Lesson 2: Solve multi-step word problems using the standard addition algorithm modeled with tape diagrams, and assess the reasonableness of answers using rounding.

Property

To model a comparative word problem where one quantity is 'more than' another, use two tapes. The first tape represents the known, smaller quantity. The second tape is drawn longer and is composed of two parts: a section equal to the first tape, plus an additional section representing the 'more than' amount. The total is the sum of both full tapes.

Examples

Property

To find a total ($T$) in a multi-step problem, you may first need to find an unknown part ($Q_{\text{unknown}}$) by relating it to a known part ($Q_{\text{known}}$).
Step 1: Find the unknown part: $Q_{\text{unknown}} = Q_{\text{known}} + \text{difference}$
Step 2: Find the total: $T = Q_{\text{known}} + Q_{\text{unknown}}$

Examples

Property

To check if an answer is reasonable, compare the exact answer to an estimated answer found by using rounded numbers. The exact answer should be close to the estimate.