# REVISED GCSE Scheme of Work Mathematics Higher Unit 6. For First Teaching September 2010 For First Examination Summer 2011 This Unit Summer 2012

Save this PDF as:

Size: px
Start display at page:

Download "REVISED GCSE Scheme of Work Mathematics Higher Unit 6. For First Teaching September 2010 For First Examination Summer 2011 This Unit Summer 2012"

## Transcription

1 REVISED GCSE Scheme of Work Mathematics Higher Unit 6 For First Teaching September 2010 For First Examination Summer 2011 This Unit Summer 2012

2 Version 1: 28 April 10

3 Version 1: 28 April 10 Unit T6

4 Unit T6 This is a working document for teachers to adapt for their own needs. Knowledge of the content of Unit T5 is assumed. Topic No. Topic Subject Content 1 Number Standard Form 2 Algebra Change of Subject 3 Number Recurring Decimals 4 Algebra Linear Inequalities 5 Algebra Simultaneous equations 6 Geometry and Measures Transformation of Shapes 7 Geometry and Measures Similarity 8 Algebra Real-life Graphs 9 Geometry and Measures Loci Constructions 10 Algebra Indices 11 Number Surds 12 Geometry and Measures Volume 13 Geometry and Measures Perimeters using arcs and Volumes 14 Geometry and Measures Units and Dimensions 15 Algebra Graphs of Reciprocal Functions 16 Algebra Graphs of Cubic, Trigonometric and Exponential Functions 17 Probability Mutually Exclusive and Exhaustive Events 18 Probability Independent Events and Tree Diagrams Version 1: 28 April 10 2

5 TOPIC 1: NUMBER Standard Index Form interpret, order and calculate with numbers written in standard index form; Be able to write very large and very small numbers presented in context in standard form; Convert between ordinary and standard index form numbers; SAM T62 Q. 7 Interpret a calculator display using standard form; Calculate with numbers in standard form using a calculator. Version 1: 28 April 10 3

6 TOPIC 2: ALGEBRA Changing The Subject change the subject of formulae including cases where the subject appears in more than one term, or where a power of the subject appears. Show examples of changing the subject with linear equations before progressing on to quadratic equations and equations in which the subject appears more than once. Transform formulae such as v = u + at, A = r 2 100(s c), p c SAM T61 Q. 4(b) understand, construct and evaluate formulae related to mathematics or other subjects or real-life situations. e.g. Work out s = ut + ½at 2 where u or a may have negative values. GMm Use the formula F = 2 to calculate one variable given the others. r SAM T61 Q. 4(a) SAM T62 Q. 8 Version 1: 28 April 10 4

7 TOPIC 3: NUMBER Recurring decimals change a recurring decimal to a fraction. Know the significance of recurring and non-recurring decimals. Recurring decimals are rational numbers and can be changed into fractions. Non-recurring decimals that are not finite are irrational, e.g.. SAM T61 Q. 13(a) In recurring decimal notation dots are placed over the first and last of the set of 124 recurring digits, e.g = = 999 To change a recurring decimal to a fraction the following method can be used: Find the length of the recurring sequence. If the recurring sequence is one digit then multiply the recurring decimal by 10, if the recurring sequence is two digits then multiply the recurring decimal by 100, etc. Subtract the original recurring decimal from the one that has just been calculated. Divide through to obtain the fractional form of the recurring decimal. e.g. n = = 0.234, multiply by n = n = subtract 999n = 234 Therefore n = Version 1: 28 April 10 5

