seegongsik
Grade 3 (age 8-9)

grade 3 Equal Sharing

Sharing equally means splitting a set of things fairly so that everyone gets the same number. If 15 apples go to 4 people, each person gets 3 and 3 apples are left over; that leftover amount is called the remainder. The remainder is always smaller than the number you divide by, and if divisor × quotient + remainder gives back the starting number, the sharing was done right. Change the number of apples and people on the plates below to see how each share and the remainder change.

Sharing Fairly

🍎 15 Apples for 4 People
①Hand out the apples one at a time in turn, and each round uses 4 apples
②After three rounds 12 apples are gone and 3 remain, which is not enough to give all four people one more
③So each share is 3, the remainder is 3, and we write 15 ÷ 4 = 3 R 3

Sharing onto Plates

15
4
💡 Why the Remainder Is Smaller
①If the leftover apples were at least as many as the people, everyone could get one more, so the sharing would not be finished
②That is why the remainder is always smaller than the divisor. With 4 people it can only be 0, 1, 2 or 3
③Change the apples to 16 and each person gets 4 with none left over. When the remainder is 0, the number divides evenly

Checking with Multiplication

🔍 Undoing the Division
①Four plates with 3 apples each hold 4 × 3 = 12 apples
②Add the 3 leftover apples and 12 + 3 = 15, the number you started with
③When divisor × quotient + remainder equals the dividend, the division is right; if a different number comes out, find the quotient or the remainder again

Summary

What Division Means
Total ÷ Number of people = Each share
It tells how many each person gets when things are shared equally
Division with a Remainder
15 ÷ 4 = 3 R 3
The quotient is 3 and the remainder is 3, which is smaller than the divisor 4
Check Equation
Divisor × Quotient + Remainder = Dividend
If it comes back to the starting number, as 4 × 3 + 3 = 15 does, the division is right
🎯 Summary
①Division splits a total into equal shares
②What is left after equal sharing is the remainder, and it is always smaller than the divisor
③When the remainder is 0, the number divides evenly
④Check the answer by seeing whether divisor × quotient + remainder equals the dividend
⑤The same idea is used when packing candy into bags or forming teams

Examples and Unit Test

Example 1
If 15 apples are shared equally among 4 people, how many does each person get and how many are left over?
1
Count how many times you can take 4 away from 15: 4, 8, 12 is three times, and one more would make 16, which is more than 15.
2
4 × 3 = 12, so 15 − 12 = 3 are left.
▸ 3 each, 3 left over
The 3 left over cannot give each of the 4 people one more, so they are the remainder.
Example 2
Check whether 15 ÷ 4 = 3 R 3 is correct.
1
The check equation is divisor × quotient + remainder = dividend.
2
4 × 3 + 3 = 12 + 3 = 15, which equals the dividend 15.
▸ 4 × 3 + 3 = 15, so it is correct
If the check does not match, either the quotient or the remainder was found wrong.
Unit Test
Which shows the correct quotient and remainder for 20 ÷ 6?
①quotient 3, remainder 1
②quotient 3, remainder 2
③quotient 4, remainder 0
④quotient 2, remainder 8
▸ ② quotient 3, remainder 2
1
6 × 3 = 18, and 6 × 4 = 24 is more than 20, so the quotient is 3.
2
20 − 18 = 2 is the remainder, and 2 is smaller than 6, so 20 ÷ 6 = 3 R 2.
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Rounding Numbers
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Plane Figures

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