having the same value.
Numerator
Proportion
Fraction
The top number in a fraction. Shows how many parts we
have.
The bottom number in a fraction.
Shows how many equal parts the item is divided into.
Proportion says that two ratios (or fractions) are equal.
A fraction is a part of a whole.
Equivalent
fraction
Equivalent Fractions have the same value, even though
they may look different.
Denominator
Example
21, 4, 0, and −2048 are
integers, while 9.75, 5 1⁄2,
and √2 are not.
9 is the sum of 2, 4 and 3
(because 2 + 4 + 3 = 9).
8 is the product of 4 and 2.
If there is 1 boy and 3 girls
you could write the ratio as:
1:3 (for every one boy there
are 3 girls).
1/4 are boys and 3/4 are
girls.
0.25 are boys (by dividing 1
by 4).
25% are boys (0.25 as a
percentage).
1 Dollar is equivalent to 100
cents.
120 seconds is equivalent to
2 minutes.
In the fraction 3/7, the
numerator is 3.
In the fraction 3/7, the
denominator is 7.
1/3 = 2/6
2/3 of a pizza. The top
number says how many
slices we have. The bottom
number says how many
slices the pizza is cut into.
These fractions are really the
same:
1
2
Linear
equation
A linear equation is an equation for a straight line
Equation of a
line
The equation of a straight line is usually written this way:
y = mx + c. m represents the gradient of the line, c
=
2
4
=
4
8
All linear equations:
y = 2x+1
5x = 6+3y
y/2 = 3 - x
If y = 3x -7, the gradient is 3
and the y-intercept is -7
Variable
represents the y-intercept.
A symbol for a number we don't know yet. It is usually a
letter like x or y.
In x + 2 = 6,
x is the variable.
Estimate
A close guess to the actual value, usually with some
thought or calculation involved.
Alex estimated that there
were 10000 sunflowers in
the field by counting rows.
Simultaneous
equation
A simultaneous equation is when we have two or more
equations working together. Each equation contains two
variables.
x+y=6
and
−3x + y = 2
are simultaneous equations
both containing variables x
and y.
Substitution
In Algebra "Substitution" means putting numbers where
the letters are.
Nth term
The 'nth' term is a formula with 'n' in it which enables you
to find any term of a sequence without having to go up
from one term to the next.
'n' stands for the term number so to find the 50th term we
would just substitute 50 in the formula in place of 'n'.
What is x + x/2 when x=5?
Put "5" where "x" is: 5 +
5/2 = 5 + 2.5 = 7.5
For the sequence
6, 11, 16, 21, …
Where there is a common
difference between terms.
nth term = dn + (a - d)
Where d is the difference
between the terms, a is the
first term and n is the term
number.
e.g. 6, 11, 16, 21, ...For this
sequence d = 5, a = 6
So the formula is
nth term = 5n + (6 - 5)
which becomes nth term =
5n + 1
Common
difference
The difference between each number in an arithmetic
sequence.
Congruence
The same shape and size.
Similarity
Two shapes are congruent when you can Turn, Flip and/or
Slide one so it fits exactly on the other.
Two shapes are Similar when the only difference is size
(and possibly the need to move, turn or flip one around).
The sequence {3, 5, 7, 9, 11
...} is made by adding 2 each
time, and has a "common
difference" of 2 (there is a
difference of 2 between each
number)
When two shapes are
similar, then:
corresponding angles are
equal, and
the lines are in proportion.
Quadrilateral
A flat shape with four straight sides.
Plane figure
A 2-dimensional shape. Has width and breadth, but no
thickness.
Inverse
proportion
When one value decreases at the same rate that the other
increases.
Square, rectangle,
trapezium, rhombus, kite,
parallelogram
Examples are square,
rectangle, triangles and
octagon.
4 people can paint a fence in
3 hours.
How long will it take 6
people to paint it?
(Assume everyone works at
the same rate)
It is an Inverse Proportion:


As the number of people
goes up, the painting time
goes down.
As the number of people
goes down, the painting
time goes up.
Direct
proportion
Directly proportional: as one amount increases,
another amount increases at the same rate.
∝
The symbol for "directly proportional" is ∝
You are paid £20 an hour.
How much you earn is
directly proportional to how
many hours you work.
Work more hours, get more
pay; in direct proportion.
This could be written:
Earnings ∝ Hours worked
If you work 2 hours you get
paid £40.
If you work 3 hours you get
paid £60.
etc ...
Sum of angles
in a triangle
Sum of angles
in a polygon
The three angles always add to 180°
Sum of Interior Angles = (n-2) × 180°
Each Angle (of a Regular Polygon) = (n-2) × 180° / n
What about a Regular
Decagon (10 sides) ?
Sum of Interior Angles
= (n-2) × 180°
Where n = the number of sides
= (10-2)×180° = 8×180° =
1440°
And it is a Regular Decagon
so:
Sequence
A list of numbers or objects in a special order.
Each interior angle =
1440°/10 = 144°
3, 5, 7, 9, ... is a sequence
starting at 3 and increasing
by 2 each time.