Why We Need These Games
Getting kids moving is a win-win. Movement refreshes your students while giving
them another take on math concepts. These games are super quick and fun for
everyone.
Teacher-led Games
•Groups (2-5 minutes)
The teacher calls out a number (3), and the students have 10 seconds to get
themselves into groups of that size. It might be impossible for everyone to get in
a group every time, but each new number gives everyone another chance. In the
basic game, just call out single numbers. Once students get the gist, you can call
out addition or subtraction problems (i.e., “get into groups of 7-4”). Don’t forget
to call out a group of 1 and a group of however many students are in the entire
class at some point in the game.
•Stand Up/Sit Down (2-5 minutes)
The rules are simple: if the teacher gives the number 10, students stand up. Any
other number, they sit down. The trick is, the teacher will say things like “7+3”
and “14 – 5” (pick appropriate sums and differences for your students to solve
mentally). This is a great game to try to “trick” the students by standing up or
sitting down on when they should be doing the opposite. There are endless
variations.
For Example:
○ stand when the number is larger than 5; sit if it is 5 or
below
○ stand when the number is even; sit when it is odd
○ stand if the digit 1 appears on the number; sit otherwise.
•Bigger/Smaller/Equal (2-5 minutes)
If the teacher says a number greater than 10, students expand their bodies to
take up as much space as they can (while keeping their feet firmly planted on
the ground—no running around). If the teacher says a number less than 10,
students shrink their bodies to take up the least space they can. If the teacher
gives the number 10 exactly, students hold their body neutrally and make an
equals sign with their arms. As before, the teacher moves to sums and
differences once students get the rules.
•Rhythmic Clapping/Counting (2-5 minutes)
The teacher claps/counts out a rhythm. Students imitate the rhythm of the clap
and the count.
•Skip Counting with Movement (2-5 minutes)
Make up a movement that comes in 2, 3, or more parts. Whisper the first parts,
and call out the final move loudly.
Example: Windmills. Whisper “1” and touch your right hand to your left foot.
Whisper “2” and touch your left hand to your right foot. Call out “3” and do a
jumping jack! Continue counting like this up to 30, calling out the multiples of 3
and whispering the numbers in between.
For Example:
http://mathandmovement.com/pdfs/skipcountingguide.pdf
•Circlecount (2-5 minutes)
Stand in a circle and try to count off as quickly as possible all the way around
the circle. Start with 1, then the student on your right says “2,” and the student
on their right says “3,” and so on until the count comes back to you. Challenge
the kids to go as quickly and seamlessly as possible. When everyone can do this
proficiently, count by twos, fives, tens, or threes. You can also start at numbers
greater than 1, or try counting backward.
Student-pair Games
•Finger Speed-Sums (1-5 minutes)
Students meet in pairs with one hand behind their back. On the count of three,
they each put forward some number of fingers. Whoever says the sum first wins.
Then the pair breaks up and each person finds a new person to play with.
Advanced players can use two hands instead of just one.
•Finger Speed-Differences (1-5 minutes)
Same as speed-sums, except whoever find the difference between the two
numbers first wins.
•Make it Five/Make it Ten (1-5 minutes)
In this cooperative game, students meet in pairs. One student throws forward
some number of fingers. The second student must throw forward however many
fingers will make the sum 5 (or 10). For example, if two students meet and one
student puts forward two fingers, the other student should, as quickly as
possible, look, think, and throw forward three fingers. Then they part and each
finds a new partner.
•Five High Fives (1 – 2 minutes, or longer with the exploration)
Students try to give a high-five to five different classmates. When they’ve gotten
their five high-fives done, they sit down. This game is part mystery: sometimes it
will be possible for everyone to get a high-five; sometimes not. The difference
(which the teacher knows but the students don’t) is that it is only possible if
there are an even number of people giving high-fives. Try this game at different
times and let students guess whether they think everyone will get a high-five or
not. Why does it only work sometimes, not always? If you make it four or six
high-fives instead of five, then everyone will be able to get their high-fives every
time.
Tips for the classroom
1. Make sure kids never feel ashamed if they don’t already know the
right answer. You can also tweak competitive games to make them
collaborative.
2. You enthusiasm is critical in these games. Figure out your favorites,
and expand on them, or get the students to come up with their own
variations. If you’re into them and having a good time, the kids will
have a good time too.
Topics: logic, deduction, mathematical argument, communication
Materials: None
Recommended Grades: K, 1, 2, 3, 4, 5, 6, 7, 8
Common Core: Variable, but especially MP3
Proving the teacher wrong. Rigorously.
