2. There is a problem of littering on our school grounds. If every student littered one item every day of the school year, how many pieces of garbage would there be? How much area would that cover in square meters? Compare this to our classroom size. Border retrieved from: http://www.go2itech.org/HTML/TT06/toolkit/development/print/graphics/powerpoint/Borders/pages/003_A_JuiceDrop_jpg.htm Oct 2/14.http://www.go2itech.org/HTML/TT06/toolkit/development/print/graphics/powerpoint/Borders/pages/003_A_JuiceDrop_jpg.htm Rich Relevant Different Approaches Mathematics Curriculum Multiplication Guided Inquiry Area Waste in our World Real World Schmidt, C. (Photographer). (2014, Oct. 7 ). Litter [Print Photo] EDUC 427: Module 2 Assignment We created this rich problem because we wanted to make it based on an issue relevant to the students’ real world. This problem fits the mathematics curriculum of multiplication and area as well as the “Waste in our World” science curriculum. Furthermore, we wanted to make the problem as close to guided inquiry as possible by giving the students the ability to approach the problem in many different ways.

3. Our Solution: 1) Student population: 621 more than twice Students’ solutions may vary depending on their approaches to finding the student population, the number of days in the school year, their average sizes for the pieces of garbage and the measurements of the classroom. 2) Number of days per school year: 3) Pieces of garbage: 4) Area of a piece of garbage: 5) Total area garbage covers: 6) Area of the classroom: 7) Compare: 10 months x 4 weeks 40 weeks - 5 weeks 35 weeks x 5 days 175 days 621 students x 1 piece 621 pieces x 175 days 108,675 pieces 10 cm long x 7 cm wide 70 cm square 108,675 pieces x 70 cm square 7,607,250 cm square 760 m square 20 m long x 15 m wide 300 m square Retrieved from http://www.ergoindemand.com/2-x-3-oak-framed-chalkboard.html Oct. 14/14http://www.ergoindemand.com/2-x-3-oak-framed-chalkboard.html

4. Without using multiplication the solution would look something like this: 5 + 5 + ____ 175 For the next part of the question, one would have to do 621 repeated additions of 175 or vice versa. Retrieved from http://www.tutoringandresumes.com/yahoo_site_admin/assets/images/frustrated.13011234_std.gif on Oct 7/14.http://www.tutoringandresumes.com/yahoo_site_admin/assets/images/frustrated.13011234_std.gif Without using multiplication, for the first part of the question, one would have to use repeated addition or skip count by 5 to find the answer. For the second part of the question, repeated addition would be the only obvious way to solve the problem. However, this method increases the number of chances to make an error in the calculation. Our goal as teachers is to challenge, not discourage.

5. Using the formula for area is more efficient. To figure out the average area of a piece of garbage students could use manipulatives. Retrieved from: http://beeconlearning.com/500unifixmathcubes.asp Oct 2/14http://beeconlearning.com/500unifixmathcubes.asp To solve the overall area the garbage covers, it is unrealistic to use manipulatives, therefore, students may opt to use graph paper. However, if they do not use multiplication, students will have to count to a very large number. Retrieved from http://www.mycutegraphics.com/graphics/school/supplies/graph-paper.htmlhttp://www.mycutegraphics.com/graphics/school/supplies/graph-paper.html Oct 7/14 Without using a formula for calculating area, the process would be time consuming. Despite this, students could use manipulatives to show the area of a piece of garbage and then count that number so that it represents a unit of measure. In this case, it will likely be in square centimeters. To figure out the overall area that the garbage will cover, the numbers will be significantly larger. Students are limited in using manipulatives due to the large number that would be required to represent the total area. However, if students are creative in their approach, they could make each manipulative represent a larger number (such as 10 or 100). An alternative to this would be using graph paper and then counting the squares to find the area.

6. Reinforcement Problem #1: If every student threw away two juice boxes per month instead of recycling them, how many juice boxes would there be? Retrieved from http://www.newoutlookorganizing.com/wp-content/uploads/2011/02/recycling-logo.jpghttp://www.newoutlookorganizing.com/wp-content/uploads/2011/02/recycling-logo.jpg Oct 2/14. Retrieved from http://blog.foodnetwork.com/healthyeats/2012/08/23/taste-test-juice-boxes/ Oct 7/14.http://blog.foodnetwork.com/healthyeats/2012/08/23/taste-test-juice-boxes/ The primary question demonstrated the efficiency of using multiplication to solve problems. Though the students could opt to use addition to solve this problem, we anticipate the students will use multiplication because of their understanding that multiplication can be more useful than addition. In this case students would multiply 621 students by 2 juice boxes per day to equal 1,242 juice boxes per month. Then they would multiply that number by the 10 months in the school year which equals 12,420 juice boxes per year. Furthermore, we chose this question due to its relevance to the Waste in our world unit in the science curriculum which aims to bring awareness to our impact on the planet. 621 students x 2 juice boxes 1,242 juice boxes x 10 months 12,420 juice boxes

7. Reinforcement Problem #2: How much money could our school get for these juice boxes if we took them to the bottle depot? What could we purchase with that money that the school would enjoy? Some possible things we could buy are: 2 Ipads Build a tire swing/swing set Sports Equipment Fun Lunch … Retrieved from http://www.notebookcheck.net/Review-Apple-iPad-3rd-Gen-2012-4G-Tablet.71925.0.htmlhttp://www.notebookcheck.net/Review-Apple-iPad-3rd-Gen-2012-4G-Tablet.71925.0.html Oct 9/14. Retrieved from http://www.sweetspot.org.za/ Oct 9/14http://www.sweetspot.org.za/ Once again, as with the primary question and the 1 st reinforcement problem, this problem is more easily solved by using multiplication rather than addition. Our online research showed us that one returned juice box is worth 10cents so we multiplied 10cents by the 12,420 juice boxes to discover that we could earn $1,242.00 thus showing that recycling is financially beneficial. By getting the students to think about what we could purchase with the money, this could spur the recycling program at the school in which the goal would be to actually purchase these items for the school. 12,420 juice boxes x $ 0.10 returned juice box $1,242.00