EDMT 7530 Mathematics Tasks/Investigation Questions
Donna McDonald
June 25, 2012
Primes and Composites
1) Is 421 prime or composite? Since 23 x 23 > 421 and 19 x 19 < 421, we only need
to consider 2,3,5,7,11,13,17, and 19 as possible factors of 421. Since none of
these primes are factors, 421 is a prime number.
2) Is 667 a prime number? No, it is divisible by 23
3) Write the prime factorization of 1836 = 22 x 33 x17
Solve the problem
4) One lighthouse light flashes every 10 seconds, and a second lighthouse light
flashes every 12 seconds. If they both flash at the same moment, how long will it
be until they will flash together again? 60
Fractions and Percents
5) Write the fraction as a terminating decimal. 3/8 0.375
6) Write the decimal as a percent. 1.4 140%
7) 847 is what percent of 2053? 41.13%
Solve the problem
8) One-fiftieth of the Earth’s crust is magnesium, and 1/20 of the Earth’s crust is
iron. Is there more iron or more magnesium in the earth’s crust? More iron
Absolute Value, Rational and Irrational Numbers
9) –I-18I – I29I 11
10) Is this number rational or irrational? .060060006… irrational, not repeating
11) Is this number rational or irrational? .21060606… rational, repeating
Algebra
12) Solve the Equation 7x + 2 = 3x + 10 Subtract 3x from both sides, 4x + 2 = 10.
Subtract 2 from each side, 4x + 8, divide each side by 4, x = 2
13) Solve the linear inequality -9x>- 28 -3
14) Solve the problem. A woman’s shoe size is given by 3x – 22, where x is the
length of her foot in inches. What is a woman’s shoe size for a length of 9
inches? 11 inches? 9 inches = size 5, 11 inches = size 11
15) Write the following polynomial in standard form. (10x5+3x2-5x)+(2x5+4x2+7x)
12x5+7x2+2x
Geometry
16) What is the sum of 2 supplementary angles? 180o
17) What is the measure of the obtuse angle formed by the hour and minute hands
of a clock if the time is 8 o’clock? 120o
18) An equilateral triangle has three sides of equal length. Fold a sheet of paper to
form an equilateral triangle, using the creases or edges of the paper. (Hint:
Obtain centerline by folding the paper in half.)
19) Find the sum of all the angles in a pentagon. A pentagon can be subdivided into
three triangles, so the total number of degrees in its angles is 3, and 3 x 180 o =
540o.
Solve the problem
20) Mr. and Mrs. Ritchie have five sons. Each son has a sister. How many people
are in the Ritchie family? There are 8 members of the Ritchie family, Dad, Mom,
the five brothers, and the one sister.
Mathematics Tasks/Investigations
Description of Solutions, Classroom Usage, and Relevance
Solve the problem #8
One-fiftieth of the Earth’s crust is magnesium, and 1/20 of the Earth’s crust is iron. Is
there more iron or more magnesium in the earth’s crust? More iron
The difficulty in finding the answer is that the denominators are unequal. To make this
determination, we must replace the two fractions by fractions having the same
denominator. Since the least common multiple of 50 and 20 is 100, this is the smallest
common denominator of 1/50 and 1/20 and these fractions can be replaced by 100. 50
will go into 100, 2 times. 2x1 (the numerator) is 2, new fraction 2/100. 20 will go into
100, 5 times. 5x1=5, new fraction 5/100. Magnesium = 2/100, Iron = 5/100.
This problem would fit in nicely with a science lesson regarding the Earth’s Geology. It
crosses subject areas well and gives practice to operations with fractions.
Solve the problem #14
A woman’s shoe size is given by 3x – 22, where x is the length of her foot in inches.
What is a woman’s shoe size for a length of 9 inches? 11 inches? x = 9 inches = size
5, x = 11 inches = size 11
A letter or symbol that is used to denote an unknown number is called a variable. In this
algebraic expression that letter is x. The x value is given in the equation, 9 and then 11.
3(9)-22=5, and 3(11)-22=11
This problem is a good warm up for the initial introduction to algebra. The students can
make a background connection as they have all tried on shoes. I used the female
context to generate a girl’s interest in the math problem. I would also provide rules so
that the students could make a personal connection to the problem.
Geometry #17
What is the measure of the obtuse angle formed by the hour and minute hands of a
clock if the time is 8 o’clock? 120o
Students will have to view that analog clock and understand that the 6 o’clock hour
would represent 180o; they must also understand that each 5 minute increment
represents 30o. Students must calculate that there are 6 (5) minute increments in the
180o. 180o divided by 6 increments equals 30o in each increment. If the minute hand is
on the 8, then 2 increments have passed, 2 x 30o=60o. 180o-60o=120o
Students have a background knowledge of clocks and understand the incremental
breakdown of telling time. Incorporating what they already know into learning a new
geometry concept should lessen the anxiety of learning new terminology. A fun add on
activity would be to have the class determine the type and degree of “time” angle for
their lunch period, and last period class start and end times. This could also segway
into single degree increments, and supplementary angle discussions.
Geometry #18
An equilateral triangle has three sides of equal length. Fold a sheet of paper to form an
equilateral triangle, using the creases or edges of the paper. (Hint: Obtain centerline by
folding the paper in half.)
1. Fold the paper in half long-ways, then open it out flat.
2. Fold a bottom corner up to touch the fold line, making a sharp point on the
other corner.
3. Now fold the two RED edges together.
4. Fold under the corner and then tuck it in out of the way. Turn over to the
smooth side.
The folding problem looks at why the angles of an equilateral triangle are 60 o
This task is a hands on and visual activity for learns.
Solve the problem #20
Mr. and Mrs. Ritchie have five sons. Each son has a sister. How many people are in
the Ritchie family? There are 8 members of the Ritchie family, Dad, Mom, the five
brothers, and the one sister.
Count the Mr. and Mrs. Ritchie as persons 1 and 2, plus the 5 sons brings your total to
7, and there is just 1 sister in total, as she is the sister to each son. This bring the total
to 8 people in the Ritchie family.
This is a fun logic problem that gets the students engaged with one another. Use is as
a warm up or throw it in as a bonus question. It is an off based question that gets a lot
of attention.