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Math Gone Wild

Scientists are finding that many species use math like we do!

Jim Brandenburg/Minden Pictures

Can a wolf work with numbers? Can a chickadee count? Mathematical skills like these might seem like they’re unique to humans. But scientists have found that many animals also seem to have a basic sense of numbers that helps them survive in the wild.

Since animals can’t talk, it’s impossible to know whether they understand numbers the same way we do, says Andreas Nieder. He’s a neurobiologist at the University of Tübingen in Germany who studies how animals think.

“Exploring how the brain gives rise to [number sense] helps us understand our own counting capability,” says Nieder. Read on to meet four species that use math in some unexpected ways.

Can a wolf work with numbers? Can a chickadee count? Math might seem like something only humans can do. But many animals also seem to have a basic sense of numbers, scientists have found. This understanding helps the animals survive in the wild.

Obviously, animals can’t talk. That makes it impossible to know whether they understand numbers the same way we do, says Andreas Nieder. He’s a scientist at the University of Tübingen in Germany. He studies how animals think.

Understanding how animals use number sense helps scientists understand where ours comes from, says Nieder. Read on to meet four species that use math.

Wolves Pick Pack Size

Wolves are fierce predators, but hunting is still dangerous. Elk and bison, their usual prey in Yellowstone National Park, have sharp hooves that can injure or even kill. Hunting in groups helps wolves subdue their prey more easily—but a group that’s too big puts more wolves in danger. So they form teams of different numbers depending on the prey they’re after.

Wolves can hunt elk alone or in small groups, says Daniel MacNulty, a wildlife ecologist at Utah State University. But a 1,000-pound bison is a much more formidable foe. “A single wolf has virtually no chance of taking down a bison by itself,” says MacNulty. He’s found that wolves seem to know this, and are more likely to attack when they have a group of the right size.

Wolves are fierce predators. But hunting is still dangerous for them. In Yellowstone National Park, wolves prey on elk and bison. These animals have sharp hooves that can injure or even kill a wolf. Hunting in groups can help wolves take down their prey more easily. But if the group is too big, that puts more wolves in danger. So they form teams of different numbers depending on the prey.

Wolves can hunt elk alone or in small groups, says Daniel MacNulty. He’s a wildlife ecologist at Utah State University. But a bison can weigh 1,000 pounds, making it much more dangerous. “A single wolf has virtually no chance of taking down a bison by itself,” says MacNulty. Wolves seem to know this, MacNulty has found. They’re more likely to attack a bison when they have a pack of the right size.

Chickadees Count

Jeff Caverly/Shutterstock.com

Chickadees are a tasty snack for predators like owls or hawks. But the tiny birds have a defense system: an alarm call that summons other chickadees to screech and fly at the predator’s face. The idea is to pester the predator until it leaves to find an easier target, says Christopher Templeton, a biologist at Pacific University in Forest Grove, Oregon. He’s found that chickadees change the number of notes in their alarm call depending on how dangerous a predator is.

A chickadee’s call sounds like its name: chick-a-dee-dee-dee. The bigger the threat a predator poses, the more “dee” notes it adds at the end. Chickadees are fast and nimble, so small predators that can maneuver easily are more dangerous than big ones. “A pygmy owl will get a whole bunch of ‘dee’ notes, while larger predators like great horned owls receive very few,” says Templeton.

Chickadees are a tasty snack for predators like owls or hawks. But the tiny birds have a defense system. Their chirpy alarm call tells other chickadees to help them attack the predator. They screech and fly at the predator’s face as a group. This annoys the predator, which leaves to find an easier target, says Christopher Templeton. He’s a biologist at Pacific University in Forest Grove, Oregon. He’s found that chickadees can change the number of notes in their alarm call. They use a different number depending on how dangerous a predator is.

A chickadee’s call sounds like its name: chick-a-dee-dee-dee. The more dangerous a predator is, the more “dee” notes it adds at the end. Chickadees are fast and nimble. That means small predators that can maneuver easily are more dangerous than big ones. “A pygmy owl will get a whole bunch of ‘dee’ notes,” says Templeton. “Larger predators like great horned owls receive very few.”

Baboons Vote

Sylvain Cordier/Biosphoto/Minden Pictures

Baboons live in tight-knit social groups called troops. As many as 100 of the central African primates stick together as they roam in search of food. But troop leaders don’t always agree on which direction they should travel. When there’s a conflict, the monkeys have a mathematical method for deciding what to do.

Meg Crofoot, an anthropologist at the University of California, Davis, tracked a baboon troop in Kenya. She found that when troop leaders disagreed, they would each start to walk in the direction they wanted to go. If the difference in directions was small, the troop compromised and took a middle path. But if the difference was large, they put it to a vote. Each baboon in the troop walked over to the leader it agreed with. The direction with the most supporters won—even if that group had only one more baboon! “There’s a strong majority rule,” says Crofoot.

Baboons live in groups called troops in central Africa. As many as 100 of them stick together as they travel to find food. But troop leaders don’t always agree on which direction the group should go. When that happens, the monkeys have a mathematical way to decide.

