For both days of this lesson, I had the students work on their fluency with the four different operations. I begin with addition and subtraction working up to the levels in the standards, including place values into the thousands. I also have the students use number lines as models to work on these solutions.
Next, I present equations for multiplication and division including missing variables. Students use arrays and other models for these situations. All students at one team are solving the same problem, and sharing their ideas for solutions with each other. Even though they are developing fluency with these operations, I still have them create models to explain and check their solutions. I find it more engaging for the students to work as a team and then rotate the equations among the teams. This allowed the students to support each other and discuss solutions. Using different equations for each team kept them focused on their own team problem rather than having all teams solving the same equation.
During this lesson students begin to learn about the order of operations and why/how using the order of operations can change the solution to a problem. I begin with modeling how to write a word problem, using multiple operations. This first example is written in the order of multiplication, division, addition, and subtraction. The context I used for the problem is bees, because they live as a group.
I suggest using math facts with multiple factors such as 24, 36, and 48. Using even numbers makes the division step easier for the students to calculate -- the goal is to make sense of the order of operations. Using odd numbers could make the division step confusing and stop the progression of the lesson.
There are four beehives in a tree, each with six bees. One of the beehives is knocked out of the tree, and the bees have to move into the remaining three hives. How many bees are living in each beehive now?
Later, more bees discover these three hives, and they join these bees. Now there are six bees more in each hive. How many bees live in the hives now? Some of the bees realize the hives are too small and 2 bees leave each hive. How many bees are living in the tree?
I display this problem for the class and I ask them to solve the problem, including creating diagrams to demonstrate each step. I remind students to use their "tools" (MP5) - number lines, arrays, and group models (MP4). I also remind the students to include labels with their problems (MP6). I discuss the importance of labels because without a label it the answer could have an entirely different meaning.
Day 1 - Once I'm confident the students are comfortable with the order of operations I release them to write their own problems. I recommend that you provide a visual / list of the order of operations - multiplication, division, addition, subtraction. I put some parameters in place, as supports for success - the problems have to use animals as their context. I choose this because it is easier for students to contextualize and make links to prior knowledge about using multiples as in legs, or groups of animals. It also relates back to my model problem.
The emphasis of this lesson is to emphasize the order of operations, and write problems in the order of operations - multiplication, division, addition, subtraction.
To allow for some personalization, I encourage students to choose their own animal - one different from their neighbor's choice.
Day 2 - Using problems written on day 1, students work on solving the problems of other students from their table group. I again emphasize the order of operations and display these on the board.
As students work on the problems, they have the opportunity to ask questions of the person who wrote the problem if they need clarification. This put the students in the role of both the student and teacher of their own problem. It also improves individual mathematical communication skills because a student whose problem is ambiguous will be learning this from a user - the classmate who is attempting to solve their word problem. This gives the word problem author an opportunity - through conversation (easier than writing!) to develop their mathematical thinking so that they can better express it.
To close this lesson each table group selects one of problems to present to the class, demonstrating a modeled solution. The student teams explain and demonstrate how they use a model with a color-coding to connect the words to the numbers. The student work focus is to create a problem that includes each operation, presented in order of operations, detailed models to represent student thinking, and correct use of labels. As students present, they use highlighters or crayons to underline and connect the word sentence matching the number sentence and model.