8 TOPIC 4: ALGEBRA Linear Inequalities Students should be able to: solve a range of linear inequalities; Introduce inequalities by how they are represented on a number line open circle means the end point is not included, closed (shaded) circle means end point is included, e.g. x < 10, y 6. Include examples of double inequalities. (Progress to examples where an inequality is multiplied or divided through by a negative number, meaning the direction of the inequality sign must be reversed.) Computer package such as Omnigraph Graph paper use straight line graphs to locate regions representing linear inequalities; Introduce locating regions of a graph by first looking at examples of inequalities parallel to one axis. e.g. x < 10, draw the x = 10 line (dotted), shade appropriate region. e.g. y 6, draw the y = 6 line (solid) and shade appropriate region. e.g. 3 < x 8 draw appropriate lines and shade region. Move on to show inequalities involving both x and y on the same graph, e.g. x < 10, y 6. Progress to several inequalities are to be drawn on the same graph, e.g. x < 10, y 6, y < 2x + 3. The solution space should be left unshaded. Show examples of how inequalities can solve problems. Omnigraph can be used to give practice at solving inequalities. SAM T62 Q. 4 Version 1: 28 April 10 6

9 TOPIC 5: ALGEBRA Simultaneous Equations Students should be able to: use algebraic and graphical methods to solve simultaneous linear equations in two unknowns; use algebraic and graphical methods to solve two simultaneous equations, one linear and the other quadratic, in two unknowns. Introduce the idea of two linear equations having only one point in common by drawing the graph of the equations. The point of intersection is the solution to the equations. Check that the coordinates work in both equations before moving on. Draw the straight line graphs and find the point of intersection. May be helpful to use Omnigraph to draw the two simultaneous equations and read off the point of intersection. Introduce the algebraic method of solving simultaneous equations by first using examples where the coefficients of x or y are equal in both equations subtract the equations to find one unknown. Then use substitution to find the second unknown. Move on to examples where the coefficients of x and y are the same but of opposite signs add the equations to find one unknown. Then use substitution to find the second unknown. Look at examples of simultaneous equations where one equation needs to be multiplied to make the coefficients equal in size. Show examples of simultaneous equations where the two equations need to be multiplied to make the coefficients equal in size. Show examples where an equation needs to be rearranged into the required format before solving. Always highlight the notion of checking that the solutions fit into the two original simultaneous equations. Progress to equations where one is linear and one is quadratic, e.g. solve y = 5x 6 and y = x 2. Computer package such as Omnigraph Version 1: 28 April 10 7

10 TOPIC 6: GEOMETRY and MEASURES Transformations of Shapes understand transformation of shapes using reflection, rotation, translation and enlargement. enlarge a shape through a given centre of enlargement, by a positive fractional or negative scale factor; recognise that enlargements preserve angle but not length; distinguish properties that are preserved under particular transformations; Ensure that the pupils understand that the term transformation encompasses reflection, rotation, translation, and enlargement. Understand that reflection, rotation and translation all preserve the size and shape of the object being transformed while enlargement just preserves shape. Consider reflections in both axes and y = x. Stress that you need the centre of rotation, the direction and the angle to fully describe a rotation. Be able to complete and describe given rotations Consider simple enlargements with positive integer scale factors. The image is larger and on the same side of the centre of enlargement as the original. Using examples and exemplars allow pupils to decide if an image is an enlargement of the original or not. All enlargements are described using a scale factor and the centre of enlargement. Stress that the enlargement is similar to the original; has the same angles and all corresponding side have the same ratio. Move on to consider positive fractional scale factors. Highlighting that the image is always smaller and on the same side of the centre of enlargement as the original. SAM T61 Q. 6 Version 1: 28 April 10 8

11 TOPIC 6: GEOMETRY and MEASURES Transformations of Shapes(cont.) use transformations to create and analyse spatial patterns; understand how transformations are related by combinations and inverses. Negative scale factors can now be clarified stressing that the image is now on the other side of the centre of enlargement from the original. Be able to complete and describe given enlargement questions Understand that the image in a translation is congruent to the original. And be able to describe a translation in using vector notation. Pupils should do set question both in class discussion and individual work involving choosing and describing which transformation or combination of transformations maps an original shape to its image. SAM T61 Q. 11(a) Pupils should then understand how to map an image back to its original ie find inverses of transformations. Version 1: 28 April 10 9

