PAGE 1: Overview OVERVIEW ======== Capacity is how much a container can hold. In this sub-strand you will measure capacity in litres, half litres and quarter litres, then add and subtract capacities written in litres. ## Strand 2.0: Measurement Sub-strand 2.4: Capacity Suggested lessons: 8 ## What this sub-strand covers • Capacity in litres • Addition and subtraction of capacity ## Source • KICD Grade 4 Mathematics Curriculum Design (Revised 2024) — Strand 2.0 Measurement, Sub-strand 2.4 Capacity • KICD Grade 4 Mathematics radio lessons: Measuring capacity; Addition of capacity; Subtraction of capacity ## Learning outcomes By the end of the sub-strand, the learner should be able to: a) measure capacity in litres in real-life situations b) measure capacity in litres and litres in real- life situations c) work out addition and subtraction of capacity in litres in real-life situations d) appreciate use of the litre as a unit of measuring capacity in real-life situations ## Key inquiry questions 1. How can you measure capacity using arbitrary units? PAGE 2: How we will learn ## Learning experiences • measure capacity of containers using a one-litre container • work with peers in making litre containers from locally available materials through filling and emptying the container with substances such as water or sand using a 1 litre container • make litre containers through filling and emptying using a 1 litre container • team up with peers to use litre and litre containers to measure capacity of other containers • add capacity involving litres • subtract capacity involving litres • play games involving capacity using containers of different capacities or use digital devices for digital games ## Core competencies • Learning to learn: learner makes 1⁄2 litre containers from locally available materials through filling and emptying the container with substances such as water or sand using a one-litre container. • Self-efficacy: learner shows confidence in measuring capacity of 1⁄2 litre and 1⁄4 litre. ## Values • Responsibility: learner makes 1⁄4 litre containers from locally available materials through filling and emptying the container with substances such as water or sand using a one-litre container. ## Pertinent and contemporary issues • Safety: learner observes precautionary measures while determining 1⁄2 litre and 1⁄4 litre containers. • Environmental Education: learner uses 1⁄2 litre containers made from locally available materials. ## Links to other learning areas • The learner is able to relate practical activities involving measurement of liquids to properties of matter in Science and Technology. PAGE 3: Lesson 1: The litre — Measuring by filling LESSON 1: THE LITRE =================== ## What you will learn • State that the litre is a unit of capacity. • Measure the capacity of a container by filling it with a one-litre container. Curriculum outcomes: a) measure capacity in litres in real-life situations; d) appreciate use of the litre as a unit of measuring capacity in real-life situations ## Introduction A jug, a bottle and a bucket do not all hold the same amount of water. Capacity is how much a container holds when it is full. The litre is the unit we use for that amount. ## Notes We write litre in short as L. A one-litre container is the measuring piece. Many water bottles used in school hold about 1 litre when they are full to the marked line. The mark matters: a bottle filled only halfway does not hold 1 litre yet. ### Measuring by filling To find the capacity of a larger container: 1. Fill the one-litre container to its litre mark. 2. Pour all of it into the larger container. 3. Fill the one-litre container again and pour. 4. Count the pours until the larger container is full. If a bucket is full after 12 pours, its capacity is 12 litres. Pour slowly. If water spills, that pour was not a full litre in the bucket, and the count will be wrong. A dry container at the start gives a true measurement. PAGE 4: Lesson 1: The litre — Fill and count the litres ### Smaller containers A cup may hold less than 1 litre. You will need several cups to fill a one-litre container. Keep counting until the litre container is full. That count tells you how the cup compares with 1 litre. ### Why the litre is useful Water for cooking, milk from a cow, juice in a bottle and fuel in a jerrycan are all described in litres. Using the same unit means a buyer and a seller agree on the amount. An unmarked gourd is an arbitrary container: two gourds may not hold the same amount. A litre container is the same every time you fill it to the mark. ## Key words • capacity — how much a container can hold • litre (L) — the unit used to measure capacity ## Worked examples ### Example 1 A bucket is filled by 12 full one-litre bottles. What is the capacity of the bucket? Working: 1. Each bottle pours in 1 litre. 2. 12 pours make 12 litres. Answer: 12 litres ## Worked examples ### Example 2 A jerrycan is filled by pouring from a one-litre cup 20 times. What is its capacity? Working: 1. 20 × 1 litre = 20 litres. Answer: 20 litres ## Activity: Fill and count the litres You will need: A one-litre container, A jug, a bucket and a cup, Water, A basin to avoid spills 1. Work outside or over a basin. Fill the one-litre container to its mark and pour it into the jug. Repeat until the jug is full, and record the number of litres. 2. Do the same for a bucket. 3. Find how many full cups fill the one-litre container. 4. Empty the containers when you finish and wipe the floor so that nobody slips. 5. Discuss one time at home when your family needs to know a capacity in litres. PAGE 5: Lesson 1: The litre — Answers to practice ## Practice 1. A tank is filled by 25 one-litre bottles. What is the capacity poured in? 2. A container becomes full after 8 pours from a one-litre jug. What is its capacity? 3. Why is a one-litre container better for measuring than two unmarked gourds? ## Answers to practice 1. 25 litres 2. 8 litres 3. The litre container holds the same amount each time it is filled to the mark, but the gourds may hold different amounts. ## Summary • Capacity is how much a container holds. • The litre (L) is the unit. • Count how many times a full one-litre container fills the container you are measuring. LESSON 2: MAKING A ONE-LITRE CONTAINER ====================================== ## What you will learn • Make a one-litre mark on a container by filling and emptying. • Use the marked container to measure another container. Curriculum outcomes: a) measure capacity in litres in real-life situations ## Introduction You may not have a measuring jug at home. If you have one true one-litre bottle, you can mark a tin or a plastic bottle so that it also holds one litre. ## Notes Borrow a container that you already trust as 1 litre. A bottle with a clear 1 L mark is a good start. PAGE 6: Lesson 2: Making a one-litre container — Filling and emptying ### Filling and emptying 1. Fill the trusted bottle with water or dry sand up to the 1 litre mark. 2. Pour all of it into the container you want to mark. 3. Keep the container upright on a flat surface. 4. Draw a line at the level of the water or sand. Write 1 L beside the line. 5. Empty it and fill it again to your line. Pour it back into the trusted bottle. It should fill that bottle to the same 1 litre mark. If the level is short, your line was too low. If it overflows, your line was too high. Mark again. Sand must be dry and level. Tap the container gently so that the sand settles, then mark. Do not pack the sand down hard in one container and leave it loose in the other. PAGE 7: Lesson 2: Making a one-litre container — Example 2 ### Using the new container A cooking pot that takes 4 fills of your marked container has a capacity of 4 litres. Write the unit. The number 4 alone could mean 4 cups or 4 bottles. ### Care Do not drink from containers that have held sand, soap or fuel. Ask an adult before you cut a bottle. Keep water off the floor. ## Key words • mark — a line that shows where the container holds a stated amount • emptying — pouring everything out so that you can check a measurement again ## Worked examples ### Example 1 A pot is filled by 4 pours from a marked one-litre tin. What is the capacity of the pot? Working: 1. Each pour is 1 litre. 2. 