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* *Reflection: Staircase of Complexity
Diving In - Section 2: Exploration of Division with Word Problems

*Staircase of Complexity: Division and decimals*

# Diving In

Lesson 7 of 7

## Objective: Students will be able to explore the two types of division (sharing or partitioning and splitting a collection) through group work and story problems.

In the last few weeks, we have been working out of our text book “My Math” by McGraw-Hill. We have focused on relating division to multiplication through factor families and introducing the terms *unknown*, or missing value, and *variable, *a letter replacing a number (MP6). Our text book is wonderful for working students through repeated algorithmic practice (MP7). I started the division unit with the text book instead of collaborative group work because it is important for the students to know their multiplication facts and the relationship between multiplication and division (5.NBT.6).

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It’s important to know there are two types of division problems. The first is sharing or partitioning. This is dividing a collection of objects into a given number of equal parts. An example would be if a student had twelve candies and they wanted to give them equally to three friends. 12 ÷ 3 = 4, each friend gets 4 candies.

The second type of division is grouping or splitting a collection of objects into groups of a known size. How many 15 cent pencils can be bought with $5.00.

Tell the following story: *Four friends were playing on the basketball court before school and found a $10.00 bill. They asked the person on duty if they could take it to the office. When they gave the $10.00 to the secretary she told them she would try to find out who lost the money, but if she could not find the owner, the money is theirs. A week later, the secretary called the four students back to the office and told them no one claimed the money. Before they could have it, though, they had to figure out how to share it equally among the four of them.* (5.NBT.6).

Have the students work together to solve the problem, record their solutions and show/explain their thinking (MP6). For those groups who finish, I have them solve a similar problem with remainders. For example: *Four students found $1.50 on the playground. How much would each get if they shared it equally?*

After the students have finished, have them share their solutions while you write math problems on the board. Adding the decimals in afterward – student will get used to seeing the decimals in with money - building prior knowledge for a unit on decimals.

Continue on with more division stories, relating the topics to things students could find in the school or related to their life outside of school – changing the divisors. For example, *Paulina came back from South Africa with 100 pieces of candy to share, how many pieces of candy will each student get? Mrs. Skinner ordered 250 pencils; if each student gets two pencils a week how long will the pencils last? **If the entire class goes to Dawson’s birthday party and there were six pizzas with ten slices each, how many slices will each student get? *

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It is important for student to reflect on their learning. This increases the retention of what they learned, and acts as that inner voice that gets students to recognize their thinking while engaged in mathematical practices.

Ask students two questions:

1. Which problems were sharing problems and which problems were grouping problems? *(reflection on the two types of division)*

2. What helped you do the math? *(reflection on thinking skills)*

#### Resources

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- LESSON 1: Multiplication Array: Part I Measuring It Out
- LESSON 2: Multiplication Array Part II Filling It In
- LESSON 3: Mulitiplication and Divsion Assessment
- LESSON 4: Multiple Ways to Multiply With Multiple Digits
- LESSON 5: Multiples in a Minute
- LESSON 6: Multiplication Timed Test 0-10
- LESSON 7: Diving In