PAGE 1: Learning outcomes OVERVIEW ======== Length tells us how long, wide, tall or far something is. In this sub-strand you will use the centimetre and the metre, measure and estimate lengths, change metres to centimetres and back, find the perimeter of shapes, and add, subtract, multiply and divide lengths in metres and centimetres. ## Strand 2.0: Measurement Sub-strand 2.1: Length Suggested lessons: 10 ## What this sub-strand covers • Centimetres as unit of length • Measure length in cm • Converting length • Perimeter of plane figures • Operations in length ## Source • KICD Grade 4 Mathematics Curriculum Design (Revised 2024) — Strand 2.0 Measurement, Sub-strand 2.1 Length • KICD Grade 4 Mathematics radio lessons: Metres to centimetres; Perimeter ## Learning outcomes By the end of the sub-strand, the learner should be able to: a) identify the centimetre as a unit of measuring length in real-life situations b) measure length in centimetres in real life- situations c) establish the relationship between metres and centimetres practically d) convert metres to centimetres and centimetres to metres in real-life situations e) work out perimeter of plane figures in different contexts f) work out addition involving length in metres and centimetres in real-life situations g) work out subtraction involving length in metres and centimetres in real-life situations h) carry out multiplication involving metres and centimetres in real life- situations i) carry out division involving metres and centimetres in real-life situations j) appreciate use of metres and centimetres in measuring distance in real life ## Key inquiry questions 1. How can you measure distance? 2. Why should we measure distance in real life? PAGE 2: How we will learn ## Learning experiences • team up with peers to identify the centimetre and mark out lengths of one centimetre using a ruler • work with peers to measure the length of a given object in centimetres using a metre ruler or a tape measure • jointly work with peers to estimate the length of a given object in centimetres • measure the actual length of the estimated length in centimetres • share tasks while measuring the length of objects in classrooms in metres and centimetres and establish the relationship between the units • work with peers to use the relationship between centimetres and metres • convert metres into centimetres and centimetres into metres using whole numbers, decimals or fractions • team up with peers to calculate the perimeter of plane figures • perform addition and subtraction involving metres and centimetres • work out multiplication involving metres and centimetres • team up with peers to work out division involving metres and centimetres • share tasks with peers while playing digital games involving length ## Core competencies • Learning to learn: learner measures length of objects in classrooms in metres and centimetres and establishes the relationship between the units. • Critical thinking and problem solving: learner demonstrates autonomy in measuring the length of a given object in centimetres using a metre ruler or a tape measure. ## Values • Responsibility: learner takes care of a metre ruler and a tape measure while measuring lengths of objects. ## Pertinent and contemporary issues • Self-awareness: learner estimates and measures the length of a given object in centimetres using a metre ruler or a tape measure. ## Links to other learning areas • The learner is able to relate the measurement of the length of objects to preparing planting sites and planting in Agriculture. PAGE 3: Lesson 1: The centimetre as a unit of length — The centimetre LESSON 1: THE CENTIMETRE AS A UNIT OF LENGTH ============================================ ## What you will learn • Identify the centimetre on a ruler. • Mark out lengths of one centimetre and more using a ruler. Curriculum outcomes: a) identify the centimetre as a unit of measuring length in real-life situations ## Introduction Look at your ruler. It has many small lines and the numbers 0, 1, 2, 3 and so on. The space between two numbers that follow each other is one centimetre. It is a small unit that helps us measure short things like a pencil, an eraser or the side of a book. ## Notes Length is how long something is from one end to the other. To say how long something is, we need a unit of length. One common unit is the centimetre. ### The centimetre We write centimetre in short as cm. On a ruler, the distance from 0 to 1 is 1 cm. The distance from 1 to 2 is also 1 cm, and so on. Every centimetre on a ruler is exactly the same length. Many school rulers are 30 cm long. A metre rule, which teachers use on the chalkboard, is 100 cm long. One