A Problem of the Day for each math class in December. Emphasis is MP7: Look for and make use of structure.

1. WINTER
Template
December
Problem Solving
MP7: Look for and make use of structure

2. 12/3
How Many Squares?
How many squares are on a
traditional 8 × 8 checkerboard?
(Hint: the answer is not 64.)

3. 12/4
Find A, B, C, D!
Determine the
values for A, B, C,
and D, which are all
positive integers,
given the following
information:

4. 12/5
Find the value of “A”
What digit should replace the “A”
in the following grid of numbers?
Explain your reasoning.

5. 12/6
Complicated... or not?
Simplify the following expression:
State your answer in fractional form.
Explain your reasoning.

6. 12/7
WINTER
The Structure of “75”
The number 75 Template
can be expressed as
the sum of consecutive whole
numbers.
For ex, 75 = 13 + 14 + 15 + 16 + 17.
Find two additional sets of consecutive
whole numbers with more than 5
addends that also sum to 75.

7. 12/10
Page Clues
A large novel is divided into a three-volume
set. The pages of the novel are numbered
consecutively, beginning with page 1 of volume
1 to the last page of volume 3 (in other words,
if the last page of volume 1 is 324, then the first
page of volume 2 is 325). There are an equal
number of pages in each volume. If the sum of
the numbers on the first page of each volume
is 1281, how many pages does each volume
have?

8. 12/11
Playing Chess
What percentage of the black squares
on a traditional checkerboard are not
occupied by red pieces at the
beginning of a game of checkers?

9. 12/12
Take a Chance
You are given two sets of numbers. You
randomly select two different numbers from
set A and add them. You randomly select
two different numbers from set B and multiply
them. What is the probability that the sum of
the two numbers in set A is greater than the
product of the two numbers in set B?

10. 12/13
Making the Grade
You took a 20-question exam that was
scored in this way: 10 points are awarded
for each correct answer and 5 points are
deducted for each incorrect answer. You
answered all 20 questions and received a
score of 125 points. How many questions
did you answer incorrectly?

11. 12/14
WINTER
What comes next?
Determine theTemplate in the
next value
following pattern of numbers:
Write your answer as a simplified
fraction.

12. 12/17
The Structure of “75”
A mathematician was using his
magnifying glass to examine an angle
measuring 14 1/2 degrees. It was
magnified 3 1/2 times. Under the glass,
how large would that angle measure?

13. 12/18
Convex Polygons
In a convex polygon, no segment
connecting any two vertices contains
points outside the polygon. What is the
maximum number of acute interior
angles that any given convex polygon
can have?

14. 12/19
Relating Length and Area
Find the diameter of a circle
whose area is quadrupled when
the length of its radius is
increased by 4 cm.

15. 12/20
Multiples and Probability
The numbers 1 to 500 in are put into a
hat. What is the probability that a
number chosen at random from the
hat is a multiple of both 6 and 13?

16. 12/21
WINTER
The Structure of “75”
Based on the values in the table, find
Template
the value of Q. Explain your reasoning
for your solution.