Download Rectangular and triangular numbers

OpenStax-CNX module: m21835
1
Rectangular and triangular
numbers
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1 MATHEMATICS
2 Estimations, Equations and Variables
3 EDUCATOR SECTION
4 Memorandum
1. (b) quadrate number
2.
(a)
(b) No not quadrate of number
(c) No 1 + 2 + 3 + 4 4 5
3.
(b) 64; 125; 216; 343
(c) 64
(d) 64 000
(e) 274 625
(f) K4: + 64
K5: + 64 + 125 = 225
(g) 1 + 8 + 27 + 64 + 125 + 216 = 441
(h) all square number
5 Leaner Section
6 Content
7 ACTIVITY: Rectangular and triangular numbers [LO 1.3.4, LO 1.7.2, LO 1.7.7,
LO 2.3.1, LO 2.3.3]
1. Do you still remember?
In module 1 we learnt about square numbers and triangular numbers.
a) Can you explain to your partner what these patterns are like?
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OpenStax-CNX module: m21835
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b) What is the synonym for square numbers?
2. Let us have a look at RECTANGULAR NUMBERS.
Did you know?
Each counting number bigger than 0 is a rectangular number. The Greeks used the term rectangular
number for the product of two consecutive numbers only,
e.g. 42 = 6 x 7.
When we draw rectangular numbers, they will look like this:
___
___
___
___
6 = 1
×
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___
6
___
___
___
___
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6 = 2
×
3
Table 1
a) Now draw as many sketches as possible to represent the rectangular number 18.
b) Is 18 a square number? ______________________________ Why/why not?
____________________________________________________________________
____________________________________________________________________
c) Is 18 a triangular number? ___________________________ Why/why not?
____________________________________________________________________
____________________________________________________________________
3. Did you know?
a) We also have numbers to the power of three!! These numbers are also known as cubed numbers. Take
a good look at the examples:
Figure 1
1 = 1
×
1
×
1
Figure 2
8 = 2
×
2
×
2
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OpenStax-CNX module: m21835
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Figure 3
27 = 3
×
3
×
3
b) Predict what the following four cubed numbers will be (you may use your pocket calculator).
___________________________;
___________________________;
___________________________;
___________________________;
c) List any of the above numbers that may be a square number:______________
d) What will the 40th cubed number be? _______________________________
e) What is 653 (to the power of 3)? ___________________________________
f) Take a good look at the following. Can you complete the table?
Cubed numbers
Sum of the cubed numbers
K1
1
K2
1+8=9
K3
1 + 8 + 27 = 36
K4
1 + 8 + 27 + ........... = 100
K5
1 + 8 + 27 + ........... + ........... = .........................
Table 2
g) Can you predict what the sum of the rst 6 cubed numbers will be?
____________________________________________________________________
h) What do you notice about the numbers in the second column?
____________________________________________________________________
8 Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their
relationships, and to count, estimate, calculate and check with competence and condence in solving problems.
Assessment Standard 1.3: We know this when the learner recognises, classies and represents the
following numbers in order to describe and compare them:
2
1.3.4: numbers in exponential form including squares of natural numbers to at least 12 , cubes of natural
3
numbers to at least 5 , and their square and cube roots.
Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and
using operations appropriate to solving problems that involve:
1.7.2: multiple operations with integers;
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OpenStax-CNX module: m21835
1.7.7:
exponents.
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The learner will be able to recognise, describe and represent patterns and
relationships, as well as to solve problems using algebraic language and skills.
Assessment Standard 2.3: We know this when the learner represents and uses relationships between
variables in order to determine input and/or output values in a variety of ways using:
2.3.1: verbal descriptions;
2.3.3: tables.
Learning Outcome 2:
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