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Math booklet
Grade 6 section ( )
1st term ( 2019 -2020 )
 Topic 1
Numbers and calculations 1

Addition of Integers
When integers have the same sign, add the integers.  The sum will have the same sign as the integers.
 Find the sums of the following integers.
Addition Problem Sum

     -7 + (+12)  

     8 + (-5)  

     -17 + 12+4  

     9 + (-14)  

    8 + (-5)+3  

-16 + 16  

-24 + 15  

6 + (-13) + 16  

-12 + 7 + (-5)  

14 + (-27) + (-13) + 8  

Subtraction of Integers
When subtracting integers, the additive inverse must be used. The additive inverse of +8 is -8  (-
8 + 8 = 0). 

-6 - (+8) = -6 + (-8) = -14

Find the difference of the following integers.
Subtraction Problem Difference
     -9 - (+12)  
     15 - (-7)-9  
     -3- - 4-9  
    -14 - (+9)  
   -5 - (+8)  
-13 - (+13)-6  
32 - (-12)  
-27 - (+17)-4  
21 - (+5)+4  
3-(+4)+2-6
-10 - (+11)-16  

Integer Multiplication

Rule 1: The product of a positive integer and a negative integer is a

negative integer.

Example: -3 × 4 = -12

Rule 2: The product of two negative integers or two positive integers is

Multiply
Multiplication Problem Product
6 × -4  
6× 4  
-6 × -4  
12 ×-3  
-25 × -4  
2 × -3 × -3  
7 × -7 × 7  
4×5×3  
-6 × -2 × - 4  
3 × -4 × -1  

Integer division
When you divide two integers with the same sign, the result is always
positive.
Positive ÷ positive = positive
Negative ÷ negative = positive
When you divide two integers with different signs, the result is always
negative.
Positive ÷ negative = negative
Negative ÷ positive = negative
Examples: 
24 ÷ (-6) = -4
24 ÷ 6 = 4
(-24) ÷ (-6) = 4
Divide
Division problem Answer
6 ÷ -2  
-14 ÷ -7  
12÷ -3  
-121 ÷ 11  
25 ÷ 5  
20 ÷ -2  
-16 ÷ -8  
120 ÷ -6  
55 ÷ -11  
3 × -4 ÷ 3  

what is a "Multiple" ?
We get a multiple of a number when we multiply it by another number.
Such as multiplying by 1, 2, 3, 4, 5, etc, but not zero. Just like the
multiplication table. 

Here are some examples:

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,...

The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

What is a "Common Multiple" ?

Say we have listed the first few multiples of 4 and 5: the common
Find the least common multiple of 4 and 10:

Find the least common multiple of 6 and 15:

Find the least common multiple of 4, 6, and 8

Find the LCM of these sets of numbers. 3, 9, 21

Highest common factor (H.C.F) such as 10, 100, and 1000:

Highest common factor (H.C.F) of two or more numbers is the greatest number which
divides each of them exactly.

Now we will learn about the method of finding highest common factor (H.C.F).

Steps 1:

Find all the factors of each given number.

Step 2:

Find common factors of the given number.

Step 3:

The greatest of all the factors obtained in Step 2, is the required highest common
factor (H.C.F).

Move the decimal point to the right as many p

For Example:
1. Find the highest common factor (H.C.F) of 14 and 18.

2. Find the highest common factor (H.C.F) of 15 and 10.

3. Find the highest common factor (H.C.F) of 24 and 36.

4. Find the highest common factor (H.C.F) of 12 and 18.

Squares and square root

• Squaring a number
• 32 means '3 squared', or 3 x 3.

• The small 2 is an index number, or power. It tells us how many times we

should multiply 3 by itself.

• Similarly 72 means '7 squared', or 7 x 7

• And 102 means '10 squared', or 10 x 10.

• A square root is the opposite of squaring a number.

• Three squared is nine, so the square root of nine is three!
Square the following numbers :

Number Squared Answer

2 22
4
9
-7
12

Solve :

1. √ 9= 11. √ 25+56=

2. √ 36= 12. √ 100+44=

3. √ 81= 13. √ 95+26=

4. √ 169= 14. √ 144+25=

 5. √ 64= 15.
√ 62 +82=

6. √ 121= 16.
√ 92+122 =

7. √ 49= 17.
√ 122+162=

8. √ 100= 18.
√ 82+15 2=

9. √ 16= 19.
√ 32 + 42=

10. √ 225= 20.

