Lesson objective: Extend prior knowledge about comparing two objects and develop the understanding that comparing lengths of objects requires taking both endpoints into account.

This lesson helps to build understanding that comparing lengths of objects requires taking both endpoints into account. Images are used here because they support the procedural skills of comparing lengths of objects. This work develops students' understanding that both endpoints must be taken into account when comparing lengths of objects.

Students bring prior knowledge of comparing two objects describing measureable attributes of objects, such as length or weight (Grade K, Unit 8, K.MD.1D), and directly compare two objects with a measureable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference (Grade K, Unit 8, K.MD.1D).

This prior knowledge is extended to taking both endpoints into account as students must determine which pieces of licorice are longer. A conceptual challenge students may encounter is considering only one pair of endpoints when comparing objects.

The concept is developed through work with linear models such as ribbons, pieces of paper, or string which allow students to physically match up and align objects at the same endpoints and compare the other endpoints.

This work helps students deepen their understanding of numbers because when students compare length they can extend this to number comparisons. It also extends understanding of equivalence and non-equivalence.

Students engage in Mathematical Practice 2 (Students** **reason quantitatively and abstractly as they use measurements of others to compare their results), Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others as students compare the measurements of others and construct a viable argument as to why the process produced correct or incorrect responses), and Mathematical Practice 6 (Attend to precision). Students will use mathematics vocabulary properly when discussing problems. Carefully showing the steps in solving comparison problems.

**Key vocabulary:**

- length
- long
- short
- measure
- endpoint