Grade 6 Maths Review
Place value
Find the place value of the underlined digit in the following numbers:
1. 7,862
Thousands
2. 13,422
Ten thousands
3. 1,044.24
Hundredths
4. 14,665,491 Millions
5. 12,000
Units
What is the value of the underlined digit:
1. 398,841
800
2. 4,564,320
4,000
3. 862,479
70
4. 197,346,825 90,000,000
0
5. 102
Significant figures
1. 1,564 =
2. 890,416 =
3. 0.44600 =
4. 10,601,900 =
5. 15,015 =
6. 3,001 =
7. 198,423.30 =
8. 17,005 =
9. 0.0032023 =
10. 3 =
1. 4 SF (Rule 1)
2. 6 SF (Rule 2)
3. 3 SF (Rule 4)
4. 6 SF (Rule 4,2)
5. 5 SF (Rule 2)
6. 4 SF (Rule 2)
7. 7 SF (Rule 4)
8. 5 SF (Rule 2)
9. 5 SF (Rule 2,3)
10. 1 SF (Rule 1)
Estimation and aproximation
Month:
January
February
March
April
May
June
Loaves of
bread
345
892
1,002
593
120
698
350
890
1,000
590
120
700
Month:
July
August
September
October
November
December
Loaves of
bread
647
352
888
988
1352
68
650
350
990
1350
70
890
Estimate how many loaves of bread a local bakery sold
this year.
Round each number to the nearest ten and then add
Approximate Answer: 7,950 Loaves
Divisibility rules
2 THE LAST DIGIT IS EVEN
3 THE SUM OF THE DIGITS IS DIVISIBLE BY 3
4 THE LAST 2 DIGITS ARE DIVISIBLE BY 4
5 THE NUMBER ENDS IN 0 OR 5
6 THE NUMBER IS DIVISIBLE BY 3 AND 2
9 THE SUM OF THE DIGITS IS DIVISIBLE BY 9
10 THE NUMBER ENDS IN 0
Indicies and roots
LAW 1. When the index of a base number is one, it means we
only have one of the base number, therefore the answer is
always the base number itself.
LAW 2. When the index of a base number is zero, the answer is
always one.
LAW 3. When an index has a base of 10 such as 102, we multiply
by 10!
Whenever we multiply a number by 10 we just need to add a 0.
LAW 4. When multiplying two of the same number with
different indexes together we add the indexes together.
This becomes the new index.
LAW 5. When dividing two of the same number with
different indexes together we subtract the indexes. This
becomes the new index.
LAW 6. When multiplying an index inside a bracket with
an index outside a bracket we must multiply the indexes
together.
A square root is the inverse of a2, where “a” can be any
number. When we use a letter to represent any number,
we call the letter a variable in maths. “Variable” means
something that can change.
16 = a
A cube root is the inverse of a3, where “a” can be any number.
3
64 = a
BIDMAS
BIDMAS is also known as PEMDAS and BODMAS.
1. Brackets/ Parentheses
2. Indices/ Exponents
3. Division
4. Multiplication
5. Addition
6.Subtraction
Remember: Which ever comes first when
going from left to right is done first.
Negative numbers
In maths, a negative number is a real number
that is less than zero.
When the signs next to each other are different
you move to the left on the number line.
When the signs next to each other are the
same you move to the right on the number
line.
Rules for Negative Numbers
Multiplication
×
- ×
+ ×
- ×
+
= +
+ = - = - = +
+
Division
÷
- ÷
+ ÷
- ÷
+
= +
+ = - = - = +
+
• If the signs are the same, the product/quotient is positive.
• If the signs are different, then the product/quotient is
negative.
Algebra
Something that is unknown in algebra is called a variable.
Some common variables we use are x,y,a,b, but we can
use any letter.
An equation is a mathematical statement that says things
are equal. Equations have equal signs(=).
Terms are the parts of an equation or expression
Like terms are terms whose variables
(and their exponents such as the 2 in x2) are the same.
