TEACHINGWEEKPMV YEAR 7 – FUNCTIONAL MATHEMATICSTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS2 hours1. NumbersRead and write and represent numbers up to 10 millions.Review reading and writing numbers up to and greater than a million:Five million, three hundred and fifty four thousand and twenty-five.Write in words: 9 234 207.Write a whole number as an expanded numeral using powers of 10.e.g. 234 567 = 200 000 + 30 000 + 4 000 + 500 + 60 + 7Rewrite using number words or numerals5 000 000five million400 000four hundred thousand30 000thirty thousand 2 000two thousand 600six hundred50fifty7sevenExample: Read 5 432 657Putting the words together, we have“Five million four hundred and thirty-two thousand six hundred and fifty-seven”TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS4 hoursDemonstrate concretely and pictorially an understanding of place value to millions.6000400 30 76000400307 6437 Read each of these numbers individually and then combine them to form the required number. Guide pupils to read this number as: “Six thousand four hundred and thirty-seven”.Number cards512037Use these digits to form- the greatest possible number,-the least possible number,- five other possible numbers,- write these numbers in words,- arrange the numbers you have formed from the least to the greatest.The police department is counting the number of cars on a certain road. The counting meter now reads47399What will it read after one more car passes by?Flash cardsTEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS2 hoursYou are given the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Put one digit in each box so that the answer will be as large as possible. 4 231 = (a digit can be used only once).Put one digit in each box so that the answer will be as small as possible. (a digit can 431 2 = be used only once).1.3 Compare numbersGuide students to arrange numbers in order of size. Use a place-value board if necessary to help pupils understand the process of comparing numbers.Activities on compare numbersPlace value boardFlash cards
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS3 hours3 hoursRound off numbers to the nearest, 10, 100 and 1000.Explain the importance of rounding off in everyday life.Review the meaning of the word “nearest”. Review rounding of whole numbers less than 100 to the nearest 10.Round numbers to the nearest 100. Use an appropriate number line.Example: 236 is nearer to 200 than 300. Therefore, 236 is rounded off as 200, to the nearest hundred.Discuss the case of 250 being round off as 300 by convention (as in the case of 25 being rounded off as 30).Round off 5-digit numbers and discuss the rounding of mid-way numbers such as 3500 is rounded off as 4000 (to the nearest 1000).Number line strip.Addition and subtraction of numbers up to 10 000.Add and subtract numbers up to two 3-digit numbers without using calculators.Use calculators for adding and subtracting 4-digit numbers.Estimate and add or subtract.287 + 156 (first estimate by rounding)= 300 + 160. Therefore the sum should be around 460.1092 - 363, (first estimate by rounding)= 1100 – 400. Therefore the difference should be around 700.Solve word problems.Check reasonableness of answers.TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS5 hours2 hoursMultiply and divide numbers up to 10 000 either by computation or by using a calculator.Review the basic facts of multiplication and division. The basic facts of multiplication are made up all multiplication involving single digit numbers from 0 × 0 up to 9 × 9.Discuss with pupils some techniques for remembering the basic facts of multiplication.Review the basic facts of division. Show pupils the connection between multiplication and division.Multiply and divide within the multiplication tables (0 × 0 up to 12 × 12) without using calculators.Use calculators for multiplication and division involving large digits.Solve word problems.1.7 Multiply whole numbers up to 4-digit by 1-digit.Multiply a 3-digit or a 4-digit number by a 1-digit number.Review basic multiplication facts. Conduct regular mental quizzes using flash cards or short written practices on these facts to ensure that all pupils have acquired mastery of basic multiplication facts to the level of rapid recall.Review multiplication of 2-digit numbers by 1-digit number. Demonstrate an example of this multiplication by using concrete materials. Relate the concrete multiplication to the symbolic form.Multiply a 3-digit number by a 1-digit number.Example: 4 314Estimate answers in calculations.Check reasonableness of answers.TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS2 hoursGuide pupils to estimate the product before multiplying. 314 is about 300. The product of 300 and 4 is 1200.The actual answer should be around 1200. 314 = 300 + 10 + 4 4 314 = 4 ( 300 + 10 + 4) = 1200 + 40 + 16 = 1256Use a similar approach to multiply a 4-digit number by a 1-digit number.Consolidate the vertical format of multiplicationMultiply a 4-digit number by 10.Discuss multiplication of 1-digit, 2-digit and 3-digit numbers by 10 before proceeding to 4-digit numbers.Examples:4 x 10 = 4035 x 10 = 350572 x 10 = 57204519 x 10 = 45190TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS3 hours1.8Divide numbers up to 4-digit by 1-digit (without remainder).Review division algorithm involving 2 and 3 digit numbers and 1-digit divisors. Use concrete materials and drawing techniques before moving on to symbolic techniques. Establish the symbolic representation by using concrete materials.27813029210Use a similar approach for 4-digit divided by 1-digit.Estimate answers in calculations.Check reasonableness of answers.Solve word problems involving division. Example:7 children shared $840 equally. How much did each child receive?TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS2 hoursFactors and multiplesDetermine if a 1-digit number is a factor of a given number.List all the factors of a given number up to 100.Find common factors of two given numbers.Recognise relationships between factors and multiples.Determine if a number is a multiple of a given 1-digit number.List the first 10 multiples of a given 1-digit number.Find the common multiples of two given numbers up to 12.2 hours1.10 Combined OperationsPerform combined operation involving up to 3 different operations.Example: 85 – 12 x 5 + 16 36 + 108 ÷ 9 – 23 Use of brackets in expression involving different operations.Example: 6 x (12 + 30) – 45 36 ÷ 6 + (30 x 4) (78 + 45) ÷ 3 + 34