centimetre is small. The width of the fingernail on a child's small finger is about 1 cm. This helps you picture the size of a centimetre, but only a ruler gives an exact measurement. ### Marking out centimetres To draw a line 1 cm long: - Put the ruler flat on the paper. - Put a dot at the 0 mark. - Put a second dot at the 1 mark. - Join the two dots with a straight line. To draw a line 6 cm long, start at 0 and stop at 6. PAGE 4: Lesson 1: The centimetre as a unit of length — Reading a length on a ruler ### Reading a length on a ruler Always start measuring from 0, not from the edge of the ruler, because some rulers have a small space before the 0 mark. If an object starts at 0 and ends at 8, it is 8 cm long. If you cannot start at 0, subtract. A line that starts at the 3 mark and ends at the 10 mark is 10 − 3 = 7 cm long. The small lines between two numbers are millimetres. You will learn about them later; for now, measure to the nearest whole centimetre. [DIAGRAM] TYPE: svg ALT: A ruler from 0 to 10 cm. The red line shows 1 cm, from the 0 mark to the 1 mark. PAYLOAD: CAPTION: A ruler from 0 to 10 cm. The red line shows 1 cm, from the 0 mark to the 1 mark. [/DIAGRAM] PAGE 5: Lesson 1: The centimetre as a unit of length — Summary ## Key words • length — how long something is from one end to the other • centimetre (cm) — a small unit of length; the space between two numbers next to each other on a ruler • ruler — a straight strip marked in centimetres used to measure and draw lines ## Worked examples ### Example 1 A line starts at the 0 mark and ends at the 9 mark on a ruler. How long is it? Working: 1. The line starts at 0. 2. It ends at 9, so it covers 9 spaces of 1 cm. Answer: 9 cm ## Worked examples ### Example 2 A crayon lies on a ruler from the 4 mark to the 12 mark. How long is the crayon? Working: 1. It does not start at 0, so subtract the start from the end. 2. 12 − 4 = 8 Answer: 8 cm ## Activity: Marking out centimetres You will need: Ruler, Pencil, Exercise book 1. Work with a partner. Each of you finds the 0 mark and the 1 mark on your ruler. 2. Draw a line exactly 1 cm long and label it 1 cm. 3. Take turns to call out a length from 2 cm to 15 cm. The partner draws a line of that length. 4. Swap books and use your ruler to check each other's lines. ## Practice 1. What is the short way of writing centimetre? 2. A line starts at 0 and ends at 13 on a ruler. How long is it? 3. A nail lies on a ruler from the 2 mark to the 7 mark. How long is the nail? 4. How many centimetres long is a metre rule? ## Answers to practice 1. cm 2. 13 cm 3. 5 cm 4. 100 cm ## Summary • The centimetre (cm) is a unit for measuring short lengths. • On a ruler, the space between two numbers next to each other is 1 cm. • Start measuring from the 0 mark, or subtract the starting mark from the end mark. LESSON 2: ESTIMATING AND MEASURING LENGTH IN CENTIMETRES ======================================================== ## What you will learn • Estimate the length of an object in centimetres. • Measure the actual length using a ruler, metre rule or tape measure. • Find the difference between the estimate and the actual length. Curriculum outcomes: b) measure length in centimetres in real life- situations ## Introduction Before a tailor cuts cloth, she measures carefully with a tape measure. Before you measure, you can make a clever guess called an estimate. Then the ruler tells you how close you were. ## Notes ### Choosing a measuring tool - A 30 cm ruler is good for short things like a pencil, an exercise book or a leaf. - A metre rule (100 cm) is good for longer things like a desk, a window or a door. - A tape measure bends, so it can go around round objects such as a water jug, a tree trunk or your head. PAGE 6: Lesson 2: Estimating and measuring length in centimetres — Estimating ### How to measure - Put the 0 mark exactly at one end of the object. - Keep the ruler straight along the edge of the object. - Read the mark at the other end of the object. - Write the answer with its unit, for example 17 cm. If the object is longer than your ruler, mark where the ruler ends with a pencil, move the ruler and keep measuring from the mark. Then add the parts. A desk measured as one full 30 cm ruler, another full 30 cm ruler and then 12 cm more is 30 + 30 + 12 = 72 cm long. ### Estimating An estimate is a sensible guess made by thinking about sizes you already know. If you know your ruler is 30 cm, you can look at a book and say, "It is a bit shorter than my ruler, maybe 25 cm." After estimating, measure the actual length. Find the difference by subtracting the smaller number from the bigger number. If you estimated 20 cm and the actual length is 17 cm, your estimate was 20 − 17 = 3 cm too long. The more you practise, the closer your estimates become. Take care of the metre rule and tape measure: do not bend, step on or play with them, so that the markings stay clear for everyone. ## Key words • estimate — a careful guess of a measurement before measuring • actual length — the length found by measuring with a ruler or tape measure • tape measure — a measuring tape that can bend around objects ## Worked examples ### Example 1 Wanjiru estimated that her exercise book is 25 cm long. She measured it and found it is 21 cm. By how much was her estimate off? Working: 1. Subtract the smaller number from the bigger one. 2. 