## Utility Container

Mount Mansfield Unified Union School District

## Branding We believe students make sense of mathematics when they learn in an environment that focuses on new concepts and builds on mathematics they have previously explored. Math class is about developing a problem solving mindset. Learning mathematics is understanding, making connections, applying knowledge, and communicating ideas.  Students learn best when the important mathematical ideas are embedded in engaging problems that they can explore, discuss, and reflect upon.  Students progress in both math content (skills & knowledge) and math practices (habits & communication) at different rates. Students build flexible thinking by considering a variety of strategies as they move towards efficiency. Depth is much more important than speed or quantity. Everyone can learn math to the highest levels. Asking questions and making mistakes are valuable tools in brain growth and learning. Math education is important to all people, not because they will see the same problems in the real world, but because they will have developed a problem solving mindset.

# Benchmark Understandings at Grade 8

## The essential building blocks for solid understanding of mathematical concepts

### Define, evaluate, and compare functions

• Model and compare functions graphically, algebraically, and in a table

### Understand connections between proportional relationships, lines, and linear equations

• Define slope and apply it to write a linear equation (y=mx+b)
• Distinguish between a proportional and nonproportional linear relationship
• Analyze and solve linear equations and their point of intersection
• Distinguish between linear and nonlinear functions

### Understand congruence and similarity of two-dimensional figures

• Prove or disprove congruence and similarity through transformations (reflections, translations, rotations and dilations)

### Descriptive Statistics - Investigate patterns of association in bivariate data

• Construct and interpret scatter plots between two quantities (line of best fit, outliers, correlations)
• Read and interpret two-way tables that compare categorical data (frequency)

### Focus at this grade level will also include:

• Estimate the value of irrational numbers and locate them on a number line (ex: square root of 2)
• Develop and apply exponent rules for all operations
• Apply square roots, cube roots, scientific notation
• Solve problems involving volume of cylinders, cones, and spheres

### Helping your student learn outside of school:

• Praise your child when they make an effort and share in the excitement when they catch and fix a mistake, solve a problem, or understand something for the first time.
• Look for everyday opportunities to have your child do mathematics with you (calculating tips at restaurants, discounts at a store, manage a personal budget).
• Encourage your child to stick with it whenever a problem seems difficult. This will help your child build stamina and see that everyone can learn math.
• Point out where you are using mathematics in your everyday life.
• Play math games that encourage strategy and reasoning with your child.

• Where are your math resources?
• What strategy are you thinking about using to solve the problem?
• How could a model or a table help you solve this problem?

# Fractional Reasoning: from concept to fluency

• Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers

• (application of previous understandings)

## High School Mathematics

• (application of previous understandings)