12 TOPIC 7: GEOMETRY and MEASURES - Similarity Students should be able to: understand the effect of enlargement for perimeter, area and volume of shapes and solids; understand and use the relationship between the surface areas of similar 3-D shapes and between the volumes of similar 3-D shapes. Understand how to make correct use of the scale factor. Pupils should consider similar 3-D shapes. An investigation could allow them to establish the relationship between the areas of corresponding surfaces of two similar 3-D shapes. Given 2 sides of one 2-D shape and the length of one corresponding side on a similar shape, pupils should be able to determine the area of the second shape. Given the area and one side of one 2-D shape a pupils should be able to determine the area of a similar 2-D shape with the corresponding side known. Given 2 sides of one 3-D shape and the length of one corresponding side on a similar shape, pupils should be able to determine the area and volume of the second 3-D shape. Given the area and one side of one 3-D shape a pupil should be able to determine the area and volume of a similar 3-D shape with the corresponding side known. SAM T61 Q. 8 SAM T61 Q. 11(b) Version 1: 28 April 10 10

13 TOPIC 8: ALGEBRA Real-life Graphs interpret and display information on graphs that describe real-life situations; For example: distance-time graphs including intersecting travel graphs. Remind pupils about the 12 and 24 hour clocks and measuring lengths of time. Do some calculations involving time. Spreadsheet package Graph paper Investigate the connection between distance, speed and time and highlight the use of compound units as a measure of rate. Progress to travel graphs and notice the connection between the steepness of the slope and the speed. Work out average speed (distance/time). Practical work could include collection of timings of races over certain distances and could link in with PE. Show examples of real life graphs and discuss the relevance of joining the points up do the values between points have any meaning? Do the lines show any trends? Progress to interpreting conversion graphs. Pupils may use a spreadsheet package to draw conversion graphs. Notice that they are always straight lines, but do not always start at the origin. Give pupils a chance to read information from conversion graphs, in both directions. Progress on to examples that use non-linear graphs. Version 1: 28 April 10 11

14 TOPIC 9: GEOMETRY and MEASURES Loci and Construction use ruler and compasses to do standard constructions including an equilateral triangle with a given side, the mid-point and perpendicular bisector of a line segment, the perpendicular from a point to a line, the perpendicular from a point on a line and the bisector of an angle; loci. Define language such as equilateral, perpendicular, and bisect. Carry the class through each of the standard constructions in steps and practise several examples of each. Explain to pupils what is meant by loci giving standard examples: The path followed by a body moving according to the rule whereby: it must always be a given distance from a fixed point it must always be a fixed distance from two fixed points it must always be a fixed distance from a given straight line it must always be a fixed distance from two fixed points it must always be a fixed distance from two straight lines Move on to use loci and construction to define regions. Region bounded by a circle and an intersecting line. For example worded problems involving maps. A prepared worksheet is particularly useful in this instance. SAM T62 Q. 6 Version 1: 28 April 10 12

15 TOPIC 10: ALGEBRA Indices use the rules of indices for integral and fractional values. Revise over the meaning of the terms index, power, and base. Look at examples of the zero index and the reciprocal. Move onto the rules of indices. SAM T61 Q. 7 When the bases are the same a m a n = a m+n, a m a n = a m n, (a m ) n = a mn Progress to examples with coefficients in front of the power terms. Simplify expressions involving positive indices only, such as: 6x 6 3x 4, 2x 2 3x 3 and (3x 2 ) 3 Introduce negative powers as being the reciprocal of the same expression with a positive power. SAM T61 Q. 13(b) a m = 1/a m A fractional power is a root of the base number a ⅓ = 3 a Version 1: 28 April 10 13

16 TOPIC 10: ALGEBRA Indices (Cont.) Use x o = 1, y 3 x ½ x 1½ = x 2 1 2, x / x 3 3 y 1 = x 1 x Introduce exponential as another word for power. An exponential equation is any equation in which the unknown is the power. Version 1: 28 April 10 14

17 TOPIC 11: NUMBER Surds use surds including rationalise a denominator; Surds are expressions with irrational square roots (they include roots that are not equivalent to integers or fractions). SAM T61 Q. 13(c) use surds and in exact calculations, without a calculator. Rules to learn: a b ab and a b To simply a surd try to find a square number, e.g. 12 = 4 3 = 2 3 a b To rationalise a surd, remove the surd from the denominator by multiplying the numerator and denominator by the value of the surd in the denominator. e.g If asked to give the exact answer, leave it in surd form. When undertaking calculations involving surds and without a calculator follow the order of precedence and the rules for surds. Version 1: 28 April 10 15

