ST. KITTS AND NEVIS MINISTRY OF EDUCATION CURRICULUM DEVELOPMENT UNIT
PRIMARY SCHOOL INTERIM CURRICULUM MATHEMATICS GRADES 5 - 6 SEPTEMBER 2015
K
INTRODUCTION AND ACKNOWLEDGEMENT The Curriculum Development Unit (CDU) has embarked upon a review of the curriculum implemented from 2000 - 2003 for Language Arts, Mathematics, Science and Technology and Social Studies. This is a mammoth undertaking that requires thoughtful planning. Nonetheless, it is a most necessary and overdue mandate. Over the years, through our visits to schools, interactions with teachers and principals, and other consultations, we have been able to identify some of the most glaring gaps in the curriculum, especially with regard to scope and sequence, which required our immediate attention. During the 2014 – 2015 academic year, we made a number of indispensable adjustments, which we are confident will help address the most glaring gaps in the interim as we proceed with the comprehensive review. This effort has resulted in what we refer to as the National (K - 6) Interim Curriculum for Language Arts, Mathematics, Science and Technology, and Social Studies for implementation in September, 2015 at all schools in the Federation of St. Kitts and Nevis. This National (K - 6) Interim Curriculum features set standards per grade and subject, clarified scope and sequence, updated content, alternative modes of assessments, and areas for integration, among others. The Interim Curriculum is a product of the combined effort of Subject Coordinators, Education Officers with responsibility for the four subject areas in both St. Kitts and Nevis, Lecturers with responsibility for the four subject areas at the Teacher Education Division (TED) of the Clarence Fitzroy Bryant College (CFBC), select teachers of Grades K – 6, select Heads of Departments at some of our Secondary Schools, our primary school principals, and other stakeholders with the relevant expertise. They have collectively prepared and / or vetted the various drafts of this most critical document, and assisted with the training sessions.
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We commend the efforts of our stakeholders. We remain grateful for their invaluable contribution to this most timely effort. We look forward to working with them in completing the overall revision of the curriculum.
The Interim Curriculum Committee members who contributed to this milestone for the subject specified are listed below: Mathematics Interim Curriculum Committee Members Sharon Burnham Cecil Diamond Sylvia Fahie Stewart Joseph Stanley Knight Lynda Moving James Morris Stanley Nisbett Natalie Phipps Laurence Richards Donato Wharton Jr.
Affiliation Teacher, Tyrell-Williams Primary Lecturer, Teacher Education Division, CFBC Education Officer responsible for Mathematics, Department of Education, Nevis Teacher, Newton Ground Primary School Former Education Officer responsible for Mathematics, St. Kitts Former Mathematics Coordinator, CDU Mathematics Coordinator, CDU Teacher, Tucker-Clarke Primary Teacher, Edgar T. Morris Primary School Education Officer, Department of Education, Nevis Teacher, Washington Archibald High School
Our hearts are indeed filled with thankfulness for your interest, commitment and availability during this process.
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…………………………………..…………………………………………….. Dr. Eva Donelly Bowrin Director, Curriculum Development Unit – Teachers Resource Centre
TABLE OF CONTENTS The Mathematics Curriculum
v
Mathematical Processes
vi
Instructional Strategies
vii
Recommended Time Allocation by Sessions
viii
Other Considerations for Curriculum Implementation
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Recommended Time Allocation by Strands
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General Statement of Learning Outcomes
1
General Objectives
2
Grade 5 Numbers & Number Sense
4
Shapes & Spaces
9
Patterns & Relations
11
Statistics & Probability
12
13
Shapes & Spaces
18
Patterns & Relations
20
Statistics & Probability
21
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Numbers & Number Sense
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Grade 6
THE MATHEMATICS CURRICULUM The St. Kitts and Nevis mathematics curriculum will strive to provide learning experiences to enable all students to appreciate the significance of mathematics to life and to gain skills and knowledge needed to function adequately in today’s society. Rationale Mathematics is being used more increasingly in other subject areas such as Social Studies, Science and Technology. Children need to master mathematical concepts and skills to find answers to questions and problems which arise in everyday life. Children need to acquire and develop knowledge of shapes and measures, the ability to calculate and to see and use relationships. Mathematics can be a means whereby children are helped to think for themselves as they learn through their own activities and enjoy what they are doing. Mathematics can help develop an inquiring mind. General Aims
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To assist pupils to: Understand and use mathematical language and symbols. See patterns and relationships in math and in their environment. Find common elements among Mathematical concepts. Search for, recognize and generate mathematic al ideas. Appreciate the role and application of mathematics in their daily activities. Understand the structure and organization of mathematics while developing proficiency in its processes and operations.
