MODULE 3 - SPACES IN THE ENVIRONMENT ……………………………………………………………………..…………………………………………....................34 - 38
MODULE 4 - MEASURING AROUND US….……….…………………………………….…………………………………………………………………………………..39 - 44
MODULE 5 - DATA HANDLING ………………..………..…….…………………………………………………………………………………………………...................45 – 50 APPENDIX I - EARNING GRID.………..………..…….…………………………………………………………………………………………………...................................51 – 53
ContentsContentsContentsContents
CCSLC/M/03/2006
i
INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION The Caribbean Examinations Council (CXC) in consultation with policy makers and educators in CXC Participating Territories identified the need for a new programme that will respond to the changing demands of the education sector. A major development is the move by all territories to universal secondary education, and so, to enable persons with a wide range of abilities to benefit from education provision at this level. The decision to implement programmes to achieve universal secondary education is based on an understanding that the region needs a well educated and trained labour force for an increasingly competitive global environment. A sound secondary education foundation is imperative for further education and training at the tertiary and para-professional levels. Several territories, recognizing the need for a programme that will meet the new needs in secondary education, had embarked on the development of national programmes. However, through consultations at the regional level, policy makers and educators recognized that a regional intervention by CXC will have several benefits including cost-effectiveness, standard-setting, portability of certification and regional and international recognition. CXC has responded to the regional need for a new secondary programme that will meet the needs of the majority of students at secondary level. Through the consultative processes employed in syllabus development, a new programme was developed by CXC for first examination in 2007. The new programme which is competency-based comprises a core of subjects – English, Integrated Science, Mathematics, Modern Languages and Social Studies. Through this core, the learner should acquire the knowledge, skills, competencies, values and attitudes that are desired in a secondary school leaver. The core developed by CXC subject panels will be examined by CXC. In addition, learners can gain additional benefit through special programmes that may be added as electives to the core at national level.
Policy makers and educators have noted that, ideally, this core programme could be taken by all students at the stage when they are ready. However, the decision, on who should take the examination and in what year it will be taken, will be decided at national level in consultation with CXC. A person who successfully completes this core should have the foundation for further education and training and for entry level employment. In developing and implementing this programme at the secondary level, CXC, working with its partners, took into consideration the cultural context and the aspirations of regional governments for a well educated and trained labour force to meet the targets set for social and economic development. A sound secondary education which this programme will provide is an imperative as a base for the development of citizens as the most valuable resource of the small states of the region. The main focus of this new programme is derived from the aspirations of regional governments and the Caribbean Community (CARICOM) which acknowledge that education is the route to healthy democracies and sustainable development. The curriculum is, therefore, competency based and encompasses the knowledge, skills, attitudes, values and attributes expected of high school graduates, by regional Governments. Some of these knowledge, skills, attitudes, values and attributes or competencies are generic and cut across all five subjects, whilst others are peculiar to each of the five subjects of the curriculum. The generic and subject specific competencies targeted for development in the curriculum are given below.
Caribbean Certificate of Secondary Level Competence
� CRITICAL THINKING � ABILITY TO FUNCTION IN A FOREIGN LANGUAGE
� INFORMED DECISION MAKING
� MATHEMATICAL LITERACY
� MANAGEMENT OF EMOTIONS � SCIENTIFIC LITERACY
� POSITIVE SELF CONCEPT
� SOCIAL AND CITIZENSHIP SKILLS
� WORKING IN GROUPS � HANDLING CONFLICT � DEALING WITH DIVERSITY AND CHANGE � INDEPENDENT LEARNING STRATEGIES � COMPUTER LITERACY
� TECHNOLOGICAL LITERACY COMPETENCIES The structure of the programme takes into consideration that the attainment of the competencies identified is the result of processes that require life-long learning and that mastery is attained by progressive steps over differing periods of time. Bearing in mind that one of the main purposes of the curriculum is to prepare individuals to participate fully as productive members of society, key competencies have been identified that are essential for daily living with emphasis on the workplace. A Learning Grid (Appendix I) lists the key competencies across the five subjects of the curriculum, identifies a reference number and indicates the subjects or group of subjects that specifically engage the learner in its development.
CCSLC/M/03/2006
iii
OUTCOMES OF THE CURRICULUM The curriculum hinges on the realization that teaching and learning are essential instruments for the development of autonomous individuals who will be able to function effectively as productive members of society. In this regard, the curriculum has identified knowledge, skills, attitudes, values and attributes or competencies that students who master the programme should have attained. These include:
� a positive image of self, family, community, region and world;
� respect for others irrespective of age, class, creed, gender, ethnicity, physical disabilities or nationality;
� an abhorrence of violence in all its forms and commitment to settle disputes through arbitration and conciliation;
� the capacity to understand that individual freedom is consonant with the acceptance of personal responsibility for one’s own actions;
� commitment to ethical and moral societies that recognize equality of opportunity, freedom of expression and association, and the right to fair judicial process.
Main Elements of the Curriculum
� It provides the foundation for further education and training and for entry level employment.
� It provides articulation between and within subject groups offered in the Caribbean Secondary Education Certificate (CSEC) examination by catering for students who continue at secondary school to take General Proficiency examinations in academic or technical and vocational or a mix of academic and technical and vocational subjects.
� It meets the needs of students who may not wish to advance to the CSEC examination, but wish to seek entry-level training for employment on
leaving school.
� It provides opportunity for students who wish to exit secondary school for first level entry jobs and to continue their education and training on the job or on their own out of school.
� It facilitates articulation within the wider school curriculum and responds to the developmental needs of the region.
CCSLC/M/03/2006
1
MATHEMATICSMATHEMATICSMATHEMATICSMATHEMATICS
♦ RATIONALERATIONALERATIONALERATIONALE
♦ AIMSAIMSAIMSAIMS
Mathematics is a precise and concise means of communicating patterns, relationships, ideas and values in a quest for a deeper and better understanding of the world around us. It requires observation, representation, investigation and comparison of patterns in social and physical phenomena.
Mathematics in the Caribbean responds to the broad spectrum of needs of the Caribbean community. Caribbean people need to be numerate and, as such, be able to calculate measure and estimate in a variety of situations. The Mathematics programme of study is, therefore, designed to help Caribbean students to be innovative, to solve problems, communicate logically and to make informed decisions after analyzing data. The programme of study aims to enable Caribbean students to develop basic understanding of mathematics in their daily endeavours, to function effectively in contemporary society and to develop creativity, practical knowledge, resourcefulness, decision making and problem solving capabilities. Students will be equipped to use mathematics for the enhancement of their environment, as well as for the empowerment of self, country and region, in order to be more competitive in an ever-changing world environment. The Mathematics programme generally recognizes that Mathematics teaching and learning may be enriched by approaching content and teaching and learning activities through the use of concrete examples and experiences, as well as, through real-life experiences. If implemented as suggested, the programme would equip all Caribbean students for the world of work or further study, and in general, for life-long learning.
The study of Mathematics is intended to assist students to:
1. develop an appreciation of mathematics and its continued contribution to modern life;
2. develop critical thinking skills and spatial awareness; 3. develop skills to analyze and solve problems arising out of real-
life situations; 4. develop the ability to identify situations where mathematical
skills can be applied; 5. develop investigative and problem solving skills; 6. develop an appreciation of the need to communicate
quantitative data accurately; 7. develop the skills to use appropriate technology to solve
mathematical problems.
CCSLC/M/03/2006
2
♦ GENERAL OBJECTIVESGENERAL OBJECTIVESGENERAL OBJECTIVESGENERAL OBJECTIVES
♦ SKILLS AND ABILITIES TO BE ASSESSEDSKILLS AND ABILITIES TO BE ASSESSEDSKILLS AND ABILITIES TO BE ASSESSEDSKILLS AND ABILITIES TO BE ASSESSED
On completion of the Mathematics programme of study, students should:
1. develop skills to use appropriate mental, written or calculator techniques to solve a variety of problems;
2. develop an appreciation for Mathematics;
3. appreciate that transactions with money are integral to everyday life; 4. develop an appreciation of the value of money, locally and
internationally; 5. understand the need for accuracy and honesty in dealing with
money; 6. develop skills to apply basic computational, estimation and
comparison skills necessary for money transactions; 7. develop skills in collecting, summarising and interpreting data in
different ways; 8. develop the ability to use data to solve problems, make decisions,
and draw conclusions and inferences; 9. develop skills to use statistics and set theory as problem solving
tools; 10. develop and apply geometric properties of straight lines, polygons
and circles; 11. develop computational and estimation competencies in using
The Aims and General Objectives can be attained by developing the related key competencies in the student:
1. apply Mathematics in practical situations; 2. use calculators or any other technological devices as mathematical
tools; 3. interpret patterns, use symbols and make generalizations; 4. read, organize, represent and interpret data; 5. estimate, compute and compare with reasonable accuracy.