25 − 21 = 4 Answer: Her estimate was 4 cm too long. ## Worked examples ### Example 2 Otieno measured the length of the teacher's table with a 30 cm ruler. The ruler fitted 4 times, and then 15 cm more. How long is the table? Working: 1. 4 full rulers: 30 + 30 + 30 + 30 = 120 cm 2. Add the extra part: 120 + 15 = 135 cm Answer: 135 cm PAGE 7: Lesson 2: Estimating and measuring length in centimetres — Practice ## Activity: Estimate, then measure You will need: Ruler, Metre rule or tape measure, Table for recording drawn in exercise books 1. In groups, choose five objects in the classroom, for example a pencil, a duster, a desk, a window and the door. 2. Draw a table with the columns Object, Estimate (cm), Actual length (cm) and Difference (cm). 3. Each member writes an estimate for each object. 4. Measure the actual length of each object together using a ruler, metre rule or tape measure, and record it. 5. Work out the difference for each estimate. Who in your group made the closest estimates? ## Practice 1. Which tool is best for measuring around a tree trunk: a ruler, a metre rule or a tape measure? 2. Amina estimated a stick to be 40 cm long. Its actual length is 46 cm. What is the difference? 3. A 30 cm ruler fits along a bench 3 times with 8 cm left over. How long is the bench? 4. Why should you place the 0 mark at the end of the object when measuring? ## Answers to practice 1. A tape measure, because it can bend around the trunk. 2. 6 cm 3. 98 cm 4. So that the number at the other end gives the true length of the object. ## Summary • Choose a ruler, metre rule or tape measure to suit the object. • An estimate is a sensible guess; measuring gives the actual length. • Difference = bigger length − smaller length. LESSON 3: METRES AND CENTIMETRES ================================ ## What you will learn • State that 1 metre is equal to 100 centimetres. • Convert metres to centimetres and centimetres to metres. • Convert lengths given in fractions or decimals of a metre. Curriculum outcomes: c) establish the relationship between metres and centimetres practically; d) convert metres to centimetres and centimetres to metres in real-life situations ## Introduction Put a 30 cm ruler next to a metre rule. You will need a little more than three rulers to cover the metre rule. Long lengths like a classroom or a football pitch are measured in metres, not centimetres. ## Notes ### The metre The metre is a bigger unit of length. We write it in short as m. Lay 1 cm rulers side by side along a metre rule and you find that: 1 metre = 100 centimetres The height of a classroom door is about 2 m. The length of a classroom may be several metres. ### Metres to centimetres: multiply by 100 Each metre has 100 cm, so multiply the number of metres by 100. - 3 m = 3 × 100 = 300 cm - 7 m = 700 cm If there are metres and centimetres, change the metres and then add the centimetres: - 4 m 25 cm = 400 cm + 25 cm = 425 cm - 2 m 8 cm = 200 cm + 8 cm = 208 cm PAGE 8: Lesson 3: Metres and centimetres — Example 1 ### Centimetres to metres: divide by 100 - 600 cm = 600 ÷ 100 = 6 m - 356 cm = 3 m 56 cm, because 300 cm make 3 m and 56 cm are left. ### Fractions of a metre - Half a metre: ½ m = 100 ÷ 2 = 50 cm - A quarter of a metre: ¼ m = 100 ÷ 4 = 25 cm - Three quarters of a metre: ¾ m = 3 × 25 = 75 cm - 2½ m = 200 cm + 50 cm = 250 cm ### Decimals of a metre A decimal can also show part of a metre. 0.5 m means 5 tenths of a metre, which is 50 cm. 1.5 m = 150 cm and 2.25 m = 225 cm. To change centimetres to a decimal of a metre, divide by 100: 175 cm = 1.75 m. ## Key words • metre (m) — a unit of length equal to 100 centimetres • convert — change a measurement from one unit to another ## Worked examples ### Example 1 Convert 5 m 60 cm to centimetres. Working: 1. 5 m = 5 × 100 = 500 cm 2. 500 cm + 60 cm = 560 cm Answer: 560 cm ## Worked examples ### Example 2 Convert 709 cm to metres and centimetres. Working: 1. 700 cm = 7 m 2. 