MATHEMATICAL PROCESSES 1. Communication Express mathematical ideas with clarity using listening & speaking, reading & writing and viewing & modelling skills.
3. Reasoning Develop skills in identifying, describing and creating patterns. Represent real-life situations as mathematical relationships. Conjecture and validate mathematical ideas. Justify thinking processes and solutions to problems. 5. Visualization Develop concepts by using mental images and diagrams. Demonstrate an understanding of concepts and procedures by using mental images and diagrams. Use models and a variety of ways to represent mathematical ideas and concepts.
2. Connections Explore links across the various units, topics and strands. Examine links between Mathematics and other disciplines. Link mathematical processes to each other. Establish links among the concrete, pictorial and symbolic modes of representing mathematical ideas. Connect mathematical skills and concepts to real-life experiences of children and the evolving needs of society. 4. Problem Solving Solve routine and non-routine problems. Verify solutions to routine and non-routine problems. Present multiple solutions to problems where applicable. Create problems based on their experiences.
6. Estimation & Mental Mathematics Use arithmetic and measurement skills to estimate in a variety of real life situations.
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Use computing technology and calculators to promote mathematical learning
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7. Technology
INSTRUCTIONAL STRATEGIES 1. Whole Class Discussion This is typically used to introduce a new concept or to determine students’ ideas for problem-solving. 2. Small-Group Exploration This cooperative strategy for problem-solving might be followed by students presenting solutions to the class. 3. Individual Exploration This strategy helps to affirm students’ knowledge by allowing the time to construct their understanding of concepts. 4. Questioning The use of non-threatening, carefully worded questions elicits explanations and reveals misconceptions. 5. Embedding Review in a Problem-Solving Context This strategy solidifies learning by using problems that encompass numerous skills and concepts previously learned. 6. Mathematical Explorations with Technology This strategy provides simulated real-life experiences which assist students in acquiring problem-solving skills.
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7. Differentiated Instruction This strategy maximizes learning for all students by accommodating individual learning needs/styles so that each student is challenged but not overwhelmed.
RECOMMENDED TIME ALLOCATIONS BY SESSIONS (PERIODS) Grade Level K–2 3–4 5–6
Session (Period) Duration 35 minutes
Total Weekly Sessions 5 7 8
Number of Single Sessions 5 3 2
Number of Double Sessions 0 2 3
OTHER CONSIDERATIONS FOR CURRICULUM IMPLEMENTATION 1. 2. 3. 4.
Integration of mathematical processes within each strand is encouraged and expected. More time should be devoted to the development of concepts. Less time should be spent on rote calculation, drill and practice and paper & pencil calculations with relatively large numbers. A minimum of 50% of available time within all strands should be dedicated to activities related to the processes of problem-solving, reasoning and connections. 5. Estimation and mental mathematics, paper & pencil exercises and the appropriate use of technology should become an integral part of the teaching and learning processes. 6. Manipulatives should be used to introduce concepts. 7. Manipulatives should be gradually developed from the concrete to semi-concrete or pictorial and then to the symbolic. The use of virtual manipulatives should also be incorporated.
RECOMMENDED TIME ALLOCATIONS BY STRANDS The curriculum is organized into four strands. Consideration must be given to specific strands. The charts below provide some guidelines for time allocations with respect to the strands. Shape & Space 20
Patterns & Relations 10
Statistics & Probability 20
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Number 50
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Strand Time Allocations (%)
GENERAL STATEMENT OF LEARNING OUTCOMES
Middle Primary Level
Upper Primary Level
K–2
3–4
5–6
By the end of Grade 2, the learner should demonstrate appreciation and understanding of key concepts and skills in the following areas: Numbers and Number Sense (whole numbers up to 999 and the four basic arithmetic operations including money, ordinal numbers up to 31st, basic concepts of fractions); Shape & Space (length, time, mass, capacity); Patterns (numerical and geometric patterns); Statistics & Probability (data collection from surveys, representing information for up to 20 subjects in tally charts, bar graphs and pictographs using one to one correspondence, outcomes).
