The next theme week of math camp is "patterns and math art," one of my very favorite subjects! But before you go, be sure to hop over to Coffee Cups and Crayons for another geometry math activity (using grapes no less!) to tide you over until next Thursday.

Previous camp mathematics fun: 

• Counting game to teach subtraction
• Magic squares

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Nim is a good early math game that supports addition and subtraction skills. I played a few rounds with my soon-to-be 5th grader and he enjoyed beating me (ahem). But then, my knowledge of mathematical theory is not what it used to be, ha ha ha.

How to play Nim

Nim can be played in various ways and with different quantities. I've chosen a simple version to share with you. We also like to call this game, "counting down."

Materials

• 11 stackable counters. 10 in one color and 1 in a different color. We used black and white poker chips, (affiliate link) which are extremely handy if you play a lot of DIY games at home. You can also use checkers, coins, or even flat blocks.
• 2 enthusiastic players

Objective

Force your opponent to pick up the black (the last) chip.

Rules:

• Stack the white chips on top of the black chip.
• Determine who will go first.
• Taking turns, players picks up 1, 2 or 3 chips from the top of the stack.
• Whoever is left with the last chip loses.

Watch the video to see the game in action:

It's that simple!

Tips and Tricks

TIP: You don't need different color chips for Nim. You can play with 11 chips and whoever is stuck with the last one, loses.

TIP: After 1 or 2 rounds, kids will learn that in order to win they need to leave 4 white counters on top of the black one. If they are able to do that, it becomes impossible for their opponent to win. This will lead to some strategizing and you can start to vary the game rules to tickle their little brains even more (see below for some variation suggestions).

A few questions to ask your kids while they play "counting down":

Is it better to go first or second?

What quantity of white chips do you ultimately want to leave on top of the black one so your opponent can't force you to pick up the black chip?

What happens if you play with 11 white chips and 1 black chip instead? (Try it!)

What happens if you can only remove 1 or 2 chips instead of up to 3? (Try it!)

Benefits of Playing Nim

What are kids learning?

• Counting backwards practices the skills needed for subtraction.
• They are learning to think strategically.
• They are using their reasoning skills.
• They are learning to plan ahead (games like this build executive function).

This post is part of our Camp Mathematics series, an easy, free summer camp curriculum based on having fun while boosting math skills.

More math games to play:

• Tens Go Fish
• Cooperative math dice games
• Magic math triangle
• Array game

The post NIM: A Simple Counting Game to Teach Subtraction Skills appeared first on What Do We Do All Day.

And since this IS Camp Mathematics, these fraction games are FUN.

What you need:

• A set of fraction cards. You can make you own, or you can print out ours and cut out the pieces. (see below for link).
• Children ready for a rowdy fraction math game. (I may have exaggerated the "rowdy" part.)

Print --> Fraction bars (Note: our printable contains more cards than are necessary for the games below. Have fun coming up with your own games that use all the pieces.)

Fractions Game #1

Each player needs:  one 1, one ½, three ¼'s, two ⅓'s, six ⅙'s,  six ⅛'s, and four 1/12's .

Keeping his longest fraction -- the "1", or the whole -- each player puts the remaining fractions in a bag or bowl.

Without looking, players alternate drawing fraction pieces until all pieces are gone.

Using their pieces, players race to put together three wholes. Players use the whole for comparison to make sure they have the correct length.

Alternative: Whoever can put the most ½'s together is the winner.

Fractions Game #2

Each player needs:  one 1, one ½, three ¼'s, two ⅓'s, six ⅙'s,  six ⅛'s, and four 1/12's .

Keeping his longest fraction -- the "1", or the whole -- each player puts the remaining fractions in a bag or bowl.

Taking turns, each player draws 10 fraction pieces. (The rest are set aside.)

Players must use ALL of their fraction pieces to make wholes.

After players have used as many pieces as possible but not all of them, they can trade each other for the pieces they need.

Notes: 

• Be aware, it is not always possible to use all the pieces to make wholes. That's part of the learning process, too.
• You could turn this into a competitive game, but we found it more fun to work cooperatively, otherwise the trading got too intense.

Extensions:

• If your kids are feeling ambitious, they can use a compass and protractor to create fraction circles for the games. You can also find plenty of templates online if they want to play with "pie pieces", but don't want to create their own.
• Kids can use pieces to "build" 2 dimensional structures.
• Kids can make up their own fractions games using the pieces!
• Make fraction cookies for a post-game snack.

Don't miss the Camp Mathematics fun at Coffee Cups and Crayons. This week Megan shows you how to turn lunch into math with fraction sandwiches!

Week 1: Counting

Counting Down Game and DIY Abacus

Week 2: Calculations

Magic Squares and Shake and Roll Math Game 

Week 3: Shapes

T Puzzle brain teaser and Grape Shapes

Week 4: Math Art

Spirolaterals and Patterns in Nature

Week 5:

You're reading it!

Week 6: Games

Cooperative dice games and Card games

The post Fraction Games for Kids that Are Actually Fun appeared first on What Do We Do All Day.

