## 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 7

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

### Recognize, represent, and solve proportional relationships between quantities

• Solve problems by finding unit rates involving fractions
• Differentiate between a proportional and a non proportional relationship
• Model proportional relationships (tables, graphs, equations, & stories)
• Compute percent markups and discounts

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

• Apply operation to add, subtract, multiply and divide positive and negative numbers (rational numbers: whole numbers and fractions)
• Apply properties of operations (the distributive, commutative, and order of operations) to evaluate expressions w/ rational numbers

### Apply properties of operations to generate equivalent expressions

• Model situations using variables to represent quantities and solve two step equations
• Use distributive property to simplify and solve equations

### Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects

• Solve problems involving surface area and volume of three-dimensional figures
• Know and apply the formulas for circumference and area of a circle

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

• Draw precise geometric two dimensional figures using tools and understand possible combinations of side lengths or angles that can form a triangle
• Apply properties of complementary, supplementary, and vertical angles to solve for an unknown
• Identify and apply scale factors to drawings of geometric figures
• Investigate chance processes and develop, use, and evaluate probability models
• Use random sampling to draw inferences about a population and draw informal comparative inferences about two populations

### 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.
• Point out where you are using mathematics in your everyday life.
• Play math games that encourage strategy and reasoning with your child.

• What are you trying to find out?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?

# Multiplicative Reasoning: from concept to fluency

• Extend understanding of area and volume to new settings (geometry)

• Solve real-world & mathematical problems involving area, volume and surface area of 2- and 3-dimensional objects (multiplicative reasoning with geometry)
• Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers (multiplicative reasoning fractions)

• (application of previous understandings)

# Fractional Reasoning: from concept to fluency

• Fluently add, subtract, multiply and divide all fractions

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

(application of previous understandings)

# Proportional Reasoning: from concept to fluency

• Understand and apply ratios to solve problems
• Write, interpret and solve variable expressions and simple equations