To begin the lesson I review division through the measurement model to include using a number line to find the number of groups. I also focus on the sentence structure of this model of division involves finding the quotient such as 12 ÷ 4 = _____.
I explain to the students the tool they will be using for today's lesson is the number line. During the warm up we practice different division problems with number lines including some that are know facts similar to 12 ÷ 4 = 3, and more complex facts such as 81 ÷ 3 = 27. I specifically choose a more complex problem because I want to the students to practice and persevere with the use of the number line.
During the modeling and practice section of the lesson, the students are using small chips as a manipulative for a concrete model to divide into groups focusing on half. Since we have already worked on fractions, my students are accustomed to the term of half. This is important in this lesson and may need to be modified to equal groups or equal shares if half is an unfamiliar term to the students.
To begin the modeling and practice, I have the students take out twenty chips and divide them in half to show two groups of ten.. I purposely choose an easy number to make sure students can demonstrate their understanding of the term half. I then ask them to divide each of these groups of ten in half. When the students have four groups of five chips, I ask, "Can you divide one of the four groups in half?"
I ask this question because I want the students to be focusing on equal groups at this time, and not working with remainders. It is important to select/use a manipulative that does not separate into even smaller pieces such as a two sided counter, or even drawing the manipulative at this time.
Using a similar problem to the one they will be solving later in the lesson, I present these numbers in a context of fish swimming together in a school.
"There are twenty fish, but they separate by half to find some food. How many fish are in each school now?" Each of these groups of 10 fish break in half when larger fish come dangerously close. How many are in each group now?"
First, I explain to the students they will be using my classroom procedure for solving the word problem for this lesson. It is important for my students to have a sequence and specific steps to follow to solve word problems. This allows for the students to look at the process rather than just jumping to a immediate answer, and possibly missing key information and steps.
Creating a plan for word problems includes:
1. Rewrite the question from that is being asked in the word problem
2. Identify the key information
3. Draw a model
4. Write the number sentence
5. Answer the question from step 1
6. Explain your solution
The last step is critical for the Common Core Standards, and one that use most often to assess student work.
The problem for this lesson is:
A monkey has a bunch of 64 bananas. Each day he eats half of the bananas he has left, and he only eats whole bananas. How many days will the bananas last?
Students work together with a partner to solve the problem. Attention to detail requires the students to focus on the second sentence and the wording "half of the bananas he has left."
This could also be modeled with counters or another type of manipulative if the students need this support.
Students are challenged to create unique presentations for the class, rather than merely reading from a chart. The focus here is on giving a clear explanation to show understanding of the division as well a solving the problem to find the number of groups/days the bananas would last.
Options for the students include using manipulatives, diagrams, acting it out, etc. Beyond not wanting students to read from their work, the presentation method is a choice for students. I do stress, though, that the presentation must focus on providing a clear explanation of their thinking.