Topic B in Module 5 is analogous to Topic B in Module 4, but while in Module 4 students composed ones and tens within 200, Module 5 expands upon this, finding students composing tens and hundreds within 1,000. The work of Topic A transitions naturally into Topic B, with students employing concrete and pictorial representations of the vertical algorithm when they encounter addition problems for which they do not have an obvious simplifying strategy. In Lessons 8–9, students continue to build their conceptual understanding as they relate manipulatives to the algorithm, recording compositions as new groups below in vertical form as they did in Module 4. As they move the manipulatives, students use place value language to express the action and physically exchange 10 ones for 1 ten and 10 tens for 1 hundred, as needed. They record each change in the written vertical method, step by step. In Lessons 10 and 11, students move from concrete conception to pictorial representation as they draw chip models to represent addition within 1,000. As they did with the manipulatives, students record each action in their drawings step by step on the algorithm (see image at right). In Lesson 12, students are presented with a variety of problems for which they must choose an appropriate strategy to solve. Students are encouraged to be flexible in their thinking and to defend their reasoning using place value language. They may choose to represent and solve problems using number bonds, the arrow way, number disks, or chip models.