~ 1 ~ BISHOPS PREP SCHOOL MATHEMATICS CURRICULUM GRADE 5

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1 ~ 1 ~ BISHOPS PREP SCHOOL MATHEMATICS CURRICULUM GRADE 5 September 2012

2 ~ 2 ~ BISHOPS PREP SCHOOL Mathematics Syllabus: Grade 5 For convenience the syllabus has been divided into sections. It is important to integrate work and set relevant problem solving tasks. Some sections will be suitable for practical assignments. It is also important to make use of the relevant software. BASIC NUMBER WORK A Whole number work 1. Revision of Grade 4 addition, subtraction, multiplication and division 2. Revision of bonds and tables 3. Numerical skills: counting in intervals- forwards and backwards working up to at least 6 digits flexibility in handling larger numbers writing numbers from words 4. Place value: value of 8 in value of diagrammatic representation of numbers using the number line using expanded notation to manipulate numbers 5. Ordering and comparing numbers: using relationship signs ascending and descending order filling in missing numbers on a sequence, number grid 6. Estimating and approximating in order to check validity of answers 7. Rounding off numbers. 8. Recognising and using commutative, associative and distributive properties with whole numbers

3 ~ 3 ~ B Work Order 1. Multiplication to be done before addition and subtraction 2. Associative rule of addition and multiplication: = C Mental Strategies 1. Estimation 2. Using short methods: rounding off to nearest 5, 10, 100 and 1000 and compensating doubling and halving building and breaking down of numbers 3. Using the associative property as a short cut: 4 x 36 x 25 = 4 x 25 x Using multiplication and division ; addition and subtraction as inverse operations. 5. Adding and subtracting units, multiples of 10, 100 and 1000 to/from any number 6. Developing mental problem solving strategies with regular mental activities. C Addition and subtraction 1. Addition and subtraction of large numbers 2. Addition as the inverse of subtraction 3. Using the correct terminology: sum, total 4. 0 in terms of its additive property D Multiplication 1. Multiplication as repeated addition 2. Multiplying by multiples of 10, 100 and 1000 mental strategies 3. Becoming proficient with a particular method of multiplication- 3 digit by 2 digit and more. 4. Working with factors and multiples

4 ~ 4 ~ 5. Using the correct terminology: multiplicand, multiplier and product. 6. Estimation: rounding off one / both 7. Multiplying by 1 and 0 8. The commutative, associative and distributive properties 9. The reciprocal relationships between multiplication and division 10. Using the calculator to check by doing division as the reciprocal operation. E Division 1. Division as repeated subtraction 2. Dividing by multiples of 10, 100 and The concept that 2 4 = 2 / 4 4. Becoming proficient with a method of division dividing a 4 digit by a 2 digit and more 5. Dealing with remainders 6. Approximation: rounding divisor, adjusting dividends 7. Using the correct terminology: dividend, divisor, quotient 8. Using the calculator to check answers and do the inverse operation F Problem solving 1. Problem solving must be done throughout the relevant sections and must be done in context to boys experience. 2. Financial and measurement contexts must be included in whole number problems. 3. Attention must be given to logical presentation and the correct use of equal signs. 4. Number sentences must be written to avoid the laborious writing of sentences practice with comprehension type questions- choosing the best number sentence to solve the problem 5. Although boys must be encouraged to develop own methods for solving problems, strategies must be discussed and taught. understanding the problem, selecting the relevant information, thinking about the possible ways to obtain the solution and reason the best methods of solving the problem. use concrete objects use drawings

5 ~ 5 ~ mimic or role play split the problem up into smaller problems use easier numbers to test ideas arrange the information and look for patterns guess and check methods eliminating possibilities. using tables 6. It is important to vary the kind of problem solving activities. G Calculator skills 1. These should be used throughout the year where applicable 2. Use as a computational tool when solving problems using large numbers using to check answers. 3. Use as an investigational aid: finding number patterns, etc 4. Calculator logic- entering correct order of operations. 5. Using the constant function. H Common Fractions Practical work with fractions is essential e.g. cutting up papers. This is essential. Progress can then be made to diagrammatic and symbolic representation. 1. Revision of concept of a fraction: correct terminology numerator and denominator 1 / 2 = 1 2 a fraction can be part of one whole or many wholes 2. Working with shaded areas of diagrams 3. Working with number lines- fractions as numbers between whole numbers 4. Equivalent fractions and fraction families 5. Simplifying fractions

6 ~ 6 ~ 6. Ordering and comparing fractions relationship signs. Not limited to fraction families. 7. Mixed numbers and conversions. 8. Counting in fraction intervals 9. Rounding off to whole numbers 10. Sharing m objects between n people where m < n m > n but not divisible. 11. Finding a fraction of a quantity where the denominator is a factor e.g. 3 / 5 of Addition and subtraction of fractions with different denominators 13. Multiplication by whole numbers- multiplication seen as repeated addition: 1 / / / 5 = 3 x 1 / Problem solving including pie charts I Decimal Fractions 1. Consolidate concept of decimal fractions up to tenths 2. Extend concept of decimal fractions up to 3 decimal places- practical and diagrammatic work. 3. Place value: 7,639 = / / / Using zero as a place holder 5. Decimals on the number line- numbers between numbers 6. Counting up and down in intervals 7. Ordering decimals using relationship signs, ascending and descending order. 8. Conversion of decimal fractions to common fractions and vice versa where the denominators are factors of 10, 100 and Rounding off of decimals 10 Addition and subtraction of decimals using zero as a place holder 11. Multiplication by 10, 100 and 100- concept of moving places 12 Division of decimals by 10, 100 and concept of moving places 13. Multiplication and division by whole numbers

