Every Problem Matters. Our expert-designed curriculum builds conceptual understanding through a deliberate instructional sequence. Breakthrough manipulative models support carefully crafted lessons that progress from concrete-representational to abstract. Students progress from virtual manipulatives to number sentences and equations, building conceptual understanding and procedural fluency.

Anatomy of a Lesson.

The following screens describe one exemplary lesson. Note how this lesson carefully scaffolds from from concrete-representational to abstract in sets of 6 problems each. The Skills Check at the end has numeric procedures only, with no visual model support.

Big Ideas 2, Topic 1, Lesson 1: Adding Unit Fractions

Note: Each step contains 6 problems.

Step 1:
Models Only

Lesson 1-6

Step 2:
Students manipulate the models further.

Step 3:
Student enters values to reflect the models.

Step 4:
Student writes the fractions and creates the models.

Step 5:
Student works with number sentences and equations only.



 

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Video: See how your students can progress from concrete-representational to abstract.