Lesson objective: Relate fractional invariance to a real life scenario.
This lesson provides an opportunity for students to apply their knowledge and understanding of the invariance of fractions to a mathematical situation. Students are asked to find start, end points, or total distance run along a ruler partitioned into different denominators.
Key Concept students will use:
 the quantitative measurement object is invariant (a toothpick's length does not change, regardless of how we align it to a ruler; the weight of a book doesn't change if we put another object on the scale with it)
Skills students will use:

unit fractions result from partitioning a whole; (Grade 3, Unit 4; 3.NF.A.1, 2a)

nonunit fractions are made up of unit fractions with the same denominator; (Grade 3, Unit 4; NF.A.1, 2a)
Students engage in Mathematical Practice 5 (use appropriate tools strategically) as they partition and align number lines and rulers in order to measure fractional lengths.
Key vocabulary:
 eighth
 fourth
 half
 number line
 partition
 ruler