Unit 6, Lesson 21
Problems with Remainders
Grade 4
Activity 1
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Han starts writing multiples of a number. When he reaches 104, he has written 8 numbers.
For each of the following questions, explain or show your reasoning.
- What number is Han writing multiples of?
- What is the 15th multiple of this number?
- Han gets to 286. How many numbers has he written at that point?
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Kiran wants to know how many multiples of 7 are between 0 and 150.
- He thinks he can use division to find out. Do you agree? Explain your reasoning.
- How many multiples will he find? Show your reasoning.
- Is 150 a multiple of 7? Show how you know.
- Han writes the number 295. He is wondering if he made a mistake. Determine if 295 is a multiple of 8 and explain your reasoning.
Student Section Summary
We solved different problems that involved dividing whole numbers.
We recalled two ways of thinking about division.
For example, if represents a situation where 274 markers are put into equal groups. The value of can tell us:
- How many markers are in each group if there were 8 groups.
- How many groups can be made if there were 8 markers in each group.
We learned that in , the is called the dividend, and the is called the divisor. We then identified many ways to find the value of a quotient —or the result of the division. For , we can:
- Think about whether one number is a multiple or factor of another number. For example, “Is 274 a multiple of 8?” or “Is 8 a factor of 274?”
- Divide by place value and think about putting 2 hundred, 7 tens, and 4 ones into 8 equal groups.
- Divide in parts and find partial quotients. For example, we can first find (which is 20), and then (which is 10), and then (which is 4).
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Think in terms of multiplication. For example, we can think of , , and so on.
Here is one way to record division using partial quotients.
Divide. 2 hundred seventy 4 divided by 8, 11 rows. First row: 34. Second row: 4. Third row: 10. Fourth row: 20. Fifth row: 8, long division symbol with 2 hundred seventy 4 inside. Sixth row: minus 1 hundred 60. Side note, 8 times 20. Horizontal line. Seventh row: one hundred 14. Eighth row: minus 80, side notes 8 times 10. Horizontal line. Ninth row: 34. Tenth row: minus 32, side note 8 times 4. Horizontal line. Eleventh row: 2.
Sometimes a division results in a leftover that can’t be put into equal groups or is not enough to make a new group. We call the leftover a remainder. Dividing 274 by 8 gives 34 and a remainder of 2.