18 TOPIC 12: GEOMETRY and MEASURES Volume Students should be able to: calculate the volume of cylinders and other simple right prisms; calculate the volume of cones and spheres; Calculate the volume of a tent. Individual work on set questions Understand the properties of a prism. Calculate the volume of prisms including cylinders. find volumes, [for example, by dissection methods]; Calculate the volume of a tent Calculate the radius of a cylinder given the volume Calculate the height of a prism given the volume and other dimensions. SAM T62 Q. 11 Calculate the surface area and volume of compound solids, including examples in everyday use. Calculate the surface area and volume of a hot water tank whose shape consists of a cylinder and a hemisphere. Version 1: 28 April 10 16

19 TOPIC 13: GEOMETRY and MEASURES Perimeters involving arcs and areas calculate lengths of circular arcs and perimeter of composite shapes; calculate areas of shapes whose perimeters include circular arcs; calculate surface areas of cylinders, cones and spheres. At this stage pupils can recall and use the equation for the circumference of a circle. Discuss the direct relationship between the angle of the sector and the arc length, this can also be investigated in pairs. Individual work on set questions involving getting arc lengths, perimeters of sectors and perimeters of shapes which involve arc lengths. Understand that a cylinder can be made using a sheet of card and what is originally the length and width of the card becomes the circumference and height of the cylinder respectively. Pupils will then understand that the curved surface area of the cylinder with a given radius or diameter is the circumference times the height. Do set applications on the surface area of cylinders. Given the curved surface area of a cylinder solve for the radius/diameter/height Do set applications on the surface area of cones, stressing that the height used is the slant height of the cone. Given the curved surface area of a cylinder solve for the radius/diameter/height Do set applications on the surface area of and spheres. Given the curved surface area of a cylinder solve for the radius/diameter Version 1: 28 April 10 17

20 TOPIC 14: GEOMETRY and MEASURES Units and dimensions distinguish between formulae for length, area and volume by considering dimensions. Review with pupils the dimensions for length, area and volume with which they are already familiar. Recognise that d is a linear measurement and that r 2 is an area measurement. Identify from a range of formulae those which denote (say) volume: 4 r 2, 4 r 3 3, 1 r 3 2 h, r 2 Remind pupils that like with algebra you can only collect like terms; you can only add a length to another length not to an area for example. Do set questions where pupils have to decide if the equation is for an area length or volume, by substituting in dimensions instead of numbers, and simplifying the expression. Pupils often respond well to examples and exemplars when learning this topic. Version 1: 28 April 10 18

21 TOPIC 15: ALGEBRA Graphs of Reciprocal Functions Students should be able to: explore the properties of reciprocal functions To include drawing graphs of: y = x a where a 0 and x 0 Graphic calculators Computer package such as Omnigraph know the forms of graphs of reciprocal functions make tables of such functions, sketch and interpret their graphs using graphical calculators and computers to understand their behaviour. Highlight the fact that this is made up of two smooth curves and is not defined when x = 0. It has both line and rotational symmetry. It may be an advantage to pupils to have seen the shape of the reciprocal graph before they attempt to draw it. Care needs to be taken when filling in the table of values. Highlight the fact that this is made up of two smooth curves and is not defined when x = 0. It has both line and rotational symmetry. It may be an advantage to pupils to have seen the shape of the reciprocal graph before they attempt to draw it. Care needs to be taken when filling in the table of values. SAM T61 Q. 10 Version 1: 28 April 10 19

