In order to gain a better understanding of how *Math Trailblazer s* is aligned with the

*Common Core State Standards for Mathematics,*this section will follow the learning progression in Fourth Grade for multiplicative reasoning.

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**Multiplicative Reasoning. **In Third Grade, students worked on developing number sense for the multiplication facts using a systematic approach. Students are provided with intentional, distributed practice as well as targeted practice throughout the year to develop fluency with the multiplication facts. Students learn strategies for solving problems involving multiplication.

In Fourth Grade, students continue to have opportunities to practice the multiplication facts through distributed practice in the *Daily Practice and Problems. *The DPP items provide targeted practice for students who need additional opportunities to build their fluency, as well as opportunities for students who know their facts to maintain and increase their fluency.

See examples from the Fourth Grade *Math Trailblazer s* curriculum that illustrate the learning progression for multiplicative reasoning at the lesson level.

Grade 4 Unit 3 *Products and Factors*

Grade 4 Unit 4 *Numbers and Number Operations*

Grade 4 Unit 5 *Using Data to Predict*

Grade 4 Unit 6 *Place Value and Large Numbers*

Grade 4 Unit 7 *Patterns in Multiplication*

Grade 4 Unit 11 *Multiplication with Larger Numbers*