By the end of Grade 4, the learner should demonstrate appreciation and understanding of key concepts and skills in the following areas: Numbers and Number Sense (whole numbers up to 99 999, decimals up to hundredths, the commutative, associative and distributive properties, factors including the HCF up to 99, multiples including the LCM, prime and composite numbers up to 50, ordinal numbers up to 100th, fractions); Shape & Space (length, time, mass, capacity, perimeter of polygons – with no more than 8 sides, area of squares and rectangles, types of lines, properties of cubes, cuboids, spheres, cylinder and cones, properties of quadrilaterals, nets of solids, classification of angles, measurement of angles of 10-degree intervals); Patterns (creating, modelling, predicting with geometric shapes, objects, pictures and numbers); Sets (elements, equality, intersections, subsets, set notation; Statistics & Probability (data collection from experiments and observations, tally charts and frequency tables, bar graphs and pictographs using 1 unit to represent 2, 5 or 10 with guidance, the mode, outcomes).
By the end of Grade 6, the learner should demonstrate appreciation and understanding of key concepts and skills in the following areas: Numbers and Number Sense (whole numbers up to 9 999 999, decimals up to thousandths, square numbers, rounding to the nearest 10 000, factor trees, four operations, unequal sharing, multiplying and dividing with fractions); Shape & Space (length, time, mass, capacity, perimeter of polygons – with no more than 8 sides, area of squares, rectangles, triangles and composite shapes, types of triangles, constructing angles up to 180 degrees); Patterns (creating, modelling, predicting with geometric shapes, objects, pictures and numbers); Sets (elements, equality, intersections, subsets, set notation; Statistics & Probability (data collection from experiments and observations, tally charts and frequency tables, bar graphs and pictographs using 1 unit to represent 2, 5 or 10 with guidance, the mode, outcomes).
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Lower Primary Level
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Descriptions of Learning Outcomes by Grade Groups
GENERAL OBJECTIVES STRAND NUMBERS & NUMBER SENSE
SHAPES & SPACES
PATTERNS & RELATIONS
STATISTICS & PROBABILITY
PATTERNS
DATA COLLECTION & ANALYSIS
SUB-STRAND NUMBER CONCEPTS NC1. Understand the meaning of numbers, the ways of representing them and the relationships among them.
MEASUREMENT M1.
Understand the measurable attributes of objects, non-standard and standard units and the processes of measurement.
P1. Identify, create and analyze numerical and non-numerical patterns
ST1. Formulate and identify questions that can be answered with data. ST2. Make inferences and predictions based on data ST3. Collect, organize and represent data.
Use appropriate instruments and simple mathematical formulae to determine measurements.
ST4. Analyze data using appropriate statistical methods
2
M2.
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NC2. Use mathematical models to represent and understand quantitative relationships.
GENERAL OBJECTIVES STRAND NUMBERS & NUMBER SENSE
SHAPES & SPACES
PATTERNS & RELATIONS
STATISTICS & PROBABILITY
SETS
PROBABILITY
SUB-STRAND NUMBER OPERATIONS NO1.
NO2.
Assign appropriate meanings to arithmetic operations on numbers and understand the relationships among the operations.
Develop computational and estimation skills.
GEOMETRY G1. Examine the properties of 2D and 3D geometric shapes and formulate arguments about geometric relationships.
S1.
Use appropriate rules and language when constructing, describing and interpreting sets.
G2. Analyze situations using symmetry.
S2.
Use the Venn diagram to represent and interpret relationships between sets.
ST5. Understand and apply concepts of probability.
G3. Solve problems by visualization and modelling with geometric objects.
Appreciate the role of money in assigning value or worth to an item or service
MO2.
Identify local currency
MO3.
Perform computations for simple financial transactions
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MO1.
3
MONEY
GRADE 5 STRAND: NUMBERS & NUMBER SENSE NUMBER CONCEPTS GENERAL OBJECTIVES Content
NC1, NC2
Specific Objectives
1.1. Communicating 1. Identify whole numbers up to with numbers 999 999 (0 – 999 999)
Code G5WRTNUM
2. Read and write whole numbers up to 999 999 in: (a) symbols (b) words 3. State word names when given whole numbers with up to 6 digits 4. State whole numbers given word names for numbers up to hundreds of thousands 1.2. Place value
1. State the value of any digit in a 6digit whole number
G5PLACEVALUE
2. State the value of any digit in a decimal number up to thousandths 1.3. Expanded form 1. Write 6-digit numbers in expanded form
G5EXPANSION
2. Write 6-digit numerals given the expanded form 1. Compare (a) whole numbers with 6 or less digits; (b) decimal numbers
G5COMPARENUM
4
2. Order (a) whole numbers with 6 or less digits; (b) decimal numbers
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1.4. Number comparisons
NUMBER CONCEPTS GENERAL OBJECTIVES
NC1, NC2
Content
Specific Objectives
Code
1.5.
