Using this Perimeter Warm Up grid, student are asked to find the perimeter of a shape. Although perimeter is not today's objective, it is important to review perimeter in order to be successful with today's problems.
I expect some students to have difficulty with this, since we are working with volume some may attempt to solve by multiplying the sides.
After some think time, students can collaborate with their table partner and discuss how they came up with their answer. I hear a lot of "Ooh!" and frantic erasing. Some students do what I expected, and are eager to fix their answer.
I use cold calling to hear student thinking so that we can (re)establish the procedure for how to find perimeter. To firmly root our discussion, I close by modeling finding perimeter on the document camera.
This problem is chosen to guide students because it reviews perimeter and conversions. I also include the context of a dog potentially ruining Jaime's garden by trampling over her roses because my students have a soft spot in their hearts for dogs, as evidenced by previous lessons. I try to throw in "dog" problems every once in a while.
I model and provide specific steps to solve each part of the problem. This way, the students see how the problem unfolds, become accustomed to using more time to solve, and increase their simpler problem in Part 2 (Independent Practice).
Jaime is building a fence around the perimeter of her rose garden, which is shaped like a rectangle. Her garden is 39 feet long and 45 feet wide. One yard of fencing costs $15. How much money will Jaime spend on fencing?
a) The perimeter of the rose garden is _____ feet.
b) Convert the perimeter in feet to yards.
A yard is _____ than a foot, so ______.
_____ ___ 3 = ______. So, ____ feet = ____ yards
c) Multiply the number of yards by the cost of one yard of fencing.
_____ yards x $_____ = ________
d) Jaime will spend _____ on fencing.
Students now have the opportunity to put into practice what they just learned; they work independently for this task. They have a clear model of the appropriate steps in converting feet into yards.
In "Part B", students are given a new perimeter. I make sure to point out that in reading the new problem some of the work is already done. They love this; it's less work for them to complete! So, now students have to:
1) Multiply 56 yards by $15 (the cost of each yard of fencing from Part 1).
2) Add on another $15 because there are 2 more feet, which is almost a yard.
I make sure we carefully read together what the question is asking for. The question doesn't ask for the new cost, but rather the change. Therefore, students have to be more analytical in how they answer this question.
Students need to write that the cost increased by $15.
About 5 minutes into independent work, I announce to students that some of the work is done for them already: 56 yards and 2 feet are now the new perimeter. Some of my students needed for me to point that out to them because more than a few of my students were "stuck", and trying to work out the perimeter again. (I want student focus on the conversion task, not the perimeter.)
Suppose the width of Jaime's rose garden is 40 feet instead of 39 feet. This would change the perimeter of the garden from 56 yards to 170 feet, or 56 yards and 2 feet. How would this change affect the answer to the problem? Here, students use MP2 to reason abstractly and quantitatively.
To extend this for early finishers, you can also ask students:
- Jamie’s dog was born on July 3, 2012. How old in years is Jamie’s dog? How many months old is Jamie’s dog?
- Did you know that every “people year” is supposed to be the equivalent of 7 “dog years”. Calculate the age of Jamie’s dog in dog years.
- Jamie’s dog likes to sleep on the couch. If Jamie’s dog is _____ inches long, how many feet long is Jamie’s dog?
The students don’t need to know the equivalencies to get the rigor -- you can provide those:
1 foot = 12 inches
3 feet = 1 yard
This type of a problem situation allows students to work at their own pace, and can encourage them to create a worthy product that is displayed, with drawings.
To close this lesson, students discuss with table partners how they arrived at their answers, with the focus on their thinking and steps. This allows students the opportunity to take low-stakes risks before reporting out before the entire class. Then, using cold calling, random students walk us through each step they took to determine the solution.