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Trainer’s outline/notes for Making Sense of Numbers the purpose of this activity is to put the participants in a situation where math does NOT make sense – where the concept is taught by procedure and not for conceptual understanding. SO…. we are going to do a Show and Tell lesson – we show and we tell…. “I am going to do a math lesson with you similar to the way that I would have done this lesson earlier in my teaching career. Your task is twofold: 1. play the role of the student – so please make notes of your attitudes, etc as we go thru the problems and 2. play the role of the observer looking for best practices or the lack thereof.” 1. Handout the 2 pages titled Making Sense of Numbers 2. Today we are going to work with base-five. In base-five, things that need to be counted are grouped in sets of 5. Explain that in the base-five number system there is no symbol for five – it is represented by a 10 (1 group of 5 and no ones and usually read “one zero”) just like our ten has no special symbol – it is represented by a 10. You may want to show them a place value chart for base-five – there is a large one in the kit – 1 copy for each site so you can write on it. Twenty-fives (52) fives ones Show them the page of dots -13 dots on the top half of the page – cover up the bottom of the page and show them how circle sets of 5 and then how to write this number in base-five. Show this number on the place value chart. Repeat for the bottom half of the page – it should have enough dots that you can also group 5 of the 5-sets. Now complete Part I – there is a large version for the document camera in the kit – one for each site so you can write on it. Continue this counting sequence for at least 8 more numbers: 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100, 101, 102, 103, 104, 110, 111… answer: (112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, …) Ask for volunteers to share their answers. 3. Have them look at the examples in Part 2. You may want to explain – make it similar to explaining how to add in base ten 42 24 + 31 + 31 123 110 2+1=3 4 + 1 = five (10) so we put down the 4 + 3 = seven (which is 12 - 1 five 0 and carry the 1 and 2 ones) 1 + 2 + 3 = six which is 11 - 1 five and 1 one 4. Have them complete the 2 problems without future help – ask them to pretend like they are in rows and cannot discuss the problems. Watch for their reactions – you will probably see the same type of reactions that would be in the classroom – some students working, some pretending to work, some trying to talk to others and/or look at others papers, and some that have shut down 5. NOW is the time to have the discussion a. how did you feel working the problems? i. confused ii. angry iii. frustrated iv. unsure about what I was doing this is how our kids feel!! b. Did the procedure make sense? c. What teaching strategies was I using? - show and tell, procedural rather than conceptual 6. Discuss base 16 where the following symbols are used 10=A, 11=B, 12= C, 13=D, 14=E, 15=F, 16=10 let them do the problems if time permits or they would like 7. Stop and show the video about Gretchen and discuss how so many of our kids try to math that does not make sense so they just follow procedures. 8. Have them look at The shepherd problem and give them the one-page handout,