# FROM THE SPECIFIC TO THE GENERAL

Save this PDF as:

Size: px
Start display at page:

## Transcription

2 CALCULATION Your original number Your result REPRESENTATION DOUBLE the number ADD 5 to the result (If we double 1 matchbox, we just get 2 matchboxes) MULTIPLY that result by 3 (We don t know what the matchbox represents so we can t add anything to it, so the easiest way is just to add 5 single objects I ve used matches.) TAKE AWAY 9 (We had to multiply EVERYTHING by 3.) DIVIDE the result by 6 (We still don t know what the matchbox represents so couldn t take anything away from there so we take it away from the 15 single matches.) TAKE AWAY your original number (Imagine dividing that lot among 6 people everyone would get 1 matchbox and 1 match.) (Your original number was the matchbox!) Now, let s do that again but this time we ll introduce the Algebra part. 2

3 Let x represent your original number. CALCULATION Your original number Your result REPRESENTATION x ALGEBRA DOUBLE the number 2x ADD 5 to the result 2x + 5 MULTIPLY that result by 3 3(2x + 5) = 6x + 15 TAKE AWAY 9 6x + 6 DIVIDE the result by 6 TAKE AWAY your original number x

4 When we DOUBLE the number, in Algebra, we just get 2 xs, or 2 matchboxes, or 2 cups, or 2 books or 2 and that s what we write. In other words, we leave out the multiplication sign, so we write 2x. So, from now on, you know that 2x means 2 times x, 3x means 3 times x, and so on. For ADD 5, we don t know what x represents, so we can t really add anything to it. All we can do is write the symbols for ADD 5 which are + 5, so we get 2x + 5. (If we use the matchboxes, then right now we have 2 matchboxes, but we don t know what they represent, so to add 5 we just use the single matches to add on the 5.) Next, we have to MULTIPLY that result by 3. This means we need to multiply everything we have by 3. We have 2 matchboxes and 5 matches, so we would get 6 matchboxes and 15 matches. We have to multiply 2x + 5 by 3, so we would get 6x TAKE AWAY 9. Remember we don t know what number x (or the matchbox) stands for, so we can t take 9 away from that, so we have to take 9 away from the number 15. We still have 6x though, so we get 6x + 6. Next, we have to DIVIDE the whole lot by 6. This means we are sharing out our 6x and our 6 (or our 6 matchboxes and our 6 matches). Each share would be one matchbox and one match, or x + 1. Lastly, TAKE AWAY your original number, which was x, and we would be left with 1. Here is just the algebra version: CALCULATION Your original number Your result x ALGEBRA DOUBLE the number 2x ADD 5 to the result 2x + 5 MULTIPLY that result 6x + 15 by 3 Take away 9 6x + 6 Divide the result by 6 x + 1 Take away your original number 1 Now to illustrate the calculation itself, using Algebra. 4

5 CALCULATION ALGEBRA NOTATION ALGEBRA RESULT Your original number x x DOUBLE the number 2x. This is the same as multiplying x by 2, or adding x and x. ADD 5 to the result 2x + 5 2x + 5 MULTIPLY that result by 3 3(2x + 5) Everything in the brackets has to be multiplied by 3. 2x 6x + 15 TAKE AWAY 9 6x x + 6 DIVIDE the result by 6 TAKE AWAY your original number 6x+6 Everything in the 6 numerator (top) has to be divided by 6. x + 1 x 1 x + 1 What has been illustrated so far has been ways of writing operations such as +,, x, and ( ) using Algebra. What has also been illustrated is that Algebra is a way of GENERALISING rather than using only specific numbers. The trick we used will always work using any number you like. Lastly, let s do the trick again, but this time we ll use the Algebra result. Here is what I mean. Say we thought of the number 11. (It s bigger than 10 so we re sure it is not your original number.) We ll use the Algebra Result and SUBSTITUTE the value of 11 for every x and see if we get the same result as if we just performed the calculation. (Please see the table over the page.) 5