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS2. Fractions3 hoursRepresent and describe proper fractions concretely, pictorially and symbolically.Recognise and name fractional parts of a whole.Illustrate and explain halves, thirds, fourths, fifths, sixths, eighths and tenths as part of a region. (use fraction circles, fraction board and geometrical shapes).Use everyday examples such as splitting a pizza, fruit etcName different fractions using a fraction charts.ONE WHOLEHalveThirdFourthFifthSixthRecognise unit fractions.Compare unit fractions and arrange them in order of size.Compare fractions using benchmarks such as half and one. (Denominators of given fractions should not exceed 12)TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS2 hoursDemonstrate and describe equivalent proper fractions concretely, pictorially and symbolically.Recognise and name equivalent fractions.List the equivalent fractions of a given fraction.With the help of fraction strips and using the fraction chart below show that ; show that .Write the equivalent fraction of a given fraction given the numerator or the denominator.Express a given fraction in its simplest form.HalvesThirdsFourthsFifthsTEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKSAli says that he can find equivalent fractions of any give fraction by multiplying the numerator and denominator by the same numeral as follows:× 3× 3 = . Is Ali correct? Use the fraction chart above to confirm Ali’s claim. Use this method to find several equivalent fraction for the following fractions: , , 2 hoursCompare proper fractions.With the help of the fraction chart put the following fractions in order of size: Discuss other methods of comparing fractions such as finding their equivalent forms; Fraction charts
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS3 hoursDemonstrate and explain meaning of improper fractions and mixed numbers and their equivalents concretely, pictorially and symbolically.Express an improper fraction as a mixed number and vice versa.Display a set of fraction pieces of the same size. Use parts of a fraction circle as shown below. Guide pupils to name the fractions represented by it. 9 pieces of is = + + = 2Lead pupils to see that an improper fraction is a number equal to or greater than 1 that is an improper fraction can be written as a whole number or a mixed number.Guide pupils to do this by computation.TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS3 hoursAdd and subtract simple fractions concretely, pictorially and symbolically.Add and subtract like fractions.The pupils have learned the concept of fractions and renaming fractions in their equivalent form. At this stage of learning fractions pupils would be familiar with adding and subtracting like fraction For example: + = 1 eighth3 eighths4 eighths orSubtraction of like fraction = Add and subtract of related fractions.In the case of related fractions, the fractions are first changed into like fractions before addition or subtraction.Example: + = + = When addition of fractions gives an improper fraction then the answer is written as a mixed number.
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS3. Decimals1 hour3.1 Read, write and interpret decimals up to 1 decimal place.Guide pupils to understand that the decimal notation is another way of recording fractional quantities.Use the place-value mat to help pupils see the extension of the place value notation to include fractional numbers such as tenths and hundredths.Introduce notation and place-values up to 3 decimal places.
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKSsGuide pupils to understand that the numbers to the right of the dot (or point) represent the fractional part.1 hour3.2 Read, write and interpret decimals up to 2 decimal places.Another way of looking at ones and tenths are as follows:699770221615Provide pupils ample practice on writing decimals based on diagrams and decimal grids.2 hoursState the value of the digits in the tenth place and the hundredth place. Twenty seven hundredths is written as: 0.27 TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKSKnow what each digit represents. Partition numbers into tenths and hundredths.Example: In the number 3.27, the digit 3 represents 3 ones, the digit 2 represents 2 tenths and the digit 7 represents 7 hundredths. Or 3.27 = 3 + 2 tenths + 7 hundredths or 3.27 = 3 + + Use the place-value mat for this purpose.Explain that 0.3 and 0.30 as representing the same value and that 3 tenths equal 30 hundredths. 2 hours3.4 Compare and order decimal numbers up to 2 decimal places.Use the models or the decimal grids to help pupils compare two decimal numbers up to 1- and 2-decimal places. Example: Circle the smaller of the two decimal numbers:(1) 2.34, 2.09(2) 34.98, 35.0Arrange 3 or more decimal numbers in order of size. Example: 0.03, 0.32, 0.4, 0.41 (ascending order)TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS3 hours3.5 Add and subtract decimals to hundredths, concretely, pictorially and symbolically.Add and subtract decimals up to 2-decimal places without using calculator.Estimate and check answers in calculations.Check reasonableness of answers.Use the decimal grid to arrange decimal numbers for addition and subtraction.Example 1: 0.3 + 0.140 . 