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 6

The essential building blocks for solid understanding of mathematical concepts

• Fluently add, subtract, multiply and divide all fractions
• Understand and apply ratios to solve problems (two cats for every three dogs)
• Write, interpret and solve variable expressions and simple equations
• Read, write and solve equations in which letters stand for numbers (use variables)and solve one-variable inequalities
• (x < 5) and graph them on a number line
• Use independent (x) and dependent (y) variables to write and graph equations
• Extend understanding of area and volume to new settings

• Solve real-world and mathematical problems involving area, surface area, and volume (using rectangles, triangles and rectangular prisms)

### FOCUS AT THIS GRADE LEVEL WILL ALSO INCLUDE:

• Compute fluently with multi-digit numbers (+, -, x, ÷)
• Use common factors and multiples to solve problems
• Compare and order positive and negative numbers (including fractions)
• Describe a set of data using mean, median, mode and/or range to answer a statistical question
• Use a variety of graphic representations to describe numerical data to solve problems

### 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.

• 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

 Grade 5 Mathematics Fluently multiply and divide multi-digit numbers with a standard algorithm by applying place value understanding and properties of operations Understand volume; and relate volume to multiplication (geometry) Grade 6 Mathematics Extend understanding of area and volume to new settings (geometry) Grade 7 Mathematics Solve real-world & mathematical problems involving area, volume and surface area of 2- and 3-dimensional objects. (geometry)

### Fractional Reasoning: from concept to fluency

 Grade 5 Mathematics Fluently add/subtract fractions using equivalent fractions and properties of operations Multiply and divide fractions Fluently add, subtract, multiply and divide decimals by applying place value understanding and properties of operations Grade 6 Mathematics Fluently add, subtract, multiply and divide all fractions Grade 7 Mathematics Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers

### Proportional Reasoning: from concept to fluency

 Grade 5 Mathematics (Not a benchmark at this grade level) Grade 6 Mathematics Understand and apply ratios to solve problems Write, interpret and solve variable expressions and simple equations Grade 7 Mathematics Recognize, represent, and solve proportional relationships between quantities Apply properties of operations to generate equivalent expressions