We have previously celebrated the *National Math Festival* by offering math games at the museum. This year, the entire in-person festival has moved online and so are we! We’re sharing fun math activities to try at home and highlighting ways to incorporate math into your everyday routines and conversations.

Check out the main *National Math Festival 2021* site here:

https://www.nationalmathfestival.org/join/2021-festival-online

Their amazing games, puzzles, books and more are here:

https://www.nationalmathfestival.org/watch-play/more-math-resources

Things like counting billboards or types of vehicles on road trips are just one way; but we also like taking walks and counting items of a chosen color and making our own picture graphs. Playing “Yahtzee” is great for practicing number sense and sequence—understanding number value displayed in different ways is a valuable skill. Stacking items like blocks or cups (then knocking them over, of course!) is a great way for the youngest of mathematicians to start their skills.

Something like skip-counting can be practiced in any number of ways. Tossing or kicking a ball back and forth between parent and child or group of children can keep children thinking on their toes. Decide before each round how many you will count by; start with 2’s, 5’s, or 10’s to keep it simple and advance to 3’s, 4’s or more. Each person counts up to the next number each time he or she receives the ball. If playing in a group, pass the ball left or right, or across to keep it fun and fast paced.

Here are some others to try.

**Round ‘Em Up – ***Intermediate Level*

*Intermediate Level*

This is a game to improve skills with rounding multi-digit numbers. Children should have knowledge of place-value before playing. *(i.e. ones, tens, hundreds place)*

**What You Need to Play**

· **Round ‘Em Up Game Pieces handout**, with numbered sheep and individual numbers (be sure to print these one-sided)

· Scissors

**How to Play**

Round ‘Em Up is a two-player game. To start, cut – up the game pieces handout. Then take the game pieces with the numbered sheep *(0 to 1000*) and place them face-down. Each person takes turns drawing five cards *(there will be one left over. You can either give this one to a player as an advantage, or set it aside)*

These numbers represent sheep that have escaped from your farm. You need to round ’em up! So how can you do this?

Shuffle the Digit Cards and draw three at random. *(If you don’t want to print the cards, you can use the 1-9 cards from a pack of cards and discard the 0 sheep. Or you could even use a ten-sided dice if you happen to have one)*

The three digits you choose can be arranged in any order. The goal is to arrange them so that the number, when rounded to the nearest hundred, matches one of your sheep!

If you can arrange the digits to round to one of your sheep, you get 1 point. If the number you create is within 20 of one of your sheep, you get 2 points. Within 10 and you get 3 points.

**Further Explanation**:

So let’s say you have the 200, 300, 600, 700, and 1000 sheep. You draw the digits 1, 5, and 7.

You could arrange them to 157 to round up to 200, or 571 to round up to 600, or 715 to round down to 700. Any of these would be a valid move, but the last one is within 20, so you would win 2 points!

You **must** make a three-digit number, even if it doesn’t round to one of your sheep. So watch out, because if it rounds to your opponent’s sheep, they get a point!

You can play as many rounds as you want, and whoever has the most points at the end of the game wins.

**Where’s the Math?**

When your child is arranging their three-digit number, they are trying to make numbers that are as close as possible to their targets. The closer they are, the more assured they can be that they’ll score a point. The game helps children make the connection between rounding and closeness explicitly, by awarding bonus points for closer and closer numbers.

The game can be adapted to rounding with tens, thousands, or even decimals. Each adaptation maintains the big idea: Build a number as close as possible to your target.

## Fold and Cut Challenge

**The Fold-and-Cut Challenge: ***Advanced*

When adults think about math, the focus tends to be on numbers and operations. There are many other important aspects of mathematical thinking that need attention as well; Geometric reasoning, spatial visualization, pattern recognition, sorting by attributes.

Fortunately, many of these domains of math can involve fun challenges.

This is actually a pair of games, one for younger elementary and one for upper elementary & older. In either case, children will practice spatial reasoning.

**Players**: 1 or more

**Ages**: 5 and up

**Math Ideas**: Symmetry, visualization, lines and angles

**Supplies needed**: Paper, scissors, something to write with

**Questions to Ask**:

*– How could you cut out this shape? – If I cut this shape out of a folded piece of paper and unfold it, what will the shape look like?*

*– What would this shape look like if you folded it in half? What if you folded it in half twice?*

**How to Play – ***Younger Elementary*

*Younger Elementary*

Parents and adults can provide an example. For children ages 5-7, take a piece of paper and fold it in half. Then draw a curvy line along the folded edge of the paper and cut it out, unfolding it to show what the shape looks like. **Download the templates.**

Then give the children a series of challenges: can you fold a piece of paper in half and then cut the paper so that the when unfolded, you have the following shapes?

