PAGE 1: Overview OVERVIEW ======== Data is information we collect, such as colours of books or types of vehicles. In this sub-strand you will gather the materials you need, collect at most 10 items, draw a table, record the data with tallies, and read the table to answer questions. You will also see why an honest table helps people make a decision. ## Strand 4.0: Data Handling Sub-strand 4.1: Data Suggested lessons: 10 ## What this sub-strand covers • Collecting data • Drawing tables • Recording data • Interpreting raw data ## Source • KICD Grade 4 Mathematics Curriculum Design (Revised 2024) — Strand 4.0 Data Handling, Sub-strand 4.1 Data ## Learning outcomes By the end of the sub-strand, the learner should be able to: a) identify materials for data collection and recording in real-life situations b) collect data of at most 10 items within the school environment c) draw a table for recording data d) record data in the table e) interpret the raw data from the table f) appreciate use of tables in representing data in real-life situations ## Key inquiry questions 1. How can you representdata? PAGE 2: How we will learn ## Learning experiences • name and gather different materials that can used for data collection and recording such as rulers, exercise books for drawing tables, and textbooks • collect and record data on different items such the types of vehicles in the environment • team up with peers to represent the raw data in simple tables • explain and interpret the raw data from the table • explain the data on the types of vehicles in relation to responding to emergencies in case they are hurt while on the road • team up with peers to use digital devices or other resources for data collection and recording ## Core competencies • Critical thinking and problem solving: learner explores new ways of gathering and sharing different items for the purposes of recording data. ## Values • Patriotism: learner exhibits honesty while gathering and sharing different items for the purposes of recording data. ## Pertinent and contemporary issues • Environmental Education: learner collects materials from the immediate classroom environment. ## Links to other learning areas • The learner is able to relate data collection and recording to Democracy in society in Social Studies. LESSON 1: MATERIALS FOR COLLECTING AND RECORDING DATA ===================================================== ## What you will learn • Explain what data is. • Name materials used to collect and record data. Curriculum outcomes: a) identify materials for data collection and recording in real-life situations ## Introduction Before a class can say how many learners are present, someone has to count and write the number down. The count is data. The book, the pencil and the ruler are the materials that keep the count clear. ## Notes Data is a collection of pieces of information. The colours of the bags in a group, the ways learners come to school, and the types of vehicles passing the gate are all data. A single number, such as '5 red bags', is useful only when we know what was counted and how it was written down. PAGE 3: Lesson 1: Materials for collecting and recording data — Materials and what each one does ### Materials and what each one does - An exercise book and a pencil are for writing the list and the table. - A ruler is for drawing straight rows and columns. A crooked line makes a table hard to read. - A textbook can be a source of a small count, for example the kinds of pictures on one page, and it can also lie under the page while you rule lines. - Bottle tops, stones or sticks can stand for the items. One object stands for one item. You move them into sets and then count the sets. - Manila paper is for a table the whole group can see. - A digital device, such as a tablet the teacher allows, can be used to type the same table. The paper record still comes first, so the group has a copy if the device is switched off. You do not need every material every time. For a count of books you need a pencil and a book to write in. For a neat table you add the ruler. Gather only what the task needs, and collect it from the classroom so that nothing is taken from another learner without asking. ### Keep the collection small In Grade 4 the data set has at most 10 items. That may be 10 books, 10 vehicles, or the choices of 10 learners. A short list is easier to check. Write what you really see. Changing a number so that your group 'wins' makes the data false, and other people cannot use it. ## Key words • data — pieces of information that have been collected • record — to write down what was collected so it can be read later ## Worked examples ### Example 1 A group gathers a ruler, an exercise book, a pencil and a textbook. How many materials is that? Working: 1. Count each material once. 2. 1 + 1 + 1 + 1 = 4. Answer: 4 ## Worked examples ### Example 2 Each of 6 lines in a table is 10 cm long. What is the total length of the lines? Working: 1. There are 6 equal lines. 2. 6 × 10 = 60. Answer: 60 cm ## Worked examples ### Example 3 One stick stands for one item. How many sticks are needed to stand for 10 items? Working: 1. Each item needs its own stick. 2. The number of sticks is 10. Answer: 10 PAGE 4: Lesson 1: Materials for collecting and recording data — Summary ## Activity: Gather the recording kit You will need: Ruler, Exercise book, Pencil, Textbook, Sticks or bottle tops 1. In a group, name each material and say what it is used for when collecting data. 2. Gather a ruler, an exercise book and a pencil from the classroom. Count the materials and write the number. 3. Decide which material you would add if you wanted one object to stand for each item. 4. Look at one page of a textbook and list the kinds of pictures you see, up to 10 pictures. 5. Say which material you would use first if the teacher allowed a digital device, and which paper material you would still keep. ## Practice 1. What is data? 2. A table uses 4 lines, each 12 cm long. What is the total length of the lines? 3. Name two materials used to draw and fill a table. 4. How many bottle tops are needed if one top stands for each of 8 books? ## Answers to practice 1. Pieces of information that have been collected. 2. 48 cm 3. A ruler and a pencil, or an exercise book and a ruler. 4. 8 ## Summary • Data is information we collect. • A ruler, an exercise book and a pencil are the basic recording materials. • Write the true count. In this grade, collect at most 10 items. LESSON 2: COLLECTING AT MOST 10 ITEMS ===================================== ## What you will learn • Collect a raw list of at most 10 items. • Count how many times each type appears. Curriculum outcomes: b) collect data of at most 10 items within the school environment ## Introduction A raw list is the data just as it was collected, item by item. If ten vehicles pass while the class watches with the teacher, the raw list is the ten names in the order they passed, not yet sorted. ## Notes Collecting data starts with a question. 'What types of vehicles pass the school gate?' is a clear question. 'Look at the road' is not, because nobody knows what to write. PAGE 5: Lesson 2: Collecting at most 10 items — How to collect ### How to collect 1. Agree the question and the types you might see, such as car, matatu, bus, lorry, bicycle and motorcycle. 2. Keep the count to at most 10 items. 3. Write each item as it comes, in order. That list is the raw data. 4. Only then count how many of each type you wrote. Here is a raw list of 10 vehicles from a teacher-led watch: car, matatu, car, bicycle, lorry, car, matatu, bicycle, bus, motorcycle. Count each type: - car: 3 - matatu: 2 - bicycle: 2 - lorry: 1 - bus: 1 - motorcycle: 1 Add the counts: 3 + 2 + 2 + 1 + 1 + 1 = 10. The total matches the number of items in the raw list. If the total were 9 or 11, a vehicle would have been missed or counted twice, and the group would count again. ### Care while collecting Stand well back from the road with the teacher. Do not step into the road to see a vehicle, and do not shout at drivers. In the classroom, count objects you are allowed to touch, such as books or bottle tops. Stop at 10 items even if you could see more. A short honest list is the task. ## Key words • raw data — the list of items just as they were collected, before they are organised • type — a kind of item, such as car or bicycle PAGE 6: Lesson 2: Collecting at most 10 items — Practice ## Worked examples ### Example 1 The raw list is car, matatu, car, bicycle, lorry, car, matatu, bicycle, bus, motorcycle. How many cars are there, and how many vehicles are there altogether? Working: 1. The word car appears in positions 1, 3 and 6, so there are 3 cars. 2. There are 10 names in the list. 3. Check: 3 + 2 + 2 + 1 + 1 + 1 = 10. Answer: 3 cars, and 10 vehicles altogether ## Worked examples ### Example 2 A group has listed 7 items and is allowed at most 10. How many more items may they collect? Working: 1. At most 10 means they stop at 10. 2. 10 − 7 = 3. Answer: 3 ## Worked examples ### Example 3 Bicycles are 2 and matatus are 2 in the list above. How many of those two types are there together? Working: 1. Add the two counts. 2. 2 + 2 = 4. Answer: 4 ## Activity: Collect a raw list of 10 You will need: Exercise book, Pencil, Classroom objects or a teacher-led view of the road 1. Agree a question that can be answered with at most 10 items, such as the colours of 10 books in the group. 2. Write the raw list in the order you collect the items. 3. Count each type and add the counts. 4. Check that the total equals the number of items in the raw list. Recount if it does not. 5. If the question is about vehicles, stay with the teacher, well back from the road, and stop at 10 vehicles. ## Practice 1. What is raw data? 2. A raw list has 4 red books, 3 blue books and 2 green books. How many books were collected? 3. You have collected 10 items. How many more are you asked to collect in this grade? 4. In the vehicle list, there is 1 bus and 1 lorry. How many vehicles are not a bus or a lorry if 10 were seen? ## Answers to practice 1. The list of items just as they were collected, before they are organised. 2. 9 3. None. At most 10 means you stop. 4. 8 ## Summary • Start with a clear question and write a raw list of at most 10 items. • Then count each type. • The counts must add up to the number of items in the list. PAGE 7: Lesson 3: Drawing a table — The parts to draw LESSON 3: DRAWING A TABLE ========================= ## What you will learn • Name the title, headings, columns and rows of a table. • Draw a table that can hold up to 10 items. Curriculum outcomes: c) draw a table for recording data ## Introduction A raw list of ten vehicles is hard to compare until it is placed in a table. A table uses a title, headings and ruled boxes so that each number sits in a place you can find again. ## Notes A table is a grid of rows and columns. Rows go across. Columns go down. Where a row and a column meet, there is one cell. ### The parts to draw 1. Write a title that says what was collected, such as 'Vehicles seen at the school gate'. 2. Draw a rectangle with a ruler. 3. Draw a vertical line to make two columns. 4. Draw a horizontal line under the top row. That row is for headings, such as 'Type of vehicle' and 'Number'. 5. Draw one more horizontal line for each type you need to record. If there are 4 types, the table has the heading row plus 4 rows, which is 5 rows. Two columns and 5 rows make 2 × 5 = 10 cells. Leave the number cells empty until the next lesson. Drawing and filling are different jobs. PAGE 8: Lesson 3: Drawing a table — A table that fits the data ### A table that fits the data Use one row for each type, not one row for each item. The raw list of 10 vehicles had 6 types, so the table needs a heading row and 6 type rows, which is 7 rows. Do not add a type you did not see, unless the question asks you to leave a row ready, such as a row for ambulance that may stay at zero. Keep the lines straight. If two groups draw tables about the same raw list, the titles and headings should match so the tables can be compared. A table with no title can be read wrongly: the number 3 might be cars, books or votes. [DIAGRAM] TYPE: svg ALT: A table has a title, a heading row, and one row for each type. The number column is still empty. PAYLOAD: CAPTION: A table has a title, a heading row, and one row for each type. The number column is still empty. [/DIAGRAM] ## Key words • table — a grid of rows and columns used to organise data • heading — the label at the top of a column, such as Type or Number • cell — the box where one row and one column meet ## Worked examples ### Example 1 A table has a heading row and 4 rows of data, and it has 2 columns. How many cells does it have? Working: 1. Rows: 1 + 4 = 5. 2. Cells: 2 × 5 = 10. Answer: 10 ## Worked examples ### Example 2 A raw list uses 6 types. How many rows should the table have, including the heading row? Working: 1. One row is for headings. 2. Six rows are for the types. 3. 1 + 6 = 7. Answer: 7 ## Worked examples ### Example 3 Each of 5 rows is 15 cm wide. What is the total width if you could lay the rows end to end? Working: 1. The rows are equal. 2. 5 × 15 = 75. Answer: 75 cm PAGE 9: Lesson 3: Drawing a table — Practice ## Activity: Rule a table You will need: Ruler, Pencil, Exercise book 1. Write the title 'Vehicles seen at the school gate'. 2. Use the ruler to draw a table with 2 columns and a heading row plus 4 empty data rows. 3. Head the columns 'Type of vehicle' and 'Number'. 4. Count the rows and the cells. Check that 2 columns times the number of rows gives the number of cells. 5. Draw a second, smaller table titled 'Colours of books', with headings 'Colour' and 'Number', ready for the next lesson. ## Practice 1. How many rows are in a table with a heading row and 6 types? 2. A table has 2 columns and 8 rows. How many cells is that? 3. What is the heading row for? 4. A table has 3 columns and a heading plus 4 data rows. How many cells is that? ## Answers to practice 1. 7 2. 16 3. It names what each column shows, such as Type and Number. 4. 15 ## Summary • A table has a title, headings, rows and columns. • Use one row for each type. • Cells = columns × rows, including the heading row. LESSON 4: RECORDING DATA WITH TALLIES ===================================== ## What you will learn • Show a count up to 10 with tally marks grouped in fives. • Record the tally and the number in a table. Curriculum outcomes: d) record data in the table ## Introduction Saying a number is quick, but a tally shows the count one mark at a time. Four upright sticks and a fifth stick across them stand for 5. You can check the number by counting the sticks. ## Notes A tally is a mark that stands for one item. To keep the marks easy to count, group them in fives. Draw four upright sticks, then draw the fifth stick across the four. That bundle is 5. Two bundles are 5 + 5 = 10. A count of 7 is one bundle and two extra sticks, because 5 + 2 = 7. A count of 4 is four upright sticks and no cross, because the bundle is not complete. PAGE 10: Lesson 4: Recording data with tallies — From the raw list to the table ### From the raw list to the table Take a raw list of 10 book colours: red, red, blue, green, red, blue, yellow, red, green, blue. Make one tally mark for each book, in the row of its colour. - red: 4 - blue: 3 - green: 2 - yellow: 1 Check: 4 + 3 + 2 + 1 = 10. Then write the number beside the tally. The table needs three columns if you keep both the tally and the number: Colour, Tally, Number. The number is what you read later. The tally is the working that shows how you got it. Sticks on the desk work the same way. Lay one stick for each item, bundle each five with a cross stick or a loop of string, then count the bundles. Five bundles would be 25, but this grade stops at 10 items, so you will have at most two bundles. Write the tally in the table on the same day you collect the data. A list left only in someone's memory is easy to change by mistake. ## Key words • tally — a mark that stands for one item, usually grouped in fives • bundle of five — four upright tally marks with a fifth mark across them ## Worked examples ### Example 1 How many items does one complete tally bundle and two extra marks stand for? Working: 1. A complete bundle is 5. 2. Two extra marks are 2. 3. 5 + 2 = 7. Answer: 7 ## Worked examples ### Example 2 Book colours: red 4, blue 3, green 2, yellow 1. How many books were recorded? Working: 1. Add the numbers in the table. 2. 4 + 3 + 2 + 1 = 10. Answer: 10 ## Worked examples ### Example 3 Two complete tally bundles stand for how many items? Working: 1. Each bundle is 5. 2. 2 × 5 = 10. Answer: 10 PAGE 11: Lesson 4: Recording data with tallies — Summary ## Activity: Tally, then write the number You will need: Sticks or pencil and paper, The table drawn in the previous lesson, Up to 10 classroom items 1. Collect a raw list of at most 10 items, such as the colours of 10 books. 2. Use sticks or tally marks, bundled in fives, to show each type. 3. Write the tally and the number in the table. 4. Add the numbers. If the total is not the same as the number of items, find the missing or extra mark. 5. Swap tables with another pair and check one row by recounting the tally. ## Practice 1. A tally shows two bundles of five. What number is that? 2. Red books 4, blue books 5, green books 1. What is the total? 3. How do you draw the tally for 5? 4. A table shows 6 and 3. How many more is 6 than 3? ## Answers to practice 1. 10 2. 10 3. Four upright marks with a fifth mark across them. 4. 3 ## Summary • One tally mark stands for one item. Bundle the marks in fives. • Record both the tally and the number. • The numbers in the table must add up to the number of items collected. LESSON 5: READING AND INTERPRETING A TABLE ========================================== ## What you will learn • Find the greatest and least numbers in a table. • Find a total and how many more one type has than another. Curriculum outcomes: e) interpret the raw data from the table ## Introduction A table does not answer a question until someone reads it. Interpreting means using the numbers to say which type has the most, which has the least, and how the types compare. ## Notes Use this order every time you interpret a table. 1. Read the title so you know what was collected. 2. Read the headings so you know which column is the type and which is the number. 3. Find the greatest number. That type has the most. Find the least number. That type has the least. If two types share the greatest number, say that they are equal. 4. Add every number in the number column. The total should equal the number of items collected. 5. Subtract to find how many more one type has than another. PAGE 12: Lesson 5: Reading and interpreting a table — A fruit table ### A fruit table Eight learners each chose one fruit. The table shows mango 3, banana 2, orange 1, apple 2. The total is 3 + 2 + 1 + 2 = 8, which matches the 8 learners. Mango has the most, because 3 is greater than 2 and greater than 1. Orange has the least. Mango has 3 − 1 = 2 more than orange. Banana and apple are equal, with 2 each. Together, banana and apple are 2 + 2 = 4, which is half of 8. ### What the table does not say The table does not say that mango is a better fruit. It says that, in this group of 8, mango was chosen most often. It also does not say what a ninth learner would choose. Keep the interpretation inside the data you have. When two groups interpret the same table, they should get the same total and the same 'how many more'. If they do not, one of them has added or subtracted wrongly, and both groups work the sum again. ## Key words • interpret — to answer questions from the numbers in a table • most — the type with the greatest number • least — the type with the smallest number ## Worked examples ### Example 1 The fruit table shows mango 3, banana 2, orange 1 and apple 2. How many learners chose a fruit? Working: 1. Add the numbers. 2. 3 + 2 + 1 + 2 = 8. Answer: 8 ## Worked examples ### Example 2 How many more learners chose mango than orange? Working: 1. Mango is 3 and orange is 1. 2. 3 − 1 = 2. Answer: 2 ## Worked examples ### Example 3 How many learners chose banana or apple? Working: 1. Banana is 2 and apple is 2. 2. 2 + 2 = 4. Answer: 4 PAGE 13: Lesson 5: Reading and interpreting a table — Practice ## Activity: Questions from our table You will need: A completed table of at most 10 items, Exercise book 1. Swap tables with another group. 2. Write the total by adding the number column. Check it against their raw list if they still have it. 3. Write which type has the most and which has the least. 4. Write one 'how many more' question and its answer. 5. Give the table back and let the owners mark your answers. ## Practice 1. A table shows dogs 4, cats 2 and hens 3. What is the total? 2. Using dogs 4, cats 2 and hens 3, how many more dogs than cats? 3. Which animal has the least: dogs 4, cats 2, hens 3? 4. How many animals are not dogs if the total is 9 and dogs are 4? ## Answers to practice 1. 9 2. 2 3. Cats 4. 5 ## Summary • Read the title and the headings before you use the numbers. • The greatest number is the most. The least number is the least. • Add for a total and subtract to find how many more. LESSON 6: VEHICLE DATA AND STAYING SAFE ======================================= ## What you will learn • Interpret a table of vehicle types. • Relate the table to how people get help if they are hurt near a road. Curriculum outcomes: e) interpret the raw data from the table; f) appreciate use of tables in representing data in real-life situations ## Introduction A table of vehicles is not only a counting exercise. It tells you how busy a road was during the watch, and it reminds you which vehicle is there to help if someone is hurt. ## Notes During one teacher-led watch, a group recorded 10 vehicles in this table. - car: 4 - matatu: 3 - lorry: 2 - ambulance: 1 The total is 4 + 3 + 2 + 1 = 10. Cars have the most. The ambulance has the least. Cars and matatus together are 4 + 3 = 7. Vehicles that are not ambulances are 10 − 1 = 9. PAGE 14: Lesson 6: Vehicle data and staying safe — If someone is hurt near the road ### What the numbers suggest about the road Cars, matatus and lorries are the vehicles learners must watch for in traffic. In this table they are 4 + 3 + 2 = 9 of the 10 vehicles. The road was busy during that short watch. A busy count is a reason to stand further back, not a reason to move closer. An ambulance is the vehicle used to carry a sick or injured person for care. Seeing 1 in the table does not mean an ambulance will be there whenever someone is hurt. It means that, in this watch, one ambulance passed. ### If someone is hurt near the road Move away from the traffic if you can do so safely. Tell a teacher or another trusted adult at once. Do not run into the road, and do not chase any vehicle. The adult is the person who calls for help. The data lesson and the safety lesson meet here: the table tells you the road has many vehicles, so getting help starts with getting away from those vehicles and telling an adult. A table is worth keeping because the numbers can be read again later. A memory of 'lots of cars' cannot be checked. The table can. PAGE 15: Lesson 6: Vehicle data and staying safe — Example 1 ## Key words • ambulance — a vehicle used to carry a sick or injured person for care • matatu — a shared minibus used for public transport in Kenya ## Worked examples ### Example 1 The table shows car 4, matatu 3, lorry 2 and ambulance 1. What is the total? Working: 1. Add the four numbers. 2. 4 + 3 + 2 + 1 = 10. Answer: 10 ## Worked examples ### Example 2 How many of the vehicles are not ambulances? Working: 1. The total is 10 and there is 1 ambulance. 2. 10 − 1 = 9. Answer: 9 ## Worked examples ### Example 3 How many more cars than lorries were recorded? Working: 1. Cars are 4 and lorries are 2. 2. 4 − 2 = 2. Answer: 2 ## Activity: Read a vehicle table You will need: A vehicle table with at most 10 vehicles, Exercise book 1. Copy the class vehicle table, or use car 4, matatu 3, lorry 2, ambulance 1. 2. Find the total, the type with the most, and how many vehicles are not ambulances. 3. Discuss, still in the classroom, what the group should do if a learner is hurt near a road: move back if it is safe, and tell an adult. 4. Write one sentence that uses a number from the table and one sentence about telling an adult. 5. Do not go to the road for this discussion. ## Practice 1. Cars 4 and matatus 3. How many is that together? 2. Lorries 2 and ambulances 1. How many more lorries than ambulances? 3. What is an ambulance used for? 4. A watch recorded 6 cars, 2 buses and 1 bicycle. How many vehicles is that? ## Answers to practice 1. 7 2. 1 3. To carry a sick or injured person for care. 4. 9 ## Summary • Add the vehicle counts and compare the types. • A large count of cars, matatus and lorries means the road is busy. • If someone is hurt, move back from traffic if you can and tell a trusted adult. LESSON 7: TABLES IN REAL LIFE ============================= ## What you will learn • Read a score table, a price list and a vote table. • Explain why the numbers must be recorded honestly. Curriculum outcomes: f) appreciate use of tables in representing data in real-life situations ## Introduction Schools, shops and games already use tables. A register, a price list and a score sheet are ordinary tables. Once you can read one table, you can read another, because the title and the headings tell you what the numbers mean. PAGE 16: Lesson 7: Tables in real life — A price list in a shop play ## Notes A table earns its place when someone needs the numbers again. ### Scores Three teams scored in a game: Team A 6, Team B 4, Team C 5. The total of the scores is 6 + 4 + 5 = 15. Team A has the highest score. Team A scored 6 − 4 = 2 more than Team B. The table settles the result. Arguing from memory does not. ### A price list in a shop play One class price list shows a pencil at 10 shillings, an exercise book at 50 shillings and a ruler at 20 shillings. These are the prices on that list, for the play. One of each item costs 10 + 50 + 20 = 80 shillings. Two pencils and one ruler cost 2 × 10 + 20 = 40 shillings. The table lets a buyer work out the cost without asking for every price again. ### A class vote Ten learners voted for a class monitor. The table shows Asha 4, Brian 3, Chebet 3. The total is 4 + 3 + 3 = 10, so every vote was recorded. Asha has the most, by 4 − 3 = 1 vote. Writing the votes in a table is a fair way to choose, because the group can see the count. This is the same idea people use when they choose a leader by votes. Changing a number after the vote would make the choice unfair. In each example the table is useful only if it is true. Record what happened, then let the addition and subtraction speak. PAGE 17: Lesson 7: Tables in real life — Example 3 ## Key words • price list — a table that shows the cost of each item • vote — a choice that can be counted in a table ## Worked examples ### Example 1 Team A scored 6, Team B scored 4 and Team C scored 5. What is the total, and how many more did A score than B? Working: 1. Total: 6 + 4 + 5 = 15. 2. How many more: 6 − 4 = 2. Answer: The total is 15. A scored 2 more than B. ## Worked examples ### Example 2 A pencil costs 10 shillings and a ruler costs 20 shillings. What is the cost of 2 pencils and 1 ruler? Working: 1. Two pencils cost 2 × 10 = 20 shillings. 2. Add the ruler: 20 + 20 = 40. Answer: 40 shillings ## Worked examples ### Example 3 Votes: Asha 4, Brian 3, Chebet 3. How many votes were cast, and by how many votes does Asha lead Brian? Working: 1. Total: 4 + 3 + 3 = 10. 2. Lead: 4 − 3 = 1. Answer: 10 votes were cast. Asha leads by 1 vote. PAGE 18: Lesson 7: Tables in real life — Three useful tables ## Activity: Three useful tables You will need: Ruler, Exercise book, Pencil 1. Draw a score table for three teams and fill it with 6, 4 and 5. Find the total and the highest score. 2. Draw a price list for a pencil at 10 shillings, an exercise book at 50 shillings and a ruler at 20 shillings. Find the cost of one of each. 3. Draw a vote table for three names. Collect up to 10 votes in the group, one each, and record them with tallies. 4. Add the votes and name the person with the most. If two share the highest number, say that the result is a tie. 5. Explain why the group should not change a tally after the count. ## Practice 1. Scores are 5, 5 and 3. What is the total? 2. An exercise book costs 50 shillings and a pencil costs 10 shillings. What do they cost together? 3. Votes are 6 and 4. How many more votes does the first person have? 4. Why should a vote table show the true count? ## Answers to practice 1. 13 2. 60 shillings 3. 2 4. So that the choice is fair and everyone can check the result. ## Summary • Score sheets, price lists and vote tables all store numbers that people need again. • Add the column to check that nothing was left out. • An honest table lets the group agree the result. LESSON 8: FROM THE QUESTION TO THE INTERPRETATION ================================================= ## What you will learn • Carry out one data task from the question to the interpretation. • Check that the table total matches the number of items. Curriculum outcomes: a) identify materials for data collection and recording in real-life situations; b) collect data of at most 10 items within the school environment; c) draw a table for recording data; d) record data in the table; e) interpret the raw data from the table; f) appreciate use of tables in representing data in real-life situations ## Introduction The separate steps become one task. You choose a question, collect at most 10 items with classroom materials, draw the table, record tallies, and only then say what the numbers mean. ## Notes Follow the steps in order. Skipping the raw list and writing numbers from memory is how counts go wrong. PAGE 19: Lesson 8: From the question to the interpretation — One complete example ### One complete example Question: Which game did 10 learners in the group choose? Materials: exercise book, pencil, ruler, and sticks for tallies. Raw list: football, football, netball, football, skipping, netball, football, tag, netball, football. Counts: - football: 5 - netball: 3 - skipping: 1 - tag: 1 The total is 5 + 3 + 1 + 1 = 10, so the table matches the raw list. Football has the most. Skipping and tag have the least, and they are equal. Football was chosen by 5 − 3 = 2 more learners than netball. Learners who did not choose football are 10 − 5 = 5. So half the group chose football and half did not. The table does not say football is a better game. It says that, of these 10 learners, football was the most common choice. ### Check before you share 1. Count the items in the raw list. It must be 10 or fewer. 2. Add the number column. 3. If the two numbers differ, find the row that was miscounted before you tell anyone the result. 