CCSLC/M/03/2006
3
♦ ORGANORGANORGANORGANIZATION OF THE IZATION OF THE IZATION OF THE IZATION OF THE PROGRAMMEPROGRAMMEPROGRAMMEPROGRAMME The programme of study is arranged in five Modules, namely: Module 1 - Number and Number Sense Module 2 - Conscious Consumer Module 3 - Spaces in the Environment Module 4 - Measuring around us Module 5 - Data Handling
♦ ASSESSMENT GUIDELINES ASSESSMENT GUIDELINES ASSESSMENT GUIDELINES ASSESSMENT GUIDELINES Assessment is an integral component of the programme of studies. Its major functions include facilitating learning, providing information which may be used by students and teachers in the planning of subsequent instructional experiences, and providing information on the highest level of proficiency demonstrated by the student. Teachers are encouraged to take advantage of the flexible structure of the programme to ensure that students demonstrate mastery of each increment of the programme before going on to the next. A student who has attained mastery should, on any subsequent occasion, and without assistance, be able to demonstrate the highest levels of proficiency on the same or an equivalent task. The assessment for each syllabus comprises two major components: Teacher Assessment (TA) and External Assessment (EA). TEACHER ASSESSMENT (TA) This assessment spans two phases. Phase 1:- Formative Assessment Teachers assess students to identify their areas of strength and weakness. This assessment may be formal or informal, and is usually continuous and integrated with teaching and learning. Some teaching and learning activities are suggested in this programme of study and the assessment tasks may either be designed or sourced by the teacher, or may be selected or adapted from those provided in the assessment column of this programme of study. Information derived from this type of assessment should be used by teachers and students in planning subsequent action. Students should be encouraged to assess themselves (self- and peer- assessment) and, wherever practical, to participate in the planning of subsequent activity. The effectiveness and management of this approach may be enhanced by sharing the assessment criteria with students before the assessment is done, or by engaging them in the development of these criteria.
CCSLC/M/03/2006
4
Phase 2:- Summative Assessment
Teachers assess students in order to create an objective record of the highest level of proficiency demonstrated. Students may be assessed any time after the teacher deems that they have attained mastery. Teachers may also provide exercises which integrate skills across the Modules. The students may be assessed individually or in groups, and the arrangements and scheduling may be influenced by the nature of the task, and logistical and administrative considerations. A single standardized summative task is required for each Module. Each subject has five modules, and for each student, the teacher will submit to CXC a single total score representing the sum of the student’s scores on the five modules. The following three specifications facilitate the standardization of the summative assessments:
(i) A generic task is outlined at the end of each Module. This task provides general specifications, and conditions which must be satisfied by the assessment undertaken by all students. However, within the limits specified, teachers may adapt the tasks to reflect local or individual interests. For each assignment, one example of an adaptation is given.
(ii) A standardized rubric or mark scheme is defined and is to be used by the teacher in scoring all students’ work. This rubric/mark scheme is
designed to clearly indicate the dimensions of interest and the relative importance of each; consequently, it may be used by teachers to verify the appropriateness of their adapted task. While the generic task may be adapted, the mark scheme is not to be adjusted. The same mark scheme is to be used by all teachers and students across all centres and territories.
(iii) It is expected that quality control and monitoring of teachers’ adherence to the specifications will be arranged and managed at local level.
In order to ensure that students have reasonable opportunity to achieve and demonstrate mastery, teachers can afford their students multiple opportunities to retake or resubmit, the summative assessment for any Module. Feedback and suggestions for improvement may be provided between attempts, however, the process should be transparent and objective, and the mark awarded should be indicative of the level of proficiency that the candidate would be able to demonstrate independently. The achievement of mastery is emphasized in this programme; thus, a student will be expected to achieve a minimum of 50% of the marks available for the teacher assessment component that will be completed in preparation for taking the external examination. EXTERNAL ASSESSMENT At any given sitting, candidates may register to write the external examination in one or more subjects. The external assessment will be a multiple-choice examination comprising 50 items. Grading Scheme Scores from the Teacher Assessment (TA) and the External Assessment (EA) will be combined to give a composite score with a maximum of 100. A single subject grade will be reported. The grade boundaries are as follows:
Composite Score Grade
75 - 100 Master
CCSLC/M/03/2006
5
50 - 74
Competent
0 - 49
Developing Competence
Reporting 1. The results of any sitting are valid for a three-year period. 2. A result slip will be provided after every sitting for which a candidate registers for the external examination in one or more subjects.
♦ FORMAT OF THE FORMAT OF THE FORMAT OF THE FORMAT OF THE AAAASSSSSESSMENTSESSMENTSESSMENTSESSMENT Teacher Assessment Five summative Module-assessments – one per Module. External Assessment 50 multiple choice items; each item will have four options. (1 hour 15 minutes) NOTES ON THE EXAMINATION 1. CXC will set and mark the external assessment. 2. The teacher will set and mark the assignments that make up the internal assessment of each Module using the Guidelines provided. 3. The teacher will combine the marks given for each Module to give a single total mark. 4. The teacher will submit the total mark to CXC no later than May 31. 5. CXC will combine the marks earned on the internal and the external assessment to produce the candidate’s overall grade.
CCSLC/M/03/2006
6
6. Three skills will be assessed across the Teacher Assessment and External Assessment:
8. The results of any sitting are valid for a three-year period. 9. A result slip will be provided after every sitting for which a candidate registers for the external examination in one or more subjects.
CCSLC/M/03/2006
7
♦ MODULE 1: MODULE 1: MODULE 1: MODULE 1: NUMBER AND NUMBER SENSENUMBER AND NUMBER SENSENUMBER AND NUMBER SENSENUMBER AND NUMBER SENSE
This Module contains the following topics: (a) Properties of Numbers; (b) Number Patterns; (c) Symbolic Representations; (d) Ratio; (e) Use of the Calculator.
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to: (a) Properties of Numbers 1. distinguish between types of
numbers: a. natural and whole
numbers, b. odd and even; c. prime and composite, d. whole numbers and
integers;
2. read and write numbers in the decimal system up to seven digits;
Natural numbers, whole numbers, odd numbers, even numbers, prime numbers, composite numbers, integers. Web diagrams; Venn diagrams; Classifications. Place value, face value; decimal system.
▪ Teacher and students could discuss the history of Roman numerals, Hindu/Arabic number system and the emergence of zero as an introduction to the Module.
▪ Teachers could initiate discussion on the importance of place value in connection with different number systems.
▪ Teachers could initiate the use of manipulatives, for example, place value charts, to form and compare numbers in the decimal system.
Have students classify natural, whole, even, odd, prime, composite numbers and integers from a given list of numbers. Have students draw web diagrams to show different sets of numbers. For example
All numbers
Integers
Whole Numbers
CCSLC/M/03/2006
8
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
Have students complete worksheets, enter decimal numbers on grids or charts and orally state value of the digits in a decimal number. Teacher could observe students’ use of manipulatives to form and compare numbers in the decimal (denary) system. On worksheets – have students compare numbers in order of size; state the value of an underlined or shaded digit in a given number; write given numbers in words or figures.
operations with: - integers, - money, - decimals, - proper fractions, - being alert to
unreasonable answers;
Decimal, integers, proper fractions, mixed numbers. Addition of up to five- digit numbers; Subtraction of up to five- digit numbers (manually); Multiplication of up to a three-digit number by a three- digit number (manually); Division by a 2 digit number. Rounding to the nearest whole number, nearest ten, hundred; estimated answers before working problems; compare estimation with real solution; calculator (to double-check).
▪ Students could solve routine problems composed by both teacher and students.
▪ Encourage students to use different approaches and strategies to perform operations on different types of numbers.
▪ Provide students with opportunities to explain the approaches used.
▪ Calculators could be used to show the results of performing operations on different types of numbers.
▪ Students could use cricket score sheets to estimate the fraction of total runs scored by particular batsmen. Have students use the results obtained to comment on each batsman’s contribution to the team’s performance.
▪ If available, interactive technology, that
Have students compose their own items and carryout calculations to derive answers. Teacher and students can assess complexity of items and variations of strategies used. Have students draw a chart (for example a flow chart) to show consecutive steps in an operation. Assess their sequencing and accuracy. (If multi-media equipment are available, students can use a projector and a screen to present their ideas). Have students do self and peer-
CCSLC/M/03/2006
9
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to: 5. solve problems involving
integers, fractions, and decimals in real life situations.
would enable students to work with different types of numbers and solve problems, could be used. Certain Websites could afford students this opportunity, for example, http://www.coolmaths4teachers.com; http://www.coolmaths.com; http://www.nctm.org; http://mathsforum.org.
assessment of accuracy of their estimates of fractions of total score made by batsmen in a cricket match. Have students solve a simple problem involving a real life situation. Have students answer questions in a problem solving interview questionnaire set by peers.