1. Round whole numbers to the nearest: (a) ten (b) hundred (c) thousand (d) ten thousand
G5ROUNDING
Rounding
2. Round decimals to the nearest: (a) tenth (b) hundredth 1.6.
Estimation
1. Estimate by: (a) rounding (b) clustering (c) G5ESTIMATING using compatible numbers (d) using the front-end method 2. Estimate then count the number of objects in a set of less than 1 000 000 objects
1.7.
Skip counting
1. Use random numbers as starting points to G5SKIPCOUNT skip count in: (a) units (b) tens (c) hundreds (d) thousands (e) tens of thousands (f) tenths (g) hundredths
1.8.
Prime & composite numbers
1. Identify prime numbers up to 100
1.9.
Factors
1. State the factors of numbers from 1 – 99
1.10.
Prime 1. Express any number up to 144 as a Factorization product of its prime factors
1.11.
Highest Common Factor
G5PRIMES
2. Identify composite numbers up to 100 G5FACTORS
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1. Determine the highest common factor of 3 or less numbers
NUMBER CONCEPTS GENERAL OBJECTIVES
NC1, NC2
Content
Specific Objectives
Code
1.12. Multiples
1. State the multiples of 1-digit and 2-digit numbers
G5MULTIPLES
1.13. Lowest Common Multiple
1. Determine the lowest common multiple of 3 or less numbers
1.14. Roman numerals
1. Read and write Roman numerals up to 3000
G5ROMAN_NUMERAL
2. Express the current year in Roman Numerals 1.15. Square numbers
1. Identify square numbers up to 144
G5SQUARE_NUMBER
1.16. Odd & even numbers
1. Classify numbers as odd or even
G5ODD_EVEN
NUMBER OPERATIONS GENERAL OBJECTIVES
NO1, NO2
Content
Specific Objectives
Code
1.17. Addition & Subtraction
1. Use addition and subtraction strategies to solve simple problems mentally
G5ADD_SUBTRACT
2. Explain addition and subtraction strategies
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3. Solve addition and subtraction problems involving: (a) whole numbers (b) fractions (c) decimals up to thousandths (d) money
NUMBER OPERATIONS GENERAL OBJECTIVES Content
Specific Objectives
NO1, NO2 Code
1.18. Multiplication 1. Determine the product of 1-digit and 2G5MULTIPLY_DIVIDE & Division digit whole numbers by: (a) using an array (b) doubling (c) repeated doubling (d) skip counting (e) skip counting from a known fact 2. Determine the quotient of 2-digit, 3-digit or 4-digit numbers and whole numbers with up to 2-digits by: (a) partitive division (b) quotative division (c) flexible division algorithms (d) long division algorithms 3. Solve multiplication and division problems involving: (a) whole numbers (b) fractions (c) decimals up to thousandths (d) money 1.19. Problemsolving techniques
1. Select appropriate operation(s) and method(s) for solving problems
G5NUM_PROBLEM
2. Justify operations and methods selected when solving problems 3. Evaluate alternate methods of solving a given problem 4. Verify solutions 5. Solve problems involving: (a) multiple steps (b) multiple operations
1.20. Number Sequences
1. Create number sequences of addition and subtraction with up to 10: (a) whole numbers (b) fractions (c) decimals
G5NUM_SEQUENCE
2. Create number sequences of multiplication and division with up to 10: (a) whole numbers (b) fractions (c) decimals 2. Use the order of operations to solve problems
G5ORDER
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1. State the order of arithmetic operations
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1.21. Order of Arithmetic Operations
NUMBER OPERATIONS GENERAL OBJECTIVES
NO1, NO2
Content
Specific Objectives
Code
1.22. Ratio
1. Represent ratios using objects
G5RATIO
2. Express a ratio using a colon (:) or a fraction 3. Identify and write equivalent ratios 4. Determine the missing term in a pair of equivalent ratios 1.23. Proportion
1. Solve simple ratio and proportion problems
G5PROPORTION
2. Solve problems involving unequal sharing 1.24. Simple 1. Determine simple percentages of given G5PERCENTAGE Percentage quantities 1.25. Fractional parts
1. Calculate fractions of given quantities
1.26. Equivalent fractions
1. Determine the equivalence of fractions
