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 3

The essential building blocks for solid understanding of mathematical concepts

• Fluently add and subtract multi-digit numbers by applying place value understanding and properties of operations
• Fluently multiply and divide within 100 by applying properties of operations and the inverse relationship
• Understand area and relate area to multiplication and division
• Develop understanding of fractions as numbers

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

• Solve problems about measurement and time.
• Organize and analyze data using tables and graphs.
• Compare the perimeter and area of various shapes.
• Identify shapes using their attributes.

### HELPING YOUR STUDENT LEARN OUTSIDE OF SCHOOL:

• Look for everyday opportunities to have your child do mathematics. Some great third grade examples.
• Point out when you are using math.
• Encourage your child to stick with it whenever a problem seems difficult. This will help your child see that everyone can learn math.
• Praise your child when he or she makes an effort and share in the excitement when he or she solves a problem or understands something for the first time.

• What do you already know in this problem? What are you trying to find out?
• What strategy are you thinking about using to solve the problem?
• Would drawing a picture help? Make a table?

### Multiplicative Reasoning: from concept to fluency

• Fluently add and subtract within 100 by applying place value and properties of operations
• Understand place value and powers of 10 to add and subtract within 1000

• Fluently add and subtract within 100 by applying place value and properties of operations
• Understand place value and powers of 10 to add and subtract within 1000

• Fluently add and subtract multi-digit numbers with a standard algorithm by applying place value understanding & properties of operations.
• Add, subtract, and multiply fractions by applying previous understandings of operations on whole numbers (additive reasoning with fractions)

### Fractional Reasoning: from concept to fluency

• Develop understanding of fractions as numbers.

• Apply equivalence and understanding of unit fractions to compare and order fractions and decimals
• Fluently add, subtract, multiply and divide fractions by applying place value understanding and properties of operations

• Fluently add/subtract fractions using equivalent fractions and properties of operations
• Multiply and divide fractions
• Fluency add, subtract, multiply and divide decimals by applying place value understanding and properties of operations