*[Feature photo (above) by Phil Roeder. (CC BY 2.0 via Flickr)]*

A frequently-asked question on homeschooling forums is, “Are my children working at grade level? What do they need to know?”

The *Council of the Great City Schools* has published a handy 6-page pdf summary of third grade math concepts, with suggestions for how parents can support their children’s learning:

Whether you are a radical unschooler or passionately devoted to your textbook — or, like me, somewhere in between — you can help your children toward these grade-level goals by encouraging them to view mathematics as mental play. Don’t think of the standards as a “to do” list, but as your guide to an adventure of exploration. The key to learning math is to see it the mathematician’s way, as a game of playing with ideas.

The following are excerpts from the roadmap document (along with a few extra tips) and links to related posts from the past eight years of playing with math on this blog…

## What Your Child Will Learn in 3rd Grade Math

In grade three, students will continue to build their concept of numbers, developing an understanding of fractions as numbers. They will learn the concepts behind multiplication and division and apply problem-solving skills and strategies for multiplying and dividing numbers up through 100 to solve word problems. Students will also make connections between the concept of the area of a rectangle and multiplication and addition of whole numbers.

Activities in these areas will include:

- Understanding and explaining what it means to multiply or divide numbers.

- Multiplying all one-digit numbers from memory (knowing their times table).

- Multiplying one-digit numbers by multiples of 10 (such as 20, 30, 40).

- Relating the measurement of area to multiplication and division.

- Understanding and identifying a fraction as a number on a number line.

- Expressing numbers as fractions and identifying fractions that are equal to whole numbers (for example, recognizing that 3⁄1 and 3 are the same number).

- Measuring weights and volumes and solving word problems involving these measurements.

- Representing and interpreting data.

Tip: Encourage your children to practice their creative math skills by making up problems for you to solve. This is from my youngest daughter, Kitten Poses a Puzzle.

## Helping Your Child Learn Math

- Play math games with your child. For example, “I’m thinking of two numbers whose product is between 20 and 30. How many pairs can you think of that would satisfy this problem?” Have your child explain the solutions. How does he or she know that all the number pairs have been identified?

- You can also play Tic-Tac-Toe on a times table.

- Encourage your child to write or describe numbers in different ways. For example, what are some different ways to make 1450? 1450 = 1 thousand, 4 hundreds, 5 tens, and 0 ones, or 1000 + 450, 14 hundreds and 50 ones, 13 hundreds + 15 tens, etc.

- Use everyday objects to allow your child to explore the concept of fractions. For example, use measuring cups to have students demonstrate how many 1⁄3’s are in a whole, how many 1⁄4 cups you need to make 11⁄4 cups, and how many times you have to refill a ½ cup measure to make 1½ cups.

- Make time for family board games, playing with tangram shapes, and other shared activities.

- 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.

*[Photo by tanakawho. (CC BY 2.0 via Flickr)]*

“The way we taught students in the past simply does not prepare them for the higher demands of college and careers today and in the future. Your school and schools throughout the country are working to improve teaching and learning to ensure that all children will graduate high school with the skills they need to be successful.

“In mathematics, this means three major changes. Teachers will concentrate on teaching a more focused set of major math concepts and skills. This will allow students time to master key math concepts and skills in a more organized way throughout the year and from one grade to the next. It will also call for teachers to use rich and challenging math content and to engage students in solving real-world problems in order to inspire greater interest in mathematics.”

—

Council of the Great City Schools

Parent Roadmaps to the Common Core Standards- Mathematics

## Additional Resources

- For wonderful advice on how to support children’s mathematical intuition, browse Talking Math With Your Kids.

- For creative ways to build a love for mathematics, follow Moebius Noodles.

- For more activity ideas, check out Helping Your Child Learn Mathematics.

- For other grade-level math standards, see the rest of the Council of the Great City Schools’ parent roadmaps in mathematics. Also available in Spanish.

- For a more detailed list of third grade math topics, read the Common Core State Standards for grade 3 mathematics. Or use this alternate check-list: World Book Typical Course of Study Curriculum Guide for Grade 3.

- And be sure to explore the many great ideas for elementary math on my Pinterest board: Playful Math for Upper Elementary & Middle School.

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