(b) Number Patterns 6. recognize patterns in sets
and sequences of numbers; 7. complete and/or extend
sequences according to some given pattern;
8. write multiples and factors
of whole numbers.
Patterns based on addition, subtraction, squaring, halving, doubling and tripling. Sets. Sets based on triangular numbers, perfect squares, primes, even numbers, odd- numbers. Multiples; factors.
▪ Teacher could discuss patterns found in nature, for example, leaves and petal of flowers. Describe and explain patterns using natural language, diagrams, charts or any other means.
▪ Students could observe patterns in buildings.
▪ Students could construct simple models to illustrate patterns.
▪ Teacher and students could find rules to describe given patterns in sequences.
▪ Students could construct patterns using simple rules.
▪ Students could use games, including video games, if available, in which
Have students complete worksheets in which they are required to complete sequences using numbers and diagrams. Have groups of students compose games relating to the topic. Students could be given a sequence of numbers and asked to describe the pattern or vice versa. Have students do a KWL chart (what we Know, what we Want to learn, and what we Learned) out of a group exploration exercise. Assess change in knowledge and teamwork related objectives.
CCSLC/M/03/2006
10
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
finding the most in a sequence is included, for example, snakes and ladders.
▪ Teacher could use peer teaching to help students grasp ideas from peers.
▪ Students could work with manipulatives in which they build rows and columns of objects and explore patterns of factors or multiples of the number of objects in rows and columns. Let them extend such patterns.
▪ Let students work in groups, explore divisibility by certain numbers such as 6 and 9 and record their observations.
(c) Symbolic
Representations
9. use symbols to represent number patterns;
10. use symbols to solve number
problems;
Algebraic terms, expressions. Grouping of terms; Simplification of expressions; values of terms and expressions. Symbolic representation of numbers and expressions; basic operations on algebraic terms; directed numbers and quantities.
▪ Teachers could engage students in representing stacks of bills and or coins of different denomination using symbols. For example, they could represent the value of a stack of 3 five dollar bills and 5 ten dollar bills as 3f + 5t. Have them quote the money value of their piles.
▪ Students could explore different combinations of notes and or coins to give different money values and generate simple problems out of this activity. Students could express distances using symbols for different units. For example, a distance of 3 meters and 5 centimetres could be
Have students assess the creations of their peers. Have their peers judge the effectiveness and usefulness of the representations made. Have students write terms and expressions to represent various quantities.
Have students complete flow charts to show how to solve a problems such as described in the teaching activity.
CCSLC/M/03/2006
11
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to: 11. use an algebraic approach to
solve and verify simple linear equations in one unknown.
represented as 3m + 5cm. Have them carry out various measurement activities and report their results
▪ Teachers could use counters to model integers in problem solving situations. Students could plan, mentally, their arrangement of counters.
▪ Teacher could also use ideas relating to temperatures (below or above zero [0]), sea level (above or below sea level) or money (owing or gaining).
▪ Teacher could use money to generate problems for students to model with both concrete objects as well as mentally.
▪ Teacher could engage students in problem solving activity in which they use both visual representations as well as think through and work out situations mentally. For example, a problem solving activity involving the use of a game is illustrated below:
Middle Tile
Have students verbalize or otherwise represent their thinking to the class. Assess reasoning for example: “I think of a number, multiply by 2, add 1 and my result is 7. What is the number?” Have students construct sample equations and verify the solution. × 2 + 1 = 7 or + + 1 = 7
3
CCSLC/M/03/2006
12
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
▪ Seven tiles and 6 students. Have the six students stand on the tiles with the middle tile free. Three students stand towards the left and the other three students stand towards the right of the free tile (see diagram above). Those on the right move left and those on the left move right. The object of the game is for all those on the left to occupy the tiles on the right and those on the right to occupy tiles on the left. A student could only shift over another if there is a free tile. Have students try this physically as well as plan mentally and or on paper, how they could solve the problem.
▪ Students could start by doing activity with concrete material in which they model equations. For example:
▪ Students could balance blocks of different weights on a flat plane object. The weight of 2 blocks on the left balance with that of 4 on the right as shown in the diagram. Students could draw conclusions about the weight of the blocks from this information.
CCSLC/M/03/2006
13
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
▪ They could do activity on equations involving number counters in which some counters are marked and the others are concealed or unmarked. Students could draw inferences about unmarked or concealed counter values for equality to exist. (See diagram below).
Unknown counters inside
▪ Teachers should present the opportunity for students to think about values of unknown quantities mentally as soon as possible. Additionally, the use of number bonds should be encouraged and problem situations presented.
(d) Ratio 12. write as a ratio the
relationship between two quantities;
13. write ratios in simplest
Ratio; relationship, comparison.
▪ Teachers should emphasize that the only way to write a ratio is 2:3 or 2 to 3.
▪ Students could work in pairs to arrange articles in different columns giving similar ratios.
Have students divide a given quantity according to particular ratios. Have students deduce the ratio, given the total quantity and one share Have students complete recipe charts to
CCSLC/M/03/2006
14
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
form; 14. divide a quantity in a given
ratio.
For example, in the diagram above:
▪ Students could work in groups to put objects in the blank spaces so that the ratio in column 1 is maintained.
▪ Students could explore possible combinations that give the same ratio.
▪ Students could make their own ratios.
▪ Students could design and compare models of real life objects in their environment.
▪ Students could share actual objects in a given ratio.
▪ Students could determine the missing terms in a given ratio.
▪ Students could solve routine and non-routine problems involving simple ratios and proportion.
▪ Students could use the unitary method to solve problems.
▪ Students could solve real life problems arising in Caribbean contexts.
reflect ratios of ingredients.
CCSLC/M/03/2006
15
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to: (e) Use of the Calculator
15. use the calculator to perform basic mathematical operations;
16. use the calculator to obtain
squares and square roots of numbers;
17. read and interpret displayed
quantities on the calculator.
Input key, output, data, display and parenthesis, order of operations.
▪ Teacher and students could discuss the order of operations in relation to the use of the calculator.
▪ Teacher and students could discuss appropriate use of the calculator.
▪ Students could perform calculations without using certain keys. For example, perform the operation 3 × 2 on the calculator without using the ‘×’ key and the ‘2’ key.
Have students use the calculator to perform operations of the form:
2+3 x 6 52 , 20 2 , 902
Have students perform operations with the calculator and the computer ( if available) and verify the answers manually. Have students compare and assess answers of their peers.
SUMMATIVE ASSESSMENT GENERIC TASK Students will compile a portfolio comprising a collection of four activities or investigations relating to Number and Number Sense. The activities and or investigation should include: 1. Number pattern; 2. Number chart; 3. Number puzzle; 4. Use of the calculator.
Each activity is marked out of 20. The students’ mark for Module 1 will therefore total 80. Students’ total mark for the portfolio must be divided by 4.
Scoring Rubric Marks
• Use of basic Mathematical operations 4
• Use of properties of numbers 4
CCSLC/M/03/2006
16
• Outlining the rule/generalization 6
• Apply rule/generalization to extend pattern/make predictions 6 Total 20
1. Number Pattern Example - Sample activity
1st 2
nd 3
rd
pattern pattern pattern
• • •
• • • •
• • •
1 dot 3 dots 6 dots
(a) Outline the rule for determining the number of dots in subsequent patterns in the sequence. (b) Extend the sequence to show the 4th and 5th patterns. (c) Use the rule/generalization to determine the number of dots in the 10th pattern. Rule/Generalization (a) The number of dots in each subsequent pattern is determined by adding 1 additional dot to the number of dots in the previous pattern.
2. Number Chart Activity Build a Number Chart to show the relationship between numbers. Example/Sample activity
Number
Number divisible by
3 9
Sum of digits Is sum divisible by
3 9
37 NO NO 10 NO NO
81 YES YES 9 YES YES
456 YES NO 15 YES NO
567 YES YES 18 YES YES
514
1356
1359
1368
2655
4997
6858
(a) Use the chart to obtain the rule which determines whether a number is divisible by 3. (b) Having studied the pattern in the chart, outline the rule which determines whether a number is divisible by both 3 and 9. (c) Extend the chart to include three 4 digit numbers which are divisible by 3 and 9.
CCSLC/M/03/2006
19
3. Number Puzzle Construct a Number Puzzle which must be solved by performing basic mathematical operations and applying knowledge of properties of Numbers.