22 TOPIC 16: ALGEBRA Cubic, Trig. & Exponential Functions explore the properties of cubic, trig. and exponential functions; make tables of such functions, sketch and interpret their graphs using graphical calculators and computers to understand their behaviour; know the form of exponential functions; use growth and decay rates and display these graphically; solve polynomial equations by graphical methods. Pupils need to be able to work out coordinates of given functions by tabulating values. Once this has been achieved, graphs may be plotted on a computer and interpreted. Begin by discussing how a graph could show the answer to f(x) = 0 i.e. y = f(x) cuts the x-axis. Progress to show that the equation f(x) = a is solved by looking at where the graph of y = f(x) cuts the line at y = a. Show that by rearranging the equation, a graph can be used to solve a whole family of equations. Introduce exponential functions by explaining that they are functions where the unknown is the power. To include drawing graphs of: y = a x where a = 2, 3, 4 These examples all show exponential growth. Progress to examples showing exponential decay. Know about rates of economic growth and decline and the half-life of radioactive elements. Trig. Functions are restricted to y = sin x and y = cos x for 0 o < x < 360 o. Computer graph plotting package such as Omnigraph Graphic calculators SAM T61 Q. 15 Version 1: 28 April 10 20

23 TOPIC 17: PROBABILITY Mutually exclusive and exhaustive events know that if there are several possible outcomes of a event (exhaustive and mutually exclusive), the total of these probabilities is 1; understand that the probability of something happening is 1 minus the probability of it not happening; understand and apply the addition of probabilities for mutually exclusive events Review probability as a measure of how likely an event is of happening. Discuss the probability scale: 0 for impossible and 1 for certain. Define the terms event and outcome. Discuss the form of a sample space diagram and possibility space. Note that the probability (theoretical probability) of an event is the number of favourable outcomes divided by the total number of outcomes. Define mutually exclusive and exhaustive events: Events are mutually exclusive if they cannot occur at the same time. Note that the sum of the probabilities of all mutually exclusive events is 1. Events are exhaustive if together they include all possible outcomes ie. at least one of them must occur. Therefore it should be noted that the probabilities of exhaustive mutually exclusive events always add up to 1. Recognise that if the probability of a machine failing is 0.05 then the probability of it not failing is 0.95 Introduce the appropriate representation of probability as a capital P with the event written in brackets e.g. P(A). Therefore the probability of an event not happening can be written as follows; P(Ā) = 1 P(A) For mutually exclusive events use the addition law of probability to find the probability of either one or other of the two events happening; P(A or B) = P(A) + P(B) SAM T61 Q. 2 SAM T62 Q. 9(b) Version 1: 28 April 10 21

24 TOPIC 18: PROBABILITY Independent events and tree diagrams understand that when dealing with two independent events, the probability of them both happening is less than the probability of either of them happening (unless the probability is 0 or 1); Know that the probability of getting two consecutive sunny days over a weekend is less than the probability of getting a sunny Saturday or Sunday. Discuss that two events are independent if the outcome of one does not affect the outcome of the other. For independent events the multiplication rule of probability is applied; P(A and B) = P(A) P(B) It should be noted that when multiplying probabilities the resulting answer is smaller than either of the separate probabilities. SAM T62 Q. 9(a) calculate the probability of a combined event given the probability of two independent events and illustrate combined probability of several events using tabulation or a tree diagram; Given that there are 2 sets of traffic lights on the way to school and the probability of getting straight through the lights without having to stop are 0.6 and 0.4 respectively, find the probability of a cyclist having to stop at one set of lights, using a tree diagram or otherwise. This is usually referred to as a tree diagram with replacement as the events can then be observed as being independent. To obtain the appropriate answer use the following procedure: multiply along the branches to get the end results; on any set of branches which meet at a point, the numbers must always add up to 1; check that the end results also add up to 1. To obtain the relevant answer to a problem simply add up the relevant end points. SAM T61 Q. 12 Conditional probability. Version 1: 28 April 10 22

25 TOPIC 18: PROBABILITY Independent events and tree diagrams(cont.) Draw a tree diagram or use a tabulation to define all of the possible outcomes eg. tossing a coin 3 times. produce a tree diagram to illustrate the combined probability of several events which are not independent An operation has a 60% success rate the first time it is attempted. If it is unsuccessful it can be repeated, but with a success rate of only 30%. The probability of success the third time is so low that surgeons are unwilling to operate. What is the probability that the operation will fail twice? Discuss that sometimes the events illustrated by a tree diagram are not independent. The outcome of the first event may affect subsequent events. This type of tree diagram is sometimes referred to as one without replacement. Version 1: 28 April 10 23

