PMV YEAR 7 – FUNCTIONAL MATHEMATICSTEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS
1. Numbers2 hours 1.1 Read and write and Review reading and writing numbers up to and greater than a million: represent numbers up a. Five million, three hundred and fifty four thousand and twenty-five. to 10 millions. b. Write in words: 9 234 207. c. Write a whole number as an expanded numeral using powers of 10. e.g. 234 567 = 200 000 + 30 000 + 4 000 + 500 + 60 + 7 Rewrite using number words or numerals Example: Read 5 432 657 5 000 000 five million 400 000 four hundred thousand 30 000 thirty thousand 2 000 two thousand 600 six hundred 50 fifty 7 seven Putting the words together, we have “Five million four hundred and thirty-two thousand six hundred and fifty- seven”
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 6000 Number cards 4 hours 1.2 Demonstrate 400 6000 concretely and 30 400 pictorially an 30 6437 understanding of 7 7 place value to Read each of these numbers individually and then combine them to millions. form the required number. Guide pupils to read this number as: “Six thousand four hundred and thirty-seven”. 1 5 2 0 3 7 Flash cards Use 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 reads 4 7 3 9 9 What will it read after one more car passes by?
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS You 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). 2 hours 1.3 Compare numbers Guide students to arrange numbers in order of size. Use a place-value Place value board board if necessary to help pupils understand the process of comparing Flash cards numbers. Activities on compare numbers
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 3 hours 1.4 Round off numbers Explain the importance of rounding off in everyday life. to the nearest, 10, Number line strip. 100 and 1000. 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). 3 hours 1.5 Addition and Add and subtract numbers up to two 3-digit numbers without using subtraction of calculators. numbers up to 10 000. Use calculators for adding and subtracting 4-digit numbers. Estimate and add or subtract. a. 287 + 156 (first estimate by rounding) = 300 + 160. Therefore the sum should be around 460. b. 1092 - 363, (first estimate by rounding) = 1100 – 400. Therefore the difference should be around 700. c. Solve word problems. d. Check reasonableness of answers.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Review the basic facts of multiplication and division. The basic facts of 1.6 Multiply and divide multiplication are made up all multiplication involving single digit numbers 5 hours numbers up to 10 000 from 0 × 0 up to 9 × 9. either by computation or by using a Discuss with pupils some techniques for remembering the basic facts of calculator. 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 Review basic multiplication facts. Conduct regular mental quizzes using numbers up to 4-digit flash cards or short written practices on these facts to ensure that all 2 hours pupils have acquired mastery of basic multiplication facts to the level of by 1-digit. 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. a. Multiply a 3-digit or Multiply a 3-digit number by a 1-digit number. a 4-digit number by Example: a 1-digit number. 4 × 314 Estimate answers in calculations. Check reasonableness of answers.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Guide pupils to estimate the product before multiplying. o 314 is about 300. The product of 300 and 4 is 1200. o The actual answer should be around 1200. 314 = 300 + 10 + 4 4 × 314 = 4 × ( 300 + 10 + 4) = 1200 + 40 + 16 = 1256 Use a similar approach to multiply a 4-digit number by a 1-digit number. Consolidate the vertical format of multiplication b. Multiply a 4-digit Discuss multiplication of 1-digit, 2-digit and 3-digit numbers by 10 before 2 hours number by 10. proceeding to 4-digit numbers. Examples: 4 x 10 = 40 35 x 10 = 350 572 x 10 = 5720 4519 x 10 = 45190
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Review division algorithm involving 2 and 3 digit numbers and 1-digit 3 hours 1.8 Divide numbers up to divisors. Use concrete materials and drawing techniques before moving on to symbolic techniques. 4-digit by 1-digit (without remainder). Establish the symbolic representation by using concrete materials. Use 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?
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 2 hours 1.9 Factors and multiples Determine 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 hours 1.10 Combined Perform combined operation involving up to 3 different operations. 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
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 2. Fractions Recognise and name fractional parts of a whole. 2.1 Represent and 3 hours describe proper Illustrate and explain halves, thirds, fourths, fifths, sixths, eighths and fractions concretely, tenths as part of a region. (use fraction circles, fraction board and pictorially and geometrical shapes). symbolically. Use everyday examples such as splitting a pizza, fruit etc Name different fractions using a fraction charts. ONE WHOLE Halve Third Fourth Fifth Sixth Recognise 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)
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 2 hours 2.2 Demonstrate and Recognise and name equivalent fractions. describe equivalent proper fractions List the equivalent fractions of a given fraction. concretely, pictorially With the help of fraction strips and using the fraction chart below show and symbolically. 1 4 1 3 that = ; show that = . 3 12 4 12 Write the equivalent fraction of a given fraction given the numerator or the denominator. Express a given fraction in its simplest form. Halves Thirds Fourths Fifths
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Ali 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 9 = . Is Ali correct? Use the fraction chart above to confirm Ali’s 4 12 ×3 claim. Use this method to find several equivalent 3 2 5 fraction for the following fractions: , , 5 7 8 2 hours 2.3 Compare proper With the help of the fraction chart put the following fractions in order Fraction charts fractions. 1 5 3 of size: , , , 2 6 4 Discuss other methods of comparing fractions such as finding their equivalent forms;
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 3 hours 2.4 Demonstrate and Express an improper fraction as a mixed number and vice versa. explain meaning of improper fractions 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 and mixed numbers by it. and their equivalents concretely, pictorially and symbolically. 9 pieces of is 9 4 4 1 = + + 4 4 4 4 1 = 2 4 Lead 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.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Add and subtract like fractions. 2.5 Add and subtract The pupils have learned the concept of fractions and renaming fractions 3 hours simple fractions in their equivalent form. At this stage of learning fractions pupils would concretely, pictorially be familiar with adding and subtracting like fraction and symbolically. For example: 1 3 4 + = 8 8 8 1 eighth 3 eighths or 4 eighths Subtraction of like fraction 4 1 3 − = 5 5 5 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: 1 3 2 3 5 + = + = 4 8 8 8 8 When addition of fractions gives an improper fraction then the answer is written as a mixed number.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 3. Decimals 1 hour 3.1 Read, write and Guide pupils to understand that the decimal notation is another way of interpret recording fractional quantities. decimals up to 1 Use the place-value mat to help pupils see the extension of the place value notation to include fractional numbers such as tenths and decimal place. hundredths. Introduce notation and place-values up to 3 decimal places.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Guide pupils to understand that the numbers to the right of the dot (or s point) represent the fractional part. Another way of looking at ones and tenths are as follows: 1 hour 3.2 Read, write and interpret decimals up to 2 decimal places. Provide pupils ample practice on writing decimals based on diagrams and decimal grids. 2 hours 3.3 State the value of the digits in the tenth Twenty seven hundredths is written as: 0.27 place and the hundredth place.TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS Know 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 +hundredth thousandth tenth 7 hundredths tenth hundredth thousandth 2 7 0.3 .34 2 or 3.27 =•3 +3 3 + 0 2 • 4 0 . 1 42 0. 0 0 • • 10 1 2 4100 0 . 4 45 4 2.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 5 hours 4.3 Time Convert 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 hours 4.4 Area and perimeter Understand 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. Find 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.TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 5. Geometry 2 hours 5.1 Parallel and Recognise and name parallel, perpendicular, horizontal and vertical lines. perpendicular lines Draw parallel and perpendicular lines using protractor, set squares and ruler only, 6 hours 5.2 Angles Use angle notation such as ABC and x to name angles.
TEACHING WEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS 6. Statistics 2 hours 6.1 Use a variety of Use various methods of collecting data. methods to collect Examples: and record data. - Observation, - Questionnaires, - Interviews and measurement. Select appropriate methods for collecting data - Designing 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 hours 6.2 Tables, bar graphs Complete a table/bar graph from given data or from data collected from and line graphs practical activities. Read and interpret tables, bar graphs and line graphs. Solve problems from information presented in tables/bar graphs and line graphs.