Example/Sample Activity
Across 5+7 300+20+27 15x11 39 ÷ 3
Down 99+36 4x6 7x11 20-4 36 ÷ 2 500+20+3
Answer
1 2
3 4
5
6 7
8
1 1 2
2
3 3
4 4
7
5 7
5 1
6 1 6 7
5
8 2
8 1 3
1 3 6
4
8
1 2 5 6 7
CCSLC/M/03/2006
20
4. Use of the Calculator Students will be required to use the calculator to perform operations in a variety of ways. Example/Sample Activity The number 2 on your calculator is damaged and cannot be used. Use a flowchart to show 4 different ways in which you can calculate 24 x 12. Solution
(d) Purchasing and Investment; (e) Rates and Taxes; (f) Wages, Salary and Commission. N.B. Throughout this Module topics of interest and importance are suggested for exploration. Teachers may want to use other relevant areas to investigate. Individual students or groups of students may choose one or two of these to investigate and then share their findings with the rest of the class. Reports from investigations along with other pieces of their work may be used for assessment. Students should be encouraged to include brief comments on their work and experiences at different stages of the Module. Where possible use available technology to enhance the learning and teaching experience.
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to: (a) Percentages 1. identify quantities in their
everyday setting that make use of percentages;
2. write the percentage equivalent
of fractions ¼, ½, ¾, and 1/10 and all its multiples;
3. use correct procedures for
conversions of fractions to percentages and percentages to fractions;
Percentages; conversion of percentages to fractions and fractions to percentages; comparisons (larger, smaller or equal); estimations; percentage increase and decrease (only 25%, 50%, 75% and 100%); use of calculator.
▪ Students could use scores from tests in various subjects to compare their performances. Example: Mary scored 15 out of 25 in History and 15 out of 20 in Science. In which subject did she score a higher percentage?
▪ Students could make a hundred square using egg boxes.
▪ Students could plant seeds in some
Have students complete charts, tables and diagrams relating to fractions and percentages. This should include changing fractions to percentages and percentages to fractions. Have students answer questions to those listed below. A local department store is having a sale. James goes to the store and finds that there is a discount of 25% on television sets. James is interested in a television set that normally sells for
CCSLC/M/03/2006
22
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to: 4. determine percentages of
numbers that are multiples of ten not exceeding 1,000,000;
5. determine rough estimates of percentages not exceeding 100;
6. increase or decrease a number
by a given percentage; 7. make simple comparisons of
percentages of quantities.
boxes, monitor their growth over a period - What percentage of the boxes contained seeds? What percentages of the seeds sprouted?
▪ Students could use newspapers and flyers to discover where, why and how percentages are used.
▪ Students could design an activity in which they shade portions of 10 x 10 grids. They then associate fractions with the shaded regions and make general statements about the corresponding percentage involved.
▪ Students should recognise for
example that 30
16 represents
slightly more than 50%.
▪ Students should make connections between certain percentages and their equivalent functions, for example, 25% - ¼, 50% -½, 75% - ¾, 10% - 1/10.
▪ Students should recognize that percentages, such as, 49% and 51% are close to 50% and can be used as
$800. If it is 25% discounted, how much will he pay for it? Have students complete tables of percentages and explain verbally how their entries are found. Example:
10% 25% 50% 100%
$100 $1000 $10000
Have students do quizzes in which they state the two numbers between which the percentage of a number lies. Have them state their reasoning. Assess reasoning and ability to think about estimates. Have students send instruction cards
CCSLC/M/03/2006
23
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
50% or ½ (one half) for purposes of estimation.
▪ Let students use their hundred squares board to increase and decrease number of squares in different sets. Let them compare added or subtracted number of squares with the number in their original set. Have them draw, construct tables or write steps they carried out in doing their computations.
▪ Skills and knowledge appropriate to achieve objective 7 could be developed simultaneously with comparison of fractions.
▪ Students need to know, for example, that 50% is not the same if it refers to quantities of different sizes or amounts.
▪ The Internet may be used to discover how percentages are applied.
telling someone what to do to increase or decrease a number by a certain percent. Have other students carry out the instructions and give comments. Assess clarity and correctness of procedures. Have students match equal, larger or smaller quantities based on percentage and size from lists of diagrams or pictures. Have them state reasoning and justify through examples.
(b) Currency 8. perform the four basic
operations using money;
9. convert the currencies of one country to another
10. solve simple routine and non-routine problems involving
Currencies of CARICOM territories; other currencies, for example, US$, British pound (£); Euro$, Japanese Yen; operations on money; currency conversion procedures; estimation of
▪ Teacher could give students a homework assignment to write a paragraph on a topic such as, ‘A world without money’. Teachers may select a number of such essays for discussion.
▪ Teacher and students could discuss
Have students make oral and written presentations on the findings into an investigation of purchasing a car from abroad. Presentations should be assessed on the following: content, application of currency conversion and communication (for example, correct use of terms, grammar), organization of
CCSLC/M/03/2006
24
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
money conversions.
values of one currency compared to another; basic operations on currency; conversion charts.
the methods of trading in early civilisations. Student could investigate the emergence of money, as we know it today – the use of credit cards, debit cards or ‘plastic money’.
▪ Students could discuss (1) the most economical method of purchasing a car (2) the advantages and disadvantages of purchasing locally or online. Students should determine the profit made by each dealer.
▪ By comparing the prices of airline tickets at various times of the week and year, students could plan a class trip to a Caribbean destination. Select a country that they see as the most economical to visit.
▪ Students could present arguments to justify purchasing of items at different times of the year or prices or in different countries;
▪ Students could create appropriate currency conversion charts and simple model bank drafts. Students could find out how much banks charge for exchanging currency.
information, summary or conclusion.
Have students complete worksheets based on currency conversions, for example: Roger received US$10 from his mother who is currently living in the USA. If 1US$ = (Jamaica) J$66; how much would Roger receive in Jamaican dollars.
(c) Household Bills 11. calculate a bill given the costs of
a number of items and Unit price estimation; charge bills; electricity bill;
▪ Teacher could encourage students to create a shopping list from a
Have students make up a personal budget for a month given a specified
CCSLC/M/03/2006
25
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
determine the change due after buying a number of items;
12. compare the prices of items to
select the best value for money; 13. solve simple problems involving
household bills.
gas bill; telephone bill; water bill; meter reading; varied rates.
number of items.
▪ Teacher could have students compare the cost of buying lunch at school and preparing lunch at home.
▪ Teacher could set up a small class shop to purchase and sell items. Accurate records of sales and purchases should be kept.
▪ Teachers could take students on a field trip to a utility company. Topics such as:
- capability of companies to
meet the demands of the population;
- methods of conserving
energy may be discussed with employees.
NB: These topics are closely related to
work that may be done in Integrated Science and Social Studies and the teacher may want to draw on the ideas of teachers in these subjects.
▪ Students may: i. use samples of actual utility bills to
calculate charges on various utility bills;
ii. find out the different costs involved
salary. Have students write a paragraph on topics (reflective writing) related to conservation, use and alternative sources of energy. Teacher and students should prepare instrument to assess class projects, for example, for individual and group projects. Instrument should assess: content, creativity, feasibility, organization, communication (correct grammar and spelling). Students should prepare entries based on individual or group investigations related to visits to utility companies. Have students complete worksheets with problems based on utility bills, for example, How many units of electricity have been used, if the meter reading is 24672 and the previous meter reading was 24269? What is the cost of electricity if cost per unit is $1.50?
CCSLC/M/03/2006
26
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
in producing electricity; iii. prepare posters, skits and jingles to
illustrate various aspects of conservation as it relates to utility use;
iv. be asked to indicate what they
learnt from these presentations; v. discuss how wastage of water
affects the water bill.
(e) Purchasing and Investment 14. distinguish between the terms
profit, loss, tax, discount and interest;
15. relate interest to: buying and selling; saving and investing;
16. calculate profit, loss, percentage profit or loss, discount, and discount price, sales tax, sales price;
17. distinguish among the terms principal, cost price, selling price, instalment and deposit;
18. calculate the profit and loss given the cost price and the selling price or percent profit or loss;
19. calculate the cost price given the selling and the profit or loss as a sum of money;
Cost price; selling price; profit; loss; discount price; hire purchase price (hp), cash price deposit, instalments, saving, investing, bank statements, cheques, overdraft, Sales tax (VAT- Value Added Tax, GCT- General Consumption Tax); simple and compound interest; depreciation.
▪ Teacher should include examples in cultural settings of bargaining, beating down price, bartering. Students may discuss in groups ways in which they use money.
▪ Teacher and students should describe and compare the functions of banks, credit unions, mortgage houses and moneylenders.
▪ The teacher and students may establish a class bank or ‘meeting turn’ or ‘partners’ or ‘sou sou’, or ‘box hand’ so that students can save small amounts of money.