1.27. Reducing fractions
1. Reduce fractions
1.28. Mixed numbers
1. Express improper fractions as mixed numbers
G5FRACTION
2. Write fractions in their simplest form G5MIXED_NUM
2. Express mixed numbers as improper fractions 1.29. Operations 1. Add and subtract fractions with: with fractions (a) like denominators (b) unlike denominators
G5FRACTION_OPS
2. Add and subtract mixed numbers 3. Multiply fractions by: (a) whole numbers (b) fractions
1.31. Converting 1. Express fractions as: (a) percentages fractions to (b) decimals percentages decimals
G5FRACTION_COMP G5_FRACTION_CONV
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1. Order and compare fractions
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1.30. Comparing fractions
MONEY GENERAL OBJECTIVES
MO1, MO2, MO3
Content
Specific Objectives
Code
1.32. Computing bills
1. Calculate shopping bills given the unit cost of items and a shopping list
G5BILLS
2. Calculate the cost of meals when given the unit cost per item and a list of orders 3. Compute the change to be given or received from bills up to $80 1.33. Profit or loss 1. Use cues in word problems to determine G5PROFIT_LOSS an item’s: (a) cost price (b) selling price 2. Identify whether a profit is made or a loss is incurred in simple financial transactions 3. Given the cost price and selling price of an item, calculate the: (a) profit or (b) loss STRAND: SHAPES & SPACE MEASUREMENT GENERAL OBJECTIVES
M1, M2
Content
Specific Objectives
Code
2.1.
1. State the relationships among mm, cm, m and km
G5LENGTH
Length
2. Convert: (a) mm to cm; cm to mm (b) cm to m; m to cm (c) mm to m; m to mm (d) m to km; km to m 3. Convert: (a) mm to cm; cm to mm (b) cm to m; m to cm (c) mm to m; m to mm 4. Estimate lengths in mm, cm and m. 5. Measure lengths in mm, cm and m. 1. Using mechanical and word problems, calculate the perimeter polygons (3 to 8 sides)
G5PERIMETER
9
Perimeter
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2.2.
MEASUREMENT M1, M2
Content
Specific Objectives
Code
2.3. Area
1.
Calculate the length of a rectangle if the area and width are known
G5AREA
2.
Calculate width of a rectangle if the area and length are known
3.
Calculate the area of regular polygons using a grid
2.5. Mass
2.6. Time
Distinguish the term volume from capacity
2.
Estimate the capacity of objects in standard units
3.
Measure the capacity of containers in standard units
4.
Arrange containers in order of capacity (standard units)
5.
Convert whole and half numbers from: (a) ml to L (b) L to ml
6.
Solve problems involving capacity
1.
Estimate, measure and record the mass of objects in standard units
2.
Compare and order the mass of objects using standard units
3.
Convert whole numbers and halves from: (a) g to kg (b) kg to g
4.
Solve problems involving mass
1.
Read and write time in hours and minutes
2.
Use addition and subtraction to determine the elapsed time between two events
3.
Convert: (a) hours to minutes (b) minutes to hours
4.
Convert between the 12-hour and the 24-hour clock
5.
Solve word problems involving time
G5CAPACITY
G5MASS
G5TIME
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2.4. Capacity 1.
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GENERAL OBJECTIVES
GEOMETRY GENERAL OBJECTIVES Content 2.7. The Circle
G1, G2, G3
Specific Objectives 1. Name the parts of a circle
Code G5GEOMETRY
2. Calculate radius of a circle when the diameter is known 3. Calculate the diameter of a circle when the radius is known
2.8. Polygons 1. Name a polygon when given: (a) the with 3 to number of sides of the polygons or (b) 12 sides diagrams of the polygon 2. State the number of edges, faces and vertices in 3-D solids 2.9. Angles
1. Distinguish types of angles from each other: acute, obtuse, right angle, reflex angle, straight angle/straight line angle 2. Use protractors to read angles between 0 and 180 degree STRAND: PATTERNS & RELATIONS PATTERNS P1
Specific Objectives
3.1. Simple patterns: Concrete & pictorial
1.
Complete numerical, geometric and G5PATTERNS picture patterns
2.
