In grade 3, students reasoned about equivalent fractions, using fraction strips, tape diagrams, and number lines. Here, they begin to revisit the idea of equivalence. Students examine fractions that have the same size but are expressed with different numerators and denominators. Students use diagrams of fraction strips, now expanded to include fractions with denominator 10 and 12, and then transition to using number lines to support their reasoning.

The relationships between fractions, such as  and , and , and and , in which one denominator is a multiple of the other, continue to be highlighted and offer many opportunities for students to look for and make use of structure (MP7).

Later in the unit, students will take a closer look at equivalence and investigate new ways to reason about equivalence.

As in earlier activities, rulers can be provided to help students draw, extend, or align partition lines, but they should not be used to measure the location of a fraction.

This lesson is students’ first experience with the number line in IM Grade 4. What understandings or misunderstandings about the number line did you observe today as students worked? Did you see students relating the idea of partitioning a tape diagram to partitioning a number line?