4 × 1 = 4 litres. Answer: 4 litres ## Worked examples ### Example 2 A learner's mark is checked by pouring back into a true 1 litre bottle. The bottle overflows. What is wrong with the mark? Working: 1. More than 1 litre was poured back. 2. The line on the learner's container is too high. Answer: The mark is above the true 1 litre level. PAGE 8: Lesson 2: Making a one-litre container — Practice ## Activity: Mark one litre You will need: A container already marked 1 litre, A plain plastic bottle or tin, Water or dry sand, A marker pen 1. In pairs, fill the trusted 1 litre container and pour it into the plain container. 2. Mark the level and label it 1 L. 3. Empty the plain container, fill it to your mark, and pour it back. Adjust the mark if it does not match. 4. Use your marked container to find the capacity of a jug or a small bucket. 5. Wash your hands if you used sand, and do not leave containers where someone might trip. ## Practice 1. A basin holds 6 fills of a marked 1 litre container. What is its capacity? 2. You pour a marked container back into a true 1 litre bottle and the bottle is not full. Was your mark too high or too low? 3. Three marked one-litre tins are poured into an empty jerrycan, and the jerrycan is then full. What is its capacity? ## Answers to practice 1. 6 litres 2. Too low 3. 3 litres ## Summary • Pour a true 1 litre into a plain container and mark the level. • Check the mark by pouring back into the true litre container. • Use the marked container to measure other capacities in litres. PAGE 9: Lesson 3: Half litres and quarter litres — Making a half litre LESSON 3: HALF LITRES AND QUARTER LITRES ======================================== ## What you will learn • Show that 2 half litres make 1 litre and 4 quarter litres make 1 litre. • Measure a capacity using half-litre and quarter-litre containers. Curriculum outcomes: b) measure capacity in litres and litres in real- life situations ## Introduction A small cup of milk may be only part of a litre. Half a litre and a quarter of a litre are the parts you can make from one litre by sharing it into equal amounts. ## Notes Half a litre is written ½ L. A quarter of a litre is written ¼ L. ### Making a half litre Fill a 1 litre container. Pour it into two matching empty bottles until the water is at the same level in both. Each bottle then holds ½ L. Two half litres poured back fill the 1 litre container exactly. 2 × ½ L = 1 L ### Making a quarter litre Share ½ L equally between two matching smaller bottles, or share 1 L equally among four. Each small bottle holds ¼ L. 4 × ¼ L = 1 L 2 × ¼ L = ½ L PAGE 10: Lesson 3: Half litres and quarter litres — Counting the parts ### Counting the parts If a jug is filled by 6 half-litre cups, its capacity is 6 × ½ L = 3 L. If a bottle is filled by 5 quarter-litre cups, its capacity is 5 × ¼ L = 1¼ L. Four of the quarters make 1 litre, and one quarter is left. Ask an adult before cutting a bottle to the water line. Cut away from your hands. A container that held chemicals should not be used for drinking water. [DIAGRAM] TYPE: svg ALT: 1 litre equals 2 half litres and also equals 4 quarter litres. PAYLOAD: CAPTION: 1 litre equals 2 half litres and also equals 4 quarter litres. [/DIAGRAM] PAGE 11: Lesson 3: Half litres and quarter litres — Example 1 ## Key words • half litre — ½ L, the amount in one of two equal parts of a litre • quarter litre — ¼ L, the amount in one of four equal parts of a litre ## Worked examples ### Example 1 How many half litres are there in 3 litres? Working: 1. Each litre contains 2 half litres. 2. 3 × 2 = 6. Answer: 6 half litres ## Worked examples ### Example 2 How many quarter litres are there in 2 litres? Working: 1. Each litre contains 4 quarter litres. 2. 2 × 4 = 8. Answer: 8 quarter litres ## Worked examples ### Example 3 A bottle is filled by five quarter-litre cups. What is its capacity? Working: 1. 5 × ¼ L = 5/4 L. 2. 5/4 L = 1¼ L. Answer: 1¼ litres ## Activity: Halves and quarters of a litre You will need: A 1 litre container, Matching plastic bottles, Water, Marker pen 1. Fill the 1 litre container. Share the water equally between two matching bottles and mark each as ½ L. 2. Pour both halves back and check that they fill 1 litre. 