Mock Test for Teachers

At yesterday's math meeting I shared my funky Midterm Rubric with my math colleagues.

I had prepared a short "midterm" to give them for five minutes, in case they wanted to experience the rubric first-hand.  (They didn't.)

It was an interesting challenge to create a few questions that my fellow math teachers would find interesting enough to want to discuss in groups.

How do you do on my mock test?

Answers are in white.  Highlight the blanks with the cursor to make them visible.

1. What is the sum of three hundred seventy two and one thousand two hundred fifteen?  Show your work in base negative ten.

(Hint: three hundred seventy two = four hundreds minus three tens plus two ones = 432.)

   432
+19395
------
 19627 (one thousand, five hundred, eighty seven)

2. Usually it is most proper to say a three-digit number using place value, as in "four hundred twelve".  Think of at least two situations in which it is proper to say a three-digit number by naming each digit, as in "four one two".

license plates, street addresses

3. A fatally ill goldfish breeder decides to give away all his fish.
(a) First he gives his niece a third of what remains, plus one-third of a fish.
(b) Then he gives his brother a fourth of what remains, plus one-fourth of a fish.
(c) Then he gives his friend a fifth of what remains, plus one-fifth of a fish.
(d) Lastly, he sells the remaining eleven goldfish.
No fish was divided or injured in any way.  How many fish did he start with?

For part (e) use the equation 1/5 y + 1/5 + 11 = y
11.2 = 0.8 y
14 = y
and so on, working backwards
eventually get (a) 29 fish -> (b) 19 fish -> (c) 14 fish -> (d) 11 fish

4a. A circus has a certain number of horses and riders.  Between them there are 50 feet and 18 heads.  How many horses and riders are in the circus?

4b. The pet shop Vince's Vertebrates sells jungle animals.  There are twice as many four-footed animals as two-footed animals.  There are 11 heads and 20 feet.  How many animals of each type are at the pet shop?
[4a]
18 heads means 18 total, so 36 haunches, so 50 - 36 = 14 forefeet
To make 14 forefeet there must be 7 horses
Then 18 - 7 = 11 riders

[4b]
There must be at least one snake with no feet!
4 four-footed makes 16 feet
2 two-footed makes 4 feet
5 snakes makes a total of 11 heads