CPS Grade 7 Math Pacing Guide 2011-12

noveg

Le téléchargement nécessite un accès à la bibliothèque YouScribe
Tout savoir sur nos offres

39 pages

English

Le téléchargement nécessite un accès à la bibliothèque YouScribe
Tout savoir sur nos offres

A propos
Informations
Extrait

Description

cours - matière potentielle : students
cours - matière potentielle : grade
cours - matière potentielle : year
exposé
expression écrite
leçon - matière potentielle : maps
revision
cours - matière potentielle : page
cours - matière potentielle : event
leçon - matière potentielle : maps
cours - matière potentielle : years

Cambridge Public Schools Grade 7 Mathematics Pacing Guide 2011 – 2012 Cambridge Public Schools Page 1 2011-2012 The 2011-2012 school year will be the start of the district's transition to the new 2011 Massachusetts Mathematics Curriculum Framework for Grades 3 through 8. The pacing guides for these grades will incorporate new concepts that students need to be successful when the framework is fully implemented in the 2012-2013 school year. In addition, the 2012 MCAS will only test a subset of standards from the 2000/2004 framework, meaning standards not tested on the MCAS will receive less of a focus in this school year.

geometric constructions
scale drawings
quadrants of the coordinate plane
proportionality through expressions
equations
problems
standards
grade
relationships
problem

Sujets

Student

Exposé

Révision

Massachusetts

Standard

Problem

Relationship

Geometry

Informations

Publié par	noveg
Nombre de lectures	33
Langue	English

Extrait

Introduction to MATLAB

Anthony J. O’Connor
School of Science, Griffith University, Brisbane, Australia

1. What is MATLAB ?

MATLAB started as an interactive program for doing matrix calculations and has
now grown to a high level mathematical language that can solve integrals and
differential equations numerically and plot a wide variety of two and three
dimensional graphs. In this subject you will mostly use it interactively and also
create MATLAB scripts that carry out a sequence of commands. MATLAB also
contains a programming language that is rather like Pascal.

The first version of Matlab was produced in the mid 1970s as a teaching tool. The
vastly expanded Matlab is now used for mathematical calculations and simulation in
companies and government labs ranging from aerospace, car design, signal analysis
through to instrument control & financial analysis. Other similar programs are
Mathematica and Maple. Mathematica is somewhat better at symbolic calculations
but is slower at large numerical calculations.

Recent versions of Matlab also include much of the Maple symbolic calculation
program.

In this lab you will cover the following basic things:

• using Matlab as a numerical calculator
• entering row vectors and column vectors
• entering matrices
• forming matrix and vector products

• doing matrix products, sums etc

• using Matlab to solve linear equations

• Matlab functions that operate on arrays

• Plotting basic graphs using Matlab.

Matlab introduction ‘ 1 1 How to get started

When the computer has started go through the following steps in the different menus

• Look for the Network Applications folder and double click on that
• Within this you will see a little icon for Matlab61 – double click on that

Within about 30 seconds Matlab will open (you may get a little message box about ICA
applications – just click OK on this)

You should now see a screen like the picture below

This is the Matlab screen – it broken into 3 parts

On the right you have the Command Window – this is where you type commands and
usually the answers (or error messages) appear here too

On the top left you have the Workspace window – if you define new quantities (called
variables) there names should be listed here.

On the bottom left you have Command History window – this is where past commands are
remembered. If you want to re-run a previous command or to edit it you can drag it from this
window to the command window to re-run it.

Matlab introduction ‘ 2 2.1 The Matlab prompt is >> .

Look at the Command Window and you will see the cursor flickerring after the >>
prompt. This means that Matlab is waiting for further instructions.

2.2 Seeing the Matlab demo.

Just type the command

>> demo (and then press Enter or Return key)

and run the simple slideshow under the Matrix manipulation option.

This briefly shows you some of the things that Matlab can do - don’t worry if you do
not know what everything means here.

Matlab introduction ‘ 3 2.3 Simple arithmetic with Matlab

The basic arithmetic operators are +, -, * (for multiplication), / (for divide) & ^ for
powers. Where necessary brackets should be used to make the order in which things
are evaluated completely clear.

