Standards: The learner will be able to:

Transcription

1 STRANDS: 1. NUMBER: THEORY, CONCEPTS AND OPERATIONS 2. MEASUREMENT 3. GEOMETRY 4. STATISTICS AND DATA HANDLING 5. ALGEBRA, PATTERNS AND FUNCTIONS 6. CONSUMER ARITHMETIC Standards: The learner will be able to: 1. Develop number sense, ways of representing numbers, relationships among numbers and number systems and perform mathematical computations 2. Construct an understanding of measurable attributes of objects and the units, systems, and the processes of measurement. 3. Investigate properties of geometric shapes. 4. Use appropriate data gathering procedures, techniques for representing data and interpreting data. 5. Discover algebraic properties and expressions and apply the operations to the solution of algebraic equations and inequalities; read and interpret graphs and use them to represent algebraic relationships. 6. Appreciate the role of the consumer in performing day-to-day transactions involving money. 7. Solve problems using a variety of problem solving strategies (See Polya.) Attainment Targets: The learner will be able to: 1 1. Apply number operations and relationships with speed and accuracy to solve problems using mental strategies, paper/pencil or technology. 2. Make and use estimation and accurate measurement by applying appropriate instruments, formulas and units to solve problems in a variety of ways. 3. Identify and describe attributes of geometric shapes and apply this knowledge to reason or solve problems about shape, size, position or motion of objects. 4. Use a variety of strategies to collect, organize, analyze, and interpret data to make decisions and solve problems. 5. Identify, describe and represent patterns and functional relationships to solve mathematical and real-life problems with speed and accuracy. 6. Apply knowledge of money to solve problems related to day-to-day transactions.

2 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: NUMBER CONCEPTS TERM: ONE UNIT: ONE DURATION: ONE WEEK Focus Questions: 1. What is the relationship between numbers and the number system? Specific Objectives Key Strategies Skills Resources Assessment Demonstrate an Place value Classifying Work sheet understanding of number up to Types of numbers test Create an solve problems involving properties of numbers 1. Create and solve problems involving factors and multiples of whole numbers 2. Read numerals up to Write numerals up to in words and numerals 4. Identify the place and total value of any digit in a number with five digits 5. Write numbers with up to five digits in expanded notation 6. Classify numbers using several number concepts: prime, odd, prime and even, prime and odd, composite and odd 7. Explain how various types of numbers are related 8. List multiples of a given number 9. List factors of a given number 10. Explain the concept of prime number 11. Write a number as a product of its prime factors 12. Calculate the least Common Multiple of two or three numbers 13. Explain the concept of Highest Common Factor 14. Find Highest Common Factor of two or three numbers by listing factors 15. Round off numbers with up to five digits to the nearest ten, hundred, or thousand Arrange a set of whole numbers in order of magnitude Expanded notation Prime Odd Even Odd Composite Multiples Factors Rounding off H.C.F L.C.M Ordering numbers Draw a place value char with place up to million Inset numbers with up to five digits in the table Question students on the place value of various digits Using manipulative like buttons and bottle caps give students the opportunity to discover why some numbers are even and others are odd numbers Teachers present each pupil with a chart with the heading odd, even, composite and prime numbers. Use flash card and give pupils a set of number. Classify the different numbers using the symbols >; <; or = Observing Manipulating Place value charts Manipulating Hundred chart 2

3 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: ROMAN NUMERALS TERM: ONE UNIT: TWO DURATION: ONE WEEK Focus Questions: What is the relationship between Roman Numerals and Hindu Arabic numerals? Specific Objectives Key Create and solve 1. Identify real life situations that involve the Roman problems involving use of Roman numerals numeral properties of numbers 2. State the Roman numerals for I, 5 and Explain how the Roman numerals for 1, 5 and 10 should be used to form other Roman numerals between 2 and 12 inclusive 4. Identify and write Roman numerals for numbers from 1 to 12 Strategies Skills Resources Assessment Introduce objects to pupils that are marked with roman numerals e.g. clock, book (chapter) Matching roman numerals with corresponding Hindu-Arabic Numbers. Allow pupils to work in group to construct calendars and clocks using Roman numerals Problem solving involving start, elapsed and end time Making Models Cards Models Clocks and calendar Quiz 5. Tell and write time using the 12 hour and 24 hour clock 6. Represent time on an analog or digital clock 7. Determine start, elapsed and end time 12- hour clock 24-hour clock 3