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

### Decide how many topics you wish to revise at a time (let s say 10).

1 Minute Maths for the Higher Exam (grades B, C and D topics*) Too fast for a first-time use but... brilliant for topics you have already understood and want to quickly revise. for the Foundation Exam

### Edexcel Maths Linear Topic list HIGHER Edexcel GCSE Maths Linear Exam Topic List - HIGHER

Edexcel GCSE Maths Linear Exam Topic List - HIGHER NUMBER Add, subtract, multiply, divide Order numbers Factors, multiples and primes Write numbers in words Write numbers from words Add, subtract, multiply,

### Introduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test

Introduction The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are

### CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers

### MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

### 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

### Ingleby Manor Scheme of Work : Year 7. Objectives Support L3/4 Core L4/5/6 Extension L6/7

Autumn 1 Mathematics Objectives Support L3/4 Core L4/5/6 Extension L6/7 Week 1: Algebra 1 (6 hours) Sequences and functions - Recognize and extend number sequences - Identify the term to term rule - Know

### In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

### Curriculum Overview YR 9 MATHS. SUPPORT CORE HIGHER Topics Topics Topics Powers of 10 Powers of 10 Significant figures

Curriculum Overview YR 9 MATHS AUTUMN Thursday 28th August- Friday 19th December SUPPORT CORE HIGHER Topics Topics Topics Powers of 10 Powers of 10 Significant figures Rounding Rounding Upper and lower

### Section 1: How will you be tested? This section will give you information about the different types of examination papers that are available.

REVISION CHECKLIST for IGCSE Mathematics 0580 A guide for students How to use this guide This guide describes what topics and skills you need to know for your IGCSE Mathematics examination. It will help

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to

### Key Topics What will ALL students learn? What will the most able students learn?

2013 2014 Scheme of Work Subject MATHS Year 9 Course/ Year Term 1 Key Topics What will ALL students learn? What will the most able students learn? Number Written methods of calculations Decimals Rounding

### Mathematics programmes of study: key stage 4. National curriculum in England

Mathematics programmes of study: key stage 4 National curriculum in England July 2014 Contents Purpose of study 3 Aims 3 Information and communication technology (ICT) 4 Spoken language 4 Working mathematically

### 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

### Number Sense and Operations

Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

### Utah Core Curriculum for Mathematics

Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions

Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### KS3 Maths Learning Objectives (excludes Year 9 extension objectives)

KS3 Maths Learning Objectives (excludes Year 9 extension objectives) blue Year 7 black Year 8 green Year 9 NUMBER N1 Place value and standard form N1.1 Place value N1.2 Powers of ten Framework Objectives

### The Australian Curriculum Mathematics

The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year

### Mathematics. GCSE subject content and assessment objectives

Mathematics GCSE subject content and assessment objectives June 2013 Contents Introduction 3 Subject content 4 Assessment objectives 11 Appendix: Mathematical formulae 12 2 Introduction GCSE subject criteria

### Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

### MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

### MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

### FOREWORD. Executive Secretary

FOREWORD The Botswana Examinations Council is pleased to authorise the publication of the revised assessment procedures for the Junior Certificate Examination programme. According to the Revised National

### Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

### McDougal Littell California:

McDougal Littell California: Pre-Algebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California Pre-Algebra Components: Pupil Edition (PE), Teacher s Edition (TE),

### Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

### National 5 Mathematics Course Assessment Specification (C747 75)

National 5 Mathematics Course Assessment Specification (C747 75) Valid from August 013 First edition: April 01 Revised: June 013, version 1.1 This specification may be reproduced in whole or in part for

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### GRADES 7, 8, AND 9 BIG IDEAS

Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

### Mathematics programmes of study: key stage 3. National curriculum in England

Mathematics programmes of study: key stage 3 National curriculum in England September 2013 Purpose of study Mathematics is a creative and highly inter-connected discipline that has been developed over

### Centroid: The point of intersection of the three medians of a triangle. Centroid

Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

### Math Grade 11 Assessment Anchors and Eligible Content

Math Grade 11 Assessment Anchors and Eligible Content Pennsylvania Department of Education www.pde.state.pa.us Updated August 2010 M11.A Numbers and Operations M11.A.1 Demonstrate an understanding of numbers,

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### NEW MEXICO Grade 6 MATHEMATICS STANDARDS

PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

### Express a whole number as a product of its prime factors. e.g

Subject OCR 1 Number Operations and Integers 1.01 Calculations with integers 1.01a Four rules Use non-calculator methods to calculate the sum, difference, product and quotient of positive and negative

### Common Core State Standards for Mathematics Accelerated 7th Grade

A Correlation of 2013 To the to the Introduction This document demonstrates how Mathematics Accelerated Grade 7, 2013, meets the. Correlation references are to the pages within the Student Edition. Meeting

### Chapter 1: Essentials of Geometry

Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

### Functional Math II. Information CourseTitle. Types of Instruction

Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade

### Syllabus. Cambridge IGCSE Mathematics

Syllabus Cambridge IGCSE Mathematics 0580 For examination in June and November 2017 and 2018. Also available for examination in March 2017 and 2018 for India only. Cambridge Secondary 2 Version 1 Changes

### Indiana State Core Curriculum Standards updated 2009 Algebra I

Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and

### Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

### Wednesday 15 January 2014 Morning Time: 2 hours

Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number

### Grade Level Expectations for the Sunshine State Standards

for the Sunshine State Standards Mathematics Grades 6-8 FLORIDA DEPARTMENT OF EDUCATION http://www.myfloridaeducation.com/ Strand A: Number Sense, Concepts, and Operations Standard 1: The student understands

### Prentice Hall Mathematics: Algebra 1 2007 Correlated to: Michigan Merit Curriculum for Algebra 1

STRAND 1: QUANTITATIVE LITERACY AND LOGIC STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS Based on their knowledge of the properties of arithmetic, students understand and reason

### WASSCE / WAEC ELECTIVE / FURTHER MATHEMATICS SYLLABUS

Visit this link to read the introductory text for this syllabus. 1. Circular Measure Lengths of Arcs of circles and Radians Perimeters of Sectors and Segments measure in radians 2. Trigonometry (i) Sine,

### Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

### Chapter 8 Geometry We will discuss following concepts in this chapter.

Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

### Curriculum Map Grade: _7 th Basic Math School: _ Middle Date: Oct. 31/2009

August/ September Review basic skills of add, subtract, multiply, and divide whole numbers and fractions. (skill with a # assessed locally.) Students will add, subtract, multiply, and divide positive rational

### Students will understand 1. use numerical bases and the laws of exponents

Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?

### Bridging Documents for Mathematics

Bridging Documents for Mathematics 5 th /6 th Class, Primary Junior Cycle, Post-Primary Primary Post-Primary Card # Strand(s): Number, Measure Number (Strand 3) 2-5 Strand: Shape and Space Geometry and

### Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013

A Correlation of Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates

### 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

### EVERY DAY COUNTS CALENDAR MATH 2005 correlated to

EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:

### with functions, expressions and equations which follow in units 3 and 4.

Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model

### WORK SCHEDULE: MATHEMATICS 2007

, K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check

### For examination in June and November 2016. Also available for examination in March 2016 for India only.

SYLLABUS Cambridge IGCSE Mathematics 0580 For examination in June and November 2016. Also available for examination in March 2016 for India only. This syllabus is approved for use in England, Wales and

### Standards and progression point examples

Mathematics Progressing towards Foundation Progression Point 0.5 At 0.5, a student progressing towards the standard at Foundation may, for example: connect number names and numerals with sets of up to