Best of all, my fellow blogger, Megan, and I did all your thinking for you! We created 6 weeks of a super budget friendly easy and fun do-it-yourself summer math camp program and that includes lesson plan activities and ideas for all ages and covers a variety of math topics in creative and engaging ways. Math camp was never so much fun! (Pssst. Be sure to check out our DIY science camp, too!)

Summer Math Camp Activities

Week 1: Counting and Numbers

•  Counting Down Game (Includes a video) This game is based on the classic game of nim, and helps kids with counting, but also with strategy skills.
•  DIY Abacus. Combine math, crafts and social studies. Kids will learn about a math tool used in other cultures.

Week 2: Simple Calculations

• Magic Squares (Includes a printable). This brain teasing math game will get kids thinking about number in a new light.
• Shake and Roll math game. Calculations made during a game are stress-free.

Week 3: Shapes and Geometry

•  T Puzzle brain teaser. (Includes a video and printable) This is a classic puzzle that kids can solve and then stump the grown-ups in their lives!
• Grape shapes. Learn about 3D shapes while having a healthy snack.

Week 4: Patterns

• Spirolaterals. (Includes a video) Spirolaterals are not just pretty patterns they will help kids learn skip counting and their multiplication tables.
• Patterns in nature. Summer means nature and nature means math discoveries!

Week 5: Fractions

• Printable fraction games. (Includes printable) Fractions can be tricky, but not if you turn them into a game.
• Fraction sandwiches. Who doesn't love a tasty math snack?

Week 6: Games

• Cooperative dice games. Cooperating instead of competing always makes things much less stressful for my kids!
• Card games. Card games sneak in lots and lots of math learning. Invite the neighborhood friends over for a tournament. Don't forget the fraction sandwiches!

Both Megan and I have loads of math activities for additional summer math camp ideas:

• Math activities at What Do We Do All Day?
• Math learning at Coffee Cups and Crayons

More summer camp ideas:

1. DIY Summer science camp

,

The post DIY Summer Math Camp: Budget-Friendly Activity Plans appeared first on What Do We Do All Day.

We always play math dice cooperatively. Currently, my youngest has a lot of difficulty with competitive games and since his 10 year old brother's math skills are more advanced than his, it makes sense to work together, thus avoiding much despair and frustration for all of us!  Plus, I don't need any more reason for my kids to one up each other! (Note: this post contains affiliate links that earn from qualifying purchases.)

We used Think Fun Math Dice for these games. The set comes with two 12-sided dice and three 6 sided dice.

Game #1

This game and its variations are based on the enclosed instructions for Think Fun Math Dice .

Roll the two white, 12 sided dice. Multiply the two numbers. This is your target number. So for example, 8 x 3 = 24. 24 is the target number.

Now, roll the three blue dice. Using the resulting numbers, players attempt to create as many equations as they can to achieve a number as close to the target number as they can.

For example, 4, 4, 3. 4 + 4 + 3 = 11; (4 x 4) + 3 = 18; (4 + 3) x 4 = 28; (4 + 4) x 3 = 24; and so forth.

Cooperative play: we took turns creating equations. If we thought we could do better than the three equations on the first round, we talked it out together to make up more equations.

Variations:

• Add the two numbers instead of multiplying them.
• Create a 2-4 digit number with the two numbers. For example, a 12 and a 4 could be 124, or 412.

MORE: We also love TENZI, a fast paced dice game. 

Game #2

This game teaches simple addition as well as understanding probability.

Roll the two white dice and use the numbers to create a new, larger target number of your choice (so, add or multiply as described for game #1).

Taking turns players roll the three blue dice. After each roll, the numbers are added up. Players continue rolling, trying to reach the target number without going over. Players consult each other as to whether or not they should keep rolling. Variation: roll only 1 or 2 dice at a time.

Notes:

Please do not feel you can't play this game if you feel "you are not good at math." I am not a math teacher. In fact, the last time I had a formal math class, I was 16 years old. When I don't know something I want my kids to see that I am willing to problem solve and apply growth mindset thinking in order to learn. In addition, I NEVER say "I'm bad at [insert subject here]" because I NEVER want my kids to think that about themselves.

This is the final week of Camp Mathematics!! Are you sad? It's been fun collaborating with Megan to bring you 6 weeks of ideas that you can use all year round, not just in the summer!

Be sure to check out Megan's ideas for simple math card games you can play with the kids.

More math dice games:

• Lu-Lu: Math Dice Game from Hawai'i
• Martinetti, fun game of chance that uses math

Don't miss the previous weeks: You can see them all here --> Camp Mathematics

• Week 1: Counting
• Week 2: Computing
• Week 3: Shapes
• Week 4: Math Patterns
• Week 5: Fractions
• Week 6: Math Games

The post Math Dice Games Kids Can Play Cooperatively! appeared first on What Do We Do All Day.