9 cm are left over. Answer: 7 m 9 cm ## Worked examples ### Example 3 A ribbon is ¾ m long. How many centimetres is that? Working: 1. ¼ m = 100 ÷ 4 = 25 cm 2. ¾ m = 3 × 25 cm Answer: 75 cm ## Worked examples ### Example 4 Write 1.5 m in centimetres. Working: 1. 1.5 × 100 = 150 Answer: 150 cm ## Activity: How many centimetres make a metre? You will need: Metre rule, 30 cm rulers, Tape measure, Chalk 1. In groups, lay a metre rule on the floor and count the centimetre marks on it. 2. Measure the length of the classroom with the metre rule. Mark each metre with chalk, then measure the part left over in centimetres. 3. Record the length in metres and centimetres, for example 7 m 40 cm, then change it to centimetres. 4. Cut strings of ½ m and ¼ m by folding a 1 m string into two and four equal parts. Measure each part to check it is 50 cm or 25 cm. PAGE 9: Lesson 4: Perimeter of plane figures ## Practice 1. Convert 9 m to centimetres. 2. Convert 3 m 45 cm to centimetres. 3. Convert 480 cm to metres and centimetres. 4. How many centimetres are in 1½ m? 5. Write 225 cm as a decimal of a metre. ## Answers to practice 1. 900 cm 2. 345 cm 3. 4 m 80 cm 4. 150 cm 5. 2.25 m ## Summary • 1 m = 100 cm. • Metres to centimetres: multiply by 100. Centimetres to metres: divide by 100. • ½ m = 50 cm, ¼ m = 25 cm, ¾ m = 75 cm. LESSON 4: PERIMETER OF PLANE FIGURES ==================================== ## What you will learn • Explain what perimeter means. • Work out the perimeter of squares, rectangles and triangles by adding the lengths of the sides. Curriculum outcomes: e) work out perimeter of plane figures in different contexts ## Introduction A farmer wants to put a fence around a rectangular vegetable garden. To know how much wire to buy, he must find the total distance around the garden. That distance is called the perimeter. ## Notes The perimeter of a shape is the total distance all the way around its edge. To find it, add the lengths of all the sides. The answer is in the same unit as the sides, such as cm or m. ### Rectangle A rectangle has two long sides of the same length and two short sides of the same length. A rectangle 8 cm long and 5 cm wide has perimeter: 8 cm + 5 cm + 8 cm + 5 cm = 26 cm You can also add the length and the width, then double: (8 + 5) × 2 = 26 cm. ### Square All four sides of a square are equal. A square with sides of 6 cm has perimeter: 6 + 6 + 6 + 6 = 24 cm, which is the same as 4 × 6 = 24 cm. ### Triangle A triangle has three sides. Add all three. A triangle with sides 5 cm, 7 cm and 9 cm has perimeter 5 + 7 + 9 = 21 cm. ### Other shapes For any shape with straight sides, measure every side and add them all. Take care not to miss a side or to count one twice. It helps to tick each side as you add it. PAGE 10: Lesson 4: Perimeter of plane figures — Perimeter in real life ### Perimeter in real life We use perimeter to find the length of fencing needed for a shamba or a school compound, the length of ribbon or lace to go around a tablecloth, and the length of a frame for a picture. Before planting, a farmer may measure around a seedbed to mark it out with pegs and string. [DIAGRAM] TYPE: svg ALT: The perimeter of a rectangle 8 cm by 5 cm is 26 cm. PAYLOAD: CAPTION: The perimeter of a rectangle 8 cm by 5 cm is 26 cm. [/DIAGRAM] ## Key words • perimeter — the total distance around the edge of a shape • plane figure — a flat shape such as a square, rectangle or triangle ## Worked examples ### Example 1 Find the perimeter of a rectangle 12 m long and 7 m wide. Working: 1. 12 + 7 + 12 + 7 2. = 38 Answer: 38 m ## Worked examples ### Example 2 A square table has sides of 90 cm. What is its perimeter? Working: 1. All 4 sides are 90 cm. 2. 4 × 90 = 360 Answer: 360 cm ## Worked examples ### Example 3 A triangular flower bed has sides 3 m, 4 m and 5 m. Find its perimeter. Working: 1. 3 + 4 + 5 = 12 Answer: 12 m ## Activity: Measuring around shapes You will need: Ruler, Tape measure, Exercise book, String 1. In pairs, measure the sides of your exercise book in centimetres and work out its perimeter. 2. Draw a square, a rectangle and a triangle in your book. Measure each side and find each perimeter. 3. In groups, use a tape measure to find the perimeter of the top of your desk or the teacher's table. 4. Lay a string along the edge of one shape, straighten it out and measure the string. Is it the same as your answer? ## Practice 1. Find the perimeter of a rectangle 10 cm long and 4 cm wide. 2. A square has sides of 15 m. Find its perimeter. 3. A triangle has sides 6 cm, 8 cm and 10 cm. What is its perimeter? 4. A school field is 50 m long and 30 m wide. How many metres of fence are needed to go around it once? ## Answers to practice 1. 28 cm 2. 60 m 3. 24 cm 4. 