### Greater Nanticoke Area School District Math Standards: Grade 6

Greater Nanticoke Area School District Math Standards: Grade 6 Standard 2.1 Numbers, Number Systems and Number Relationships CS2.1.8A. Represent and use numbers in equivalent forms 43. Recognize place

### Grade 6 Grade-Level Goals. Equivalent names for fractions, decimals, and percents. Comparing and ordering numbers

Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

### Tennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes

Tennessee Mathematics Standards 2009-2010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical

### Algebra 1 Course Information

Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

### SAT Subject Math Level 2 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Arithmetic Sequences: PEMDAS (Parentheses

### 20 Maths Wordsearch Puzzles

20 Maths Wordsearch Puzzles Licence Duncan Keith 2005 (maths@subtangent.com) This document is released under the Creative Commons Attribution-NonCommercial- ShareAlike 1.0 (UK) licence. You can find the

### Specimen paper MATHEMATICS HIGHER TIER. Time allowed: 2 hours. GCSE BITESIZE examinations. General Certificate of Secondary Education

GCSE BITESIZE examinations General Certificate of Secondary Education Specimen paper MATHEMATICS HIGHER TIER 2005 Paper 1 Non-calculator Time allowed: 2 hours You must not use a calculator. Answer all

### Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

### Illinois State Standards Alignments Grades Three through Eleven

Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other

### Mathematical Procedures

CHAPTER 6 Mathematical Procedures 168 CHAPTER 6 Mathematical Procedures The multidisciplinary approach to medicine has incorporated a wide variety of mathematical procedures from the fields of physics,

### Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test

Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan

### Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter B. Middle School

Middle School 111.B. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter B. Middle School Statutory Authority: The provisions of this Subchapter B issued under the Texas Education

### 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

### 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

### Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

### 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 Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

### Pennsylvania System of School Assessment

Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read

### Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade)

Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade) Teacher: School Phone: Email: Kim Schnakenberg 402-443- 3101 kschnakenberg@esu2.org Course Descriptions: Both Concept and Application

### MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

### Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### SHAPE, SPACE AND MEASURES

SHPE, SPCE ND MESURES Pupils should be taught to: Understand and use the language and notation associated with reflections, translations and rotations s outcomes, Year 7 pupils should, for example: Use,

### Introduction to the Instructor TERM 1

Introduction to the Instructor TERM 1 This calendar of lessons was prepared as a textbook independent sequence of lessons and the order of topics can be modified based on the textbook selection. The columns

### Everyday Mathematics GOALS

Copyright Wright Group/McGraw-Hill GOALS The following tables list the Grade-Level Goals organized by Content Strand and Program Goal. Content Strand: NUMBER AND NUMERATION Program Goal: Understand the

### 4. An isosceles triangle has two sides of length 10 and one of length 12. What is its area?

1 1 2 + 1 3 + 1 5 = 2 The sum of three numbers is 17 The first is 2 times the second The third is 5 more than the second What is the value of the largest of the three numbers? 3 A chemist has 100 cc of

### Geometry. Higher Mathematics Courses 69. Geometry

The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

### Algebra 1-2. A. Identify and translate variables and expressions.

St. Mary's College High School Algebra 1-2 The Language of Algebra What is a variable? A. Identify and translate variables and expressions. The following apply to all the skills How is a variable used

### KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007

KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and

### GEOMETRY COMMON CORE STANDARDS

1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

### ModuMath Algebra Lessons

ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations

### Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below.

Infinite Algebra 1 Kuta Software LLC Common Core Alignment Software version 2.05 Last revised July 2015 Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below. High School

### CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are

### Core Maths C1. Revision Notes

Core Maths C Revision Notes November 0 Core Maths C Algebra... Indices... Rules of indices... Surds... 4 Simplifying surds... 4 Rationalising the denominator... 4 Quadratic functions... 4 Completing the

### Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel

### Senior Phase Grade 8 Today Planning Pack MATHEMATICS

M780636110236 Senior Phase Grade 8 Today Planning Pack MATHEMATICS Contents: Work Schedule: Page Grade 8 2 Lesson Plans: Grade 8 4 Rubrics: Rubric 1: Recognising, classifying and representing numbers...22