Welcome to division at the Grade 3 level! Division means sharing equally or making equal groups. For example, if you have 12 cookies and want to share them equally among 3 friends, how many cookies does each friend get? Let's solve this by dividing 12 by 3.
Another way to understand division is as repeated subtraction. For our example of 12 divided by 3, we can subtract 3 from 12 repeatedly until we reach zero. Let's count: 12 minus 3 equals 9, 9 minus 3 equals 6, 6 minus 3 equals 3, and finally 3 minus 3 equals 0. We subtracted 3 a total of 4 times, so 12 divided by 3 equals 4.
Division is closely connected to multiplication. They are inverse operations. If we know that 3 times 4 equals 12, then we also know that 12 divided by 3 equals 4, and 12 divided by 4 equals 3. These related facts form what we call a fact family. In division, we use specific vocabulary: the dividend is the number being divided, in this case 12; the divisor is the number we divide by, which is 3; and the quotient is our answer, which is 4. We can visualize this using an array of 12 dots arranged in 3 rows of 4, showing both the multiplication 3 times 4 equals 12 and the division 12 divided by 3 equals 4.
Let's practice solving a division word problem. Here's our problem: There are 20 stickers to be shared equally among 5 children. How many stickers will each child receive? To solve this, we follow these steps: First, identify what we're dividing, which is 20 stickers. Second, identify the divisor, which is 5 children. Third, set up the division equation: 20 divided by 5 equals what? Fourth, solve the equation: 20 divided by 5 equals 4. Finally, state our answer: Each child gets 4 stickers. We can visualize this by showing 20 stickers being distributed equally among 5 children, with each child receiving 4 stickers.
Let's summarize what we've learned about division at the Grade 3 level. Division means sharing equally or making equal groups. It can be understood as repeated subtraction, where we subtract the divisor repeatedly until we reach zero. Division is the inverse operation of multiplication - they undo each other. Important vocabulary includes the dividend, which is the number being divided; the divisor, which is the number we divide by; and the quotient, which is our answer. We can solve real-world problems using division. There are several methods to solve division problems: equal sharing, where we distribute items one by one; repeated subtraction, where we subtract the divisor repeatedly; and using multiplication facts, where we use our knowledge of multiplication to find the answer. Regular practice with division facts will help build fluency and confidence with division.