√ 72+24 2=

Let’s practice, complete the following cubes.

a.) 13= Cubesb.)and

2= cube root c.) 3 =
3 3

d.) 63 = e.) 83 = f.) 103=

How to Cube a Number: 3 = 3 x 3 x 3 = 27

Example: What is 3 cubed? 3

3 3

Note: We write 3 cubed as 3^3

 Let’s practice, complete the following cubes.
a.) 13= b.) 23= c.) 33=

d.) 63 = e.) 83= f.) 103=

The inverse of cubing a number is……
3.) √3 8 = 4.) √3 512=

5.)√3 125= 6.) √3 64=

Indices
Indices are a useful way of more simply expressing large numbers.

What are Indices?

The expression 25 is defined as follows:

We call "2" the base and "5" the index..imal numbers by numbers such as 10, 100,
and 1000:
Expand each expression then evaluate:

1) 55 

2) 211 

3) 63 

4) 93 

5) 1002 

6) 65 

7) 107 

8) 35 

9) 48 

10) 124 

Math worksheet- Topic 2

Numbers and calculations 2
1 d.p = 1 decimal place
2 d.p = 2 decimal place
Write correct: (Round )

Numbers Rounding

985 to nearest 10  

1.746 to 1 d.p  

14.7 to nearest 10  

22567 to nearest 100  

58.361 to nearest whole number  

2.489 to 1 d.p  

574516 to nearest 1000  

431 to nearest 10  

12.975 to nearest whole number  

 
92146 to nearest 100
231 to nearest ten
1411 to nearest ten
1054 to the nearest thousand
2545 to nearest hundred
437012 to nearest thousand
21.73 to nearest tenth
1.443 to two decimal places
21.95 correct to ( 1 d.p)
13.3327 correct to (2 d.p)
7.9949 correct to (2 d.p)

Put these decimals in order from smallest to largest

U . t h th

1) 5.6 5.3 5.8 5.4 5.0 6.0

2) 7.9 7.2 7.7 8.0 7.1 7.5

3) 12.4 10.8 7.3 9.4 3.8 18.2

4) 6.16 6.19 6.14 6.11 6.13 6.18

5) 4.41 4.45 4.39 4.57 4.54 4.50

6) 3.89 3.83 3.93 3.46 3.42 3.51

7) 8.76 8.84 8.34 8.01 8.51 8.15

8) 8.6 8.66 8.576 8.5 8.57 8.55

9) 6.95 7.09 6.65 6.9 7.9 6.99

10) 7.632 7.6 7.567 7.765 7.675 7.7

11) 5.555 5.565 5.050 5.055 5.505 5.5

Multiply
Multiplication Problem Product
5.14×10=      
4.006×10=  
583.2×10=  
0.7761×10=  
90.5×100=  
6.33×100=  
0.0047×100=  
62.11×1000=  
0.0577×1000=  
71.55×10,000=  
Divide
Multiplication Problem Answer
5.14 ÷10=      
4.006 ÷10=  
583.2÷ 10=  
0.7761÷ 10=  
90.5÷ 100=  
6.33÷100=  
0.0047÷100=  
62.11÷1000=  
0.0577÷1000=  
71.55÷10,000=  
Work out
 ÷ 0.001 = 0.37 ÷ 0.01 =

0.79
8.13 ÷ 0.1
27.1 ÷ 0.01 = 3.39 ÷ 0.1 =
=
0.338 ÷ 0.001
0.08 ÷ 0.01 = 55.6 ÷ 0.1 =
=
0.003 ÷ 0.001
0.4 ÷ 0.01 = 68.14 ÷ 0.1 =
=
512.4 ÷ 0.1
9.46 ÷ 0.01 = 3.5 ÷ 0.001 =
=
0.17 ÷ 0.1
6.62 ÷ 0.001 = 53.2 ÷ 0.01 =
=
0.079 ÷ 0.001
0.54 ÷ 0.01 = 13.5 ÷ 0.1 =
=