4 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: COMPUTATION TERM: ONE UNIT: THREE DURATION: TWO WEEKS 1. What are the basic facts of addition, subtraction, multiplication, and division of whole numbers Create and solve real-life problems involving addition and subtraction with numbers up to Create and solve real-life problems involving multiplication and division of numbers up to 3 digit numbers Specific Objectives 1. Recall the basic facts for addition, subtraction, multiplication and division of whole numbers 2. Create and solve problems involving addition, subtraction, multiplication and / or division of whole numbers 3. Add sets of numbers with totals up to , without and with regrouping 4. Carry out subtraction involving whole numbers with up to five digits, without and with regrouping 5. Multiply two and three-digit numbers by one- and two-digit numbers 6. Divide whole numbers with up to five digits by one- and two-digit numbers, without and with remainder Key Computation vocabulary: sum, product, total Suggested activities Skills Resources Assessment Engage pupils in a bingo game involving addition, subtraction, multiplication or division of whole numbers. Use arrow graph to draw pupils their knowledge of addition, subtraction, multiplication or division. Use calculator, mental strategies, pen and paper to investigate number pattern and relationships. Use the lattice methods to multiply Use rules for divisibility Problem solving Lolly sticks Buttons Beans Test 4

5 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: FRACTIONS TERM: ONE UNIT: FOUR DURATION: ONE WEEK Focus question: 1. What is the relationship between decimal numbers and whole numbers? 2. Which decimal is larger or smaller? Specific Objectives Key Strategies Skills Resources Assessment Solve simple problems Fractions Fraction strips Worksheet involving basic fractions and decimals Test 1. Use diagrams/pictures to represent unit, proper and improper fractions and mixed numbers 2. Convert an improper fraction to a mixed number and vice versa 3. Explain the concept of lowest terms and its relationship to equivalent fractions 4. Express fractions in their lowest terms 5. Generate fractions that are equivalent to a given fraction 6. Calculate the lowest common denominator for fractions with unlike but related denominators 7. Arrange a set of fractions in order of magnitude Mixed numbers Fractions: Improper Equivalent Least Common Denominator Ordering fractions Let pupils work in groups Give each pupil a paper shape vary the size of the paper as much as possible in each group and let different students fold their paper shapes into different fractions Engage pupils in a domino or matching game Allow pupils compare different fractions Shading Drawing Comparing and contrasting GRADE 6: 5

6 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: FRACTIONS TERM: ONE UNIT: FIVE DURATION: TWO WEEKS 1. What is the relationship between different kinds of fractions? 2. Which fraction is smaller or bigger? Solve simple problems involving basic fractions and decimals Specific Objectives 1. Add proper fractions with like or unlike but related denominators 2. Add a whole number to a proper fraction 3. Add a proper fraction and a mixed number with like denominators 4. Add a proper fraction and a mixed number with unlike but related denominators 5. Carry out subtraction involving proper fractions with like denominators 6. Carry out subtraction involving proper fractions with unlike but related denominators 7. Subtract a proper fraction from a mixed number with like denominator, without regrouping 8. Subtract a proper fraction from a mixed number with unlike but related denominator without regrouping 9. Subtract a proper fraction from a whole number 10. Multiply a proper fraction by a whole number 11. Multiply a whole number by a proper fraction 12. Multiply two proper fractions 13. Divide a proper fraction by a whole number Key Fraction Proper fraction Improper fraction Denominator Numerator Improper fraction Mixed numbers Suggested activities Skills Resources Assessment Put pupils into groups and provide opportunities for them to use fraction strips to compare fractions. Engage pupils in a domino game Draw and shade fractions Using diagrams to illustrate how multiple or divide proper fraction by a whole number Describing Testing hypotheses Constructing Shading Drawing 3D`shapes worksheet Test 6

7 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: DECIMALS TERM: ONE UNIT: SIX DURATION: ONE WEEK Focus question: What is the relationship between decimals numbers and whole numbers? Specific Objectives Key Strategies Skills Resources Assessment Solve simple problems 1. Explain how decimal numbers and whole Relationship Draw a shape of the board and then Observation Hundred quiz involving basic fractions numbers are related between divide it into 10 parts shade part 6 Ordering and charts and decimals 2. Identify the place and total value of the digits decimals and Ask what fraction is shaded comparing Crayons in a decimal number with up to two decimal whole numbers Let pupils interpret shaded fraction as places decimals 3. Represent simple decimal numbers with up Place value & Explain with the use of a number line the to two decimal places using diagrams total value sequence of decimal ascends 4. Read and Using a hundred chart point out that each 5. Write decimal numbers with up to two Relationship square is 1/100 decimal places between 6. Arrange a set of decimal numbers with up to two decimal places in order of magnitude fractions and decimals 7. Explain how fractions and decimals are related Conversions 8. Write a decimal number as a fraction 9. Write a fraction as a decimal number 7

8 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: DECIMALS TERM: ONE UNIT: SIX DURATION: ONE WEEK 1. What is the relationship between decimals and whole numbers? Solve simple problems involving basic fractions and decimals Specific Objectives Key Suggested activities Skills Resources Assessment 1. Explain how computation procedures for whole numbers can be applied to decimal numbers 2. Add decimal numbers with up to two decimal places, without and with regrouping 3. Carry out subtraction involving decimal numbers with up to two decimal places, without and with regrouping 4. Multiply a decimal number with up to two decimal places by a one-digit number Whole numbers Tenths Hundredths Decimal point Teacher demonstrate how to compare decimals with the uses of place value chart and number line Engage pupils in a decimal cross number puzzle Describing Testing hypotheses Constructing Dice ; cards Worksheet 8

9 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: PERCENTS TERM: ONE UNIT: SEVEN DURATION: TWO WEEKS Focus Questions: How are percentages relevant in everyday life? Specific Objectives Key Solve simple problems Percent involving basic fractions and decimals 1. Explain the concept of percent 2. Represent a given percent using pictures/diagrams and symbols 3. Explain the meaning of a given percent 4. Describe and 5. Analyse situations in real life that involve percents 6. Explain the relationship between fractions, decimals and percents 7. Express a percent as a decimal or fraction 8. Express simple proper fractions and decimals as percents 9. Create 10. Solve and 11. Analyse problems involving fractions, decimals and percent Decimals Relationship between fractions, decimals and percents Real life situations Strategies Skills Resources Assessment Through the use of a paper containing 100 squares. Explain that a percentage is a fraction of 100 Engage pupils in a domino games Matching Comparing Charts Crayons text test 9

10 STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: PERCENTS TERM: ONE UNIT: SEVEN DURATION: TWO WEEKS 1. What does percent means? 2. How relevant is percentage in everyday life? Solve simple problems involving basic fractions and decimals Specific Objectives 1. Calculate a percent of a number 2. Express one number as a percent of another 3. Calculate profit or loss, given the cost price and selling price of an article 4. Calculate profit or loss as a percent of the cost price of an article Key Percentage Profit Loss Cost price Suggested activities Skills Resources Assessment Present picture representing priced items and allow pupils to calculate percentage of each item Put pupils in groups and give them worksheet with problems involving percentages Question pupils on whether there is a loss or profit. Calculating Problem solving 3D`shapes Picture Text brochures Quiz Selling price GRADE 6: 10