160 m ## Summary • Perimeter is the distance around a shape. • Add the lengths of all the sides. • Square: 4 × side. Rectangle: length + width + length + width. PAGE 11: Lesson 5: Adding and subtracting metres and centimetres — Addition LESSON 5: ADDING AND SUBTRACTING METRES AND CENTIMETRES ======================================================= ## What you will learn • Add lengths in metres and centimetres, regrouping 100 cm as 1 m. • Subtract lengths in metres and centimetres, changing 1 m into 100 cm when needed. Curriculum outcomes: f) work out addition involving length in metres and centimetres in real-life situations; g) work out subtraction involving length in metres and centimetres in real-life situations ## Introduction Mama Achieng bought 2 m 50 cm of cloth for a dress and 1 m 75 cm for a shirt. How much cloth did she buy altogether? To answer, you add metres and centimetres. ## Notes Write lengths in two columns, one for metres (m) and one for centimetres (cm). Always work on the centimetres column first. ### Addition Add 2 m 50 cm and 1 m 75 cm. - Add the centimetres: 50 + 75 = 125 cm. - 125 cm is more than 100 cm. 125 cm = 1 m 25 cm. Write 25 in the cm column and carry 1 to the m column. - Add the metres: 2 + 1 + 1 (carried) = 4 m. - Answer: 4 m 25 cm. Check using centimetres: 250 cm + 175 cm = 425 cm = 4 m 25 cm. ### Subtraction Subtract 3 m 45 cm from 7 m 20 cm. - Look at the centimetres: 20 − 45 cannot be done. - Take 1 m from the 7 m and change it to 100 cm. Now there are 6 m and 100 + 20 = 120 cm. - Subtract the centimetres: 120 − 45 = 75 cm. - Subtract the metres: 6 − 3 = 3 m. - Answer: 3 m 75 cm. Check using centimetres: 720 cm − 345 cm = 375 cm = 3 m 75 cm. PAGE 12: Lesson 5: Adding and subtracting metres and centimetres — Remember ### Remember - The centimetres column should never be 100 or more in the final answer; regroup it into metres. - In subtraction, when the top centimetres are fewer than the bottom, borrow 1 m and change it to 100 cm. - Add to check a subtraction: 3 m 75 cm + 3 m 45 cm should give back 7 m 20 cm. These skills help when joining pieces of rope or pipe, finding how much of a roll of wire is left, or comparing two jumps in a long jump race. ## Key words • regroup — change 100 cm into 1 m, or 1 m into 100 cm, when adding or subtracting • difference — the answer when one number is subtracted from another ## Worked examples ### Example 1 Add 4 m 65 cm and 2 m 50 cm. Working: 1. cm: 65 + 50 = 115 cm = 1 m 15 cm. Write 15, carry 1 m. 2. m: 4 + 2 + 1 = 7 m Answer: 7 m 15 cm ## Worked examples ### Example 2 A roll had 5 m 40 cm of wire. A fundi used 2 m 75 cm. How much wire is left? Working: 1. cm: 40 − 75 cannot be done. Change 1 m to 100 cm: 140 − 75 = 65 cm. 2. m: 4 − 2 = 2 m Answer: 2 m 65 cm ## Worked examples ### Example 3 Kiprop jumped 3 m 8 cm and Halima jumped 2 m 96 cm. How much further did Kiprop jump? Working: 1. cm: 8 − 96 cannot be done. Change 1 m to 100 cm: 108 − 96 = 12 cm. 2. m: 2 − 2 = 0 m Answer: 12 cm PAGE 13: Lesson 5: Adding and subtracting metres and centimetres — Practice ## Activity: Joining and cutting strings You will need: Balls of string, Tape measure or metre rule, Scissors 1. In groups, cut two pieces of string and measure each in metres and centimetres. 2. Add the two lengths in your books. Then tie the pieces end to end, measure the long string and compare with your answer. (The knot uses a little string, so the measured length may be slightly shorter.) 3. Measure a long string, cut off a piece and measure the piece. 4. Subtract to find the length left, then measure the remaining string to check. ## Practice 1. Add 3 m 40 cm and 5 m 35 cm. 2. Add 6 m 80 cm and 1 m 45 cm. 3. Subtract 2 m 30 cm from 9 m 70 cm. 4. A pipe was 8 m 15 cm long. A piece of 3 m 60 cm was cut off. What length is left? ## Answers to practice 1. 8 m 75 cm 2. 8 m 25 cm 3. 7 m 40 cm 4. 4 m 55 cm ## Summary • Work on the centimetres first, then the metres. • 100 cm = 1 m: carry when adding, borrow when subtracting. • Check by changing everything to centimetres. LESSON 6: MULTIPLYING AND DIVIDING METRES AND CENTIMETRES ========================================================= ## What you will learn • Multiply lengths in metres and centimetres by a whole number. • Divide lengths in metres and centimetres by a whole number. • Describe where metres and centimetres are used in daily life. Curriculum outcomes: h) carry out multiplication involving metres and centimetres in real life- situations; i) carry out division involving metres and centimetres in real-life situations; j) appreciate use of metres and centimetres in measuring distance in real life ## Introduction A carpenter needs 4 pieces of timber, each 2 m 35 cm long, to make a bed