## Students in charge of their own learning

### Preparing for college and career readiness

**Integer Operations**

Students use integer tiles to create expressions that are equivalent to a given value or another expression. When given an incomplete equation such as –12 = __ ÷ 4 × __ , students use integers to create a true equation such as –12 = –8 ÷ 4 × 6 or –12 = 4 ÷ 4 × –12. Beneath the equation, students see DreamBox’s panel of ‘lights’ that visually represents the values and then animates sequentially to help students understand the operations and how the expression simplifies in a mathematically valid order of operations. Because multiplication and division are both multiplicative, they are solved in order from left to right. Therefore in the equation above, students visually see the division step solved first and the multiplication step solved second.

**Supplementary and Vertical Angles**

In this lesson, students deepen their understanding of angle measurement and rotation while fluently reasoning about and using supplementary and vertical angle relationships. Students use DreamBox’s engaging digital tool – which points simultaneously in opposite directions – to make rotations, aim for targets, and determine angle measurements. Students must use valid deductive reasoning to figure out how to aim for specific targets in ways that require critical thinking and mental math. Students deepen their understanding of vertical angles congruence and use supplementary angle relationships to make specific rotations.

**Constructing and Measuring Polygons III**

In this lesson: The students are given a shape with marked angles and side lengths, then asked to create a new shape using scale factor. Students construct different types of triangles, quadrilaterals, regular polygons, and scaled polygons using specified restraints, and use a ruler and protractor to measure their sides and angles.

Grade 7 Teacher Tools for interactive whiteboards