▪ Students may be asked to complete bank slips as shown in the diagram overleaf.
To assess knowledge of terms, profit, loss and the other terms, have students draw web diagrams to display the connection between terms and the situations in which they arise. Have them display their charts for peers to assess. To assess students ability to relate interest to buying, selling, saving and investing, have them do flow charts in which they show where interest arises in these transactions. Calculations could be assessed through having students complete missing steps in a procedural approach and having them determine whether or not the inserted step is reasonable for the desired result. Have students do characterizations or tell stories to model procedures to obtain profit and other quantities. Have
CCSLC/M/03/2006
27
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
20. calculate total hire purchase price;
21. calculate selling price given cost price and profit or loss as a sum of money;
22. solve problems involving profit
and loss; 23. solve problems involving hire
purchase; 24. calculate the simple interest
and total amount for a period of terms, including months and years;
25. calculate the amount of an
investment after a period of time, including months and years;
Bill/coin TOTAL X$2 X$5 X$10 X$50 X$100
▪ Students could visit the local store to find out the cash prices of furniture or appliances and calculate the hire purchase prices for these items. Work out the difference between hire purchase price and cash price.
▪ The teacher could invite a small businessperson to share his or her experiences in setting up a business.
▪ Teacher and students should discuss interest as applied in banking, credit unions and other lending agencies, including those in a cultural context. Let class discussion determine the most profitable way in saving money. Encourage role-play and set up models.
▪ Teacher and students could discuss the value of ‘meeting turn’ or ‘partners’ or ‘sou sou’, or ‘box hand’, credit unions, banks and money
them carry out the procedures with actual money and assess their reasoning, application and understanding. To assess problem solving, ask students to model the problem using a chart. Conduct interviews to assess students’ knowledge of what is given, what is required and strategies to obtain a solution. Students could also be asked to critique solutions and strategies presented by teacher and peers. Given a specified sum of money, have students assess whether they have too much, enough or too little money to make purchases in which percentage quantities are to be added or taken out. Assess their ability to make correct judgements and reasonable
CCSLC/M/03/2006
28
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to: 26. calculate the compound interest
for not more than two years (the use of formula is not required);
27. use knowledge of simple and
compound interest to make decisions;
28. calculate depreciation for not
lenders to investors.
▪ Teacher could review using everyday examples, types of bank accounts and use of credit cards.
▪ Teacher and students could discuss the need to be thrifty and honest in dealing with money.
▪ Students could use advertisements from newspapers or flyers to calculate hire purchase prices of household furniture and appliances. Have students compare the price of items, if bought for the cash price rather than on hire purchase.
▪ Students could discuss when simple interest and compound interest are used. Teacher may invite a resource person from a bank to discuss these options. Students (as a group activity) may be assigned an activity in which they borrow then repay at simple or compound interest rates. The more beneficial option may be determined by comparison.
▪ Teacher could use the tape recorder and/or video camera to record the question and answer session with bank personnel and the information collected used for reflection and feedback.
justifications. Let students use knowledge of simple interest and compound interest to make decision related to the activity. Have students complete pen and paper tests involving depreciation, for example: 1. A car is bought for $57000 and
after a year it is valued at $52000. Find by how much the car has depreciated in value.
2. If a car valued at $16000
depreciates by 10% per year, what is its value after two years?
CCSLC/M/03/2006
29
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
more than 2 years (the use of formula is not required).
▪ Students could discuss local situations in which depreciation occurs. For example, machinery such as vehicles. Students could discuss the effect that depreciation has on insuring vehicles. Discussion can be extended to include the cost of maintaining a car. For example, licence, insurance, repairs, gasoline and depreciation.
(f) Rates and Taxes 29. solve problems involving
charges and or taxes given not more than two different rates;
30. distinguish between taxable
income, tax-free income, allowance and income tax;
31. distinguish between income tax and purchase tax;
Income; Income tax; taxable income; taxpayer. Charges; taxrate, electricity rates; telephone rates; water rates.
▪ Students could do role-play with play money, workers, income tax board members and simplified versions of tax forms. Let them deduct tax from different amounts of money, make a list of terms important for income tax.
▪ Students could discuss the reasons for taxation, for example, income tax, national insurance.
▪ Students could draw diagrams to show the steps in income tax deduction. Let them draw cartoons to express feelings of the taxpayer and the tax collector.
Have students draw a flow chart to demonstrate their knowledge of the steps involved in computing income tax based on two rates. For example: Fact: Tax is money from those who get income.
Feelings: I feel hurt if tax is not used on me. Have students demonstrate their ability
CCSLC/M/03/2006
30
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
32. estimate cost of postage.
Postage rate; estimation
▪ Students could prepare letters and packages of different sizes and weights that they post abroad. They could make charts and diagrams and take pictures of packages. They could record approximate weights and sizes and cost of postage based on information from the post office.
to use the terms in context by being able to prepare or draw protest placards about the high taxes paid. Direct the protest to someone in authority. Assess ability to use terms in context.
Assess understanding based on whether these feelings match with what they are associated.
Have students post letters and packages to peers in the class in imaginary countries. Have peers assess whether the postage stamps attached were correct. The teacher could also assess students’ based on their ability to detect incorrect postage stamps. (This needs to be carefully planned).
(d) Wages, Salary and Commission 33. solve problems involving wages,
salaries, overtime and commission;
34. perform simple calculations to obtain total annual salary;
35. calculate overtime salary and total monthly salary;
36. calculate commission due on sales given amount of sales and percentage commission.
Wages, minimum wage; hourly rate; total annual salary; monthly salary; overtime; piece work; commission, national insurance scheme deductions.
▪ Teacher should distinguish between the terms: wages, hourly rate, minimum wage, overtime, basic salary, piece work, salaries and commission.
▪ Students could discuss the advantages or disadvantages of working for wages with tips or salary with commission as compared to a fixed wage or salary.
▪ Students could report on the best way to buy a car if they were receiving a given salary.
▪ Students could be given two or three employment scenarios with
Have students complete worksheets to solve problems involving wages and salaries, overtime and commission.
Have students give oral presentation on their findings from the investigations about salaries and wages of different types of workers.
Have students develop an instrument to assess the group presentations.
CCSLC/M/03/2006
31
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
ASSESSMENT
Students should be able to:
specified conditions such as living expenses, deductions and travel expenses. They should determine which scenario provides optimal benefits.
▪ Teacher and students could discuss why national insurance is paid. The issue of equity as it relates to employer/employee contribution could provide a valuable learning opportunity for critical thinking among students.
Have students prepare a weekly or monthly budget to determine living expenses. Include savings.
SUMMATIVE ASSESSMENT
GENERIC TASK
Students will undertake an investigation in which they make a comparison with two similar items, or two decisions to determine which is more feasible.
The decision must be informed by appropriate calculations and mathematical judgement.
Examples of possible Investigations:
1. which of two similar appliances/equipment/vehicles is, “the better buy” 2. which of two vacation packages is, “better”-“cheaper” 3. build versus buy a house 4. use washing machine or take clothes to the laundry
The task will be assessed in five areas, namely 1. comparison 2. use of mathematical concepts and operations 3. accuracy of calculation 4. decision 5. inference /generalization/conclusion
CCSLC/M/03/2006
32
CCSLC/M/03/2006
33
Scoring Rubric
1. Comparison Marks (a) Sufficiently Reasonable 3 (b) Reasonable but partly sufficient 2 (c) Reasonable but insufficient 1
2. Use of mathematical concepts and operations (a) Use appropriate and varied mathematical concepts and operations 4 (b) Use appropriate mathematical concepts and operations 2-3 (c) Use mathematical concepts and operations 1
3. Accuracy of Calculation (a) Accurate calculations 5-6 (b) Most calculations accurate 3-4 (c) Some calculations accurate 1-2
Sample Task: Determine by calculation which of two stoves: Gas versus Electricity is the “better buy”. 1. Comparison
(a) Cost of acquiring both stoves by cash and hire purchase (b) Cost of operating both stoves- that is, cost of Gas versus cost of Electricity.
2. Use of Mathematical concepts and operations.
Concepts Operations Cash Price Addition Hire Purchase Subtraction Total Cost Multiplication Interest Division Difference Average
3. Accuracy of Calculation
(a) Accurate calculations - 90% - 100%
CCSLC/M/03/2006
34
(b) Most calculations accurate - 75% - 89% (c) Some calculations accurate – less than 75%
4. Decision All cost factors must be taken into consideration, in order to arrive at a sound decision.
5. Inference/Generalization/Conclusion
Compare and contrast each aspect of choice in order to make the final decision.
