Lesson objective: Understand that numbers can be represented in various ways and still be equivalent.

Students bring prior knowledge of using parentheses to signify grouping and ungrouping Grade 3 (3.NBT.1). This prior knowledge is extended to include different representations of numbers and larger numbers. A conceptual challenge students may encounter is thinking that numbers have the same value even though they are written in different ways.

The concept is developed through work with a sorting activity which explains how different numbers are similarly grouped.

This work helps students deepen their understanding of equivalence because numbers that are written in different forms still have the same value.

Students engage in Mathematical Practice 6 (attend to precision) as they use base ten numeral form, expanded notation, number name, and base 10 representations to discuss equivalency of numbers.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as students will create categories for their sort in order to show equivalency.

**Key vocabulary:**

- base-ten
- expanded form
- equivalency
- representation
- standard form
- type
- word form

**Special materials needed:**

- pencil and paper
- print out the numbers for students to sort