Lesson objective: Understand that we can express a number in multiple ways with both mixed numbers and fractions and flexibly move between the representations to more efficiently add and subtract mixed numbers.

Students bring prior knowledge of decomposing a mixed number from 3.NF.A1. This prior knowledge is extended to applying it to adding mixed number and fraction problems as students add orders of sandwiches tallied by the whole and half. A conceptual challenge students may encounter is accounting for an equivalence with the entire number and not just a single whole number.

The concept is developed through work with a tally tables, where students interpret the number represented by the total of tallies.

This work helps students deepen their understanding of equivalence because they recognize equivalent numbers and choose which equivalence will be most helpful in solving addition and subtraction of mixed number problems.

Students engage in Mathematical Practice 4 (model with mathematics) as they interpret tally tables and use diagrams to assist in writing equivalent forms of the numbers represented.

**Key vocabulary:**

- fraction
- mixed number