11 STRAND: MEASUREMENT UNIT TITLE: LENGTH, CAPACITY, MASS TERM: TWO UNIT: ONE DURATION: FOUR WEEKS 1. What is the metric unit to measure length, capacity, and mass? 2. Create and solve problems using different units of length Create and solve real life problems involving basic standard units of mass Specific Objectives 1. Estimate and measure lengths and heights using the metre, centimetre and / or millimeter as the units of measure 2. Estimate and measure distances using the metre / and / or centimeter as the units of measure 3. Identify and interpret the scale that was used in a scale drawing 4. Use scale drawings to determine actual measurements in metres or kilometers 5. Male simple scale drawings 6. Estimate and measure the mass of objects using kilograms, grams, and / or milligrams as the units of measure Metre Key Centimeter Kilometer Kilogram Gram Milligram Celsius Scale Suggested activities Skills Resources Assessment Let pupils measure different objects in the classroom Divide class into group in which pupils are allowed to measure length of various objects. Given a map draw to scale Pupils will find the actual distance on the ground by using the scale drawing Pupils will draw their own dream house floor plan using scale Measuring Estimating Recording Drawing Cube Cuboid Beam Balance Thermometer Accuracy of measurement Convert measurements from one unit to another. Compare the lengths/height of objects given in the same units Create and solve real life problems involving basic standard units of capacity 7. Estimate and measure the capacity of containers using litres, centiliters, and / or milliliters as the units of measure 8. estimate and measure temperatures using the Celsius scale 11

12 STRAND: MEASUREMENT UNIT TITLE: MONEY TERM: TWO UNIT: TWO DURATION: TWO WEEKS 1. What role does money play in trade/everyday life? Create and solve real life problems involving simple profit and loss. Specific Objectives Key Suggested activities Skills Resources Assessment 1. Read and write amounts of money up to $ Describe situations that involve the use of large amounts (thousands) 3. Describe the role of cheques in transactions involving money 4. Represent amounts of money in a variety of ways 5. Calculate the total cost of a set of items, given the cost of one item and / or the cost of multiple of items 6. Make up bills 7. Calculate change 8. Explain the concepts of cost price, selling price, profit, and discount 9. Use the concepts of cost price, selling price, profit, loss and discount in descriptions of situations involving buying and selling Cost price Selling price Profit Loss Discount Buying and selling Role play a shop keeper dealing with his/her customers using paper money etc Put pupils into groups and give groups a set of invoices. Let the shopkeeper calculate the amount owed. The pupils will pay the required amount or more than the required amount and so get change. Lead, discuss and allow each shop keeper to say whether he makes a profit or loss. Describing Problem solving Calculating Fake money Empty milk tin etc. Oral test Presentation arrangement of shop 12

13 STRAND: GEOMETRY UNIT TITLE: SHAPES TERM: TWO UNIT: THREE DURATION: ONE WEEK 1. What is the relationship faces, edges and vertices of 3D shapes? 2. How are 3D shapes useful in everyday life? Demonstrate understanding of 3- D shapes to construct models Specific Objectives 1. Describe three-dimensional shapes in terms of the number and type of faces and the number of edges and vertices 2. Use the attributes of a 3Dimensional shape to formulate reasons for its uses in every day life 3. Identify and describe cubes, cuboids, cylinders, cones and spheres 4. Make nets of cubes, cuboids and cylinders 5. Identify nets that will form a cube, cuboid or cylinder 6. Construct cubes, cuboids and cylinder Key 3Dimensional shapes Edges Vertices Suggested activities Skills Resources Assessment Given concrete objects pupils will describe them in terms of types of faces and the number of edges and vertices. Students bring in examples of cube, cuboid and cylinders (match box, shoe box, gift box, Pringles container) The open out/cut containers apart and observe how they were made up (put together). Students ten make their own nets using Manila paper. Engage pupils in making models of cubes, cuboids and cylinders Describing Testing hypotheses Constructing 3D`shapes Nets of 3D shapes Picture Charts Shapes in the environment Quiz Drawing and describing figures Reports construct models GRADE 6: 13