frame. What total length should he buy? Later he cuts a long plank into equal pieces. Both jobs need multiplication and division of lengths. ## Notes ### Multiplication Multiply 2 m 35 cm by 4. - Multiply the centimetres: 35 × 4 = 140 cm = 1 m 40 cm. Write 40, carry 1 m. - Multiply the metres: 2 × 4 = 8 m, then add the carried 1 m: 9 m. - Answer: 9 m 40 cm. Check in centimetres: 235 cm × 4 = 940 cm = 9 m 40 cm. PAGE 14: Lesson 6: Multiplying and dividing metres and centimetres — Why metres and centimetres matter ### Division Divide 9 m 60 cm by 3. - Divide the metres: 9 ÷ 3 = 3 m, nothing left. - Divide the centimetres: 60 ÷ 3 = 20 cm. - Answer: 3 m 20 cm. Sometimes metres are left over. Divide 5 m 60 cm by 4. - Metres: 5 ÷ 4 = 1 m, remainder 1 m. - Change the remainder to centimetres: 1 m = 100 cm. Add it to the 60 cm: 160 cm. - Centimetres: 160 ÷ 4 = 40 cm. - Answer: 1 m 40 cm. Check by multiplying back: 1 m 40 cm × 4 = 4 m 160 cm = 5 m 60 cm. Another way is to change the whole length to centimetres first: 5 m 60 cm = 560 cm, and 560 ÷ 4 = 140 cm = 1 m 40 cm. ### Why metres and centimetres matter Many people use these units every day: - Tailors measure cloth and body sizes in centimetres. - Carpenters and masons measure timber, doors and walls in metres and centimetres. - Farmers measure spaces between rows and holes when planting. - Athletes run races measured in metres, such as the 100 m race. - Shops sell rope, wire, cloth and pipes by the metre. Measuring correctly saves money and materials, because nothing is cut too short or wasted. ## Key words • remainder — the amount left over after dividing • equal pieces — parts that all have the same length ## Worked examples ### Example 1 Multiply 3 m 45 cm by 3. Working: 1. cm: 45 × 3 = 135 cm = 1 m 35 cm. Write 35, carry 1 m. 2. m: 3 × 3 = 9, plus 1 = 10 m Answer: 10 m 35 cm PAGE 15: Lesson 6: Multiplying and dividing metres and centimetres — Equal pieces of string ## Worked examples ### Example 2 A rope 8 m 40 cm long is cut into 4 equal pieces. How long is each piece? Working: 1. m: 8 ÷ 4 = 2 m 2. cm: 40 ÷ 4 = 10 cm Answer: 2 m 10 cm ## Worked examples ### Example 3 Share 7 m 20 cm of cloth equally among 3 learners. Working: 1. m: 7 ÷ 3 = 2 m, remainder 1 m 2. 1 m = 100 cm; 100 + 20 = 120 cm 3. cm: 120 ÷ 3 = 40 cm Answer: 2 m 40 cm each ## Activity: Equal pieces of string You will need: String, Metre rule or tape measure, Scissors 1. In groups, measure a piece of string that is 1 m 20 cm long. 2. Work out how long each piece would be if the string is shared equally among the 4 members of the group. Then fold, cut and measure to check. 3. Each member measures their arm span in metres and centimetres. Work out what the total would be if 3 learners had the same arm span as you. 4. Discuss with your group three jobs at home or in your community where people measure in metres and centimetres. ## Practice 1. Multiply 1 m 25 cm by 5. 2. Multiply 4 m 60 cm by 2. 3. Divide 6 m 90 cm by 3. 4. A 9 m 50 cm plank is cut into 5 equal pieces. How long is each piece? 5. Name two people in your community who use metres and centimetres in their work. ## Answers to practice 1. 6 m 25 cm 2. 9 m 20 cm 3. 2 m 30 cm 4. 1 m 90 cm 5. Any two, for example a tailor, a carpenter, a mason, a farmer or a shopkeeper who sells cloth or wire. ## Summary • Multiply: centimetres first, regroup 100 cm into 1 m, then metres. • Divide: metres first, change any remainder to centimetres, then divide the centimetres. • Changing everything to centimetres is a quick way to check. PAGE 16: Lesson 7: Measuring longer lengths in metres and centimetres — Measuring past one metre LESSON 7: MEASURING LONGER LENGTHS IN METRES AND CENTIMETRES ============================================================ ## What you will learn • Measure a length longer than one metre and record it in metres and centimetres. • Change that measurement into centimetres. • Compare an estimate in metres with the measured length. Curriculum outcomes: b) measure length in centimetres in real life- situations; c) establish the relationship between metres and centimetres practically; j) appreciate use of metres and centimetres in measuring distance in real life ## Introduction A desk may fit on a 30 cm ruler, but a classroom wall, a path or a seedbed is much longer. For those lengths you use a metre rule or a tape measure and record both metres and centimetres. ## Notes A metre rule is 100 cm long. If an object is longer than the rule, one placement is not enough. ### Measuring past one metre Put the 0 mark at one end of the object. Where the rule ends, make a small chalk mark. Move the rule so that 0 sits on that mark, and measure again. Count the full