Use concrete objects to represent relationships in (function) tables
3.
Determine the rule which represents a given relationship
3.2. Pattern 1. development
Construct and extend patterns
3.3. Problemsolving with patterns
Complete multi-step problems e.g., sums of sequences
1.
Code
11
Content
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GENERAL OBJECTIVES
SETS GENERAL OBJECTIVES Content 3.5.
Sets
S1, S2
Specific Objectives
Code
1. Identify equal sets
G5SETS
2. List proper subsets from given data 3. Use symbols to represent: (a) elements (b) subsets (c) intersections of sets and (d) unions of sets 4. Use Venn diagrams to show intersection(not more than 2 sets) 5. Solve problems using Venn diagrams STRAND: STATISTICS & PROBABILITY STATISTICS GENERAL OBJECTIVES Content
ST1, ST2, ST3, ST4
Specific Objectives
Code
4.1.
Data Collection
1. Distinguish between a total population G5DATA_COLLECT and a sample of that population.
4.2.
Charts & Graphs
2. Read information using: (a) tally charts (b) frequency tables
G5CHARTS_GRAPHS
Choose a suitable scale to display data on: (a) pictographs (b)bar graphs Read and interpret pictographs/bar graphs where a single picture/bar represents 2 to 10 objects Read and interpret line graphs in the first quadrant 4.3.
The Mean
3. Calculate the mean from given information
4.4.
Predictions 4. Use data to make inferences and draw conclusions PROBABILITY
4.5.
Specific Objectives Outcomes 1. Distinguish between possible and expected outcomes
Code G5PROBABILITY
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Content
ST1, ST2, ST3, ST4
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GENERAL OBJECTIVES
GRADE 6 STRAND: NUMBERS & NUMBER SENSE NUMBER CONCEPTS GENERAL OBJECTIVES Content
NC1, NC2
Specific Objectives
1.1. Communicating 1. Identify whole numbers up to with numbers 9 999 999 (0 – 9 999 999)
Code G6WRTNUM
2. Read and write whole numbers up to 9 999 999 in: (a) numerals (b) words 3. State word names when given whole numbers with up to 7 digits 4. Write numerals given word names for numbers up to 9 999 999 1.2. Place value
1. State the value of any digit in a 7digit number
1.3. Expanded form 1. Write 7-digit whole numbers in expanded form
G6PLACEVALUE G6EXPANSION
2. Write numerals of 7-digit whole numbers given the expanded form 1.4. Number comparisons
1. Compare (a) whole numbers with 7 or less digits; (b) decimal numbers up to thousandths
G6COMPARENUM
2. Order (a) whole numbers with 7 or less digits; (b) decimal numbers up to thousandths 1. Round whole numbers to the nearest: (a) ten (b) hundred (c) thousand (d) ten thousand (e) hundred thousand
G6ROUNDING
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2. Round decimals to the nearest: (a) tenth (b) hundredth
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1.5. Rounding
NUMBER CONCEPTS GENERAL OBJECTIVES
NC1, NC2
Content
Specific Objectives
1.6.
1. Estimate by: (a) rounding (b) clustering (c) G6ESTIMATING using compatible numbers (d) using the front-end method
Estimation
Code
2. Estimate then count the number of objects in a set of less than 10 000 000 objects 1.7.
Skip counting
1. Use random numbers as starting points to skip count, forwards and backwards in: (a) units (b) tens (c) hundreds (d) thousands (e) tens of thousands (f) tenths (g) hundredths
G6SKIPCOUNT
1.8.
Prime & composite numbers
1. Identify prime numbers up to 100
G6PRIMES
Factors
1. State the factors of numbers from 1 – 99
1.9.