7 ~ 7 ~ PATTERNS, FUNCTIONS AND ALGEBRA 1. Investigate and extend numeric patterns looking for rules of patterns. multiples, factors, odd and even numbers sequences involving a constant difference or ratio doubling, halving prime and composite numbers square numbers 2. Determining input values, output values and rules for patterns using flow diagrams and tables. Flow diagrams using 2 operations- link to use of brackets to ensure correct work order. m x (m + 3) x 2 3. Finding the missing number in a series 4. Solving and completing number sentences by inspection and trial and error and improvement methods; b + 4 = 10 b = Investigate and extend geometric patterns looking for relationships and rules. 6. Describing observed relationships or rules in words. SPACE AND SHAPE The work in this section should be done with concrete aids and sketches. Make use of models and illustrate on dotty paper. A Lines 1. Concept of a line 2. Classifying vertical, horizontal, oblique, perpendicular, parallel B Angles 1. Concept of an angle- using straws and split pins. No formal measurement needed 2. Classifying angles: acute; right; obtuse; straight; reflex and revolution 3. Recognising the different angles on polygons and drawings 4. Compass points and angles

8 ~ 8 ~ 5. Moving through angles on the clock- clockwise and anticlockwise 6. Whole, half and quarter turns C Polygons and 2D Figures 1. Concept of a polygon- a plane figure bound by straight lines 2. Classifying polygons and recognising: regular and irregular convex and concave 3. Using the correct terminology - vertex and sides 4. Investigation of quadrilaterals: creating using the geoboards, paper strips drawing using dotty paper sorting into categories according to length of sides and vertices identifying the quadrilaterals similarities and differences between squares and rectangles terminology diagonal and parallel correct markings for equal and parallel on a drawing 5. Recognising and drawing line of symmetry on polygons and other mathematical shapes D 3D Figures 1. Identifying 3D figures around us 2. Correct terminology: faces, vertices, edges 3. Recognising similarities and differences between: cones, spheres, cylinders, pyramids and prisms 4. Similarities and differences between cubes and rectangular prisms 5. Cutting open models to trace their nets 6. Drawing shapes on grid paper

9 ~ 9 ~ E Transformations 1. Tracing and moving 2D shapes in one or more of the following ways: rotation reflection translation 2. Make tessellated patterns by tracing and moving 2D shapes in the following ways: rotation reflection translation F Viewing of objects, position and movement 1. Describing and sketching views of 3D objects in different positions. 2. Locate position of objects, drawings or symbols on a grid and map with alpha- numeric grid references. 3. Follow directions to trace a path between positions on a map. MEASUREMENT Where necessary practical work must precede written work. Use Multe- Maths software for diagrammatic representation. A Length, capacity and mass 1. Estimation and accurate measuring 2. Introduction of ton in mass 3. Reading from tape measures and scales with different calibrations 4. Using the most sensible unit for measuring various objects or quantities 5. Conversions between the units- using the decimal comma 6. Rounding off to whole numbers 7. Using maps and scale drawings

10 ~ 10 ~ B Perimeter 1. Concept and practical measurement 2. Perimeter of irregular shapes- using string for circles, etc. 3. Perimeter of square and rectangles. C Area 1. Find area of regular and irregular shape by counting squares on a grid to develop an understanding of the concept of area. D Volume 1. Find volume/ capacity of objects by packing and filling them to develop an understanding of the concept of cubic units. 2. Counting the number of cubes which make up the volume of given shapes. E Time 1. Calendar and timetable work. 2. Conversions and calculations with units of time 3. Pie charts for time division F Temperature 1. Reading and interpreting thermometers. 2. Introduce the concept of negative numbers as sub zero temperatures.

11 ~ 11 ~ DATA HANDLING Integrate into all areas of work where applicable 1. Collect data by using a survey and tally chart. 2. Order data 3. Draw a variety of graphs to display and interpret data: pie charts line graphs bar graphs 4. Drawing graphs on the computer 5. Critically interpreting and analysing data by answering posed questions. 6. Drawing conclusions from data and making predictions 7. Examine ungrouped numerical data to determine the most frequently occurring score in the data set i.e. mode 8. Probability Performing simple repeated events and list possible outcomes for experiments using coins, dice, spinners Counting and comparing the frequency of actual outcomes for a series of trials. ASSESSMENT 1. Assessment should be done after each relevant section. 2. Assessment should be varied and include basic number work as well as problem solving where possible. 3. Formal assessment for mark report purposes should always be preceded by diagnostic assessment to see if intervention is necessary. This can take the form of informal observations, verbal questioning or quick class exercises. 4. Projects and assignments must form part of each term s assessment.

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