14 STRAND: GEOMETRY UNIT TITLE: 2D SHAPES TERM: TWO UNIT: FOUR DURATION: ONE WEEK 1. What types of angels are present in 2D? Create and solve simple problems with 2-D Specific Objectives 1. Describe two-dimensional shapes in terms of the number and type the type of angles 2. Explain the concept of circumference of a circle 3. State the relationship between radii and diameters of circles 4. Draw circles 5. Identify the following parts: circumference, radius, diameter, centre 6. Identify 2Dimensional shapes that have the same size and shape 7. Explain the concept of congruent figures 8. Classify two-dimensional shapes using a variety of attributes Key 2Dimensional shapes Edges Vertices Parts of a circle: Circumference Radius Diameter Centre Attributes: open, closed, symmetrical, congruent, number of sides and angles, types of angles and sizes Suggested activities Skills Resources Assessment Divide class into group of mixed abilities. Each group is given a set of 2 dimensional shapes Provide opportunities for pupils to describe and compare shapes Teacher and pupils classify 2 dimensional objects, open and closed, symmetrical, types of angles etc. Students are given symmetrical drawings, and asked to fold diagrams so that halves cover each other exactly. Students unfold drawings and note the fold line to be line of symmetry of the diagram Help students to develop an understanding of the further identify lines of symmetry of given drawing of diagrams/letters Students are given exercises where they are asked to draw the lines of symmetry of given drawing/letters. Students are given drawing where they fold paper along the edge of the drawing and trace the image. Students then unfold paper and copy image they are to complete. Students now practice free hand completing drawing of a diagrams that are symmetrical. Describing Drawing Classifying 2D`shapes Pictures Cutouts Dot and squared paper Making models of shapes Congruent figures GRADE 6: 14

15 STRAND: GEOMETRY UNIT TITLE: PERIMETER & AREA TERM: TWO UNIT: FIVE DURATION: ONE WEEK 1. How do perimeters and areas help to relate everyday situation? Solve simple real life problems involving area Specific Objectives Key Suggested activities Skills Resources Assessment 1. Calculate the perimeter of a two-dimensional shape 2. Identify appropriate units for the measurement of small and large areas 3. Calculate the area of a rectangle triangle or square by using the formula, Area = length X width 4. Calculate the area of irregular figures that are comprised of triangle squares, and / or rectangles 5. Sketch squares, rectangles, or irregular figures with a given area and / or perimeter 2 Dimensional Perimeter Area Irregular figures Squares Rectangles Given two dimensional shape, pupils will calculate the perimeter by counting on the grid and by using the formulae where applicable. Given irregular shapes, pupils will dissect them into squares and rectangles then find their areas by using the grid and appropriate formulae. Calculating Sketching 3D`shapes worksheet GRADE 6: 15

16 STRAND: GEOMETRY UNIT TITLE: PLANE SHAPES TERM: TWO UNIT: SIX DURATION: ONE WEEK 1. What angles are presented in 3D shapes 2. How are angles useful in everyday life? Create and solve problems involving plane shapes Specific Objectives 1. Identify angles in threedimensional and plane shapes 2. Draw and label angles 3. Explain what is a right angle 4. Classify angles according to size, as equal to, larger than, or smaller than a right angle 5. Identify acute and obtuse angles 6. Describe acute and obtuse angles 7. Draw and label line segments 8. Explain the concepts of horizontal, vertical, parallel and perpendicular lines 9. Identify horizontal and vertical line segments 10. Draw horizontal and vertical line segments 11. Identify parallel and perpendicular lines 12. Draw parallel and perpendicular lines Key 3Dimensional shapes Edges Vertices Comparing size of angles Acute angles Obtuse angles Right angles Horizontal, Vertical, Parallel, Perpendicular lines Suggested activities Skills Resources Assessment Idnetify angles in the classroom Trace out angles on a piece of paper and compare them with right angles to see which are smaller, larger or the same Fro a project, compile a scrapbook of angles and lines Identifying Classifying Drawing Sketching Describing 3D`shapes Pictures text Work sheets Projects 16