Why We Need Counterexamples
Every kid loves to prove the teacher wrong. With Counterexamples, they get to
do this in a productive way, and learn appropriate mathematical skepticism and
communication skills at the same time.
It is possible to play Counterexamples with kids as young as kindergarteners as
a kind of reverse “I Spy” (“I claim are no squares in this classroom. Who can find
a counterexample?”). What’s great, though, is that you can transition to
substantial math concepts, and address common misconceptions.
Counterexamples is a perfect way to disprove claims like “doubling a number
always makes it larger” (not true for negative number or 0) or sorting out why
every square is a rectangle, but not every rectangle is a square. For older kids,
you can even go into much deeper topics, like: “every point on the number line is
a rational number.”
The language of counterexamples is crucial to distinguish true and false claims
in mathematics; this game makes it natural, fun, and plants the skills to be used
later. Counterexamples is also a great way to practice constructing viable
arguments and critiquing the reasoning of others (CCSS.Math.Practice.MP3).
How it works
Counterexamples is a fun, quick way to highlight how to disprove conjectures by
finding a counterexample. The leader (usually the teacher, though it can be a
student) makes a false statement that can be proven false with a
counterexample. The group tries to think of a counterexample that proves it
false.
The best statements usually have the form “All ______s are _______” or “No
______s are _______.” You can also play around with statements like “If it has
______, then it can _______.” For instance:
● All birds can fly. (Counterexample: penguins)
● No books have pictures in them.
● All books have pictures in them.
● If something produces light, then it is a light bulb.
● If something has stripes, then it is a zebra.
● (harder) No square has a perimeter equal to its area.
(Counterexample: a 4 by 4 square.)
Example
Teacher: I claim all animals have four legs. Who can think of a counterexample?
Student 1: A person!
Student 2: A spider.
Student 3: A fish.
Teacher: Why is a person a counterexample?
Student 4: Because it has two legs.
Teacher: Right. I said every animal has four legs, but a human being is an animal
with just two legs. So I must have been wrong. What about this one: everything
with four legs is an animal.
Student 5: A spider.
Teacher: A spider is an animal with eight legs, so it proves that not every animal
has four legs. But I claimed that if you have something with four legs, it must be
an animal. To prove me wrong, you have to give me something with four legs that
isn’t an animal.
Student 5: Like a table?
Teacher: Who can tell me if a table is a counterexample to my claim?
And so on.
Tips for the Classroom
1. Start simple.
2. Try using silly claims, e.g., “The only one who likes cookies is cookie
monster.”
3. Use Number Talk mechanics. Have students raise a thumb at their
chest quietly when they have a counterexample, and raise more
fingers if they can think of more.
4. Kids can think of their own false claims, but sometimes these aren’t
the right kind, and they often have to be vetted.
5. Once you introduce the language of counterexamples, look for places
to use it in the rest of your math discussions.
6. You can also use Counterexamples to motivate a normal math
question. Instead of saying “draw a triangle with the same area as
this square,” you can say, “I claim there is no triangle with the same
area as this square.” If students know to look for counterexamples,
this will set them to work trying to disprove the claim right away.
Counter examples in Action: Pattern Blocks
Here are a series of Counterexample challenges that launch an exploration with
pattern blocks. These level up in difficulty to the main exploration (challenges 4
& 5).
1. “It’s impossible to make a hexagon with pattern blocks that isn’t
yellow.”
2. “It’s impossible to make a hexagon that isn’t yellow or red (assuming
they made a red hexagon from two trapezoids).”
3. (If they’ve made hexagons with 1, 2, 3, and 6 blocks) It’s impossible to
make a hexagon using exactly 4 or 5 blocks.
4. “Ok, it’s definitely impossible to make a hexagon that uses MORE
than 6 blocks.”
5. You can launch them onto their own with this question: Is it possible
to build a hexagon with ANY number of blocks? To start, can you build
a hexagon using 7 blocks? 8 blocks? 9 blocks? … up to 20 blocks?
6. Bonus (harder): “Is is impossible to build a hexagon with 50
blocks/100 blocks.”
7. Bonus: “It is impossible to make a hexagon using only squares”
Along the way, you can draw kids attention to any nonstandard hexagons that
get built. That fifth question is the key one for them to work on on their own for
a longer time. Ideally, they can build hexagons with larger numbers of blocks,
and check off the numbers they’re able to get. It would be cool if, as a class, you
could get all the numbers from 7 to 20, or even higher.