3. Share 1 litre equally among four small matching containers and mark each as ¼ L. 4. Find how many of your ½ L containers fill a jug. 5. Wipe up spills. Do not cut bottles unless an adult is helping. PAGE 12: Lesson 3: Half litres and quarter litres — Summary ## Practice 1. How many half litres make 5 litres? 2. How many quarter litres make 1 half litre? 3. Seven half-litre cups fill a jug. What is the capacity of the jug? 4. How many quarter litres are there in 3 litres? ## Answers to practice 1. 10 half litres 2. 2 quarter litres 3. 3½ litres 4. 12 quarter litres ## Summary • 2 × ½ L = 1 L and 4 × ¼ L = 1 L. • 2 × ¼ L = ½ L. • Count the half-litre or quarter-litre pours, then change the count into litres. LESSON 4: MEASURING WITH LITRES, HALF LITRES AND QUARTER LITRES ============================================================ ## What you will learn • Record a capacity that is a mixture of litres and parts of a litre. • Change a count of quarter litres into litres. Curriculum outcomes: a) measure capacity in litres in real-life situations; b) measure capacity in litres and litres in real- life situations ## Introduction A container is not always a whole number of litres. It might hold 3 full litres and then one more half litre. You record both parts. ## Notes Use the biggest container that fits, then the smaller ones for what is left. Suppose a jerry can takes four full litres, and the leftover water fills one half-litre container and one quarter-litre container. The capacity is 4 L + ½ L + ¼ L. Change the parts into quarters so that you can add them: - 1 L = 4 quarters, so 4 L = 16 quarters. - ½ L = 2 quarters. - ¼ L = 1 quarter. 16 + 2 + 1 = 19 quarters. That is 4 litres and 3 quarters, or 4¾ L, because 16 quarters make 4 litres and 3 quarters remain. PAGE 13: Lesson 4: Measuring with litres, half litres and quarter litres — Example 1 ### A shorter way ½ + ¼ = ¾. So 4 L + ½ L + ¼ L = 4¾ L. ### Checking a measurement Pour the water back with your measuring containers and count again. Two groups measuring the same full container should get the same result if nobody spills. Write the unit every time. A capacity of 4¾ without a unit is not a finished answer. Water and sand both show capacity, but do not mix them in the same container during one measurement. Use one substance, empty the container, and start the next measurement clean. ## Key words • mixed capacity — a measure with whole litres and a fraction of a litre, such as 4¾ L • quarter — one of four equal parts ## Worked examples ### Example 1 A container holds 4 L + ½ L + ¼ L. Write the capacity as one mixed number. Working: 1. ½ + ¼ = ¾. 2. 4 + ¾ = 4¾. Answer: 4¾ litres ## Worked examples ### Example 2 A jug is filled by seven half-litre cups. Write the capacity in litres. Working: 1. 7 × ½ = 7/2. 2. 7/2 = 3½. Answer: 3½ litres PAGE 14: Lesson 4: Measuring with litres, half litres and quarter litres — Whole litres and parts ## Activity: Whole litres and parts You will need: 1 L, ½ L and ¼ L containers, A jug, Water, Basin 1. In a group, fill a jug using the 1 litre container as many times as you can. 2. Measure what is still needed with the half-litre container, then the quarter-litre container. 3. Write the capacity as whole litres and a fraction. 4. Empty the jug and let another pair measure it. Compare the two results. 5. Pour the water onto plants if it is clean, or back into a storage container. Do not leave the floor wet. ## Practice 1. Write 3 L + ½ L as a mixed number of litres. 2. Write 2 L + ¼ L + ¼ L in litres. 3. Nine quarter litres fill a bottle. What is its capacity? 4. How many quarter litres are in 4¾ litres? ## Answers to practice 1. 3½ litres 2. 2½ litres 3. 2¼ litres 4. 19 quarter litres ## Summary • Measure whole litres first, then halves and quarters. • ½ L + ¼ L = ¾ L. • Check by measuring the same container a second time. PAGE 15: Lesson 5: Adding capacity in litres — Whole litres LESSON 5: ADDING CAPACITY IN LITRES =================================== ## What you will learn • Add whole-litre capacities, regrouping when a column is 10 or more. • Add capacities that include half litres and quarter litres. Curriculum outcomes: c) work out addition and subtraction of capacity in litres in real-life situations ## Introduction A family may collect 326 litres of water in the morning and 174 litres in the afternoon. To know the total, add the litres in the same way you add whole numbers. ## Notes Write the numbers in columns: hundreds, tens and ones. Add the ones first. If a column is 10 or more, write the ones digit of that sum and carry the tens digit to the next column. ### Whole litres Add 326 L and 174 L. - Ones: 6 + 4 = 10. Write 0, carry 1 ten. - Tens: 2 + 7 + 1 = 10. Write 0, carry 1 hundred. - Hundreds: 3 + 1 + 1 = 5. - The total is 500 L. Add 87 L and 232 L. - Ones: 7 + 2 = 9. - Tens: 8 + 3 = 11. Write 1, carry 1 hundred. - Hundreds: 2 + 1 = 3. - The total is 319 L. Check by adding in the other order. 232 + 87 must also give 319. ### Fractions of a litre Add the fraction parts, then the whole litres. Change 2 quarters into a half, or 2 halves into a litre, when you can. 2½ L + 1¼ L = 2 L + 1 L + ½ L + ¼ L = 3 L + ¾ L = 3¾ L. 1½ L + 1½ L = 3 L, because ½ + ½ = 1. Always write litres in the answer. A total of 500 could be mistaken for metres or shillings if the unit is missing. PAGE 16: Lesson 5: Adding capacity in litres — Example 1 ## Key words • total capacity — the amount when two or more capacities are added • carry — to move 10 from one column into 1 in the next column when adding ## Worked examples ### Example 1 Add 326 litres and 174 litres. Working: 1. Ones: 6 + 4 = 10. Write 0, carry 1. 2. Tens: 2 + 7 + 1 = 10. Write 0, carry 1. 3. Hundreds: 3 + 1 + 1 = 5. Answer: 500 litres ## Worked examples ### Example 2 Add 87 litres and 232 litres. Working: 1. Ones: 7 + 2 = 9. 2. Tens: 8 + 3 = 11. Write 1, carry 1. 3. Hundreds: 2 + 1 = 3. Answer: 319 litres ## Worked examples ### Example 3 Add 2½ litres and 1¼ litres. Working: 1. Wholes: 2 + 1 = 3. 2. Fractions: ½ + ¼ = ¾. 3. Total: 3¾ litres. Answer: 3¾ litres PAGE 17: Lesson 5: Adding capacity in litres — Pour two amounts together ## Activity: Pour two amounts together You will need: Two containers of known capacity, A larger basin, A one-litre container, Water 1. Measure 2 litres into one container and 3 litres into another. 2. Pour both into a basin. Predict the total, then measure it with the one-litre container. 3. In your book, add 154 litres and 163 litres in columns. Check by adding the numbers in the reverse order. 4. Add 2½ litres and 1½ litres. Explain where the two halves make an extra litre. 5. Empty the basin where the water can be used, and dry the working place. ## Practice 1. Add 467 litres and 192 litres. 2. Add 923 litres and 69 litres. 3. Add 1½ litres and ¾ litres. 4. A tank received 1,250 litres and then 875 litres. How much water was received altogether? ## Answers to practice 1. 659 litres 2. 992 litres 3. 2¼ litres 4. 2,125 litres ## Summary • Add litres in columns, starting at the ones, and carry when a column is 10 or more. • Add fraction parts separately, and change 2 halves into 1 litre. • Check by adding the two numbers in the other order. PAGE 18: Lesson 6: Subtracting capacity in litres — Whole litres LESSON 6: SUBTRACTING CAPACITY IN LITRES ======================================== ## What you will learn • Subtract litres, regrouping when a digit is too small. • Subtract half litres and quarter litres from whole litres. Curriculum outcomes: c) work out addition and subtraction of capacity in litres in real-life situations; d) appreciate use of the litre as a unit of measuring capacity in real-life situations ## Introduction A tank held 2,958 litres. After a week the family had used 839 litres. Subtraction tells you how many litres are left. The same skill works for a cup of milk when you pour some out. ## Notes Set the subtraction in columns. Start at the ones. If the top digit is smaller than the bottom digit, regroup 1 ten as 10 ones. ### Whole litres Subtract 19 L from 32 L. - Ones: 2 is smaller than 9. Regroup 1 ten. The tens become 2, and the ones become 12. - 12 − 9 = 3. - Tens: 2 − 1 = 1. - 13 litres remain. Subtract 839 L from 2,958 L. - Ones: 8 − 9 cannot be done. Regroup: 18 − 9 = 9. - Tens: 4 − 3 = 1, after the regroup left 4 in the tens. - Hundreds: 9 − 8 = 1. The thousands digit 2 stays. - 2,119 litres remain. Check by adding: 2,119 + 839 = 2,958. ### Parts of a litre Take the whole litres away first, then the fraction. 