6 CALCULATION Your original number DOUBLE the number USING 11 to calculate ALGEBRA RESULT 11 x 11 SUBSTITUTING 11 into ALGEBRA RESULT 11 X 2 = 22 2x 2 x 11 = 22 ADD 5 to the result = 27 2x x = = 27 MULTIPLY that result by 3 27 x 3 = 81 6x x = = 81 TAKE AWAY = 72 6x x = = 72 DIVIDE the result by = 12 x = 12 TAKE AWAY your original number = Notice that the results in the SUBSTITUTION column are exactly the same as they are in the USING 11 to calculate column. Please try this experiment with ANY other number. You can choose decimals, fractions, even negative numbers will work. You can use the table over the page. 6

7 CALCULATION Your original number USING your new number to calculate ALGEBRA RESULT x SUBSTITUTING your new number into ALGEBRA RESULT DOUBLE number the 2x ADD 5 to the result 2x + 5 MULTIPLY result by 3 that 6x + 15 TAKE AWAY 9 6x + 6 DIVIDE the result by 6 TAKE AWAY your original number x This brings us to the next part of Algebra: 7

8 SUBSTITUTION You might have come across formulas in all sorts of situations. Some examples could be: calculating repayments on a mortgage; finding the area of the floor of a room to be carpeted or tiled; working out the amount of tax to pay. For each of these types of calculations you can use a formula, no matter what the size of the mortgage, the dimensions of the room, or whatever amount you have earned. This is because formulas are simply a way of generalising from specific numbers, so that we can apply the same formula, or method, or procedure, to the same concept every time. Probably the simplest example from the ones above is to find the area of the rectangular floor of a room. You might know that we multiply the length of the floor by the width of the floor. (If you want to know more, please refer to CONNECT: Calculating Areas.) Let s say the length of a floor is 3 metres and the width is 2.5 metres. We multiply 3 x 2.5 and get 7.5 m 2 as the area. But we are not going to always have a length of 3 and a width of 2.5. Maybe we ll need to calculate the area of a floor that is 7.2 m by 5.1 metres and someone else wants to calculate This is where Algebra comes in. We can generalise and say that the length of the floor can be represented by l and the width can be represented by w. Then the Area, which we can represent using A, is the result of multiplying l by w, which can be written as A = l x w, or just A = l w. Whatever the length and width might be, we can simply SUBSTITUTE their values into our formula and find the answer. (To be able to substitute correctly into a formula, it helps to know about the Order of Operations for calculating and how to use your calculator. If you are unsure about either of these, please refer to CONNECT: Calculations: ORDER OF OPERATIONS IN MATHEMATICS and CONNECT: Calculators: GETTING TO KNOW YOUR SCIENTIFIC CALCULATOR.) Another common formula: The area of a circle. A = πr 2. A represents the value of the area of a circle and r represents the value of the radius of that circle. These values will change depending on the size of the circle. We say that A and r are variables because they can change or vary. With this formula, we also meet a new concept, π. π is what is called a constant, that is, unlike other letters for which we can substitute any value, π always remains the same. You can pick up any calculator and press the button for π and you will always see the same result. It is not a variable like A, 8

9 r, (or l and w in the rectangle formula). That is, π does not vary, it is always the same. Using the formula A = πr 2, we can find the area of any circle we like. The radius, r, can be any value, and by substituting that value into our formula, we can find the area of that circle. For example, let s find the area of a circle with radius 4.1 cm. We multiply π by the result of squaring 4.1 (which is 16.81) so we get π x 16.81, which is equal to (rounded) cm 2. We would write this calculation as follows: A = πr 2 = π x = π x (the means the value has been rounded and is approximate). So the area of the circle is approximately 52.81cm 2. Another formula. We can calculate the average speed (or velocity) with which we travelled on a trip. We do this by recognising that speed is just the distance travelled in a certain amount of time, example, kilometres per hour (km/h), metres per second (m/s) and so on (per hour means during each hour or during 1 hour). For example, you might have travelled 100 km in 1 hour, which gives you an average speed of 100 km/h. If you had taken 2 hours to do the 100km, you would have had an average of 50 km/h. If you had taken 4 hours to do the 100km, you would have had an average of 25 km/h. All we have done each time has been to divide the distance by the time taken, so the average speed can be calculated by using the formula v = d t where v is the velocity (speed), d is the distance travelled and t is the time taken. The units of distance and time will determine the units of velocity. Example: Calculate the average speed (velocity) on a trip of 350 km which took 5 hours. (we can leave this line out because we can just enter the previous line into the calculator and get the answer straight away) 9