Algebraic sequences
A sequence can be finite or infinite.
A finite sequence is one with a fixed number of terms.
6, 11, 16, 21, 26, 31, 36, 41
8 terms
An infinite sequence continues forever, we show this by adding
three dots at the end.
6, 11, 16, 21, 26, 31, 36, 41 . . .
infinite terms
nth term
4, 9, 14, 19, 24 ...
Find the 65th term in this sequence
nth term expression is 5n - 1
Substitute n = 65
5 (65) - 1 =
The 65th number in this sequence is 5 (65) - 1 = 324
Angles
1. Right angle
90
3. Obtuse angle
Larger than 90,̊ but smaller
than 180
2. Acute angle
Less than 90
4. Reflex angle
Greater than 180
Types of Triangles by side
Equilateral
• All sides are equal length.
• All angles are equal size.
Isosceles
• Two sides are equal length.
• Two angles are equal size.
Scalene
• No sides are equal.
• No angles are equal.
S
e
i
Missing Angles in Quadrilaterals
How many degrees are in a triangle?
a + b + c = 180ᵒ
All quadrilaterals are made of two triangles.
180ᵒ
180ᵒ
So how many degrees are in a quadrilateral?
180ᵒ + 180ᵒ = 360ᵒ
Missing Angles in Quadrilaterals
Parallelogram
b
a
c
a = 80ᵒ c = 80ᵒ
b =100ᵒ d =100ᵒ
d
We know a = c and b = d, so if a = 80ᵒ, c must be what?
80ᵒ+ b + 80ᵒ+ d = 360ᵒ
160ᵒ + 2b = 360ᵒ
360ᵒ - 160ᵒ = 2b
200ᵒ = 2b
100ᵒ = b100ᵒ = d
Since b and d are the
same, let's change d to b
to simplify
Converting Fractions
Decimals
• What does convert mean?
to change form
• How do you make a fraction into a
decimal?
you divide the numerator by the
denominator
1
2
FRACTION
0.5
=
2 1
calculations
=
0.5
DECIMAL
Converting Decimals
Percentages
• How do you make a decimal into a percentage?
you multiply the decimal by 100
0.5 x 100
0.50
move the
decimal 2
places to the
right
= 50 %
add your
percent sign!
Converting Percentages
Fractions
• How do you convert a percentage into a fraction?
you put the percentage over a denominator of
100 and simplify
50%
50
1
=
100
2
Ratios
A ratio is used to compare two or more
quantities.
Example:
The ratio of triangles to squares is
4:3
Probability
• Probability or chance is how likely something is to happen.
• It is similar to a prediction in the scientific method.
• If something has a low probability, it is unlikely to happen.
• If something has a high probability, it is likely to happen.
Calculating probability
If I flip a coin, what is the probability of getting a head?
(coins have two sides, heads and tails)
0.5, ½ or 50%
Calculating probability
If I flip the coin twice, I will get one of these combinations:
1. Heads, Heads
1. H, H
2. Heads, Tails
or
2. H, T
3. Tails, Heads
3. T, H
4. Tails, Tails
4. T, T
What is the probability of getting two heads?
Only one of the four combinations is two heads.
1/4, 25%, 0.25
A Sample Space is a list of all the possible outcomes,
e.g. HH, HT, TH, TT
We can show this in a Sample Space Diagram:
First Coin
Second Coin
H
T
H H, H H, T
T T, H
T, T
There are 4 possible outcomes if you toss a coin twice.
So the probability of two heads is ¼
Statistics
There are three kinds of averages:
• Mean- The sum of a set of numbers divided by how
many numbers there are.
• Median- The middle number in a set of numbers.
• Mode- The most frequent(common) number in a set
of numbers.
Other Statistical Vocab
• Range- The difference between the highest and
lowest numbers in a set.
5, 3, 12, 17, 9, 8, 2
Highest number: 17
Lowest number: 2
Range: 17-2= 15
End of grade 6
Review
Have fun in grade 7!