Lesson objective: Use cluster estimation to estimate sums and products when the numbers being added or multiplied cluster near or are close in value to a single number.

This lesson helps to build procedural skill with cluster estimation and help students determine which estimation strategies are most efficient for different contexts of problems. Bar models are used here because it helps students visualize the relationship amongst the quantities and models efficient problem solving with more complex tasks. This work develops students' understanding that in addition to rounding, we can use mental computation strategies to assess the reasonableness of responses. By introducing and comparing a variety of strategies to estimate, students can begin to recognize there is no "right" estimate, but different estimation strategies may produce different estimates and some estimates will be closer to the actual answer than others.

A conceptual challenge students may encounter is making an adjustment to correct for the digits or numbers that were ignored using a particular estimation strategy. Discussing if an estimation strategy changed the exact numbers involved to be a little more or less may help students begin to reason about adjusting estimates. Students should also consider the context of a problem to reason about the level of precision needed when estimating.

Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they explain to themselves the meaning of the problem and how to go about solving it. They should check their thinking and solutions by asking themselves, "Does this make sense?"

**Key vocabulary:**

- approximation
- cluster estimation
- reasonableness

**Special materials needed:**

- Smartboard, document camera, or overhead projector