Mental Math Helps Families on Sleep Habits

Dec 21, 2018 | Cambridge

If your kids seem cranky or distracted when doing homework, think about their sleep habits. Just as their bodies need sleep to be healthy, their brains also need sleep for them to be happy and to function well.

A good night’s sleep will help everyone in the family process and retain information, problem-solve, and concentrate during the day. Adequate sleep helps achieve the alertness needed for complex mental processes and mental stamina.

Life Hack #1: Know How Many Hours of Sleep Each Family Member Needs

Kids need sleep to be healthy—in body and brain! Here are 3 math-related life-hacks to help your family sleep better and feel healthier!

While individuals vary in how much sleep they need, you can use these age guidelines as a starting place. Adults need 7-9 hours of sleep each night. Children ages five to thirteen need regular bedtimes and about 9-11 hours of sleep. Teens need 8-10 hours of uninterrupted sleep.

Unfortunately, many doctors consider sleep deprivation to be an epidemic, with parents often modeling poor sleep habits for their children.

The Center for Disease Control reports that one in three adults don’t sleep the minimum recommended hours per night. According to the Sleep in America Poll, over fifty percent of adolescents and seventy-five percent of teens are sleep deprived. Sleep scientist Wendy Troxel encourages teenagers to sleep more in order to improve their mental health and do better in school. This makes sense, because a high-school math class, or math tutoring session, requires significant mental stamina.

Sleep deprivation in younger children is less prevalent than it is with teens and adults, but it is still a problem. Tired children simply can’t learn as well.

Life Hack #2: Understand the Math and Science to Change the Habit

Enforcing bedtime habits may be easier when you understand the research on sleep needs. You may even want share some of this information with your children, so they understand why you enforce bedtime. (Just don’t start the conversation at bedtime!)

Sleep researchers observe people sleeping and measure physiological changes in heart rate, brainwaves, breathing, and movement. They use statistics to analyze the data they collect and to help the rest of us understand sleep.

The Stages of Sleep

Kids need sleep to be healthy—in body and brain! Here are 3 math-related life-hacks to help your family sleep better and feel healthier!

One stage of sleep is Rapid Eye Movement, or REM. In REM, our eyes move back and forth, as seen in this video. REM is the stage when we dream. When we dream, brainwaves are small and fast, at 60-70 waves per second.

There is also non-Rapid Eye Movement, or non-REM sleep, which is broken down into stages from light to deep sleep. In light sleep, we have theta brainwaves of 4-7 Hz. In deep sleep, we have slow, delta brainwaves of about 0.4-4 HZ.

Every night we cycle between REM and non-REM about every ninety minutes. We spend 25% of our night in the REM stage and 75% is non- REM.

Scientists believe that non-REM sleep promotes healing and helps us create neural pathways for cognitive development, while the dreams in REM sleep help us process emotions and memories. Perhaps the future generation of scientists will solve these mysteries.

Trouble Falling Asleep

A common reason for sleep deprivation is trouble falling asleep. Teens (as well as adults and some children) often experience this because their minds go into overdrive at night. Knowing that they have a challenging day of school ahead, teens may feel anxious about not sleeping — which makes sleep even more elusive. Which leads us to life hack #3…

Life Hack #3: Do Mental Calculations to Relax and Fall Asleep

Kids need sleep to be healthy—in body and brain! Here are 3 math-related life-hacks to help your family sleep better and feel healthier!

When we are still thinking about the day as we try to sleep, our brainwaves are too fast to allow sleep to take over. Next time your child has trouble falling to sleep, suggest they do a mental math exercise to slow down their brainwaves.

Regular counting, or counting sheep, is too easy to effectively slow brain waves. Instead, slightly more challenging mental calculations, such as the ideas listed below, should slow the brainwaves from fast beta waves, to slower alpha waves, and then into theta waves of a light sleep.

You and your child can create a “bank” of mental math activities that are close to the level of math they are learning. Then they can find the ones that work the best, or rotate activities.

Ideas for ages 5-7:

Ideas for ages 8-10:

  • Count by threes or fours.
  • Count backward from 300 by twos, fives, or tens.
  • Count by a non-integer like ½ or .25.
  • Practice multiplication facts.

Ideas for ages 11-14:

  • Count backward from 300 by threes or ½.
  • Work on the Fibonacci sequence for as long as possible. It is a series of numbers where every number (after the first two in the series) is the sum of the previous two. For example, 0, 1, 1, 2, 3, 5… and so on.
  • Find all the prime numbers up to 100
  • Pick two numbers, and then find the least common denominator.
  • Practice squaring numbers.

Ideas for ages 15 and up:

  • Find the square root to the second decimal place of the age of people in your family.
  • Practice cubing numbers.
  • Recite formulas from chemistry, math, or physics.
  • Do any of the ideas from the 11-14 age category.


We love how math helps us describe, understand, and analyze everything, from politics, to art, to sleep. It’s also cool that math helps us fall asleep faster. Life, including math class, goes better when we get the sleep we need. If you’re looking for a math-related book to share together at bedtime, try one of the ones from our recommended list. Sweet dreams!