For a week prior to this lesson, I ask students to bring in healthy ingredients for a trail mix. This was an activity that our school did together for testing week, but it can be used at any time. This works well just prior to the high stakes test because it is meaningful real-world math practice that is different enough to distract them a bit from the pressures they are feeling about the upcoming test.
I suggest specific foods but give them a wide leeway. We're being "sold" through advertising to believe that cheese crackers and granola bars and cereal are healthy, so that's often what I get.
For the opener for this lesson, we just take a moment to look through the different items we received and thank the different students who brought good in. Then I ask students to think about how we will go about measuring the nutritional content (grams of sugar, grams of protein, and so on) for the total amount of trail mix we make. How about the amount per serving?
What makes this task complex is that to obtain the nutritional content for each item, the number of servings per package will have to be multiplied by the grams/serving for each item. This is why the activity is done as a completely guided activity. There are too many steps to reasonably expect a 3rd grader to complete it successfully on their own.
Recording the Ingredients
The first step is to list all the different ingredients on the blank trail mix table. (I sound out the ingredients phonetically and ask students to sound them out as they write them on their table. These little occasions for spelling and phonics practice are just as essential, if not more so, than weekly spelling tests).
Nutrition labels list quantities per serving size, rarely for the entire package. So the next step is to multiply the quantity (5 grams of protein, for example) times the total number of servings (3 per package, for example). This product is the total grams of protein (sugar, fat, and so on) per package. The total nutritional content per package of food put into the trail mix is necessary because then we will divide the trail mix into 100 servings. (1 per day for 29 kids for 3 days with some left over).
Using Division to Determine Grams Per Serving
The final step is to divide each total by the number of servings. When I teach this lesson again, I will use a smaller number of food items and simply divide it by 30 (the number of students in my class).
This lesson revolves around Mathematical Practice 8, "Look for and express regularity in repeated reasoning." Students are directed to look for patterns - something that repeats in this case within the computation. From that point, exposure to the ideas of others, and more sophisticated strategies, will make sense. For example, a student could use the distributive property as a strategy - using products they know to solve products that they don’t know. For example, if students are asked to find the product of 6 x 29, they might decompose 29 into 20, 5, and 4 and then multiply 6 x 20 and 6 x 5, and 6 x 4 to arrive at 120 + 30 + 24. Another possibility would be to multiply 6 x 30, and then subtract 6.
I choose 4 students (randomly) to be the judges and they sit at a panel at the front of the room. They are the first students to taste the trail mix and they get to rate it and make an explanatory comment in the following categories:
The top score is 5 and the minimum score is 1.
All students get to take home a mini bag of the trail mix so they can complete their homework assignment. They will get to score, using a 1-5 scale, the trail mix on the following criteria:
Tomorrow we will combine this data and, for fun, come up with the mean, median and mode for each category. These factors will be combined into a total score then be multiplied by 4 to give us a percentage score.