0.03 ÷ 0.001 = 0.05 ÷ 0.1 = 1.811 ÷ 0.01 =

835.5 ÷ 0.001 = 0.15 ÷ 0.1 = 0.04 ÷ 0.001 =

0.939 ÷ 0.1
6.1 ÷ 0.001 = 0.399 ÷ 0.1 =
=
 Math
GRADE 6

Topic 10
Fractions and decimals
 Ordering decimals
Ordering decimals can be tricky. Because often we look at 0.42 and 0.402 and say
that 0.402 must be bigger because there are more digits. But no!

We can use this method to see which decimals are bigger: 

 Set up a table with the decimal point in the same place for each number.
 Put in each number.
 Fill in the empty squares with zeros.
 Compare using the first column on the left.
 If the digits are equal move to the next column to the right until one number
wins.

If you want ascending order you always pick the smallest first

If you want descending order you always pick the largest first

Put these decimals in order from smallest to largest

U . t h th

1) 5.6 5.3 5.8 5.4 5.0 6.0

2) 7.9 7.2 7.7 8.0 7.1 7.5

3) 12.4 10.8 7.3 9.4 3.8 18.2

4) 6.16 6.19 6.14 6.11 6.13 6.18

5) 4.41 4.45 4.39 4.57 4.54 4.50

6) 3.89 3.83 3.93 3.46 3.42 3.51

7) 8.76 8.84 8.34 8.01 8.51 8.15

8) 8.6 8.66 8.576 8.5 8.57 8.55

9) 6.95 7.09 6.65 6.9 7.9 6.99

10) 7.632 7.6 7.567 7.765 7.675 7.7

11) 5.555 5.565 5.050 5.055 5.505 5.5

Adding and substracting
The Basic Steps:
• Line up the numbers by the decimal point.
• Fill in missing places with zeroes.
• Add or subtract.

Multiplying decimals
Multiplying decimals is the same as multiplying whole
numbers except for the placement of the decimal point in
the answer. When you multiply decimals, the decimal
point is placed in the product so that the number of
decimal places in the product is the sum of the decimal
places in the factors.
 
Let’s compare two multiplication problems that look
similar: 214  36, and 21.4  3.6.

 
Multiplying a Decimal by a Power of Ten
 
To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count
the number of zeros in the power of ten. Then move the decimal point that number of
places to the right.
 
For example, 0.054 · 100 = 5.4. The multiplier 100 has two zeros, so you move the
decimal point in 0.054 two places to the right—for a product of 5.4.

Dividing decimals

To divide decimals, you will once again apply the

methods you use for dividing whole numbers. Look at
the two problems below. How are the methods similar?

Notice that the division occurs in the same way—the

only difference is the placement of the decimal point in
the quotient.
Work out :

Work out :
 Writing fractions as decimals
 

To convert a Fraction to a Decimal manually, follow these steps:

 Step 1: Find a number you can multiply by the bottom of the fraction to
make it 10, or 100, or 1000, or any 1 followed by 0s.
 Step 2: Multiply both top and bottom by that number.
 Step 3. Then write down just the top number, putting the decimal point in the
correct spot (one space from the right hand side for every zero in the bottom number)
 Math
GRADE 6

Topic 2
Expressions and functions
Simplifying and expanding
Before you evaluate an algebraic expression, you need to simplify it. This will make all
your calculations much easier. Here are the basic steps to follow to simplify an algebraic
expression:

1. remove parentheses by multiplying factors

2. use exponent rules to remove parentheses in terms with exponents
3. combine like terms by adding coefficients
4. combine the constants
 Math
GRADE 6

Topic 8
Expressions , equations and formulae
Substitution into expression
What does substitution mean?
In algebra, when we replace letters in an expression or equation with numbers we call it
substitution.
 Math
GRADE 6

Topic 9

Geometry

All about angles

Find the measure of all the missing angles.

1. 2. 3.

a = _____ a = _____ a = _____

b = _____ b = _____

c = _____ c = _____

d = _____

4. 5. 6.

a = _____ a = _____ a = _____

b = _____ b = _____ b = _____

c = _____ c = _____ c = _____

d = _____ d = _____

e = _____ e = _____

Fill in each blank with a true statement.