10 Here, d = 350 and t = 5. Using v = d, we get t v = = 70 So the average speed was 70km/h. Many people like to use the units as part of their calculations, so we could also write: v = 350km 5h = 70 km/h Another common formula is to find the perimeter of a rectangle. This means we are finding the measurement of the outside of the rectangle. You can imagine walking on the outside of the rectangle this is the perimeter. If we measure the outside of the rectangle, it would mean we have measured the length twice (top and bottom, say) and the width twice (left and right) and have added them together to find the total. So we have 2 lengths and 2 widths altogether. If the length is l and the width is w, then the perimeter must be P = 2l + 2w For the rectangular floor with length 3 m and width 2.5 m, the perimeter is P = 2 x x 2.5 = = 11 So the perimeter is 11 m. 10

11 Another commonly used formula, especially when people travel to the USA, is the one which converts temperature between Fahrenheit ( F) and Celsius ( C). Fahrenheit is still used in the USA, Australia uses Celsius. The formula to convert from F to C is: C = 5 (F 32). 9 So, if the temperature in the US is 95 F, then the Celsius value would be: C = 5 (95 32) 9 = 5 9 (63) = (5 x 63) 9 (there are also other ways to calculate this) = 35 So the Celsius equivalent of 95 F is 35 C. And finally, putting everything together, a more difficult one: To find the monthly repayment on a fixed rate mortgage, one formula is c = Pr (1 + r)n (1 + r) N 1, where c is the monthly payment on a fixed rate mortgage, r is the monthly interest rate expressed as a decimal, N is the number of monthly payments, and P is the amount borrowed *. Let s borrow \$ over 25 years, at the annual interest rate of 6.35%. Before we substitute into the formula, we need to do a few calculations, mainly to work out the values of N and r. * 11

12 Because N is the number of monthly repayments, we need to know how many months there are in 25 years. So, N = 25 x 12 = 300. The interest rate, 6.35%, is given for a year. We need to work out how much that will be for a month, so we divide 6.35% by 12. To do this, it is easiest to work in decimals, so 6.35% = and = We now know: P = \$ , r = and N = 300 so we are ready to substitute. c = c = Pr (1 + r)n (1 + r) N ( )300 (( ) 300 1) So, our monthly repayment rate would be \$ (If you had any problems reaching that answer, you might like to refer to CONNECT: Calculators: GETTING TO KNOW YOUR SCIENTIFIC CALCULATOR. If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) , or Level 3 (top floor), Building 11, or through your campus. Acknowledgement: Matches and matchboxes idea from TAFENSW Career Education for Women course Author(s) unknown. 12

### CONNECT: Areas, Perimeters

CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES A plane figure or shape is a two-dimensional, flat shape. Here are 3 plane shapes: All of them have two dimensions that we usually call length and width

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a three-dimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.

