Amber Clinton

June 26, 2012

EDMT 7530

Mathematics Task Investigations

5 Tasks and Solutions:

1. The distance between place A and place B is 81.9 km. The distance between place B and place C is 27.76 km. Find the distance between place A and place C, if one wants to travel via place B.

Solution: Step 1: The distance between place A and place C = the distance between place A and place B + the distance between place B and place C.

=81.9+27.76 (Substitute distances)

Step 2: 81.90 +27.76_____________

109.66 (Line up decimal points and put zeros to make columns even)

Step 3: So the distance between place A and place C is 109.66 km.

This task could be used in the math classroom when learning how to decipher word problems into actual mathematic problems and we could start with something simple, like this addition problem. My middle grades students would learn the basis for word problems and how to substitute values for numbers.

2. Sheena is making a design in the form of a rectangle, with small red and green cubes. The design is 9 cubes wide. She arranges 3 rows of green cubes, 2 rows of red cubes, 3 rows of green cubes and so on. If she wants to make 100 rows of cubes in all, how many red cubes will she need?

Solution: Step 1: The rectangular design is 100 cubes long and 9 cubes wide.[Length of the rectangle = total number of rows.]

Step 2: The arrangement of cubes along the 100 rows is: 3G2R3G2R. . . or the pattern is 3, 2, 3, 2, . . .[There are 3 rows of green cubes, 2 rows of red cubes, 3 rows of green cubes and so on.]

Step 3: There are 3 × 20 = 60 rows of green cubes and 2 × 20 = 40 rows of red cubes. [Group the 3 rows of green cubes and 2 rows of red cubes. You get 100(3+2)= 20 such groups.]

Step 4: So, number of red cubes required = 40 × 9 = 360.[Each row is 9 cubes wide. So, 40 rows of red cubes will have (40 × 12) cubes in it.]

This task could be used in the mathematics classroom to introduce a lesson on patterns and students would learn how to turn patterns into doable mathematics problems.

 3. Victor's income (in $) per month is a four-digit number. The last digit is three less than the third, the third digit is six less than the second, the first digit is one more than the third. The second digit is 9. Find Victor's income.  

Solution: Step 1: Let abcd be the four-digit number.

Step 2: abcd = a9cd[The question says that the second digit, b = 9.]

Step 3: d = c - 3[The last digit (d) is three less than the third (c).]

Step 4: c = b - 6[The third digit (c) is six less than the second (b).]

Step 5: So, c = 9 - 6 = 3[Substitute b = 9 in step 4.]

Step 6: a = c + 1[The first digit (a) is one more than the third (c).]

Step 7: So, a = 3 + 1 = 4[Substitute c = 3 in step 6.]

Step 8: d = c - 3 = 3 - 3 = 0[Substitute c = 3 in step 3.]

Step 9: So, abcd = 4930.

Step 10: Therefore Victor's monthly income is $4930.

This could be used in the mathematics classroom when teaching algebra. Students would learn algebra patterns, relationships, and algebraic thinking from this task

4. Mr. Andrew is 25 years older than his daughter Katie. Katie is 5 years older than Mary, her sister. The sum of the ages of both his daughters is 25. How old is Katie?

Solution: Step 1: Let the age of Mary be x years.

Step 2: Age of Katie = 5 + x[Katie is 5 years older than Mary.]

Step 3: x + (x + 5) = 25[Sum of the ages of both his daughters is 25..]

Step 4: 2x = 20, x = 10[Simplify.]

Step 5: Therefore, age of Katie = 5 + x = 5 + 10 = 15 years

This could be used in the mathematics classroom when teaching algebra. Students would learn algebra patterns, relationships, and algebraic thinking from this task

5.   In the quadrilateral ABCD, ∠ABC = ∠BCD = 90° and ∠CDA = 63°. What is the measure of ∠DAB?

Solution:

Step 1: ∠ABC = ∠BCD = 90° and ∠CDA = 63°.

Step 2: In a quadrilateral, the sum of the four angles = 360°.

Step 3: ∠DAB + ∠ABC + ∠BCD + ∠CDA = 360°

Step 4: ∠DAB + 90° + 90° + 63° = 360°[Substitute ∠ABC = ∠BCD = 90° and ∠CDA = 63°.]

Step 5: ∠DAB + 243° = 360° [Add.]

Step 6: ∠DAB = 360° - 243° [Subtraction property for equality.]

Step 7: ∠DAB = 117°

Step 8: The measure of ∠DAB is 117°.

These could be used in the mathematics classroom to teach a beginning lesson in Geometry, specifically angles. Students would be expected to learn various angles and geometrical patterns.

15 Other Tasks (No solutions):

1.  Tommy's microwave repair bill was $68. This included $13.6 for each hour of labor and $27.20 for parts. Find the number of hours of labor.

2. Marissa planned to distribute 2 chocolate bars each, to her 20 friends on her birthday. She distributed the chocolates she had and they were enough for only 16 of her friends. How many chocolate bars was she short?

3. A truck driver drove a total distance of 1880 miles in a week. On the first day, he traveled a distance of 200 miles and on the rest of the days, he travels the same distance on each day. How many miles did he travel from the second day onward?

4. Laura drives from Atlanta to Savannah, a distance of 156 miles. She then drives from Savannah to Tallahasee, a distance of 120 miles, taking 6 hours on the whole. Determine her average speed for the whole journey.

5. Jasmine walks from her home to school and back home. Her sister Susan walks from school to their home and back to school. They both walk with the constant speeds. They start exactly at the same time and meet for the first time, 7 km from school. Each one continues on the way to their destination when they both turn around without any loss of time. They meet for the second time, 4 km from their home. What is the distance from their home to school?

6.  The area of a square is given by the formula A = c2. What will be the total area of 5such similar squares, if the side of a square is 7 in?   

7. Sarah had some roses and 23 of them were red-colored. She used 910 of the red-colored roses to make a bouquet. What fraction of the total rose was used for bouquet?  

8. Patrick walks 13th of a kilometer in 16th of one hour. Find the distance covered by Patrick in an hour. 

9. Sunny was given 18 problems to solve as homework, of which he solved 10 in the evening and the rest at night. Find the decimal equivalent to the fraction of problems he solved at night to the total number of problems he had for homework. B

10. Josh spent $49.25 for a pair of jeans, $43.45 for a book and $3.41 for a lunch at a mall. Write the decimal number that is equivalent to the fraction of money spent by him for the lunch to the total money spent by him at the mall.

11.   Evaluate the expression 16 × (12)n, for n = 1, 2, 3, and 4, and identify the sequence formed.

12. If the hour hand in a clock covers 60o in two hours, then what will be the angle covered by the hour hand after 5 hours?  

13.   A cow is tied with a rope in a meadow so that it can graze a maximum area of 28.26 ft2.What is the length of the rope?

14.   All the children in a school were made to stand in a square formation. Out of 687 children, 11 were left after forming the square. How many children are there in each row?  

15. The population of Texas in 1986 was 660,000. The population decreased to 485,000 in 1996. If the decrease in population was the same every year, then what was the change in population each year? ee77