7.

are
8.
supplementary,

9.

If an angle is obtuse, then its supplement must be an __________________ angle.

10.
 Math
GRADE 6

Topic 3

Shapes and mathematical drawing

Construction of Triangles and Circles

Types of Diagrams
A sketch is a rough diagram which does not have to be
too accurate.
A drawing is more accurate and can be drawn using a
ruler and a protractor for measuring lengths and angles.
A construction in mathematics is an accurate drawing
done usually using only instruments such as a ruler as a
straight edge and a pair of compasses. 
When drawing a construction, leave all of your
construction arcs and lines.
.

Construction of Triangles and Circles

Triangles are three-sided polygons. Types of triangles include isosceles,
scalene and equilateral.
To make a construction certain information is needed about the size of the
angles and sides of the shape.
The instruments used for constructions, which include ruler, compasses and
protractors are described in What is Geometry?, Topic 29.
Some of the types of constructions with circles and triangles are described
below:

Draw a circle of radius 2 cm

 
Step 1: Extend compasses to 2 cm,
using ruler.
Step 2: Draw the circle.
 
 

Construct a triangle ABC with sides of lengths 2 cm, 3 cm and 4 cm.

Step 1 
Draw side AB, say 4 cm long, with
ruler.
Step 2 
Draw an arc, center B, radius 3 cm.

Step 3 
Draw an arc, center A, radius 2 cm.

Step 4 
Let the arcs intersect at a point C and
then
join A and B to C.

Draw a triangle PQR with sides PQ = 5 cm RQ = 3 cm and PQR = 57°

Step 1 Draw a line PQ of length 5 cm.

Step 2 Draw an angle of 57° at Q, using

a protractor.

Step 3 Draw an arc of 3 cm, center Q

and label it R.

Step 4 Join R and P to form triangle

PQR.

Draw a triangle XYZ with angle Y = 45°angle X= 75° and side XY = 6 cm

Step 1 Draw the line XY of length 6
 cm.

Step 2 Draw an angle of 45° at Y using

a protractor.

Step 3 Draw an angle of 75° at X.

Z is the point where the lines intersect.

1.Construct a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm.

2. Construct a triangle PQR in which PQ = 5.8 cm, QR = 6.5 cm, PR = 4.5 cm.

3. Construct a triangle LMN in which LM = LN = 5.5 cm, MN = 7 cm.

4. Use a compass to draw a circle of radius 5 cm.

5.   Use a compass to draw a circle of diameter 12 cm.

Bisecting angles

to bisect an angle, you use your compass to locate a point that lies on the
angle bisector; then you just use your straightedge to connect that point to
the angle’s vertex.
 Try an example.

Refer to the figure as you work through this construction:

1. Open your compass to any radius r, and construct arc (K, r)

intersecting the two sides of angle K at A and B.

2. Use any radius s to construct arc (A, s) and arc (B, s) that
intersect each other at point Z.
Note that you must choose a radius s that’s long enough for the two arcs to
intersect.

3. Draw line KZ and you’re done.

Congruent Triangles
Congruent triangles are triangles that have the same size
and shape. This means that the corresponding sides are
equal and the corresponding angles are equal.
The following diagrams show the Rules for Triangle
Congruency: SSS, SAS, ASA, AAS and RHS. Take note that
SSA is not sufficient for Triangle Congruency.
 Math
GRADE 6

Topic 18

Probability

 Probability
 How  likely  something is to happen.

Many events can't be predicted with total certainty. The best we can say is
how likely they are to happen, using the idea of probability.

Tossing a Coin
 When a coin is tossed, there are two possible outcomes:

 heads (H) or
 tails (T)

We say that the probability of the coin landing H is ½

And the probability of the coin landing T is ½

Throwing Dice 

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of any one of them is 1/6

Words
Some words have special meaning in Probability:

Experiment or Trial: an action where the result is uncertain.

Sample Space: all the possible outcomes of an experiment

Sample Point: just one of the possible outcomes

Event: a single result of an experiment