Divisibility Rules

Don't forget! Math quiz on Monday! (factors, multiples, greatest common factor GCF, least common multiple LCM)



Memorize these rules!

Divisible By

"Divisible By" means "If you divide one number by another, is the result a whole number?"

Example, 14 is divisible by 7, because 14÷7 = 2 exactly

But 15 is not divisible by 7, because 15÷7 = 2 ¹/₇ (i.e., the result is not a whole number)

The Divisibility Rules

These rules let you test if one number can be evenly divided by another, without having to do too much calculation!

A number is divisible by:	If:	Example:
2	The last digit is even (0,2,4,6,8)	128 is 129 is not
3	The sum of the digits is divisible by 3	381 (3+8+1=12, and 12÷3 = 4)Yes 217 (2+1+7=10, and 10÷3 = 3 1/3) No
4	The last 2 digits are divisible by 4	1312 is (12÷4=3) 7019 is not
5	The last digit is 0 or 5	175 is 809 is not
6	The number is divisible by both 2 and 3	114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes 308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
7	If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)	672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes 905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
8	The last three digits are divisible by 8	109816 (816÷8=102) Yes 216302 (302÷8=37 3/4) No
9	The sum of the digits is divisible by 9 (Note: you can apply this rule to that answer again if you want)	1629 (1+6+2+9=18, and again, 1+8=9) Yes 2013 (2+0+1+3=6) No
10	The number ends in 0	220 is 221 is not
11	If you sum every second digit and then subtract all other digits and the answer is: 0, or divisible by 11	1364 ((3+4) - (1+6) = 0) Yes 3729 ((7+9) - (3+2) = 11) Yes 25176 ((5+7) - (2+1+6) = 3)No
12	The number is divisible by both 3 and 4	648 (6+4+8=18 and 18÷3=6, also 48÷4=12) Yes 916 (9+1+6=16, 16÷3= 5 1/3)No

How does exercise help our bodies stay healthy?

Aim: How does exercise help our bodies stay healthy?

Exercise Makes Your Heart Happy

You may know that your heart is a muscle. It works hard, pumping blood every day of your life. You can help this important muscle get stronger by doing aerobic (say: air-o-bik) exercise.

Aerobic means "with air," so aerobic exercise is a kind of activity that requires oxygen. When you breathe, you take in oxygen, and, if you're doing aerobic exercise, you may notice you're breathing faster than normal. 

Aerobic activity can get your heart pumping, make you sweaty, and quicken your breathing.

When you give your heart this kind of workout on a regular basis, your heart will get even better at its main job — delivering oxygen (in the form of oxygen-carrying blood cells) to all parts of your body.

So you want to do some aerobic exercise right now? Try swimming, basketball, ice or roller hockey, jogging (or walking quickly), inline skating, soccer, cross-country skiing, biking, or rowing. And don't forget that skipping, jumping rope, and playing hopscotch are aerobic activities, too!

Exercise Strengthens Muscles

Another kind of exercise can help make your muscles stronger. Did you ever do a push-up or swing across the monkey bars at the playground? Those are exercises that can build strength. By using your muscles to do powerful things, you can make them stronger. For older teens and adults, this kind of workout can make muscles bigger, too.

Here are some exercises and activities to build strong muscles:

• push-ups
• pull-ups
• tug-of-war
• rowing
• running
• inline skating
• bike riding

Exercise Makes You Flexible

Can you touch your toes easily without yelling ouch? Most kids are pretty flexible, which means that they can bend and stretch their bodies without much trouble. This kind of exercise often feels really good, like when you take a big stretch in the morning after waking up. Being flexible is having "full range of motion," which means you can move your arms and legs freely without feeling tightness or pain.

It's easy to find things to do for good flexibility:

• tumbling and gymnastics
• yoga
• dancing, especially ballet
• martial arts
• simple stretches, such as touching your toes or side stretches

Exercise Keeps the Balance

Food gives your body fuel in the form of calories, which are a kind of energy. Your body needs a certain amount of calories every day just to function, breathe, walk around, and do all the basic stuff. But if you're active, your body needs an extra measure of calories or energy. If you're not very active, your body won't need as many calories.

Whatever your calorie need is, if you eat enough to meet that need, your body weight will stay about the same. If you eat more calories than your body needs, it may be stored as excess fat.

Exercise Makes You Feel Good

It feels good to have a strong, flexible body that can do all the activities you enjoy — like running, jumping, and playing with your friends. It's also fun to be good at something, like scoring a basket, hitting a home run, or perfecting a dive.

But you may not know that exercising can actually put you in a better mood. When you exercise, your brain releases a chemical called endorphins (say: en-dor-funz), which may make you feel happier. It's just another reason why exercise is cool!

Social Studies & Science notes

Aim:Why did Portugal claim territory in the Americas?

Spanish colonization helped Spain to grow wealthy. The king wanted the leaders to treat the Indians well, but instead they were treated as slaves.

Pedro Alvares Cabral arrived in Brazil. Although the indigenous people didn’t have gold or silver they had wood, wild animals, fish, and gem stones. Portugal and Spain claimed land for economic, political, and religious reasons. 

The Portuguese started a colony in Brazil 1532. They forced Indians to work on sugar plantations. Many Indians died because of disease and cruel treatment. People moved to Brazil to make money and convert natives to Catholicism. 

Why is it important for people to exercise? 

Being physically active makes you stronger, helps you feel good and improves your self-image. Exercise helps your entire respiratory system. Your respiratory system is made up of all the parts of your body that helps you get oxygen into your blood and carbon dioxide out of it. Your blood gets oxygen when air goes through your nose, in the trachea into the lungs and then into the alveoli. Your heart and lungs work better with regular physical activity.