### Welcome to Basic Math Skills!

Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots

### Measurements 1. BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com. In this section we will look at. Helping you practice. Online Quizzes and Videos

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Measurements 1 In this section we will look at - Examples of everyday measurement - Some units we use to take measurements - Symbols for units and converting

### OPERATIONS: x and. x 10 10

CONNECT: Decimals OPERATIONS: x and To be able to perform the usual operations (+,, x and ) using decimals, we need to remember what decimals are. To review this, please refer to CONNECT: Fractions Fractions

### Characteristics of the Four Main Geometrical Figures

Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

### To Evaluate an Algebraic Expression

1.5 Evaluating Algebraic Expressions 1.5 OBJECTIVES 1. Evaluate algebraic expressions given any signed number value for the variables 2. Use a calculator to evaluate algebraic expressions 3. Find the sum

### CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS

### Revision Notes Adult Numeracy Level 2

Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands

### Wheels Diameter / Distance Traveled

Mechanics Teacher Note to the teacher On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions and distance. Students will use formulas relating

### Chapter 2 Formulas and Decimals

Chapter Formulas and Decimals Section A Rounding, Comparing, Adding and Subtracting Decimals Look at the following formulas. The first formula (P = A + B + C) is one we use to calculate perimeter of a

### Mathematics. Steps to Success. and. Top Tips. Year 5

Pownall Green Primary School Mathematics and Year 5 1 Contents Page 1. Multiplication and Division 3 2. Positive and Negative Numbers 4 3. Decimal Notation 4. Reading Decimals 5 5. Fractions Linked to

### CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED

This resource has been produced as a result of a grant awarded by LSIS. The grant was made available through the Skills for Life Support Programme in 2010. The resource has been developed by (managers

### Unit 3: Algebra. Date Topic Page (s) Algebra Terminology 2. Variables and Algebra Tiles 3 5. Like Terms 6 8. Adding/Subtracting Polynomials 9 12

Unit 3: Algebra Date Topic Page (s) Algebra Terminology Variables and Algebra Tiles 3 5 Like Terms 6 8 Adding/Subtracting Polynomials 9 1 Expanding Polynomials 13 15 Introduction to Equations 16 17 One

### Pre-Algebra Lecture 6

Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals

### Numeracy and mathematics Experiences and outcomes

Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different

### Order of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A.

Order of Operations Section 1: Introduction You know from previous courses that if two quantities are added, it does not make a difference which quantity is added to which. For example, 5 + 6 = 6 + 5.

### ACCUPLACER MATH TEST REVIEW

ACCUPLACER MATH TEST REVIEW ARITHMETIC ELEMENTARY ALGEBRA COLLEGE ALGEBRA The following pages are a comprehensive tool used to maneuver the ACCUPLACER UAS Math portion. This tests your mathematical capabilities

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18

### Dŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet

Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils

### Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together

Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a

### CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure.

CALCULATING PERIMETER WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. HOW DO WE CALCULATE PERIMETER? The formula one can use to calculate perimeter depends on the type of

### 7 Literal Equations and

CHAPTER 7 Literal Equations and Inequalities Chapter Outline 7.1 LITERAL EQUATIONS 7.2 INEQUALITIES 7.3 INEQUALITIES USING MULTIPLICATION AND DIVISION 7.4 MULTI-STEP INEQUALITIES 113 7.1. Literal Equations

### AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)

AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square

T92 Mathematics Success Grade 8 [OBJECTIVE] The student will create rational approximations of irrational numbers in order to compare and order them on a number line. [PREREQUISITE SKILLS] rational numbers,

### COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13

COMPASS Numerical Skills/Pre-Algebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre

### Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower

Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including

### Measurement and Geometry: Perimeter and Circumference of Geometric Figures

OpenStax-CNX module: m35022 1 Measurement and Geometry: Perimeter and Circumference of Geometric Figures Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the Creative

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Maths Module 2. Working with Fractions. This module covers fraction concepts such as:

Maths Module Working with Fractions This module covers fraction concepts such as: identifying different types of fractions converting fractions addition and subtraction of fractions multiplication and

### LESSON 10 GEOMETRY I: PERIMETER & AREA

LESSON 10 GEOMETRY I: PERIMETER & AREA INTRODUCTION Geometry is the study of shapes and space. In this lesson, we will focus on shapes and measures of one-dimension and two-dimensions. In the next lesson,

### 2.3 Applications of Linear Equations

2.3 Applications of Linear Equations Now that we can solve equations, what are they good for? It turns out, equations are used in a wide variety of ways in the real world. We will be taking a look at numerous

### MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 3 EQUATIONS This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

### Preliminary Mathematics

Preliminary Mathematics The purpose of this document is to provide you with a refresher over some topics that will be essential for what we do in this class. We will begin with fractions, decimals, and

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

### Temperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.

Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is

### Surface Area of Prisms

Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism

### ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

### Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in

### Maths Targets Year 1 Addition and Subtraction Measures. N / A in year 1.

Number and place value Maths Targets Year 1 Addition and Subtraction Count to and across 100, forwards and backwards beginning with 0 or 1 or from any given number. Count, read and write numbers to 100

### Maths Workshop for Parents 2. Fractions and Algebra

Maths Workshop for Parents 2 Fractions and Algebra What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator 2 7 This is a proper (or common)

### Unit 5 Length. Year 4. Five daily lessons. Autumn term Unit Objectives. Link Objectives

Unit 5 Length Five daily lessons Year 4 Autumn term Unit Objectives Year 4 Suggest suitable units and measuring equipment to Page 92 estimate or measure length. Use read and write standard metric units

### Lesson 21. Circles. Objectives

Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine

### Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

### EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

### Circumference and area of a circle

c Circumference and area of a circle 22 CHAPTER 22.1 Circumference of a circle The circumference is the special name of the perimeter of a circle, that is, the distance all around it. Measure the circumference

### Math syllabus Kindergarten 1

Math syllabus Kindergarten 1 Number strand: Count forward and backwards to 10 Identify numbers to 10 on a number line Use ordinal numbers first (1 st ) to fifth (5 th ) correctly Recognize and play with

### Fractions. Cavendish Community Primary School

Fractions Children in the Foundation Stage should be introduced to the concept of halves and quarters through play and practical activities in preparation for calculation at Key Stage One. Y Understand

### Free Pre-Algebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters.

Free Pre-Algebra Lesson 3 page 1 Lesson 3 Perimeter and Area Enclose a flat space; say with a fence or wall. The length of the fence (how far you walk around the edge) is the perimeter, and the measure

### ALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite

ALGEBRA Pupils should be taught to: Generate and describe sequences As outcomes, Year 7 pupils should, for example: Use, read and write, spelling correctly: sequence, term, nth term, consecutive, rule,

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### Section 1.5 Exponents, Square Roots, and the Order of Operations

Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Oral and Mental calculation

Oral and Mental calculation Read and write any integer and know what each digit represents. Read and write decimal notation for tenths and hundredths and know what each digit represents. Order and compare

### Numeracy Targets. I can count at least 20 objects

Targets 1c I can read numbers up to 10 I can count up to 10 objects I can say the number names in order up to 20 I can write at least 4 numbers up to 10. When someone gives me a small number of objects

### T. H. Rogers School Summer Math Assignment

T. H. Rogers School Summer Math Assignment Mastery of all these skills is extremely important in order to develop a solid math foundation. I believe each year builds upon the previous year s skills in

### The GED math test gives you a page of math formulas that

Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

### Draft copy. Circles, cylinders and prisms. Circles

12 Circles, cylinders and prisms You are familiar with formulae for area and volume of some plane shapes and solids. In this chapter you will build on what you learnt in Mathematics for Common Entrance

### MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume.

MAT104: Fundamentals of Mathematics II Summary of Section 14-5: Volume, Temperature, and Dimensional Analysis with Area & Volume For prisms, pyramids, cylinders, and cones: Volume is the area of one base

### What You ll Learn. Why It s Important

These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

### Geometry Notes VOLUME AND SURFACE AREA

Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

### Mathematical goals. Starting points. Materials required. Time needed

Level A3 of challenge: C A3 Creating and solving harder equations equations Mathematical goals Starting points Materials required Time needed To enable learners to: create and solve equations, where the

### Lesson 8: Velocity. Displacement & Time

Lesson 8: Velocity Two branches in physics examine the motion of objects: Kinematics: describes the motion of objects, without looking at the cause of the motion (kinematics is the first unit of Physics

### Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.

-NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has

### To Multiply Decimals

4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by

### Scale Factors and Volume. Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor

Scale Factors and Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor Find the volume of each prism 1. 2. 15cm 14m 11m 24m 38cm 9cm V = 1,848m 3 V = 5,130cm

### Numeracy Preparation Guide. for the. VETASSESS Test for Certificate IV in Nursing (Enrolled / Division 2 Nursing) course

Numeracy Preparation Guide for the VETASSESS Test for Certificate IV in Nursing (Enrolled / Division Nursing) course Introduction The Nursing course selection (or entrance) test used by various Registered

### Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

### 10-4-10 Year 9 mathematics: holiday revision. 2 How many nines are there in fifty-four?

DAY 1 Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fifty-four? 54 9 = 6 6 3 What number should you add to negative three to get the answer five? 8 4 Add two point five to

### All the examples in this worksheet and all the answers to questions are available as answer sheets or videos.

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Numbers 3 In this section we will look at - improper fractions and mixed fractions - multiplying and dividing fractions - what decimals mean and exponents

### Week #15 - Word Problems & Differential Equations Section 8.1

Week #15 - Word Problems & Differential Equations Section 8.1 From Calculus, Single Variable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 25 by John Wiley & Sons, Inc. This material is used by

### Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving

Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words

### ARITHMETIC. Overview. Testing Tips

ARITHMETIC Overview The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### The Crescent Primary School Calculation Policy

The Crescent Primary School Calculation Policy Examples of calculation methods for each year group and the progression between each method. January 2015 Our Calculation Policy This calculation policy has

### Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

### Solutions of Equations in Two Variables

6.1 Solutions of Equations in Two Variables 6.1 OBJECTIVES 1. Find solutions for an equation in two variables 2. Use ordered pair notation to write solutions for equations in two variables We discussed

### Grade 4 Mathematics Measurement: Lesson 2

Grade 4 Mathematics Measurement: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

### Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER

Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

### Mathematics. What to expect Resources Study Strategies Helpful Preparation Tips Problem Solving Strategies and Hints Test taking strategies

Mathematics Before reading this section, make sure you have read the appropriate description of the mathematics section test (computerized or paper) to understand what is expected of you in the mathematics

### Sequences. A sequence is a list of numbers, or a pattern, which obeys a rule.

Sequences A sequence is a list of numbers, or a pattern, which obeys a rule. Each number in a sequence is called a term. ie the fourth term of the sequence 2, 4, 6, 8, 10, 12... is 8, because it is the

### Mathematics. Steps to Success. and. Top Tips. Year 6

Pownall Green Primary School Mathematics and Year 6 1 Contents Page 1. Multiply and Divide Decimals 3 2. Multiply Whole Numbers 3. Order Decimals 4 4. Reduce Fractions 5. Find Fractions of Numbers 5 6.

### Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3

Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels

### COMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh

BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

### Fundamentals of Geometry

10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount

### Number Skills for Public Health

Number Skills for Public Health Rounding, Percentages, Scientific Notation and Rates These notes are designed to help you understand and use some of the numerical skills that will be useful for your studies

### The Area is the width times the height: Area = w h

Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

### Florida Math Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper

Florida Math 0022 Correlation of the ALEKS course Florida Math 0022 to the Florida Mathematics Competencies - Lower and Upper Whole Numbers MDECL1: Perform operations on whole numbers (with applications,

### Now that we have a handle on the integers, we will turn our attention to other types of numbers.

1.2 Rational Numbers Now that we have a handle on the integers, we will turn our attention to other types of numbers. We start with the following definitions. Definition: Rational Number- any number that

### The theory of the six stages of learning with integers (Published in Mathematics in Schools, Volume 29, Number 2, March 2000) Stage 1

The theory of the six stages of learning with integers (Published in Mathematics in Schools, Volume 29, Number 2, March 2000) Stage 1 Free interaction In the case of the study of integers, this first stage

### DATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation

A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal