--- title: "Venn diagrams and two-way tables" subtitle: "Data and chance · Chance · Lesson 11" --- # Venn diagrams and two-way tables **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** In a class of 30, 20 play sport and 13 play music. That adds to 33, more than the class. Nobody miscounted. What is going on? :::teacher-note **In one sentence:** Students read, build and convert between Venn diagrams and two-way tables for two yes/no properties (AC9M8P02, node 1). **Students should be able to say:** I can sort a group into one, the other, both and neither. I can build a Venn diagram or a two-way table from a story. I can change a Venn diagram into a two-way table, and back. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **In a class of 30, 20 play sport and 13 play music. 20 + 13 = 33. How can that be?** ☐ Some play neither ☐ Someone made a mistake ☐ Some play both, and were counted twice My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Some play both. They were counted once with sport and again with music. Here 8 play both. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Build them from a story :::keep-together ### Neither Here is the routine. Start in the middle. 1. $25 \text{ students: } 15 \text{ dog},\ 10 \text{ cat},\ 4 \text{ both}$ — Read the story. 2. $\text{both} = 4$ — Write the overlap first. 3. $\text{dog only} = 15 - 4 = 11,\ \text{cat only} = 10 - 4 = 6$ — Take the overlap from each total. 4. $\text{neither} = 25 - (11 + 4 + 6) = 4$ — Everyone else. **40 people: 22 like tea, 18 like coffee and 7 like both. How many like neither?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 7 Tea only 22 − 7 = 15, coffee only 18 − 7 = 11. 15 + 7 + 11 = 33, so 40 − 33 = 7 like neither. ::: :::keep-together ### Find the mistake **Lia draws the Venn diagram for the same 40 people. Click the line where she goes wrong.** ``` 1 In a group of 40 people, 22 like tea, 18 like coffee and 7 like both. 2 Lia writes 7 in the overlap of the Venn diagram. 3 She writes 22 in the tea-only part and 18 in the coffee-only part. 4 Neither: 40 − 22 − 18 − 7 = −7. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: 22 like tea, but 7 of them are already in the overlap. Tea only is 15 and coffee only is 11. A negative count shows something went wrong. ::: :::keep-together ### Tables or diagrams **Which is easier to read from a two-way table than from a Venn diagram?** ☐ Nothing: they show different people ☐ Who is in neither ☐ Who is in both groups ☐ The totals, such as how many play sport in all ::: :::teacher-note **Answer:** The totals, such as how many play sport in all The table has total rows and columns; in a Venn diagram you add the parts yourself. ::: :::typical ## From one to the other **Diagram to table.** **Table to diagram.** **Exactly one.** **Outside the circles.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Tables and diagrams :::keep-together ### Row total **A two-way table: 18 students walk and own a bike, 7 walk and don't own a bike. How many students walk in all?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 25 The Walk row: 18 + 7 = 25. ::: :::keep-together ### Case only **60 people: 35 have a phone case, 20 have a screen protector, 12 have both. How many have a case but no screen protector?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 23 35 − 12 = 23. ::: :::keep-together ### Neither **In that group of 60, how many have neither?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 17 Case only 23, both 12, protector only 8: 43. So 60 − 43 = 17 have neither. ::: :::keep-together ### Review: complement **Review: a bag has 7 counters, 2 of them green. What is P(not green)?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5/7 1 − 2/7 = 5/7. ::: ## Make: your own survey The board shows a finished example (bus and bike) to compare with. Ask your two questions to your class or family, then draw both pictures. Which is quicker to read, and for which question? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **50 students: 30 study French, 25 study Japanese, 10 study both. How many study neither?** {{lines-3}} ::: :::teacher-note **Answer:** French only 20, Japanese only 15, both 10: 45, so 5 study neither. :::