Mathematics Grade 9 - CNX

[Pages:218]Mathematics Grade 9

By: Siyavula Uploaders

Mathematics Grade 9

By: Siyavula Uploaders

Online: < >

CONNEXIONS

Rice University, Houston, Texas

This selection and arrangement of content as a collection is copyrighted by Siyavula Uploaders. It is licensed under the Creative Commons Attribution 3.0 license (). Collection structure revised: September 14, 2009 PDF generated: October 28, 2012 For copyright and attribution information for the modules contained in this collection, see p. 208.

Table of Contents

1 Term 1 1.1 Numbers - where do they come from? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Easier algebra with exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Why all the fuss about Pythagoras? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.4 How long is a piece of string? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5 Money Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2 Term 2 2.1 The algebra of the four basic operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Geometry of lines and triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.3 Space and shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.4 Congruency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.5 Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.6 Worksheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3 Term 3 3.1 Number patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.2 Understanding what graphs tell us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 112 3.3 Understanding how equations are represented on a graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 3.4 Finding the equation of a straight line graph from a diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.5 Solving simple problems by forming and solving equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.6 Collecting information to answer general questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 3.7 Analyse data for meaningful patterns and measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 3.8 Extract meaningful information from data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 3.9 Understanding the context and vocabulary of probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

4 Term 4 4.1 Explore and identify the characteristics of some quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 4.2 Compare quadrilaterals for similarities and dierences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 4.3 Understanding quadrilaterals and their properties in problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 4.4 Drawing plan and side views of three-dimensional objects to scale . . . . . . . . . . . . . . . . . . . . . . . . . . 196 4.5 Understand and use the principle of translation, learning suitable notations . . . . . . . . . . . . . . . . 200

Attributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

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Chapter 1

Term 1

1.1 Numbers - where do they come from?1

1.1.1 MATHEMATICS 1.1.2 Grade 9 1.1.3 NUMBERS 1.1.4 Module 1 1.1.5 NUMBERS WHERE DO THEY COME FROM?

Numbers where do they come from? CLASS WORK 1 Our name for the set of Natural numbers is N, and we write it: N = { 1 ; 2 ; 3 ; . . . } 1.1 Will the answer always be a natural number if you add any two natural numbers? How will you

convince someone that it is always the case? 1.2 Multiply any two natural numbers. Is the answer always also a natural number? 1.3 Now subtract any natural number from any other natural number. Describe all the sorts of answers

you can expect. Try to write down why this happens. 2 To deal with the answers you got in 1.3, we have to extend the number system to include zero and

negative numbers we call them, with the natural numbers, the integers. They are called Z and this is one

way to write them down: Z = { 0 ; ?1 ; ?2 ; ?3 ; . . . }

2.1 Complete the following denitions by writing down what has to be inside the brackets:

? Counting numbers N0 = {.........................} ? Integers Z = {.........................} in another way!(Integers are also called whole numbers)

3 Is the answer always another integer when you divide any integer by any other integer (except zero)?To

allow for these answers we have to extend the number system to the rational numbers:

3.1

Q

(rational

numbers)

is

the

set

of

all

the

numbers

which

can

be

written

in

the

form

a b

where

a

and

b

are integers as long as b is not zero. Explain very clearly why b is not allowed to be zero.

4 Q` (irrational numbers) is the set of numbers which cannot be written as a common fraction, and are

therefore not in Q. Putting Q en Q` together gives the set called R, the real numbers.

4.1 Write down what you think is in the set R` . They are called non-real numbers.

end of CLASS WORK

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CHAPTER 1. TERM 1

Quipu is an Inca word meaning a string (or set of strings) with knots in it. This system was used for remembering things, mainly numbers. It was used widely in the ancient world; not only in South America. At its simplest, it was just one string with each knot representing one item. In more advanced systems, more strings were used, often of dierent colours; sometimes a system of place-values was used.

HOMEWORK ASSIGNMENT 1. What is the importance of having a symbol for zero? Think about all the things we'll be unable to do if we didn't have a zero. 2 Find out what we call the set of numbers we get when putting R and R` together. Can you say more about them? 3 Design your own set of number symbols like those in table 1. Show how any number can be written in

your system. Now think up new symbols for + and and ? and [U+F0B8], and then make up a few sums

to show how your system works. end of HOMEWORK ASSIGNMENT ENRICHMENT ASSIGNMENT Let's check out the rational numbers

? Do the following sums on your own calculator to conrm that they are correct:

? Remember to do the operations in the proper order.

1. 2 + 3 [U+F0B8] 100 + 1 + 1 [U+F0B8] 10 = 3,013

Is 3,013 a rational number? Yes! Look at this bit of magic:

3,013

=

3 1

+

13 1000

=

3000 1000

+

13 1000

=

3000+13 1000

=

3013 1000

It is easy to write it down straightaway. Explain the method carefully.

Figure 1.1

4

Only

terminating

and

repeating

decimal

fractions

can

be

written

in

the

form

a b

.

4.1 Here are some irrational numbers (check them out on your calculator): [U+F010] 2 3 11 3,030030003000030. . .

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