6 L − 1½ L = 6 L − 1 L − ½ L. First, 6 − 1 = 5. Then 5 − ½ = 4½. So 4½ L remain. 1 L − ¼ L = ¾ L. ½ L − ¼ L = ¼ L. Measuring what is left in a real container checks a small subtraction. For a large tank you check by adding the remainder to the amount used. PAGE 19: Lesson 6: Subtracting capacity in litres — Example 1 ## Key words • remainder — the capacity left after some has been used or poured out • regroup — to change 1 ten into 10 ones so that subtraction is possible ## Worked examples ### Example 1 A container held 32 litres. 19 litres were poured out. How much is left? Working: 1. Ones: regroup 1 ten, 12 − 9 = 3. 2. Tens: 2 − 1 = 1. Answer: 13 litres ## Worked examples ### Example 2 A tank held 2,958 litres. The family used 839 litres. How much water is left? Working: 1. 2,958 − 839. 2. Check: 2,119 + 839 = 2,958. Answer: 2,119 litres ## Worked examples ### Example 3 Subtract 1½ litres from 6 litres. Working: 1. 6 − 1 = 5. 2. 5 − ½ = 4½. Answer: 4½ litres PAGE 20: Lesson 6: Subtracting capacity in litres — What is left in the container? ## Activity: What is left in the container? You will need: A one-litre container, A half-litre container, A basin of water, Exercise book 1. Pour 2 litres into a basin. Take out ½ litre. Measure what is left and write the subtraction. 2. In your book, subtract 19 litres from 32 litres and check by adding. 3. Solve: a tank had 7,535 litres and 3,229 litres were used. How many litres remain? 4. Share one story from home where someone needs to know how much water, milk or juice is left. 5. Play a capacity game with containers of different sizes, or a digital game if your teacher provides one. Record one subtraction you worked out. ## Practice 1. Subtract 174 litres from 500 litres. 2. A school tank had 7,535 litres. Learners used 3,229 litres. How many litres remain? 3. Subtract ¼ litre from 1 litre. 4. How can you check that 2,958 − 839 = 2,119? ## Answers to practice 1. 326 litres 2. 4,306 litres 3. ¾ litre 4. Add 2,119 and 839. The sum should be 2,958. ## Summary • Subtract litres in columns and regroup when the top digit is smaller. • Check a subtraction by adding the answer to the amount taken away. • 1½ litres taken from 6 litres leaves 4½ litres. PAGE 21: Revision quiz REVISION QUIZ ============= Answer all the questions, then mark yourself on the Answers tab. 1. A bucket is filled by 15 one-litre bottles. What is its capacity? A. 15 litres B. 16 litres C. 14 litres D. 1 litre 2. You pour a marked container back into a true 1 litre bottle and the bottle overflows. What does that show? 3. How many half litres make 4 litres? A. 2 B. 4 C. 8 D. 6 4. How many quarter litres are there in 3 litres? 5. Seven half-litre cups fill a jug. What is the capacity of the jug? A. 7 litres B. 3½ litres C. 14 litres D. 2 litres 6. Add 326 litres and 174 litres. 7. Add 2½ litres and 1¼ litres. 8. Subtract 19 litres from 32 litres. A. 13 litres B. 11 litres C. 21 litres D. 51 litres 9. A tank held 2,958 litres and 839 litres were used. How many litres are left? 10. Why do we use litres instead of unmarked cups when we buy milk or juice? PAGE 22: Quiz answers ANSWERS ======= 1. A. 15 litres Each full bottle is 1 litre, so 15 bottles fill 15 litres. 2. The mark is too high, so the container held more than 1 litre. A correct 1 litre mark fills the true bottle exactly. 3. C. 8 Each litre has 2 half litres, so 4 × 2 = 8. 4. 12 quarter litres Each litre has 4 quarters, so 3 × 4 = 12. 5. B. 3½ litres 7 × ½ = 3½ litres. 6. 500 litres 326 + 174 = 500. 7. 3¾ litres 2 + 1 = 3 and ½ + ¼ = ¾, so the total is 3¾ litres. 8. A. 13 litres 32 − 19 = 13. 9. 2,119 litres 2,958 − 839 = 2,119. Adding 2,119 + 839 returns 2,958. 10. A litre is the same amount every time, so the buyer and the seller agree on the capacity. Unmarked cups can hold different amounts.