17 STRAND: GEOMETRY UNIT TITLE: PLANE SHAPES/COORDINATES TERM: TWO UNIT: FIVE DURATION: ONE WEEK 1. How are geometric concepts used in the environment? Create and solve problems involving plane shapes Create and solve problems involving simple co-ordinate systems Specific Objectives 1. Explain how various groups of persons use geometric concepts 2. Create and solve problems involving plane shapes 3. Describe a simple co-ordinate system with only positive numbers 4. Plot points on a simple coordinate system 5. Identify points on a simple coordinate system Key : angles, symmetry, congruency Co-ordinates Suggested activities Skills Resources Assessment Organize and display data in a line graph. Using y axis with intervals of 1,2,4,5, or 10 and x axis with no more than 10 time intervals and whole numbers Use information on line graph to answer comprehension questions. Creating Plotting Solving problems 3D`shapes 17

18 STRAND: STATISTICS AND DATA HANDLING UNIT TITLE: DATA COLLECTION TERM: THREE UNIT: ONE DURATION: TWO WEEKS Focus Questions: 1. When do I collect data? 2. Where do I collect data? 3. How do I collect data? Collect data to solve simple problems using a variety of methods Use, construct and interpret simple graphs using a variety of methods Specific Objectives 1. Describe procedures for collecting data using observation, interview, or simple questionnaire 2. Identify similarities and differences between interviews and questionnaire 3. Explain when it is appropriate to use interviews and questionnaire to collect data 4. Select the data collection method that is appropriate for a particular problem situation, and 5. Give reasons for their selection 6. Plan data collection activities 7. Create problems whose solutions require data Key Observation Interview Data collection Suggested activities Skills Resources Assessment Identify and describe situations where data collection, representation, and interpretation could be used to solve problems Lead a discussion on the importance of data Allow pupils to observe and analyze data form tally chards and pictographs. Draft up questionnaire to collect data formulate and discuss problems that involve collecting data with pupils Discussing Selecting Problem solving Newspaper Magazines Clippings of graphs Squared paper Data collection research GRADE 6: STRAND: STATISTICS AND DATA HANDLING 18

19 UNIT TITLE: REPRESENTING DATA TERM: THREE UNIT: TWO DURATION: TWO WEEKS 1. What are the different methods to represent data? 2. What is the best method to represent data? Use, construct and interpret simple graphs using a variety of methods Specific Objectives 1. Select appropriate methods to represent data 2. Select appropriate scales to represent data graphically 3. Explain why a selected data representation method or scale is appropriate 4. Represent data using pictographs or bar charts 5. Identify similarities and differences between bar graphs and line graphs 6. Explain when it is appropriate to use bar graphs and line graphs to represent data Key Data Scales Tables Bar graphs Line graphs Pictographs Charts Suggested activities Skills Resources Assessment Through pictorial representation pupils are allowed to idnetify and select appropriate methods to represent data. Elicit form pupils the similarities and differences between two graphs Observing Researching Drawing Interpreting Presenting Interviewing Analyzing Individuals in class Handouts: Charts Graphs Pictographs Data Oral test GRADE 6: 19

20 STRAND: STATISTICS AND DATA HANDLING UNIT TITLE: INTERPRETING DATA TERM: THREE UNIT: THREE DURATION: TWO WEEKS 1. What are the different methods to represent data? 2. What does the data mean? Specific Objectives Key Suggested activities Skills Resources Assessment Use, construct and interpret simple graphs using a variety of methods 1. Read data presented in tables, pictographs, bar charts and line graphs 2. Interpret data presented in tables, pictographs, bar charts and line graphs 3. Calculate the mean / average mode, median and range of a set of data Data Scales Tables Bar graphs Line graphs Pictographs Charts Provide opportunity for pupils to read and interpret tables, bar charts and line graphs Determine the mean, mode, median and range of given data displayed using no more than 8 pieces of data and whole numbers without remainder. Apply the mean, mode, medium and range to solve problems or answer questions. Identifying information Reading data Answering questions Interpreting Presenting Calculating Data presented by students Handouts / sample: Charts Graphs Pictographs Data Work sheets Test Reports 20