1.10. Prime Factorization
2. Identify composite numbers up to 100 G6FACTORS
1. Express any number up to 144 as a product of its prime factors
1.11. Highest 1. Determine the highest common factor of 3 Common Factor or less numbers 1.12. Multiples
1. State the multiples of 1-digit and 2-digit numbers
1.13. Lowest Common Multiple
1. Determine the lowest common multiple of 3 or less whole numbers
1.14. Roman numerals
1. Read Roman numerals up to 3000
G6MULTIPLES
G6ROMAN_NUMERAL
2. Write Roman numerals up to 3000
1. Identify square numbers up to 144
G6SQUARE_NUMBER
1.16. Odd & even numbers
1. Classify numbers as odd or even
G6ODD_EVEN
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1.15. Square numbers
14
3. Express the current year in Roman Numerals
NUMBER OPERATIONS GENERAL OBJECTIVES
NO1, NO2
Content
Specific Objectives
Code
1.17. Addition & Subtraction
1. Use addition and subtraction strategies to G6ADD_SUBTRACT solve simple problems mentally 2. Explain addition and subtraction strategies 3. Solve addition and subtraction problems involving: (a) whole numbers (b) fractions (c) decimals up to thousandths (d) money
1.18. Multiplication 1. Multiply 1-digit by 2-digit numbers &Division 2. Divide 2-digit, 3-digit or 4-digit numbers by: (a) 1-digit numbers (b) 2-digit numbers
G6MULTIPLY_DIVIDE
3. Solve multiplication and division problems involving: (a) whole numbers (b) fractions (c) decimals up to thousandths (d) money 1.19. Problemsolving techniques
1. Select appropriate operation(s) and method(s) for solving problems
G6NUM_PROBLEM
2. Justify operations and methods selected when solving problems 3. Evaluate alternate methods of solving a given problem 4. Verify solutions 5. Solve problems involving: (a) multiple steps (b) multiple operations
1.20. Number Sequences
1. Create number sequences of addition and G6NUM_SEQUENCE subtraction with up to 10: (a) whole numbers (b) fractions (c) decimals 2. Create number sequences of multiplication and division with up to 10: (a) whole numbers (b) fractions (c) decimals 2. Use the order of operations to solve problems
G6ORDER
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1. State the order of arithmetic operations
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1.21. Order of Arithmetic Operations
NUMBER OPERATIONS NO1, NO2
Content
Specific Objectives
Code
1.22.
1.
Represent ratios using objects
G6RATIO
2.
Express a ratio using a colon (:) or a fraction
3.
Identify and write equivalent ratios
4.
Determine the missing term in a pair of equivalent ratios
1.
Solve simple ratio and proportion problems G6PROPORTION
2.
Solve problems involving unequal sharing
Proportion
1.24.
Simple 1. Percentages
Determine simple percentages of given quantities
G6PERCENTAGE
1.25.
Fractional parts
1.
Calculate the fractional parts of given quantities
G6FRACTION
1.26.
Equivalent fractions
1.
Determine the equivalence of fractions
1.27.
Reducing fractions
1.
Select the fraction in lowest terms from a set of equivalent fractions
2.
Write fractions in their simplest form
1.
Express improper fractions as mixed numbers
2.
Express mixed numbers as improper fractions
1.28.
1.29.
Mixed numbers
Operations 1. with fractions
Add and subtract fractions with: (a) like denominators (b) unlike denominators
G6MIXED_NUM
G6FRACTION_OPS
2.
Add and subtract mixed numbers
3.
Multiply fractions by: (a) whole numbers (b) fractions
1.
Order and compare fractions
G6FRACTION_COMP
Express fractions as: (a) percentages (b) decimals
G6_FRACTION_CONV
1.30.
Comparing fractions
1.31.
Converting 1. fractions to percentages decimals
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1.23.
Ratio
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GENERAL OBJECTIVES
MONEY GENERAL OBJECTIVES
MO1, MO2, MO3
Content
Specific Objectives
Code
1.32. Computing bills
1. Calculate shopping bills given the unit cost of items and a shopping list
G6BILLS
2. Calculate the cost of meals when given the unit cost per item and a list of orders 3. Compute the change to be given or received from bills under $100 1.33. Hire purchase
1. Distinguish the hire purchase price from the cash price of an item
G6HIRE_PURCHASE
2. Evaluate the benefit of purchasing an item by: (a) cash (b) hire purchase agreement 3. Determine the hire purchase price of items when given the number of instalments, the value each instalment and the deposit (downpayment), expressed as a percentage of the marked price 1.34. Profit or loss 1. Use cues in word problems to determine an item’s: (a) cost price (b) selling price
G6PROFIT_LOSS
2. Identify whether a profit is made or a loss is incurred in simple financial transactions 3. Given the cost price and selling price of an item, calculate the: (a) profit or (b) loss G6CURRENCY
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1. Convert foreign currency to local currency using exchange rates
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1.35. Currency conversion
STRAND: SHAPES & SPACE MEASUREMENT GENERAL OBJECTIVES Content 2.1.
M1, M2
Specific Objectives Length
Code
1.
State the relationships among mm, cm, G6LENGTH m and km
2.
