Activities & Lessons

8 Free California Elementary Math Activities

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Mathematics has been regarded as a universal language for a long time. The truth is a bit more complicated. We learn math in the language in which it is taught, meaning that math and language are inextricably connected. Regardless, math is a subject taught worldwide, and one thing’s for sure: hands-on math activities can help young learners practice various concepts—from counting to recognizing number patterns—no matter where they’re from or where they are on their mathematical journey.

Try These Math Activities in Your Classroom

Get your students hooked on math with these eight games and activities. Many of these activities turn mathe-matics into mathe-magic! Not only will students get to perform magic tricks for one another, but you get to explore the math behind the curtain.

Activity 1: Penny Baggies (Kindergarten)

  • Key Standard: Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings.

Decomposition is the act of breaking a whole number down into parts. Students learn this concept in kindergarten, and what better way to help them sharpen this skill than by playing a game! In this game, five to ten pennies are placed in a resealable baggie with a line drawn down the center. After shaking and placing the bag on the table, students identify and discuss the addends—the numbers you add together to make a whole number. In this game, the addends are two groups of pennies divided by the line on the baggie.

Activity 2: Cool Counting (Kindergarten)

  • Key Standard: Represent addition and subtraction with drawings.

This counting activity lets young learners practice basic addition and subtraction. After picking a number from five to ten and following instructions, your students should always land on the same spot on the board game. After exploring the game, ask your students to try the magic trick on a friend or sibling.

To explain how this trick works, show how you are counting the same number of units forward and backward along a number line every time. However, when you go backward and get to 4, you can either go up and end at “START” or go down and end with the elephant. Both “START” and the elephant represent 0 on a number line, and no matter what number someone picks, that number minus itself is always 0.

Activity 3: Sums-of-Ten Go Fish (Grades K–2)

  • Key Standard: For any number from 1 to 9, find the number that makes 10 when added to the given number.
  • Key Standard: Demonstrate fluency for addition within 10.

Go Fish…with a twist? Go Fish is a common card game, and there are plenty of variations out there. In Sums-of-Ten Go Fish, students pair cards representing number bonds for 10 (think 5 & 5, 6 & 4, and so on). By the end of the game, the player with the most number bonds wins. Download the full instructions below. Are your students ready for larger numbers? For a challenge, check out these activities that let students practice counting and adding up to 100.

Activity 4: Scaled Drawings (Grades 3 and up)

  • Key Standard: Multiply two 1-digit numbers, and illustrate the calculation.

Art can help students deepen their understanding of math. Art can manifest mathematics, and mathematics can manifest art, sometimes in unexpected ways (read this article that breaks down the math of famous art). Students create scaled drawings on centimeter paper using multiplication in this art-meets-math activity.

Activity 5: The Amazing Prediction (Grades 4 and up)

  • Key Standard: Use place value understanding and properties of operations to perform multi-digit arithmetic, including addition, subtraction, multiplication, and division.

Have your students get their magician hats and wands ready! This activity lets students do a magic trick on a friend, sibling, or classmate. First, students should cut out the prediction available in the downloadable activity and attach it to a piece of cardboard. Then students get to perform a magic trick where they can seemingly read their partner’s mind! How’s that for mathemagic!

If your students are ready to think about variables, this activity is a fun way to introduce algebra ideas and show how important the order of operations can be. If you think of the original secret number as x, you can illustrate each of the steps as operations on x:

  1. x
  2. 2x
  3. 2x + 12
  4. (2x + 12) ÷ 2, or x + 6
  5. x + 6 – x, or 6
  6. The 6th letter of the alphabet is F. The rest of the steps follow from there.

Activity 6: Crazy Curves (Grades K and up)

  • Key Standard: Analyze and compare two-dimensional shapes, using information language to describe their similarities, differences, and attributes.
  • Key Standard: Express the length of an object as a whole number of length units.
  • Key Standard: Reason abstractly and quantitatively.
  • Key Standard: Represent a problem in multiple ways.

An optical illusion (sometimes called a visual illusion) is a trick on the eyes. In 1889, psychologist Joseph Jastrow discovered an optical illusion known as the Jastrow illusion: when two carefully-constructed identical figures of the same size are placed next to each other, one appears to be larger. In this activity, your students try the trick for themselves by carefully cutting out two paper curves and following instructions that will have the objects appear as if they’re growing and shrinking.

This trick has broader standards coverage in younger grades, where students are first learning how to describe shapes in terms of color, shape, edges, and corners. However, students of all ages can appreciate the trick it plays with our minds. Use this lesson to have students not only look for language to describe what they’re seeing (e.g., “the shape appears to grow by a small fraction of its original size”) but also find quantitative ways to verify their observations. You can encourage students to measure the shapes’ length or describe how introducing a third dimension (i.e., placing one shape on top of the other) stops the illusion.

Activity 7: Lucky Number (Grades K and up)

  • Key Standard: Add within 15.
  • Key Standard: Make sense of problems and persevere in solving them.
  • Key Standard: Use patterns and structure to understand mathematical concepts.

Magic squares were first mentioned in Chinese literature over 2,500 years ago and have existed in many parts of the world. A magic square is a square grid with a special arrangement of numbers so that every row, column, and diagonal adds up to the same number. Magic square puzzles help build students’ mental math skills, and this activity allows them to construct one and try the concept with one another.

This magic trick is appropriate for students of all ages, and it is particularly effective for students in kindergarten and first grade, where students are beginning to learn to add to 15. For students who are ready, consider offering advanced challenges to construct a different magic square that uses the same numbers (hint: try rotating the shape) or has nine different numbers altogether (hint: try adding the same number to everything).

Activity 8: Magic Calculator Cards (Grades 2 and up)

  • Key Standard: Use addition with 32 to solve problems involving situations with unknown values.

Who needs a regular calculator when you can have a magic calculator? Hand this activity, which consists of five magic calculator cards, out to your students. Students should ask their partners to think of a number between 1 and 31 and keep it a secret. After receiving the cards that feature the secret number only, students should be able to figure out what the number is by adding the numbers at the top-left corner of the cards. Any number that’s secretly chosen is a unique combination of the number at the top left-hand corner of each card.

Teachers, are you unsure why this works? It has to do with converting between base 10 and base 2. Every number between 1 and 31 in base 10 can be written as a 5-digit number in base 2. For example:

  • 1 = 00001
  • 7 = 00111
  • 12 = 01100
  • 25 = 11001
  • 30 = 11110

Every card refers to a place value. One of the cards has all of the numbers with a “1” in the first place value. A second card has all of the numbers with a “1” in the second place value, and so on. In the same way a base ten number like “25” means 2 tens and 5 ones, or 2•10 + 5•1, a base two number like “11001” means 1•16 + 1•8 + 0•4 + 0•2 + 1•1, where 16, 8, 4, 2, and 1 are all powers of 2. Notice that these powers of 2 are the numbers in the top-left corner of every card.

Share Your Favorite Math Activities!

How do you get your students’ brains churning in the classroom? Do you use puzzles, stories, or online games to help them engage with mathematical ideas? Share your math activities with us on Twitter (@HMHCo) or Facebook or email us at


Contact your California HMH Account Executive for more information on all our math solutions.

Contact your California HMH Account Executive to learn more about our math solutions.