Lesson objective: Understand that equal shares can have a different shape or the same shape.

Students bring prior knowledge of equal shares from 1.G.A.3. This prior knowledge is extended to equal shares that look different as students practice partitioning shapes into fourths in new ways. A conceptual challenge students may encounter is realizing that fair shares may not always look exactly the same.

The concept is developed through work with partitioning rectangles, which will allow students many opportunities to prove to themselves that equal shares can be created differently.

This work helps students deepen their understanding of equivalence because they will be extending their understanding of equal parts of whole shapes.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they use their knowledge of equal parts to partition shapes in ways that result in equal shares having different or similar shapes. Students engage in Mathematical Practice 3 (Construct viable arguments) as they articulate their thinking of why parts are equal or unequal, as well as understand and critique the explanations of others.

**Key vocabulary:**

- equal
- fourth
- partition
- share
- unequal

**Special materials needed:**

- yarn or string (optional)