#### Course II

The MATH 180 Course II curriculum transitions students to pre-algebra with an emphasis on building proportional reasoning with rates, ratios and linear relationships, and functions. Visual models bring coherence to instruction, making abstract concepts more concrete.

Course II Learning Matrix

MATH 180 is organized into 9 Blocks of instruction. Each Block relates its mathematical theme to high-interest contexts, stories, and careers. Click on a number to see detailed information about each Block.

• RATES IN TIME

#### Moving Forward

Students represent motion and compare rates using graphs and tables. They solve problems related to motion and logistics.

• RATE AND RATIO

#### Bright Future

Students find rates and make connections between rates and ratios. They solve problems related to environmental science.

• RATIO RELATIONSHIPS

#### The Bottom Line

Students represent and apply ratios to compare quantities and use models to understand percent. They solve problems related to sales and marketing.

• PERCENT AND PROPORTIONAL REASONING

#### For the People

Students apply percent to solve problems and understand proportionality. They solve problems related to public services.

• PROPORTIONAL RELATIONSHIPS

#### Imagine That

Students use graphs and equations to understand proportional relationships. They solve problems related to art and design.

• LINEAR RELATIONSHIPS

#### On the Money

Students use models, graphs, and equations to extend their understanding of linear relationships. They solve problems related to entrepreneurship and business.

• GRAPHS IN THE PLANE

#### Make Yourself Heard

Students use graphs to reason about properties of negative numbers and extend their understanding of linear relationships. They solve problems related to information technology.

• FUNCTIONS

#### Crack the Code

Students represent and analyze functions and use graphs to understand the relationship between squares and square roots. They solve problems related to entertainment.

• SYSTEMS OF EQUATIONS

#### Take Care

Students use graphs to find and interpret solutions to systems of linear and non-linear systems. They solve problems related to health science.

#### MATH 180 Course II: Making Sense of Math

Some traditional methods of teaching mathematics rely on memorization of procedures. Instead, MATH 180 focuses on reasoning and using visual models to make sense of the math and build conceptual understanding.

• #### RATE

The Traditional MethodLearners often struggle to understand the meaning underlying rate and confuse quantities when calculating unit rate.

The MATH 180 ApproachMATH 180 shows students how the bar model can be used to represent and compare quantities and visualize unit rate.

• #### RATIO

The Traditional MethodStruggling learners often have difficulty understanding the meaning behind the cross-multiplication algorithm.

The MATH 180 ApproachMATH 180 shows students how visual models can be applied to solve ratio problems and gives students a problem-solving approach they can make sense of.

• #### PERCENT

The Traditional MethodStruggling learners often forget which numbers to multiply when solving percent problems.

The MATH 180 ApproachIn MATH 180, students use the double number line to visualize the relationship between the part, percent, and whole in a percent problem.

• #### FUNCTIONS

The Traditional MethodLearners often struggle to evaluate functions by substitution and using the order of operations.

The MATH 180 ApproachMATH 180 has students use graphs and estimation to make sense of functions and how to evaluate them.

• #### EQUATIONS

The Traditional MethodLearners often struggle when applying inverse operations to solve multi-step equations.

The MATH 180 ApproachIn MATH 180, students make sense of the structure of equations to reason about their solutions without using complicated algorithms.

• #### LINEAR RELATIONSHIPS

The Traditional MethodStruggling learners often confuse the slope and y-intercept when writing the equation of a line.

The MATH 180 ApproachIn MATH 180, students use a graph to build on their knowledge of proportionality to understand linear relationships.