# NEW! Journey to Mt. Fraction (Grade 5)

Students will strengthen multiplication and division skills as they prepare to go on a virtual expedition!

**OBJECTIVE**

Strengthen students' skills in multiplication and division with fractions by solving real-world problems and using visual fraction models.

**MATERIALS**

- Mt. Fraction Trail Mix Student Printable (PDF)
- EXPO
^{®}Low Odor Dry Erase Markers (fine and medium-tipped) - Whiteboard
- Pencils
- Ingredients for Mt. Fraction Trail Mix (optional)

**DIRECTIONS**

**Background Discussion (30 minutes)**1. Bring students into the thrilling world of adventure hiking as you use EXPO

^{®}Low Odor Dry Erase markers to draw the outline of a trail winding up a mountain on the center third of the whiteboard. Invite students to add features to the class drawing of Mt. Fraction such as trees, plants, and animals as they visualize the journey. Share with students that a successful climb to the summit of a mountain requires careful planning and prep work. For their imaginary journey to the top of Mt. Fraction, they will need to calculate their route and divide the necessary supplies they will need to take with them for the hike.

2. Divide students into "expedition teams" of 3 to 4 students. Write the following "expedition details" on the left third of the board:

Trip length: 192 miles round-trip

Speed of the average hiker: 3 miles per hour

Number of hours hiking each day: 8

Food and Water Supplies for an Expedition Team of Four People:

50 gallons of water

5 ^{2}⁄_{3} lbs. of pinto beans

4 ^{1}⁄_{4} lbs. of soup mix

6 lbs. of peanut butter

2 lbs. of honey

3 loaves of bread

12 lbs. of granola

3 ^{1}⁄_{2} gallons of boxed milk

21 ^{1}⁄_{3} lbs. of apples

10 lbs. of bananas

7 lbs. of carrots

4 lbs. of chocolate

3. Ask students to calculate the number of days required to hike up Mt. Fraction 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.) Mark points along the trail using a black fine-tipped EXPO^{®} Low Odor Dry Erase marker on the whiteboard showing each of the eight days. Next to each mark, create a visual representation using colored fine-tipped EXPO^{®} Low Odor Dry Erase markers showing the fraction of the journey that has been completed at that point ^{1}⁄_{8}, ^{1}⁄_{4}, ^{3}⁄_{8}, ^{1}⁄_{2}, etc.). 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.

4. Review working with mixed numbers, simplifying fractions and the process of multiplying and dividing fractions as you 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) Demonstrate how to represent this fraction visually.

**Time for Calculations (15 minutes)**5. Allow teams time to calculate how much of each supply item should be stocked at each of the eight stashes.

6. On the right third of the whiteboard using an EXPO^{®} Low Odor Dry Erase marker, 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, and draw a visual representation of the fraction using both fine-tipped and medium Expo^{®} Low Odor Dry Erase markers. Review students' findings.

(Answer: 6 ^{1}⁄_{4} gallons of water

17/24 lb. of pinto beans

4 ^{1}⁄_{4} lbs. of soup mix^{3}⁄_{4} lb. of peanut butter^{1}⁄_{4} lb. of honey^{3}⁄_{8} loaves of bread

1 ^{1}⁄_{2} lbs. of granola

7/16 gallons of boxed milk

2 ^{2}⁄_{3} lbs. of apples

1 ^{1}⁄_{4} lbs. of bananas^{7}⁄_{8} lbs. of carrots^{1}⁄_{2} lb. of chocolate)

**Using the Student Printable (20 minutes)**7. Distribute copies of the Mt. Fraction Trail Mix Student Printable. Invite students to work independently or in pairs to complete the printable, encouraging them to use visual representations of fractions as they work. (Answers will vary based on expedition team size and class size.)

**Lesson Wrap-up (20 minutes)**8. Review the recipes the students derived for the expedition-size recipe of Mt. Fraction trail mix and the class-size version. If desired, invite students to help measure and mix as you prepare a batch of trail mix to share in celebration of your successful journey through the realm of fraction math. If not making real trail mix, have students "add ingredients" to a virtual bowl by using EXPO

^{®}Low Odor Dry Erase markers to draw the correct quantity of each ingredient on the board.

**Extension Activity**Mix math and storytelling as you invite your students to compose a number-filled account of a day on the trail to the top of Mt. Fraction. Ask students to imagine one day on their hike and write a journal entry using not only vivid details to describe the scenery, but also as many numbers as possible. Encourage students to include several fractions in addition to whole numbers. Once the journal entries are finished, have students swap their work with a friend and tally up the total number of numbers used in each other's journal entry as they read.

**COMMON CORE STANDARDS**CCSS.Math.Content.5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

CCSS.Math.Content.5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole num