Lesson 4:  Division with remainders

1. In the problem  26 ÷ 7 what is the dividend? What is the divisor? What is the quotient? What is the remainder?

26 is the dividend; 7 is the divisor; 3 is the quotient, 5 is the remainder.

2. Write the number sentence shows how the dividend, divisor, quotient and remainder in the following division problem are related using multiplication and addition:

26 ÷ 8 = 3  R 2

8 × 3+2 = 26

3. Interpret 26 ÷ 8 = as a partition division problem.   What does it mean? (26 divided into .....?) Sketch what it would look like if you make a partition division diagram for the problem.

If 26 is/are divided into 8 groups,  how many are in each group?

 

4. Interpret 26 ÷ 8 = as a measurement division problem.   What does it mean? (26 divided into .....?) Sketch what it would look like if you make a measurement division diagram for the problem.

If 26 is/are divided into groups of 8,  how many are in each group?

5. For each word problem, tell your answer, and tell whether the answer is the quotient, the remainder or something else (explain what else it is).

A. 20 pencils are shared between 6 children.  How many pencils should each child get?

Each child gets 3 pencils (and 2 are left over). The answer is the quotient

B. 10 brownies are shared by 4 children.  How many brownies should each child get?

Each child gets 2 1/2 brownies (the answer is the whole number quotient plus a fraction--this is also called the fractional quotient)

C. 6 eggs can fit in a small egg carton.  I need to put 20 eggs in egg cartons.  How many egg cartons do I need?

I need 4 cartons to hold all of my eggs. The answer is the quotient + 1

D. Ms. Jensen has 40 pencils.  She wants to put the same number of pencils at each of 6 tables, and she will put any extra pencils away in her drawer.  How many pencils will she put in her drawer?

She will put 4 pencils in her drawer.  The answer is the remainder.

6. Write a division word problem for 14 ÷ 4 where the answer is

A. The quotient

This should be a word problem that asks for the number of sets or the number in each set where it isn't appropriate to have sets that are not "full"

B. The remainder

This should be a problem that asks how much is left over

C. One more than the quotient

This should be a word problem that asks for the number of sets where it isn't appropriate to have any left overs--all items must be in a set.

D. The quotient plus a fractional amount.

This should be a problem about an item that can be cut up into parts in order to be shared. At this level, it should be a partition division problem (fractional amounts in a set are easier conceptually than fractional sets).

7. Choose either partition or measurement division, and use it to show how to divide using manipulatives:

8. Write out how to divide numerically using either long division notation or scaffolding division notation.