Backwards Mapping

As a California resident, I have chosen to take a closer look at the Common Core State Standards adapted for California. I hope to teach elementary school, so I have selected a standard for 4th grade mathematics. The California math standards can be accessed at:
http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf 

Standard 4.MD.3 (The abbreviation should be read - 4th Grade.Measurement and Data.Standard 3) Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

I selected this standard because it focuses on applying mathematics to a real world problem. Common Core curriculum is focused on application and helping students to reach an endpoint where they are successful mathematicians who can apply their learning to life outside the classroom. To me, this standard has a clear endpoint and can also be taught in exciting ways. There is no need to teach this standard traditionally. Instead, students will be able to explore through measurement and real life calculations. This standard will allow me to create several fun, engaging lessons for a 4th grade class.

Common Core has developed 8 standards of mathematical practice. When beginning the backwards mapping process, I have found it is very important to first take a careful look at these practices. Common Core has created these practices as an end result for all students, whether they are in Kindergarten or in 12th grade. The chart below details the mathematical practices: 

With these ideas in mind, I can move forward with the backwards mapping process and take a careful look at my selected standard: 

Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

First, I must consider the skills or proficiencies that students should develop by the time they have completed this unit. 

• Students will be able to find the area of any given rectangular shape, building, or room by applying the area formula (A=lw).
• Students will be able to use their knowledge of multiplication and division to find the length of a missing side when given one side and the area of a rectangular shape. 
• Students will be able to find the perimeter of a rectangular shape, room, or object when given only two side lengths. 
• Students will understand the two perimeter formulas and how to apply them. They will also understand that the formulas mean the same thing, but sometimes one formula is more beneficial to use than the other. (P = 2L + 2W or P = L + L + W + W). 
• Students will be able to find the missing side length using multiplication and division when given the perimeter and the length of a different side. 

Next, it is time to plan assessments that will ensure that students have learned the material and can apply their knowledge. 

• Karl's Garden: This will be an assessment to ensure students understand area, but it does not cover perimeter. Please see- https://www.illustrativemathematics.org/content-standards/tasks/876
• Quiz: Students will take a quiz where they are given 6 word problems. 3 will be dealing with area and 3 will be dealing with perimeter. Students will demonstrate their knowledge by drawing diagrams of the situation and calculating the correct answers. 
• House Design: Students will be given a floorpan of a house on a piece of rectangular land. Students will be asked to use their knowledge of area and perimeter to find how much carpet they would need (in square feet) to re-carpet the entire house. Students will also have to find the perimeter of the yard, so that a fence can be installed. This will be the final assessment for the unit. 

Finally, it is time to plan the learning experiences that will take place so that students can learn the content: 

• Area Exploration Activity: Students will be given clipboards, yardsticks, pencils, and a data recording sheet. They will be instructed to go around the room and find the area of 5 rectangular objects. They will fill in the length of each object and the width of each object, and record the data. Students will then compute the area of the object. 
• Perimeter Exploration Activity: Students will be given clipboards, yardsticks, pencils, and a data recording sheet. They will be instructed to go around the room and find the perimeter of 5 rectangular objects. They will fill in the length and the width of each object, and record the data. Students will then compute the perimeter of the object. 
• Missing Sides Activity: Students will work in partners for this assignment. Each set of partners will be given a basket with 3 rectangular items. There will be missing information from each item. The idea is that students will explore how to find missing lengths when given the area or perimeter. Students will need to think a bit deeper and figure out how else they can apply the formula. The items will be as follows: 
• Textbook with a label indicating the length of one side of the textbook and the area of the textbook. 
• A small square box indicating the perimeter of the box, but no side lengths.
• A picture frame listing the length of one side and the perimeter of the frame. 

The procedure of backwards mapping is an excellent way to make sure that I, as the teacher, have thought through the learning process carefully. As I worked on this task, I carefully considered what activities and assessments would help students to achieve the end result. 

Chart was accessed at: http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf