Lesson objective: Solve real-world problems involving multiplicative comparisons where a fraction is multiplied by a whole number.

This lesson provides an opportunity for students to apply their knowledge and understanding of multiplicative comparisons involving a fractional amount to a problem situation. Students are asked to determine how far away locations at a nature preserve are, given the distance of a few locations and information about how far away locations are relative to each other. Students use these distances to determine possible hikes someone might take to reach a goal of a four to six mile hike.

Key Concept students will use:

- Because fractions are numbers, the meaning of multiplicative comparison does not change when fractions are involved.

Skills students will use:

- solving multiplicative comparison problems
- adding fractions (Grade 4, Unit 3)

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they work to solve a multi-step word problem. Students choose combinations of hikes for a character who wants to walk at least 4 miles, but no more than six miles. Many of the distances are described in relation to other distances, so students consider carefully what information they know and what information will help them complete the task.

**Key vocabulary: **

- comparison factor
- multiplicative comparison
- product