SWBAT multiply & divide with fractions by solving real-world problems & using visual fraction models.

Hike Mt. EOG, but take a few rests along the way to re-fuel yourself for this journey.

5 minutes

We watch Kids Hiking Equipment Review, which is a 3 minutes video clip to get a good picture of what we'll be talking about.

Ahead of time, I draw the outline of a trail winding up a mountain on the center third of the whiteboard. You can solicit input from students to then add features to the class drawing of Mt. EOG such as trees, plants, and animals as they visualize the journey if you'd like. (I am using Mt. EOG because our end-of-the-year state test is called the E.O.G.--End of Grade Test, but you can substitute your state testing acronym here of course.) Here I set up the “problem” of the Hiking Company supplies us with food, and delivering some to each pit stop, but they need exact measurements, otherwise there won’t be enough for everyone at each pit stop.

I share with students that a successful climb to the summit of a mountain requires careful planning and prep work. We review test-taking strategies together. For their imaginary journey to the top of Mt. EOG, they will need to do two things: they will 1) calculate their route & 2) divide to determine the necessary supplies they will need to take with them for the hike. Here, we also discuss the importance of teamwork both in climbing a real mountain, & when solving a problem.

20 minutes

I divide students into "expedition teams" of 3 to 4 students. I write the "expedition details" on the left third of the board: (I use expedition instead of "trip" to increase contextual vocabulary.) We've also read a few stories about sled dog teams during the Iditarod race, as they travel on an expedition through the Alaska wilderness, so my students are familiar with "pit spots" to re-fuel/re-nourish hikers & dogs. T/s determine based on rate, how long it will take to get up the mountain (and how many pit stops there will be. ) T gives the quantities of food/supplies needed for the trip. T/s work together to divide up the supplies into the 8 “pit stops”. T represents this visually with pipe cleaners & signs with fractions pre-written on them.

**Trip length: 192 miles round-trip****Speed of the average hiker: 3 miles per hour****Number of hours hiking each day: 8**

I have students calculate the number of days required to hike up Mt. EOG and back. (Answer: At a rate of 3 mph, teams hiking for eight hours in a day would travel 24 miles each day. It would take eight days to cover the 192 miles of trail.)

We mark points along the trail showing each of the eight days. Next to each mark, I use colored markers to show the fraction of the journey that has been completed at that point ^{1}⁄_{8}, ^{1}⁄_{4}, ^{3}⁄_{8}, ^{1}⁄_{2}, etc.). (I tell the teams that at each of these stops along the trail, the hike organizer will have a stash of supplies waiting so that teams won't have to carry such heavy packs.)

We review working with mixed numbers, simplifying fractions and the process of multiplying & dividing fractions as we model calculating the quantity of pinto beans needed at each of the eight supply stashes. (Answer: 5 ^{2}⁄_{3 }→ 17/3 divided by 8 → 17/3 x ^{1}⁄_{8} = 17/24 lb. of pinto beans for each supply stash).

I then allow teams about 15 minutes to calculate how much of each supply item should be stocked at each of the eight stashes. On the right third of the whiteboard, write the heading "Quantity of Supplies at Each Stash" and invite representatives of each expedition team to write the name of an item, the appropriate quantity, & draw a visual representation of the fraction. I facilitate & review student's answers.

Note: Though on the same sheet, to aid in transition time, students don't the the trail mix activity until the Practice section during the next section of the lesson. To also aid in transition time, I always trim their papers with the paper cutter prior to giving them out. This means less time wasted cutting; my students glue almost everything we do into an InterActive Notebook which holds all of their work. (It's just a composition or spiral bound notebook.) A regular photocopied sheet will not fit onto the pages neatly without being trimmed. I am not a big fan of worksheets, so you won't find too many in my lessons, but they're meaningful today to help my students make sense and persevere in problem solving.

15 minutes

Now that we've worked together with the basic necessities for each "pit stop", the students are given an opportunity to do something similar with trail mix. I use trail mix because it leads into science content - chemical & physical change. Trail mix is a heterogeneous mixture. When we put the ingredients together the result is a physical change; it does not involve a chemical change.

Students now work on the second half of the worksheet, Mt EOG Trail Mix Student Sheet and students work in groups of 3 or 4 to complete the printable, encouraging them to use visual representations of fractions as they work to find servings of each ingredient for their team and the class. (Answers will vary based on expedition team size and your class size.) Then, I call on teams to summarize their findings.

20 minutes

To close, I have students combine math and writing by having students write to a prompt about the Hiking Company.

**Have we created enough information for the Hiking Company to accurately manage our supplies?**

Students exchange their Mount EOG supply list, and taking the role of a company employee, work with their table partner to determine the accuracy of the list.

Once the journal entries are finished, students swap their work with their table partner, and tally up the total number of numbers used in each others' writing piece as they read. This task can include a celebration - students measure and mix to make trail mix. As time allows, you can also use an Author's Chair, where some students read aloud their journal entry.

I'll be looking for the following: specificity of language, correct math language, labels, and clearly stating the solution to the problem, giving each a category a score of 0-3. Scores will range from 0-12.