sow for year 7

TEACHINGWEEK TOPICS AND OUTCOMES INSTRUCTIONAL APPROACHES AND STRATEGIES RESOURCES REMARKS

2 hours1. Numbers

1.1 Read and write and represent numbers up to 10 millions.

Review reading and writing numbers up to and greater than a million:a. Five million, three hundred and fifty four thousand and

twenty-five.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

Putting the words together, we have

“Five million four hundred and thirty-two thousand six

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

PMV YEAR 7 – FUNCTIONAL MATHEMATICS

6000

400

30

7

6000400

307

6437

51 2 0 3 7

hundred and fifty-seven”


4 hours1.2 Demonstrate

concretely and pictorially an understanding of place value to millions. 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 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

Flash cards

4 7 3 9 9

What will it read after one more car passes by?


2 hours 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).

1.3 Compare numbers

Guide 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 numbers

Place value boardFlash cards


3 hours 1.4 Round 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.

Number line strip.

3 hours

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).

1.5 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.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.


5 hours

2 hours

1.6 Multiply 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.

a. 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: 4 314

Estimate answers in calculations.

Check reasonableness of answers.


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

2 hours 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 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 = 40

35 x 10 = 350

572 x 10 = 5720

4519 x 10 = 45190


3 hours1.8Divide numbers

up to 4-digit by 1-digit (without

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

remainder). materials.

Use a similar approach for 4-digit divided by 1-digit.

Estimate answers in calculations.


Solve word problems involving division.

Example:

7 children shared $840 equally. How much did each child receive?


2 hours1.9 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 hours1.10 Combined

Operations

Perform 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


2. Fractions

3 hours2.1 Represent 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 etc

Name different fractions using a fraction charts.

Recognise unit fractions.

Compare unit fractions and arrange them in order of size.

Compare fractions using benchmarks such as half and one.

ONE WHOLE

Halve

Third

Fourth

Fifth

Sixth

(Denominators of given fractions should not exceed 12)



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

13= 412 ; show that

14= 312 .

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

× 3

× 3


Ali says that he can find equivalent fractions of any give fraction by multiplying the numerator and denominator by the same numeral as follows:

34 =

912 . 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:

35 , 27 ,

58

2 hours2.3 Compare

proper fractions. With the help of the fraction chart put the following

fractions in order of size:

12,56,34,

Discuss other methods of comparing fractions such as finding their equivalent forms;

Fraction charts

4

9



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.

94 =

44 +

44 +

14

= 2

14

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.

1 eighth3 eighths4 eighths

Guide pupils to do this by computation.


3 hours 2.5 Add 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:

18 +

38 =

48

or

Subtraction of like fraction

45−15 =

35

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:

14 +

38 =

28 +

38 =

58

When addition of fractions gives an improper fraction then the

answer is written as a mixed number.


3. Decimals1 hour 3.1 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.


Guide 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

Another way of looking at ones and tenths are as follows:

s

decimal places.

Provide pupils ample practice on

writing decimals

based on diagrams and decimal grids.

2 hours3.3 State the value of

the digits in the tenth place and the hundredth place.


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 + 7 hundredths

Twenty seven hundredths is written as: 0.27

or 3.27 = 3 +

210 +

7100

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 hours 3.4 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, 35.0

Arrange 3 or more decimal numbers in order of size.

Example:

0.03, 0.32, 0.4, 0.41 (ascending order)


3 hours3.5 Add and subtract

decimals to hundredths, concretely,

Add and subtract decimals up to 2-decimal places without using calculator.

Estimate and check answers in calculations.


2 . 3 4 0 . 2 2 . 5 4

tenth

32hundredth

24

thousandth

0

pictorially and symbolically. Use the decimal grid to arrange decimal numbers for

addition and subtraction.

Example 1: 0.3 + 0.14

Example 2: 2.34 + 0.2

Solve word problems involving decimals including adding and subtracting money.

Shopping list.


4. Measurement

3 hours 4.1 Basic units of measurements

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.

Measuring devices.

a. Appreciate the basic units for measuring length, mass and volume.

- 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).

4 hours b. Carry 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.


Convert 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 600ml

4 hours 4.2 Add and subtract units of measurement

Add and subtract units of measurement involving compound units.Example

20m 75cm + 35m 55cm

5kg 370g – 2kg 500g

Solve word problems involving units of measurement of length, mass and volume.


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.


5. Geometry

2 hours 5.1 Parallel and perpendicular lines

Recognise and name parallel, perpendicular, horizontal and vertical lines.

Draw parallel and perpendicular lines using protractor, set squares and ruler only,

6 hours5.2 Angles Use 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 wedges

Introduce 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?


Place 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 x

Draw angles using a protractor.

Use the following properties to find unknown angles,- angles on a straight line- angles at a point,- vertically opposite angles,- alternate angles- corresponding angles

(exclude drawing and measuring reflex angles).

3 hours5.3 Rectangles and squares

Investigate 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).


6. Statistics

2 hours6.1 U

se 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 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 hours6.2

Tables, bar graphs and line graphs

Complete 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.

sow for year 7

Documents

digit numbers

possible numbers

round numbers

subtraction of numbers

number words

rounding of midway numbers

greatest possible number

number of cars