- Rectangle
- Square
- Circle
- Heart
- Triangle
- Star
- Plus sign
- The letter H
- The letter X
- The letter M
- A person

You can try other shapes if you like. It’s a good idea to keep a copy of each shape so children can see how they’ve progressed to more and more complicated shapes.

The triangle in particular is tricky because the children may cut triangles out of the paper, only to unfold them to find diamonds, kites, and all sorts of shapes that have more than three sides. Once they discover the trick for triangles, they can make all sorts of different shapes from folded paper.

**How to Play – ***Upper Elementary*

*Upper Elementary*

Once your children feel comfortable with the simpler activity, you can give them this fun extension: Can you take a piece of paper and fold it so that with a single, straight cut you can cut a square out from the middle of the paper?

It seems like quite a challenge, so grab some nearby scissors and paper and give it a try yourself. If you want a demonstration, you can watch the first couple of minutes of this delightful Numberphile video.

Once you’ve seen the video, try out the challenge. See the attached handout with increasingly difficult shapes to fold and cut out. (Credit to Joel David Hamkins). All the shapes are possible to cut out with a single straight cut, but they are not easy! Try them out yourself and see how your own math brain gets a workout.

**Where’s the Math?**

The fold-and-cut challenge gets your children thinking about symmetry, congruence, angle relationships, all in the context of cutting a shape out of a piece of paper.

Although the shapes start out pretty simply, they quickly become a challenge, even to adults. As it turns out, the math behind the fold-and-cut challenge is pretty complicated! A few mathematicians have even proven that every shape made of straight edges can be folded and cut out with a single straight cut. It takes quite a lot of folding to get a turtle, but it’s mathematically possible.

*Questions to Ask*

*Questions to Ask*

A favorite question for younger children is “what shapes are impossible to cut out from a folded sheet of paper?” This gets a great conversation started about symmetry and what sorts of shapes do and do not “match” themselves.

When children were struggling to visualize and cut out a shape, ask them “What does a circle look like when it’s folded?” Once they could imagine a folded circle, they could cut it out more easily.

This question has children visualizing the answer and then working backwards to find the path forward. This skill of working backwards is a valuable tool in any mathematician’s toolkit.

**Up and Down – A Jumping Game: ***Beginner*

*Beginner*

This game can help players practice and remember how to count backwards from 10 to 0; in a fun and physically – active way!

**Players**: 2 or more *(if possible, at least one adult) *

**Ages**: 4 and up

**How to Play**

You can play Up and Down indoors with cards or outdoors with numbers written in chalk. In either case, place each of the numbers about a foot apart.

To start, the adult can be the Pointer, and the child is the Jumper.

When the Pointer is pointing upward, the Jumper can jump from number to number, counting up as he goes. But when the Pointer starts pointing downward, the Jumper has to jump backwards and count down as he heads back toward zero.

A typical round might go, “1-2-3-4-5-6-…5…4…3…4-5-6-7-..6…7…6…7-8-9…8…7…8-9-10!”

It’s important that each participant takes a turn at being the Pointer and the Jumper. Children enjoy seeing adults participate and they also enjoy being the one to give the directions.

**Where’s the Math?**

“Up and Down” involves physical activity, which makes it fun and engaging for younger children. That physical aspect is also being a learning tool.

Counting is a set of skills that your child learns over time. They must learn the sequence of words to count, match those with the numerals like 1, 2, 3, and so on.

The physical layout of the game gives your child a spatial model for thinking about the number line. When they hop forward from 1 to 2 to 3 to 4, they are using the numbers in the way they’re used to. But when the Pointer begins to point downward, your child has to remember what number came just before 4.

Now this is hard to do when you’ve just memorized a sequence of number words. *(It’s even hard for us adults. For example: What word comes before “one” in the pledge of allegiance?)*

But because they’ve been hopping along a line of numbers, they might have a stronger memory of where they just were. They were standing on the 3 and yelling “three!”

So when they hop back, it’s easier to remember the number they’re returning to. Information with a physical environment helps you remember things more clearly.