metres, then read the centimetres that are left. If the rule fits 6 times and 35 cm remain, the length is 6 m 35 cm. A tape measure is often easier for a path or the length of a room, because the metres and centimetres are already printed on it. Keep the tape straight. A sagging tape gives a length that is too long. PAGE 17: Lesson 7: Measuring longer lengths in metres and centimetres — Why the measurement is worth doing ### Changing the record into centimetres Use 1 m = 100 cm. - 6 m 35 cm = 600 cm + 35 cm = 635 cm - 3 m 4 cm = 300 cm + 4 cm = 304 cm The 4 cm in 3 m 4 cm is not 40 cm. The tens place stays empty, so you write 304 cm, not 34 cm and not 340 cm. ### Estimate, then measure Picture how many metre rules would fit. A classroom door is about 2 m high. Write the estimate, measure, and subtract the smaller length from the larger one. If you estimated 6 m, that is 600 cm. If the actual length is 6 m 45 cm, that is 645 cm. The difference is 645 − 600 = 45 cm. ### Why the measurement is worth doing A farmer measures a seedbed so that planting rows fit the land. A person buying rope, wire or pipe needs the right length, so money and material are not wasted. Take care of the metre rule and the tape measure: do not bend them, step on them or leave them in the rain. [DIAGRAM] TYPE: svg ALT: Two full metres and 35 cm left over make 2 m 35 cm, or 235 cm. PAYLOAD: CAPTION: Two full metres and 35 cm left over make 2 m 35 cm, or 235 cm. [/DIAGRAM] PAGE 18: Lesson 7: Measuring longer lengths in metres and centimetres — Summary ## Key words • metre rule — a straight measuring stick that is 1 metre, or 100 centimetres, long • mixed units — a length written with both metres and centimetres, such as 6 m 35 cm ## Worked examples ### Example 1 A metre rule fits along a wall 6 times, and 35 cm are left. Write the length in metres and centimetres, and also in centimetres only. Working: 1. 6 full metres and 35 cm make 6 m 35 cm. 2. 6 × 100 = 600 cm, and 600 + 35 = 635 cm. Answer: 6 m 35 cm, which is 635 cm ## Worked examples ### Example 2 Cherono estimated a path to be 8 m long. She measured 7 m 40 cm. By how many centimetres was the estimate off? Working: 1. 8 m = 800 cm. 2. 7 m 40 cm = 740 cm. 3. 800 − 740 = 60 cm. The estimate was too long. Answer: 60 cm ## Activity: Metre by metre around the classroom You will need: Metre rule or tape measure, Chalk, Exercise book 1. In a group, choose three long objects or distances: the length of the classroom, the width of the classroom and the length of the chalkboard. 2. Each person first writes an estimate in metres. 3. Measure each one. If you use a metre rule, mark each metre with chalk, then measure the leftover centimetres. 4. Record every length in metres and centimetres, then change it to centimetres and find the difference from your estimate. 5. Discuss one job, such as marking a seedbed or buying rope, where this kind of measuring saves material. ## Practice 1. A metre rule fits along a bench 4 times, with 18 cm left. How long is the bench in centimetres? 2. Write 9 m 5 cm in centimetres. 3. Baraka estimated a rope to be 2 m. It measured 1 m 95 cm. What is the difference in centimetres? 4. Why should a tape measure be kept straight while you measure a path? ## Answers to practice 1. 418 cm 2. 905 cm 3. 5 cm 4. A sagging tape is longer than the straight distance, so the reading would be too big. ## Summary • Count full metres, then read the centimetres that are left. • To change metres and centimetres into centimetres, multiply the metres by 100 and add the centimetres. • Compare an estimate with the measurement by subtracting. PAGE 19: Lesson 8: Mixed problems on length LESSON 8: MIXED PROBLEMS ON LENGTH ================================== ## What you will learn • Choose whether a length problem needs conversion, perimeter, addition, subtraction, multiplication or division. • Solve a problem that uses more than one of these skills. • Check the answer by working in centimetres. Curriculum outcomes: d) convert metres to centimetres and centimetres to metres in real-life situations; e) work out perimeter of plane figures in different contexts; f) work out addition involving length in metres and centimetres in real-life situations; g) work out subtraction involving length in metres and centimetres in real-life situations; h) carry out multiplication involving metres and centimetres in real life- situations; i) carry out division involving metres and centimetres in real-life situations ## Introduction Real measuring jobs rarely use only one skill. A farmer may find the distance around a seedbed and then change metres into centimetres. A carpenter may add two lengths and later cut a plank into