Meg Crofoot is a scientist at the University of California, Davis. She tracked a baboon troop in Kenya to see what happened when leaders disagreed. She found that each leader started to walk in the direction they wanted to go. If the difference in directions was small, the troop compromised and took a path down the middle. But if the difference was large, they put it to a vote. Each baboon in the troop walked over to the leader it agreed with. The direction with the most supporters won. It happened even if that group had only one more baboon! “There’s a strong majority rule,” says Crofoot.

Kea Parrots use Probability

Amalia Bastos

Six kea parrots live at the Willowbank Wildlife Reserve in Christchurch, New Zealand. Biologist Amalia Bastos recently discovered that the birds have some mathematical smarts. Bastos and her colleagues first taught the birds to hand humans black plastic tokens in exchange for food. Then the scientists played a game of “pick a hand”: They filled two jars with both black and orange tokens, pulled one token from each jar, then held each token in a closed fist and let the keas choose.

The birds could see the contents of each jar, but not which token the researcher pulled from it. If a jar contained a higher proportion of black tokens, a kea was more likely to pick the hand that had pulled a token from that jar. In other words, says Bastos, they knew how to boost their odds of getting a treat. “They can use probability,” she says.

The Willowbank Wildlife Reserve is in Christchurch, New Zealand. Six kea parrots live there.  Biologist Amalia Bastos studies them. She recently discovered that the birds have some mathematical smarts. Bastos first taught the birds to give humans black plastic tokens in exchange for food. Then she and her colleagues played a game of “pick a hand.” They filled two jars with both black and orange tokens. They pulled one token from each jar. Then they held each token in a closed fist and let the keas choose.

The birds could see the contents of each jar. But they couldn’t see which token the researcher pulled from it. If a jar contained more black tokens, a kea was more likely to pick the hand that had pulled from that jar. In other words, they knew how to improve their odds of getting a treat. “They can use probability,” says Bastos.

Annotate the word problems in the following questions and solve. Use the online answer sheet to record your work and answers.

Annotate the word problems in the following questions and solve. Use the online answer sheet to record your work and answers.

A. Researchers found that wolves have the best chance of catching an elk if 4 wolves hunt together. The optimal group size for hunting a bison is 7 wolves larger than that. How many wolves should hunt together for the best chance of catching a bison?

A. Researchers found that wolves have the best chance of catching an elk if 4 wolves hunt together. The optimal group size for hunting a bison is 7 wolves larger than that. How many wolves should hunt together for the best chance of catching a bison?

B. In January 2020, they counted 94 wolves in Yellowstone National Park. The wolves had divided themselves into 8 packs. What’s the average size of each pack, rounded to the nearest whole number?

B. In January 2020, they counted 94 wolves in Yellowstone National Park. The wolves had divided themselves into 8 packs. What’s the average size of each pack, rounded to the nearest whole number?

C. Would an average-size pack have enough members to hunt a bison? Explain.

C. Would an average-size pack have enough members to hunt a bison? Explain.

A. When a chickadee sees a great gray owl, it usually uses 2 “dee” notes in its alarm call. This owl’s average wingspan is 132 centimeters. On average, chickadees add one dee note for every 50 cm smaller a predator’s wingspan is. What’s the approximate wingspan of the pygmy owl, which causes chickadees to use 4 “dee” notes?

A. When a chickadee sees a great gray owl, it usually uses 2 “dee” notes in its alarm call. This owl’s average wingspan is 132 centimeters. On average, chickadees add one dee note for every 50 cm smaller a predator’s wingspan is. What’s the approximate wingspan of the pygmy owl, which causes chickadees to use 4 “dee” notes?

B. How many “dee” notes would you expect them to make for a Cooper’s hawk with a wingspan of 81 cm?

B. How many “dee” notes would you expect them to make for a Cooper’s hawk with a wingspan of 81 cm?

A. Crofoot placed tracking collars on 25 baboons. They represented 80% of the total number of monkeys in the troop. How many baboons were in the troop, rounded to the nearest whole number?

A. Crofoot placed tracking collars on 25 baboons. They represented 80% of the total number of monkeys in the troop. How many baboons were in the troop, rounded to the nearest whole number?

B. More than  of the monkeys needed to agree for the troop to travel in a particular direction. What is the minimum number of baboons in this troop that need to be on the “winning” side for the group to make a decision?

B. More than  of the monkeys needed to agree for the troop to travel in a particular direction. What is the minimum number of baboons in this troop that need to be on the “winning” side for the group to make a decision?

A. One jar the scientists used was filled with 20 black and 100 orange tokens. What’s the probability of picking a black token, rounded to the nearest percent?

A. One jar the scientists used was filled with 20 black and 100 orange tokens. What’s the probability of picking a black token, rounded to the nearest percent?

B. A second jar had 20 black and 4 orange tokens. What’s the probability of picking a black token, rounded to the nearest percent?

B. A second jar had 20 black and 4 orange tokens. What’s the probability of picking a black token, rounded to the nearest percent?

C. A scientist pulls one token from each jar described above and plays “pick a hand.” Which hand should the kea choose for the best odds of receiving a black token—and a treat?

C. A scientist pulls one token from each jar described above and plays “pick a hand.” Which hand should the kea choose for the best odds of receiving a black token—and a treat?

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