4. Then state the most, the least, and one comparison. A digital device can hold a copy of the finished table if the teacher agrees. Type the same title, headings and numbers. The sticks and the paper table are still the record you can touch and recount. Sharing a checked table is how data becomes useful to someone who was not there when you collected it. ## Key words • total — the result of adding every number in the table • comparison — a statement of how many more one type has than another ## Worked examples ### Example 1 Games chosen by 10 learners: football 5, netball 3, skipping 1, tag 1. Show that the table total matches the number of learners. Working: 1. Add the counts. 2. 5 + 3 + 1 + 1 = 10. 3. The raw list also has 10 names. Answer: The total is 10, which matches. ## Worked examples ### Example 2 How many more learners chose football than netball? Working: 1. Football is 5 and netball is 3. 2. 5 − 3 = 2. Answer: 2 ## Worked examples ### Example 3 How many of the 10 learners did not choose football? Working: 1. Football is 5. 2. 10 − 5 = 5. Answer: 5 PAGE 20: Lesson 8: From the question to the interpretation — Practice ## Activity: One data task for the group You will need: Ruler, Exercise book, Pencil, Sticks or bottle tops, A digital device only if the teacher provides one 1. Choose a question about at most 10 items in school, such as favourite games or ways of coming to school. 2. Write the raw list, then draw a table with a title and headings. 3. Record tallies with sticks or marks, write the numbers, and add them. 4. If the total does not match the raw list, recount before you go on. 5. Tell another group the most, the least, and one 'how many more'. If a device is available, type a copy of the checked table. ## Practice 1. Walk 6, bus 2, bicycle 1. How many learners are in the table? 2. How many more learners walk than take the bus if walk is 6 and bus is 2? 3. Football 5, netball 3, skipping 1, tag 1. Which two types are equal and least? 4. What should you do if the numbers in the table add up to 9 but the raw list has 10 items? ## Answers to practice 1. 9 2. 4 3. Skipping and tag, with 1 each. 4. Recount. One item is missing from the table. ## Summary • Question, materials, raw list, table, tally, number, then interpret. • The total in the table must match the number of items collected. • Say what the data shows, and do not claim more than the table can support. PAGE 21: Revision quiz REVISION QUIZ ============= Answer all the questions, then mark yourself on the Answers tab. 1. Which set is the best kit for drawing and filling a table? A. A ball and a rope B. A ruler, a pencil and an exercise book C. Only a textbook D. A whistle 2. One bottle top stands for one book. How many tops show 9 books? A. 1 B. 8 C. 9 D. 10 3. A raw list has 6 items. How many more items can be added if the limit is 10? 4. The list is car, car, bus, car, bicycle. How many cars are there? A. 2 B. 3 C. 4 D. 5 5. A table has a heading row and 4 data rows, with 2 columns. How many cells is that? A. 6 B. 8 C. 10 D. 12 6. What does the title of a table tell you? A. The colour of the pen B. What was collected C. The name of the school bell D. How tall the ruler is 7. Two tally bundles of five stand for which number? A. 2 B. 5 C. 8 D. 10 8. A table shows red 4, blue 3 and green 2. What is the total? 9. Mango 3, banana 2, orange 1. How many more mangoes than oranges? A. 1 B. 2 C. 3 D. 4 10. Car 4, matatu 3, lorry 2, ambulance 1. How many vehicles are not ambulances? 11. Votes are Asha 4, Brian 3, Chebet 3. Who has the most votes? A. Brian B. Chebet C. Asha D. They all have the same number 12. Why is a table useful when a class chooses a monitor? PAGE 22: Quiz answers ANSWERS ======= 1. B. A ruler, a pencil and an exercise book The ruler makes straight lines, and the pencil and book record the data. 2. C. 9 Each book needs its own top, so 9 books need 9 tops. 3. 4 10 − 6 = 4. 4. B. 3 Car appears three times. The list has 5 vehicles in all. 5. C. 10 There are 5 rows. 2 × 5 = 10 cells. 6. B. What was collected The title says what the data is about, so the numbers are not mistaken for something else. 7. D. 10 Each bundle is 5. 5 + 5 = 10. 8. 9 4 + 3 + 2 = 9. This should match the number of items collected. 9. B. 2 3 − 1 = 2. 10. 9 The total is 10. 10 − 1 = 9. 11. C. Asha 4 is greater than 3. The total 4 + 3 + 3 = 10 shows every vote was recorded. 12. It shows each person's votes so the group can check who has the most. An honest table lets everyone see the same count.