equal pieces. ## Notes Read the whole question before you calculate. The words tell you the operation. - Altogether, total or perimeter: add. - Left, how much more or difference: subtract. - Each, times or equal pieces of the same length: multiply. - Shared equally or cut into equal pieces: divide. - Change between metres and centimetres: multiply or divide by 100. ### Work in one unit when it helps A rectangle is 9 m long and 6 m wide. The perimeter is 9 + 6 + 9 + 6 = 30 m. If the wire is sold by the centimetre, change the answer: 30 × 100 = 3,000 cm. PAGE 20: Lesson 8: Mixed problems on length — More than one step ### More than one step A tailor has 3 m 55 cm of cloth and buys 2 m 70 cm more. - Centimetres: 55 + 70 = 125 cm = 1 m 25 cm. - Metres: 3 + 2 + 1 = 6 m. - She has 6 m 25 cm. Check in centimetres: 355 + 270 = 625 cm = 6 m 25 cm. Five pieces of ribbon, each 1 m 40 cm, have total length 140 × 5 = 700 cm = 7 m. A wire of 9 m 60 cm cut into 6 equal pieces gives 960 ÷ 6 = 160 cm = 1 m 60 cm each. ### A check you can trust Change every length to centimetres, do the operation, then change back if the question asks for metres and centimetres. The two methods must agree. If they do not, go back to the step where you regrouped 100 cm as 1 m. ## Key words • mixed problem — a question that needs more than one operation or a change of units • operation — addition, subtraction, multiplication or division ## Worked examples ### Example 1 A seedbed is 9 m long and 6 m wide. What is its perimeter? Working: 1. Add the length and the width: 9 + 6 = 15 m. 2. Double that distance: 15 × 2 = 30 m. Answer: 30 m ## Worked examples ### Example 2 Add 3 m 55 cm and 2 m 70 cm. Working: 1. 55 + 70 = 125 cm = 1 m 25 cm. 2. 3 + 2 + 1 = 6 m. Answer: 6 m 25 cm ## Worked examples ### Example 3 A wire 9 m 60 cm long is cut into 6 equal pieces. How long is each piece? Working: 1. 9 m 60 cm = 960 cm. 2. 960 ÷ 6 = 160 cm = 1 m 60 cm. Answer: 1 m 60 cm PAGE 21: Revision quiz ## Activity: Choose the operation You will need: Metre rule or tape measure, String, Exercise book 1. In pairs, measure two lengths of string in metres and centimetres. 2. Write four questions about your strings: an addition, a subtraction, a multiplication by 2 or 3, and a division into 2 equal pieces. 3. Swap books with another pair and solve their questions. Show a check by changing the lengths to centimetres. 4. Measure the sides of a rectangular table and find its perimeter in metres and centimetres, then in centimetres only. ## Practice 1. A triangle has sides 5 m, 5 m and 6 m. Find its perimeter. 2. Subtract 3 m 75 cm from 8 m 20 cm. 3. Multiply 2 m 15 cm by 4. 4. Divide 7 m 50 cm by 5. ## Answers to practice 1. 16 m 2. 4 m 45 cm 3. 8 m 60 cm 4. 1 m 50 cm ## Summary • The words of the question tell you which operation to use. • Perimeter is still the sum of all the sides. • Changing every length to centimetres is a reliable check. REVISION QUIZ ============= Answer all the questions, then mark yourself on the Answers tab. 1. A line on a ruler goes from the 5 mark to the 14 mark. How long is it? A. 19 cm B. 9 cm C. 14 cm D. 5 cm 2. Which tool would you use to measure the distance around a football? A. A 30 cm ruler B. A metre rule C. A tape measure 3. Jabali estimated a stick to be 50 cm long. Its actual length was 58 cm. What was the difference? 4. How many centimetres make 1 metre? A. 10 B. 100 C. 1,000 D. 50 5. Convert 6 m 5 cm to centimetres. A. 65 cm B. 650 cm C. 605 cm D. 6,005 cm 6. How many centimetres are in ¼ m? 7. Find the perimeter of a rectangle 9 cm long and 6 cm wide. A. 15 cm B. 54 cm C. 30 cm D. 24 cm 8. Add 5 m 70 cm and 3 m 55 cm. 9. Subtract 4 m 85 cm from 8 m 30 cm. 10. One piece of timber is 2 m 60 cm long. What is the total length of 3 such pieces? 11. A wire 6 m 40 cm long is cut into 4 equal pieces. How long is each piece? A. 1 m 60 cm B. 1 m 10 cm C. 2 m 10 cm D. 1 m 40 cm 12. Why do tailors measure carefully before cutting cloth? PAGE 22: Quiz answers ANSWERS ======= 1. B. 9 cm Subtract the start from the end: 14 − 5 = 9 cm. 2. C. A tape measure A tape measure bends around round objects. 3. 8 cm 58 − 50 = 8 cm. 4. B. 100 1 m = 100 cm. 5. C. 605 cm 6 × 100 = 600 cm, plus 5 cm = 605 cm. 6. 25 cm 100 ÷ 4 = 25 cm. 7. C. 30 cm 9 + 6 + 9 + 6 = 30 cm. 8. 9 m 25 cm 70 + 55 = 125 cm = 1 m 25 cm; 5 + 3 + 1 = 9 m. 9. 3 m 45 cm Borrow 1 m: 130 − 85 = 45 cm; 7 − 4 = 3 m. 10. 7 m 80 cm 60 × 3 = 180 cm = 1 m 80 cm; 2 × 3 + 1 = 7 m. 11. A. 1 m 60 cm 6 ÷ 4 = 1 m remainder 2 m. 2 m = 200 cm; 200 + 40 = 240 cm; 240 ÷ 4 = 60 cm. Each piece is 1 m 60 cm. 12. So that the cloth is not cut too short and no cloth or money is wasted. Accurate measurement saves materials and money.