Download Trainer`s outline/notes for Making Sense of Numbers

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,