The great thing about spirolaterals is that not only are they gorgeous but in the process of making them, kids who love numbers can work on their skip counting and multiplication skills. Creating spirolateral math art also involves graphing and patterning so there is a whole host of awesome math and art integration going on.

Let's get down to business, shall we?

What are Spirolaterals?

Very simply, spirolaterals are spiraled, structured designs based on a repeated series of commands using length and angle.

Clear as mud?

The way I explained it to my son is that, "we would use the times tables to create spirals."

Spirolaterals can range from very basic to elaborate, depending on the angle and number patterns used. The simplest type of spirolateral is a square -- a 90 degree angle turn with a 1,1,1,1 sequence. (See some more complex patterns here.) It sounds complicated, but once you understand what's going on, it's very easy and fun to do.

Watch the grooviness and then get the full instructions below:

Choose a number and write its multiplication sequence. I'll use 5 as an example.

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55

Now, turn it into a sequence of single digits by adding the two digits of each number together. For example 10 becomes 1+0=1, 1+5=6 and so forth.

5, 1, 6, 2, 7, 3, 8, 4, 9, 5, 1

Once you see the pattern start to repeat you can stop. So we would be left with 5, 1, 6, 2, 7, 3, 8, 4, 9 as our final sequence.

Now you are ready to draw!

• Get your graph paper.
• Draw a line 5 squares long.
• Make a 90 degree turn to the right.
• Draw a line 1 square long.
• Make a 90 degree turn to the right.
• Draw a line 6 squares long.
• See the pattern?
• When you complete the final line in your sequence, start over with the first number.
• Repeat until the spirals connect back to the very first line.

Here's how to get started with multiples of 1:

TIPS:

• With younger children, start with the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9.
• Some of the numbers make very large spirals. Graph paper with more squares per inch is better.

EXTENSIONS:

• Compare the patterns of different sequences. Do some of them look similar?
• Color in your spirolateral to make it snazzy.
• Advanced kids can try 45 degree angles instead of 90 degree.
• You don't have to use times tables, what other number patterns can you use?

All the photos of my son working on this came out lousy since we did it in the evening, but he had the cool idea to make each line a different color.

MORE: Be inspired with our favorite math art projects.

Now it's time to head over to Coffee Cups and Crayons to see how Megan and her kids explored patterns in nature!

MORE: Favorite  math art books

Previous Camp Mathematics activities:

Week 1: Counting Down Game and DIY Abacus

Week 2: Magic Squares and Shake and Roll Math Game 

Week 3: T Puzzle brain teaser and Grape Shapes

The post Spirolateral Math Art: Fun Way to Practice Multiplication appeared first on What Do We Do All Day.

(Whisper voice: After you read this post, don't forget to get another hands-on math game at Coffee Cups and Crayons, our Camp Mathematics partner.)

Although there are numerous (pun!) variations of magic squares, I decided to keep it simple with a 3x3 square, especially since my 6 year old would want to try it. For more magic square fun, see the extension ideas, below.

What is a magic square?

Magic squares are grids in which distinct numbers are arranged so that the sum of the numbers in each row and column is always the same.

You can, of course, whip up your own magic square template with a few strokes of a pencil, but I've also made a snazzy magic square printable you can print out for free. Get it here --> Magic Square Printable.

How to do a 3x3 magic square math puzzle

Using the numbers 1-9, place numbers in the squares so that the sum of any three numbers in a horizontal, vertical or diagonal row equals 15. You may only use each number once.

TIP: For younger kids, start out by placing a five in the center square.

Notes from our experience:

My 10 year old got stuck at first, but what helped him out was using counters instead of numerals. This way he didn't have to keep erasing.

I worked on the puzzle with my 6 year old. It was excellent math practice for him. I made it a bit easier for him and we started out with one complete row (1, 5, 9). I asked questions like, "Does 2+3 plus any of those numbers equal 15?" When he responded, "No," then I pointed out that 2 and 3 could not be in a row or column together. Then we worked through the remaining pairs of numbers along those lines until logic could tell us at least one square.

Variations:

Make it slightly more challenging by not telling your kids that the sum of each row/column will be 15.

Try a 4x4 magic square, known as Dürer's Magic Square. What will the sum of each row be?

If you have a super math nerd, have them learn more about the workings of magic squares.

A little magic square history:

The earliest known records of magic squares are in China and the Islamic world. The Chinese 3x3 magic square is called Lo Shu (or "river map"). According to a legend, the emperor and his court were sailing down the River Lo when a turtle appeared. The design on the turtle's back was the numbers (represented by circles) in the magic square.

See more of our favorite math games in action:

More math games: 

• Fraction Games for Kids
• Lu-lu dice math game
• Math Tic Tac Toe
• T Puzzle (Boggle Your Mathematical Mind)
• Magic triangle math game

This week's camp theme is computing. Solving magic squares not only requires logic and patience, kids practice their basic addition skills, adding 3 or more numbers. Head over to Coffee Cups and Crayons for an awesome and easy hands on math game.

The post Magic Squares Math Fun appeared first on What Do We Do All Day.