CCSLC/M/03/2006
35
♦ MODULE 3: MODULE 3: MODULE 3: MODULE 3: SPACES IN THE ENVIRONMENTSPACES IN THE ENVIRONMENTSPACES IN THE ENVIRONMENTSPACES IN THE ENVIRONMENT
This Module contains the following topics:
(a) Lines and Angles; (b) Cardinal Points; (c) Plane Shapes; (d) Solids: Cylinder, Cuboid and Cube; (e) Pythagoras’ Theorem.
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to: (a) Lines and Angles
1. identify types of lines;
2. differentiate between types of angles;
3. calculate unknown angles of
polygons using the properties of the particular polygon.
Line and line segment, Ray, Point. Parallel, perpendicular and intersecting lines; Types of angles: Angles around a point, acute, obtuse, reflex, right, equal, vertically opposite, alternate angles, co-interior (allied) angles, corresponding and adjacent angles. Clockwise and anti-clockwise rotation. 360 degrees.
▪ Students could explore angle size and properties of plane shapes using protractors and pre-drawn shapes.
▪ Students could use spirit levels and set square to test whether tables, chairs, walls, surfaces and other objects are square (90 degrees) corners or are straight (180 degrees or level).
Have students differentiate between lines and line segments. Have students classify a given set of angles by type. Have students sketch examples of various types of angles.
(b) Cardinal Points 4. describe directions
appropriately using cardinal Cardinal Points: North, South, East, West
▪ Teacher could have students facing different directions and then give
Given four places on the school compound, have students give the
CCSLC/M/03/2006
36
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
points. North East, South West, North West, South East.
instructions to move to the left. This scenario creates confusion as each person’s left movement is different. This establishes the need for standardized means of giving direction.
▪ Locating places on the school compound.
location of three of the places relative to the fourth, using cardinal points.
(c) Plane Shapes 5. state the properties of a
given plane shape; 6. use the properties to classify
regular shapes into sets and subsets of polygons.
Plane shapes: quadrilaterals, triangles, circle (regular and irregular shapes within quadrilaterals and triangles)
▪ The teacher could initiate a class discussion on “A world without the understanding of shapes”.
▪ Students could investigate the value of Pi from experiment with circles of varying radii, by having students measure circumference and radii/diameter and making the appropriate deduction.
▪ Students could investigate the ideal shape for efficient packaging of goods in terms of utilization of space. For example, packaging of boxes into a barrel of a given shape and size.
▪ In the local environment, students could observe geometric features in the design of buildings and observe and sketch tessellations in pavings, floorings, gates, fences.
Have students show that they could classify given shapes using Venn diagrams or build trees according to the properties of shapes. Have students estimate diameter of a circle from a given circumference.
(d) Solids: Cylinder, Cuboid and Cube
7. classify solids as cubes, cuboids and cylinders;
▪ Students could collect items from their homes that represent the cylinder, cube
Given a set or objects or photographs of objects classify them in their correct
CCSLC/M/03/2006
37
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to: 8. identify characteristics of
regular solids, edges, vertices and faces;
9. draw nets of these solids.
(universal, subsets, intersection)
and cuboid. Let them investigate and state the characteristics of each solid. (Items could also be identified from school canteen).
▪ Teacher could supply students with sets of solids drawn on graph paper and have them cut out and assembled them.
▪ Students could make decorations for Christmas and other festivals using the nets of solids.
category of solids.
Given solids, draw corresponding nets.
Given sets, identify corresponding solids.
(e) Pythagoras’ Theorem 10. use Pythagoras’ Theorem to
find unknown side in right angled triangles.
Pythagoras’ Theorem, right angled triangle.
▪ Teacher could use available references, for example, encyclopaedia and or Internet to investigate the contribution of Pythagoras to Mathematics.
▪ Students could identify areas in the environment starting with the classroom where right angled triangles are used.
▪ Teacher and students could discuss the use of Pythagoras’ Theorem and right angled triangles in the construction or building industry.
▪ Teacher could provide students with a number of right angled triangles of different sizes drawn on graph paper with squares drawn on each side. Let students calculate the area of the squares (for example, counting the squares).
Have students verbally explain Pythagoras’ Theorem. Have students complete a worksheet to find the unknown side of right angled triangles using Pythagoras’ Theorem.
CCSLC/M/03/2006
38
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
▪ Students could Investigate Pythagoras’ Theorem using semi-circles. They should also investigate and report findings with equilateral triangular shapes on the sides of right- angled triangular shapes.
▪ Teacher could guide students to deduce (by cutting and fitting the 2 smaller squares into the larger square) that the square on the longest side is equal to the sum of the squares of the other 2 sides. This activity must be repeated for non-right angled triangles to establish that Pythagoras’ Theorem only works for right angled triangles.
SUMMATIVE ASSESSMENT
GENERIC TASK
Students will construct a model of a building or a piece of equipment or object using cardboard or Bristol board or any other suitable material. The project may be done individually or in groups. The teacher may provide students with the dimensions of the figure to be modelled.
The model must include: - at least 3 shapes and solids (square, rectangle, triangle, circle, cylinder, cube, cuboid) - at least 3 types of angles (straight, right, acute, obtuse)
CCSLC/M/03/2006
39
Scoring Rubric Mark
Suitable scale 1 Accurate use of Scale 2 Inclusion of 3 shapes/solids 3 Effective/creative use of shapes/solids 3 Inclusion of 3 types of angles 3 Accuracy of angles 3 Accurate labeling of model 3 Overall appearance and aesthetic appeal 2 Total 20
CCSLC/M/03/2006
40
♦ MODULE 4: MODULE 4: MODULE 4: MODULE 4: MMMMEASURING AROUND USEASURING AROUND USEASURING AROUND USEASURING AROUND US
This Module contains the following topics:
(a) The S I System (The International System of Units);
(b) Measurement associated with Plane Shapes;
(c) Solids: Cylinder, Cube and Cuboid;
(d) Temperature;
(e) Time, Speed and Distance.
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to: (a) The S I System (The International System of Units) 1. identify the appropriate
measuring instrument for measuring length and mass;
2. identify the most
appropriate unit for measuring a given quantity;
3. manipulate measuring instruments with a high degree a accuracy;
4. convert from one system of
measure to another.
Ruler, measuring tape, meter, scale, rule, scales. Millimetre (mm), centimetre (cm), metre (m), kilometre (km); gram (g), kilogram (kg); Estimations and conversions. measuring instruments. Converting:
▪ Given various quantities, students could determine the appropriate form of units in which to quote measures. For example, when is it more appropriate to represent a mass of flour as 4kg or when to use 400g.
▪ Teacher could generate a discussion that will lead to the need for standardized measure. For example, the teacher could have 2 or 3 students measure lengths of desks using hand span. They should discover the inconsistencies in the measuring instrument (hand span) used.
▪ Students could estimate a classmate’s height and verify using a metre rule.
▪ Students could estimate the mass of different objects and verify by weighing on a scale.
Given a list of various quantities of mass and length students determine the most appropriate unit for recording and reporting. Given a set of objects, students estimate mass and length where appropriate and verify by measuring and weighing. Use the conversion tables to convert measures in recipes, for example, kilograms to pounds and vice versa, or reduce amounts, for example, if recipe
CCSLC/M/03/2006
41
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
1. kilograms (kg) to pounds (lbs)
2. meters (m) to Yards 3. kilometres (km) to
miles
▪ Students could use measuring instruments graduated in both systems of units and report on the mass of the same object. Do the same for lengths or distances.
▪ Students could dramatize one or more of the following: what will happen without uniform units of measurement and appropriate instruments with respect to taking medications, purifying water, and building structures.
▪ Students could design a conversion table for each unit and across units, for example, grams to kilograms; equivalence with teaspoon/ tablespoon/drop.
for 4 people and it is needed for 2 people instead, then convert kilograms to grams. Where possible, have students write a small programme to do the conversions. Have students complete tables to show equivalent measures of length and mass using different units as shown in the example below.
1km 1000m 1m 100cm 2km --- -----
(b) Measurement associated with Plane Shapes 5. find the perimeter and the
area of regular and irregular plain shapes;
Perimeter of triangles, circles, quadrilaterals (square, rectangle) Centre, radius, diameter, chord, circumference and semicircle.
▪ Students could explain how they would find the distance around an irregular and regular shape, for example, school buildings.
Have students design a flow chart to give instructions on how to find the area and perimeter of given shapes.
6. solve problems relating to plane shapes.
Units)2 Area of triangles, circles, quadrilaterals (square, rectangle) Centre, radius, diameter, chord, circumference and semicircle.
▪ Students could use car park in the school yard to investigate how many cars can be parked in the yard without touching one another and with the flexibility to manoeuvre safely and comfortably.
CCSLC/M/03/2006
42
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
▪ Students could use graph or grid paper with shapes drawn to establish ways of finding area by counting squares. Draw other shapes to establish similar rules.