Convert: (a) mm to cm; cm to mm (b) cm to m; m to cm (c) mm to m; m to mm (d) m to km; km to m
3.
Estimate lengths in mm, cm and m.
4.
Measure lengths in mm, cm and m.
2.2.
Perimeter 1.
Use standard units to determine the perimeter of: (a) regular shapes (b) irregular shapes
G6PERIMETER
2.3.
Area
Use standard units to determine the area of: (a) regular shapes (b) irregular shapes (c) triangles (d) segments of regular shapes
G6AREA
2.4.
Capacity
1.
1. Distinguish the term volume from capacity
G6CAPACITY
2. Estimate the capacity of objects in standard units 3. Measure the capacity of containers in standard units 4. Arrange containers in order of capacity (standard units) 5. Convert whole numbers, halves and decimal numbers from: (a) ml to L (b) L to ml Volume
1. Calculate the volume of a: (a) cube (b) G6VOLUME rectangular prism
Page
2.5.
18
6. Solve problems involving capacity
MEASUREMENT GENERAL OBJECTIVES Content 2.6.
Mass
M1, M2
Specific Objectives
Code
1. Use standard units to: (a) estimate the mass of objects (b) measure the mass of objects (c) record the mass of objects
G6MASS
2. Compare the mass of objects using standard units 3. Arrange objects in order of increasing or decreasing mass expressed in standard units 4. Convert measurements expressed as whole numbers, decimals and fractions from: (a) g to kg (b) kg to g 5. Solve problems involving mass 2.7.
Time
1. Read and write time in hours and minutes
G6TIME
2. Determine the elapsed time between two events using: (a) addition (b) subtraction 3. Convert: (a) hours to minutes (b) minutes to hours 4. Solve word problems involving time GEOMETRY GENERAL OBJECTIVES The Circle 1. Name the parts of a circle
Code G6GEOMETRY
2. Calculate radius of a circle when the diameter is known 3. Calculate the diameter of a circle when the radius is known
19
2.8.
Specific Objectives
Page
Content
G1, G2, G3
GEOMETRY GENERAL OBJECTIVES Content 2.9.
G1, G2, G3
Specific Objectives Types of triangles
Code
1. Recall that the sum of the interior angles of a triangle is 180o 2. Distinguish the types of triangles from each other using: (a) the lengths of the sides (b) the value(s) of one or more interior angles 3. Determine the value of an unknown angle in a triangle when the other two are known
2.10.
Angles
1. Use protractors to: (a) measure angles expressed in integral values from 0 to 180 degrees (b) construct angles expressed in integral values from 0 to 180 degrees STRAND: PATTERNS & RELATIONS PATTERNS
GENERAL OBJECTIVES Content 3.1.
P1
Specific Objectives Pattern 1. Generate patterns using: (a) objects development (b) pictures or images (c) numbers
Code G6PATTERNS
2. Extend patterns 3. Summarize patterns 1. Complete multi-step problems e.g., sums of sequences
20
Problemsolving with patterns
Page
3.2.
SETS GENERAL OBJECTIVES
S1, S2
Content
Specific Objectives
Code
3.3. Sets
1.
Identify equal sets
G6SETS
2.
List proper subsets from given data
3.
Use the symbol for ‘is a subset of’, intersections, element of and union
4.
Use Venn diagrams to show intersection(not more than 2 sets)
5.
Solve problems using Venn diagrams STRAND: STATISTICS & PROBABILITY STATISTICS
GENERAL OBJECTIVES Specific Objectives
Code
4.1. Data Collection
1.
Distinguish between a total population G6DATA_COLLECT and a sample of that population.
4.2. Charts & Graphs
1.
Read information using: (a) tally charts (b) frequency tables
2.
Choose a suitable scale to display data on: (a) pictographs (b)bar graphs
3.
Read and interpret pictographs/bar graphs where a single picture/bar represents 2 to 10 objects
4.
Read and interpret line graphs in the first quadrant
1.
Calculate the mean from given information
4.4. Predictions 1.
Use data to make inferences and draw conclusions
GENERAL OBJECTIVES Content
ST5
Specific Objectives
Code G6PROBABILITY
4.5. Outcomes
1.
Distinguish between possible and expected outcomes
4.6. Probability
1.
Calculate the probability of a single event
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4.3. The Mean
G6CHARTS_GRAPHS
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Content
ST1, ST2, ST3, ST4
