Name:
A
X123 456789
10
1123 456789
10
2 2 4 6 8101214161820
3 3 6 9 12151821242730
4 4 812 16202428323640
5 51015 20253035404550
6 61218 24303642485460
7 71421 28354249566370
8 81624 32404856647280
9 91827 36455463728190
10102030 405060708090
100
B
Take a closer look at this multiplication table up to 10 x 10.
Place your ruler diagonally from point A to point B. The numbers on that line are
called square numbers.
Examples of square numbers:
1 = 1 x 1
4 = 2 x 2
9 = 3 x 3
16 = 4 x 4
1. a) Complete the following:
25 =
49 =
36 =
64 =
81 =
100 =
b) Provide the square numbers from 121 = 11 x 11
=
=
=
=
=
=
=
=
up to 400 = 20 x 20
=
=
=
© e-classroom 2013 www.e-classroom.co.za
Grade 7 Mathematics Term 3: Patterns, Functions and Algebra - Numeric and Geometric Patterns
GRADE 7
Square and Triangular Numbers
2. We can also make geometric patterns of these numbers:
1x1=1
2 x 2=4
3x3=9
4x4=16
5x5=25
The pattern of each shape is a square, as all 4 sides are equal in length
a) Using squared paper, provide the geometric pattern for the squares of numbers up to 10 x 10.
b) The number pattern of 1;4;9;16;27;36;49;64;100 is the numeric pattern of squared numbers up to 100.
What is the number pattern of squared numbers 100 up to 20 x 20?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
3. Triangular Patterns can also be made using squared numbers.
1
4
9
© e-classroom 2013 16
www.e-classroom.co.za
Grade 7 Mathematics Term 3: Patterns, Functions and Algebra - Numeric and Geometric Patterns
GRADE 7
Square and Triangular Numbers (2)
36
b) Use counters to show the triangular patterns up to 20 x 20 (work in groups)
4) Record your findings of triangular numbers in the table below:
1x111
2x21+33
3x31+3+59
4x41+3+5+716
5x5
6x6
7x7
8x8
9x9
10x10
11x11
12x12
13x13
14x14
15x15
16x16
17x17
18x18
19x19
20x20
a) What do you notice about the numeric patterns of triangular numbers? Write down a rule for the pattern of triangular numbers:
© e-classroom 2013 www.e-classroom.co.za
Grade 7 Mathematics Term 3: Patterns, Functions and Algebra - Numeric and Geometric Patterns
a) Draw the triangular patterns for:
25
GRADE 7
Square and Triangular Numbers (3)
Name:
X123 456789
10
1123 456789
10
2 2 4 6 8101214161820
3 3 6 9 12151821242730
4 4 812 16202428323640
5 51015 20253035404550
6 61218 24303642485460
7 71421 28354249566370
8 81624 32404856647280
9 91827 36455463728190
10102030 405060708090
100
B
Take a closer look at this multiplication table up to 10 x 10.
Place your ruler diagonally from point A to point B. The numbers on that line are
called square numbers.
Examples of square numbers:
1 = 1 x 1
4 = 2 x 2
9 = 3 x 3
16 = 4 x 4
1. a) Complete the following:
25 = 5 x 5
49 = 7 x 7
36 = 6 x 6
64 = 8 x 8
81 = 9 x 9
100 = 10 x 10
b) Provide the square numbers from 121 = 11 x 11 up 400 = 20 x 20
121 = 11x11
144 = 12x12
196 = 14x14 400 = 20x20
169 = 14x14 225 = 15x15
256 = 16x16 © e-classroom 2013 289 = 17x17
324 = 18x18
361 = 19x9
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GRADE 7
Grade 7 Mathematics Term 3: Patterns, Functions and Algebra - Numeric and Geometric Patterns
Square and Triangular Numbers: Answer sheet
2. We can also make geometric patterns of these numbers:
1x1=1
2 x 2=4
3x3=9
4x4=16
5x5=25
The pattern of each shape is a square, as all 4 sides are equal in length
a) Using squared paper, provide the geometric for the squares of numbers up to 10 x 10.
6x6=36 7x7=49
8x8=64 9x9=81 10x10=100
b) The number pattern of 1;4;9;16;27;36;49;64;100 is the numeric pattern of squared numbers up to 100.
What is the number pattern of squared numbers100 up to 20 x 20?
1; 4; 9; 16; 25; 36; 49; 64; 81; 100; 121; 144; 169; 225; 256; 289; 324; 361; 400
3. Triangular patterns can also be made from using squared numbers.
1
4
9
16
© e-classroom 2013 www.e-classroom.co.za
GRADE 7
Grade 7 Mathematics Term 3: Patterns, Functions and Algebra - Numeric and Geometric Patterns
Square and Triangular Numbers : Answer Sheet (2)
a) Draw the triangular patterns for:
25
36
b) Use counters to show the triangular patterns up to 20 x 20 (work in groups)
4) Record your findings of triangular numbers in the table below:
1x1
2x2
3x3
4x4
5x5
6x6
7x7
8x8
9x9
10x10
11x11
12x12
13x13
14x14
15x15
16x16
17x17
18x18
19x19
20x20
1
1+3
1+3+5
1+3+5+7
1+3+5+7+9
1+3+5+7+9+11
1+3+5+7+9+11+13
1+3+5+7+9+11+13 +15
1+3+5+7+9+11+13+15+17
1+3+5+7+9+11+13+15+17+19
1+3+5+7+9+11+13+15+17+19+21
1+3+5+7+9+11+13+15+17+19+21+23
1+3+5+7+9+11+13+15+17+19+21+23+25
1+3+5+7+9+11+13+15+17+19+21+23+25+27
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39
1
3
9
16
25
36
49
56
81
100
121
144
169
196
225
256
289
324
361
400
a) What do you notice about the numeric patterns of triangular numbers? Write down a rule for the pattern of triangular numbers:
Add the next uneven number to the total each time.
© e-classroom 2013 www.e-classroom.co.za
GRADE 7
Grade 7 Mathematics Term 3: Patterns, Functions and Algebra - Numeric and Geometric Patterns
Square and Triangular Numbers: Answer Sheet (3)