3 0 . 1 4 0 . 4 4tenth30hundredth14thousandth0Example 2:2.34 + 0.22 . 3 4 0 . 2 2 . 5 4tenth32hundredth24thousandth0Solve word problems involving decimals including adding and subtracting money.Shopping list.TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS4. Measurement3 hours4.1 Basic units of measurementsAppreciate the basic units for measuring length, mass and volume.Select and use the most appropriate unit to measure a given length mass and volume.Provide students with measuring devices to measure and perform calculations.Measure the length of different items in the classroom using millimetre, centimetres and metres as the unit of measure. Determine the most suitable unit for measuring different length. What other units would you have chosen?Example: Ask pupils to measure the length of their desk in mm. Is this unit the most appropriate unit for measuring the length of the desk? Practical activities on length of different items.Try similar activities for mass and volume.Practical activities on estimation for length mass and volume of different items (restricted to whole and half of compound unit).Measuring devices.4 hoursCarry out conversions between units in each of these measurements.Review basic units of measurement. Measure in compound units: Length: kilometre (km), metre (m), centimetre (cm), millimetre (mm).Mass:kilogram (kg), gram (g)Volume:litres (l), millilitres (ml)Make measurement using real measuring instruments such as measuring tapes, measuring cylinders and weighing scales. TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKSConvert a unit of measurement from a smaller unit to a larger unit in decimal form and vice versa,Kilometres and metres,Millimetres and centimetres,Metres and centimetres,Kilograms and grams,Litres and millilitres.(use practical activities where necessary)Guide pupils to carry out the following conversion.Examples: 4m 50cm = 450cm 2060m = 2km 60m. 5kg 400g = 5400g 1600ml = 1l 600ml4 hours4.2Add and subtract units of measurementAdd and subtract units of measurement involving compound units.Example 20m 75cm + 35m 55cm 5kg 370g – 2kg 500gSolve word problems involving units of measurement of length, mass and volume.
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS5 hours4.3 TimeConvert units of time.Find the duration of a time interval.Introduce the 24-hour clock.Convert time between the 12-hour clock and the 24-hour clock.Read time-tables involving the 24-hour clock such as flight schedules, and shipping schedules.Solve word problems involving time.Examples:1. Royal Brunei Airlines flight to Singapore departs BSB for Singapore at 18:15 and arrives in Singapore at 20 15. Write this time using the 12-hour notation.2. A parking bay shows the sign “No Parking” from 15 00 to 17 30. Write this time in the 12-hour notation.5 hours4.4 Area and perimeterUnderstand perimeter as the distance around the outer boundary of a shape or figure.Find the perimeter of a rectilinear figure.Review area of square and rectangle.Find the area of a figure made up of rectangles and squares.98742547625Find one dimension of a rectangle or square given the other dimension and its area or perimeter.Solve word problems involving area/perimeter of squares and rectangles.TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS5. Geometry2 hours5.1 Parallel and perpendicular linesRecognise and name parallel, perpendicular, horizontal and vertical lines.Draw parallel and perpendicular lines using protractor, set squares and ruler only,6 hours5.2 AnglesUse angle notation such as ABC and x to name angles.Estimate and measure angles in degrees.Use wedges to estimate the size of angles.Example: The size of this angle is about 4 wedgesIntroduce the wedge protractor.The size of each wedge must be kept constant and draw a wedge protractor with 12 wedges as shown in the diagram. Carry out activities to measure given angles (acute and obtuse angles) drawn on paper using the wedge protractor. Ask: how many wedges make this angle?TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKSPlace the wedge protractor over an angle that is to be measured and read off the value of the angle in terms of the number of wedges. Discuss the similarity between the wedge protractor and the real protractor. Use the real protractor to measure angles. Name angles using conventions such as ABC or xDraw angles using a protractor.Use the following properties to find unknown angles,angles on a straight lineangles at a point,vertically opposite angles,alternate anglescorresponding angles (exclude drawing and measuring reflex angles).3 hours5.3 Rectangles and squaresInvestigate the properties of squares and rectangles.Draw rectangles and squares from a given dimension using ruler, protractor and set squares. (exclude the term “diagonals” and its related properties).
TEACHINGWEEKTOPICS AND OUTCOMESINSTRUCTIONAL APPROACHES AND STRATEGIESRESOURCESREMARKS6. Statistics2 hoursUse a variety of methods to collect and record data.Use various methods of collecting data.Examples: Observation,Questionnaires, Interviews and measurement. Select appropriate methods for collecting dataDesigning and using simple questionnaire;Observations;Interviews;Surveys. Note:This section of the syllabus lends itself to useful practical activities. Teachers are expected to guide students to conduct practical activities in the design of questionnaire and the collection and tabulation of data. Data can be collected from within the school or from sources outside of school.4 hours6.2 Tables, bar graphs and line graphsComplete a table/bar graph from given data or from data collected from practical activities.Read and interpret tables, bar graphs and line graphs.Solve problems from information presented in tables/bar graphs and line graphs.