(c) Solids: Cylinder, Cube and Cuboid 7. calculate the surface area
and volume of cylinder, cube and cuboid;
8. solve practical problems
relating to surface area and volume;
9. make reasonable estimates
of volumes.
Surface area, volume of solids. Measuring liquids in millilitres, litres. Convert between gallons and litres.
▪ Given the capacity of containers, for example, capacity of water tank in gallons, students convert to litres.
▪ Students could apply their knowledge of surface area and volume to solve practical problems, for example, given the volume of an aquarium, students estimate how many 2 litre bottles of water will be required to fill the aquarium completely. They could assess the accuracy of their estimates by carrying out the filling exercise and comparing the estimate with the result from the experiment.
▪ Students could distinguish between capacity and volume by solving problems that involve making reasonable estimates of space, and the number of objects that could realistically hold in a given space.
▪ Students could classify items that have volume only, and those items that have capacity only. They should compare the capacities of various containers using standard and non-standard units.
▪ Teacher could distribute various objects
Have Students find the surface area and volume of given solids.
CCSLC/M/03/2006
43
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to:
(cuboids and cylinders, for example, toilet rolls, cans, boxes) to the students and have them determine the surface area of each.
(d) Temperature 10. measure temperature using
a thermometer; 11. convert from Celsius to
Fahrenheit and vice versa; 12. make reasonable estimate of
temperature equivalent on Celsius and Fahrenheit scales;
13. given temperature in Celsius
give reasonable estimate in Fahrenheit and vice versa.
Celsius; Fahrenheit; thermometer, temperature estimates. - safe use of
thermostat; - ways of reading body
temperature; - types of thermostat; - use of clinical
thermostat.
▪ Students could examine the impact of temperature on: - Food storage
- The body
▪ Students could design a conversion table by taking each other’s body temperature; temperature of water under different conditions (room, boiling, ice) using thermometers that have Fahrenheit and Celsius scales.
Using the conversion chart developed in class, have students complete a table.
(e) Time, Speed and Distance 14. add times and make
calculations involving time differences;
15. convert between 12 hour and 24 hour clocks;
12 and 24 hour clocks. Time zones and lines of longitude. Speed = Distance Time
▪ Students should read time in 12 and 24 hour formats.
▪ Students could calculate the time that lapses between leaving home and arriving at school. If they are consistently late then make time adjustments where possible. The importance of punctuality can be discussed at this point.
▪ Students could design tables showing
Have students complete tables to show comparison between times in at most three countries. Have students use conversion table developed in class to complete
CCSLC/M/03/2006
44
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
ASSESSMENT
Students should be able to: 16. calculate speed given
distance and time;
17. solve problems relating to time, distance and speed.
time in different countries based on time zones.
▪ Students could design conversion tables for 12/24 hour clock and, using both tables, design arrival charts for passengers taking flights from one country to at most 5 destinations around the world. Dual time of arrival could be quoted.
▪ Students could time each other running or walking 50yd or 100m. Estimate the speed.
worksheets to show relationship between 12 hour and 24 hour clocks. Have students perform simple calculation involving time, distance and speed.
SUMMATIVE ASSESSMENT
GENERIC TASK Students will undertake an investigation in which they use knowledge of the concepts of measurement. They will be required to keep a log of the activities undertaken.
Example/Sample Assessment Task
Students will investigate the amount of water wasted by or lost through a dripping tap.
1. Estimate how much water drips from the tap in 10 minutes. Indicate the method you used for arriving at your estimate.
2. Use an appropriate measuring instrument to test the accuracy of your estimate.
3. Repeat for 15 minutes, 45 minutes.
4. Use your results to find how much water would drip away in a day, a week and a month.
CCSLC/M/03/2006
45
5. Compare your results for a month in both metric and imperial measure.
6. Given the current cost of water in your country, calculate the cost to the consumer of the wasted water over one year.
Scoring Rubric Marks Appropriate choice of instruments 1 Appropriate Unit of Measurement 1-2 - > 75% appropriate usage 2 - < 50% appropriate usage 1 Reasonableness of estimates 1-2
- estimates very reasonable 2 - estimates reasonable 1
Accurate recording of measurements 1-3 - record measurement with a high degree of accuracy 3 - record measurement with some degree of accuracy 2 - record measurement 1 Calculations 8 - conversion 1-2 - use of mathematical operations 3 - computation 2 - reasonableness of solution 1 Decision /Conclusion/Inferences/Generalization (D/C/I/G) 4 - informed D/C/I/G supported by calculation 3-4 - reasonable D/C/I/G supported by calculation 1-2 Total 20
This Module contains the following topics: (a) Data Collection; (b) Organization of Data; (c) Typical Measures; (d) Interpretation of Data; (e) Chance and Risk.
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
(a) Data Collection 1. identify a typical
representation of a given population;
2. use different data collection
methods to obtain data; 3. make and use tally charts to
count items in a data set;
Population, samples and sampling, bias. Data collection methods: direct measurement, questionnaire, observation, interview, recording (electronic and otherwise). Classifying, grouping, counting, occurrence, tally chart.
Suggested introductions
▪ In a study about the class - students drawn from the class is the sample. The whole class is the population. However if a study is about boys in the school all boys in the school is the population. Boys drawn from the class are part of a sample.
▪ Compare sampling with taking a taste of a drink from a bottle or a piece of cake from a whole cake.
▪ Let students take samples of various items and state the population.
▪ Collect data relative to students in class: - their height, shoe size, day on
which they celebrate birthday this year.
Have students give an example of a good representation of their school if asked to attend an independence parade. Have students select from a set of data collection methods, the most appropriate one that may be used to obtain data relevant to students’ height. Have students use a tally chart to count the occurrences of each vowel in a given paragraph. Have students exhibit (class) samples of all data collected. Have students select piece(s) of their work that may be used to complete the final assessment for this Module.
CCSLC/M/03/2006
47
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
▪ Actual collection of data – rainfall, months in which students were born.
▪ Simple data collection and presenting tasks such as displaying a check of the frequency of each vowel in a given paragraph.
(b) Organization of Data 4. tabulate data extracted from
familiar sources in the immediate surroundings;
5. construct simple bar charts,
line graphs and ungrouped frequency tables.
Simple ways of organising and classifying data: Pictograph Frequency tables (ungrouped) Raw data Tally chart Line graphs Bar charts Language: occurrence, most of the time, some times, frequency.
▪ Students could work in groups to organise raw data in different ways. For example, given a set of data on rainfall over a period of months, one group of students may be asked to present the information in the form of a line graph, another group may be asked to construct a vertical bar chart, while another construct a horizontal bar chart.
▪ Students may then exhibit or display the different representation and or organisation of the same data as produced by each group.
▪ Teacher and students could study and discuss statistical representations as found in textbooks, newspapers.
▪ Students could construct tables, charts to highlight occurrences at school, within country, for example, road accidents, crime, absence from school, tourist arrival.
▪ Where available, teacher and students could use computer software such as
Have students construct a frequency table from a given set of raw data or tally chart. Have students construct line graphs or bar charts from given frequency tables. Have students construct frequency tables from given bar charts or pictographs. Have students construct a frequency table given bar charts or vice versa.
CCSLC/M/03/2006
48
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
Excel to input data and generate bar charts and other graphical representations.
(c) Typical Measures 6. state the minimum and
maximum value in a set of values;
7. identify extreme values in a
data set; 8. determine the range, mean,
median, mode of a data sets;
9. use calculation to show how an extreme value may affect the mean of a set of scores;
10. make relevant and
appropriate comments about the mean, range, median and mode;
Comparison, typical value, maximum, minimum. Organization, smallest to largest, frequency, most often, occurrence, majority, minority Mode, mean, range, median.
▪ Teacher and students could look at terms such as always, sometimes, most of the time. Discuss situation in which they are used; Do they mean the same thing to different users?
▪ Teacher could discuss situations relating to the use of these statistical measures (mean, median, mode, range).
▪ Teacher and students could discuss why a teacher was more likely to use the mean score to determine whether a student pass or fail?
▪ Students could calculate averages, for example, what is the mean score of 6, 4, 6, 8, 7.
▪ Teacher could give examples of real life data in which there are extreme values and state how they affect the mean.
▪ Teacher could use situations to discuss the utility and appropriateness of each average
▪ Teacher and students could discuss why a shoe vendor was most likely to use the mode.
Have students state the maximum and minimum value from a given set of scores. Have students pick out an extreme value from a given source. Have students state the range of a set of data and or comment on how extreme values affect the range. Have students determine the mode, given a set of raw scores, a frequency table or a bar chart. Have students determine the median of a given set of data (such data set may be a total, an odd or even number of scores, and may or may not be arranged in order of size). Have students calculate the mean of a set of scores with and without an extreme value and to comment on how the extreme value affects the mean.