Enter the following commands to learn the basic way that formulas can be evaluated in
Matlab (press enter after you have typed in the command. Record the answer beside
the command.

>> 3 + 5 -7 ........................................................................................

The result of this calculation is stored in the temporary variable called ans.
It is changed when you do another calculation.

If you want to save the answer from a calculation you can give it a name e.g.

>> t = 3 + 5 - 7 ..........................................................................

This line creates a variable t to save the answer in. If you want to find out what t is use

>> t ...................................................................................

Equally you can use t in a formula

>> 2*t + 2 ........................................................................................

Matlab introduction ‘ 4 2.4 The order of operations and putting brackets in can matter

In the following calculation does Matlab do the * or the ^ first

>> 3^2*4 ………………………………………….

To find this out think about the two possible options

• One way to do the calculation is that powers are done before multiplication.
2This 3*4 = 9* 4 = 36

2*4 8• The other option is to do the multiplication first is 3 = 3 = 6561

In this case you should have obtained the answer 36 – this is because Matlab does
3^2 first and then multiplies the answer by 4 – generally powers are done first, then
multiplication and division and finally additions and subtractions.

One way to force Matlab (or any software) to do calculations in a defined order is to
use brackets.

Compare the following commands and make sure that you understand what is
happening and why you get the answer

>> 3 – 4/4 –2 …………………………………………………..

>> (3-4)/(4-2) .....................................................................................

>> (3-4)/4 –2 ..

The rules for evaluating expressions involving numbers are

• things inside brackets are done first

• within a bracket or expression generally operations closest to a value are done
first
Matlab introduction ‘ 5 2.5 Extended arithmetic (IEEE)

You need to understand the following section to interpret the output from some calculations –
particularly when we make accidental errors.

What does Matlab produce if you ask it to find:

>> 1/0 ..................................................................

>> -1/0 .................................................................

>> 0/0 ................................................................

>> 1/Inf .......................................................................

The symbols Inf (meaning infinity) and NaN (not a well defined number) are part of a special
standard for computer arithmetic. This is the IEEE international standard for extended
arithmetic.

Typically you get Inf from 1/0 and NaN from 0/0 type calculations.

While Inf and NaN are usually signs of bad problem setup Matlab will try to manipulate these
results consistently

For example extended arithmetic will ensure that 1/( 1/x) always equals x.

Test this out by asking Matlab to calculate

>> 1/(1/0) …………………………………………

Matlab can also handle complex numbers – they are entered as 1 + i or -1+3*i etc
The symbol i is best kept as a reserved symbol (Matlab also interprets j as a complex number to
fit in with usage in electrical engineering)

Matlab introduction ‘ 6 2.6 Matlab works to 15 significant figures but usually only shows 5
figures

Type pi and you will normally get 3.1416

You can change to the long format in which all 15 figures are displayed

>> pi ……………………………………………………

>.> format long

>> pi ...............................................................................

An easier and more flexible format is scientific notation with 5 significant figures

>> format short e

>> pi ....................................................................................................

Mostly we work in the short format.

To go back to short format

>> format short ……………………………..

23Very large or small numbers use exponential format - e.g. 6.00e+23 = 6*10

Matlab introduction ‘ 7 2.7 The consequences of finite accuracy on a computer

Matlab only has limited accuracy (although it is more than enough for most uses)

Computers are normally set up to store numbers in a fixed amount of memory
308Matlab uses 64 bits and this lets it store numbers as large as 2*10 or as small as
−3082*10 But no matter which number you work with Matlab can only store it to
15 significant figures

For example:

Matlab could handle 1.234 567 890 234 56 (fifteen figures)

But a 20 digit number like 1. 234 567 890 234 567 890 12 is truncated to 15 figures.

This is an example of a round-off. Other cases of round-off occur if you add or
multiply 15 figure numbers and then only store the first 15 significant figures of the
answer. Round-off cannot be avoided in computer calculations.

This type of unavoidable ‘error’ can affect the answers you get

What is the exact value of sin