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Mount Mansfield Unified Union School District

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 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.

HOW TO RESPOND WHEN YOUR CHILD ASKS FOR HELP:

• Tell me what you know about this problem.  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?
• Why is your answer reasonable?

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Multiplicative Reasoning: from concept to fluency

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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)

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Grade 6 Mathematics

• Extend understanding of area and volume to new settings (geometry)
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Grade 7 Mathematics

• Solve real-world & mathematical problems involving area, volume and surface area of 2- and 3-dimensional objects. (geometry)
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Fractional Reasoning: from concept to fluency

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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
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Grade 6 Mathematics

• Fluently add, subtract, multiply and divide all fractions
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Grade 7 Mathematics

• Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers
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Proportional Reasoning: from concept to fluency

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Grade 5 Mathematics

• (Not a benchmark at this grade level)
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Grade 6 Mathematics

• Understand and apply ratios to solve problems
• Write, interpret and solve variable expressions and simple equations
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Grade 7 Mathematics

• Recognize, represent, and solve proportional relationships between quantities
• Apply properties of operations to generate equivalent expressions
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