CCSLC/M/03/2006
49
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
(d) Interpretation of Data 11. interpret information in
frequency tables, ungrouped data, bar chart, pie charts and line graphs;
12. identify patterns (trends)
from a given set of data; 13. draw simple inferences from
data; 14. use data to make
predictions; 15. extract information from
pictographs, bar charts, frequency tables.
Summarising information; making inferences; drawing conclusions.
▪ Teacher and students could visit Documentation Centre – Statistical Institute in one’s country to source relevant data.
▪ Teacher and students could source for study in class, statistics on cultural, environmental, social and health issues in student’s country or region, for example, deforestation, HIV/AIDS cases, migration, tourism – look at patterns trends; make predictions; discuss implications for health, the environment, future planning, education.
▪ Teacher could analyse data; making predictions; decision making; use data previously collected by students: heights of students in the class; rainfall over a period of a week or month; data from statistical departments.
▪ Students could collect bar charts and line graphs found in local newspapers and magazine.
▪ Teacher and students could critically analyse other persons’ interpretation of the same data
▪ Teacher could assist students to develop and use guidelines to examine and make critical judgements about whether data are organized and presented properly.
Have students answer questions based on information presented in bar charts, line graphs, and simple pie chart consisting of no more than five sectors. For example, based on information presented in a line graph showing rainfall over a six month period, students may be asked to state which month had the highest rainfall; calculate the difference in the amount of rainfall between the first three and the last three months. Have students make predictions based on observed trends. Pencil and paper test. For example, students may be given a bar chart with five bars and asked to draw a sixth bar based on the pattern as seen in the first five bars. Have students comment orally or in writing on trends depicted in data.
CCSLC/M/03/2006
50
SPECIFIC OBJECTIVES
CONTENT
SUGGESTED TEACHING AND LEARNIG
ACTIVITIES
ASSESSMENT
Students should be able to:
(e) Chance and Risk 16. identify and give examples
of events that have a chance of occurring, those that will definitely occur and those which have no chance of occurring;
17. use the idea of risks to make
sensible decisions.
Chance; probability range (0 to 1). Risk possibility impossibility decision making Language: always, often, most likely, maybe, sometimes, never.
▪ Teacher and students could discuss the likelihood of different events occurring. - I will die one day - I will fly one day - It will rain on a cloudy day - I will win the lottery
▪ Teacher could carry out simple experiments, for example, tossing coins, rolling die and pulling a card from a deck.
▪ Teacher and students could discuss the probability of pulling a student’s name from a box containing the names of all students in the class.
▪ Students could create charts to display results of experiments.
▪ Teacher could discuss the relationship between risks, choices and planning.
▪ Teacher and students could make predictions and check at a future date.
Have students carry out a simple performances task, for example, making a simple plan in which risk is involved. Have students indicate on number line, ranging from 0 to 1, the likelihood of something happening.
SUMMATIVE ASSESSMENT
GENERIC TASK Students will conduct a small investigation from which they will produce a written report of about 500 words. The report will be assessed in five areas, namely: - collection and organization of data - interpretation of data
CCSLC/M/03/2006
51
- conclusion - inferences - presentation Scoring Rubric Marks Collection and Organization of data 3 - appropriate use of tables and charts 2-3 - use of tables and charts 1 Use of appropriate forms 4 - use a variety of pictorial forms 3-4 - suitable labelling of pictorial forms 1-2 Interpretation of data 4 - correct interpretation of data 3-4 - reasonable interpretation of data 1-2 Conclusion 4 - valid conclusion based on data 3-4 - reasonable conclusion based on data 1-2 Inference 3 - draw reasonable inference based on data 2-3 - draw inference based on data 1 Presentation 2 - overall cohesiveness of report 1-2 Total 20
Key skills and abilities Learners will be able to:
Eng. Mod. Lang.
Math. Int. Sc. Soc. Stud.
Eng. 1 � communicate information, orally and in writing ● √ √ √ √ Eng. 2 � read and interpret information at the literal and
inferential levels ● √ √ √ √
Eng. 3 � evaluate information read and viewed ● √ √ √ √ Eng. 4 � source relevant information ● √ √ √ √ Eng. 5 � respond appropriately to information read and
viewed ● √ √ √ √
Ability to communicate orally and in writing
Eng. 6 � write appropriately for a variety of purposes ● √ √ √ √ Math. 1 � add, multiply, subtract and divide √ Math. 2 � use calculator to perform basic mathematical
operations ● √ √
Math. 3 � convert fractions to percentages and percentages to fractions
●
Math. 4 � calculate profit, loss, percentage profit or loss, discount and discount price, installment and deposit
●
Math. 5 � calculate the amount of an investment after a period of time
●
Math. 6 � determine the cost of posting letters and parcels, locally, regionally and globally
●
Math. 7 � convert major international currencies into local and regional currencies
●
Math. 8 � calculate salaries and commissions ● Math. 9 � calculate utility bills ● ● Math. 10 � complete income tax forms ● Math. 11 � make and use tally charts ● √ ●
Mathematical literacy
Math. 12 � extract information from pictographs, bar charts and frequency tables
● √ ●
CCSLC/M/03/2006
53
CURRICULUM LEARNING GRID
Subjects of the Curriculum KEY COMPETENCY
Ref. No.
Key skills and abilities Learners will be able to: Eng. Mod.
Lang. Math. Int. Sc. Soc.
Stud. Math. 13 � determine range, mean, median and mode ● ● Math. 14 � use data to make predictions ● ● ● Math. 15 � estimate the size of standard units of length and
mass ● ●
Mathematical literacy (cont’d)
Math. 16 � make reasonable estimates of areas and volumes ● ● Mod. Lg. 1
� convert short, meaningful conversation into Spanish or French
●
Mod. Lg. 2 � respond appropriately to brief instructions given in Spanish or French
●
Mod. Lg. 3 � read, understand and respond appropriately to material written in Spanish or French
●
Ability to function in a foreign language
Mod. Lg. 4 � have meaningful dialogue with a native speaker of Spanish or French
●
Int. Sc. 1 � use appropriate equipment to measure length, weight, density, volume and temperature
● ●
Int. Sc. 2 � observe precautions related to the use of drugs ● ● Int. Sc. 3 � observe precautions related to diseases including
sexually transmitted diseases ● √
Int. Sc. 4 � take care of bodily organs including skin, breast, testes, lungs and teeth
● √
Int. Sc. 5 � adhere to a nutritionally- balance diet ● √
Science Literacy
Int. Sc. 6 � care for the natural environment ● √ Soc. St. 1 � cope with stressful situations ● Soc. St. 2 � behave in a socially-acceptable manner ● Soc. St. 3 � use strategies to manage conflict ● Soc. St. 4 � differentiate between fact and opinion ● Soc. St. 5 � relate positively to family, friends and groups ● Soc. St. 6 � conduct a healthy life-style √ ● Soc. St. 7 � cope with domestic and social problems ● Soc. St. 8 � apply for a job or create a business ●
Social and citizenship skills
Soc. St. 9 � complete all types of forms including job application forms
● ● ●
CCSLC/M/03/2006
54
CURRICULUM LEARNING GRID
Subjects of the Curriculum KEY COMPETENCY
Ref. No.
Key skills and abilities Learners will be able to:
Eng. Mod. Lang.
Math. Int. Sc. Soc. Stud.
Soc. St. 10 � interpret and use information pertaining to the rights and responsibilities of workers
●
Soc. St. 11 � observe desirable consumer practices ● ● Soc. St. 12 � contribute to national goals and aspirations ● Soc. St. 13 � prepare a budget √ √ ● Soc. St. 14 � cope with changes brought about by globalization
and trade liberalization √ ●
Social and citizenship skills (cont’d)
Soc. St. 15 � cope with peer pressure resulting from the youth culture
●
TL 1 � use modern technologies to conduct research and solve problems
√ √ ● ● ●
TL 2 � use modern technologies to conduct consumer transactions
● ●
TL 3 � use computer technology to access and evaluate information
● ● ● ● ●
Technological Literacy
TL 4 � cope with the changes brought along by the use of new technologies in medicine, agriculture, transportation, manufacturing, energy and communication
√ √ √ ● ●
KEY TO GRID
Eng = English Mod. Lang. = Modern Languages Math. = Mathematics Int. Sc. = Integrated Science Soc. Stud. = Social Studies TL = Technological Literacy
● indicates the subject that specifically engages the learner in the development of the competency √ indicates the related subjects that engage the learner in the development of the competency
![Educated Jan2012[1]](https://static.documents.pub/doc/80x56/577d22731a28ab4e1e976a46/educated-jan20121.jpg)
