Routines....for reasoning??

Ask any teacher what they consider to be the most important topic they teach their students and routines is bound to be near the top of their list. Routines are the expectations that someone regularly follows. Established routines help students gain a sense of safety and familiarity with their classroom.

What happens when routines are not established?

If we would all agree that routines are important, why not establish routines for reasoning as well? What if there was a set of expectations that students had when solving math math problems and discussing their thinking? The book Routines for Reasoning explores how teachers can use the mathematical practices as a means to develop rich mathematical reasoning in their students.

Let’s take a look at how to develop the routine of Capturing Quantities.

MP2-Reason abstractly and quantitatively

What is a quantity? A quantity can be described as something that can be counted or measured, including the amount and label(ex. 5 blocks, 17 fish)

Part 1: Launch the Routine

“Today, we are going to focus on finding the quantities in number stories and the relationships between them.”

For Parts 2-4, steps are as follows:

1. Think time

2. Turn and Talk

3. Share whole group

Part 2: Identify Quantities and Relationships

Uncle Andre wants to make apple and pumpkin pies for his family reunion. He baked 12 pies. His family likes pumpkin pies, so he made twice as many pumpkin pies as apple pies.

**There is no question associated with this number story on purpose**

What quantities can you name in the scenario above?

-The total number of pies

-The number of apple pies

-The number of pumpkin pies

-The number of pies baked

After discussing the quantities with students, begin to move students towards describing the relationship between the different quantities.

-The number of pumpkin pies is twice(two times) as many as apple pies.

-The number of apple pies combined with the number of pumpkin pies is the same as the total number of pies baked.

Part 3: Create Diagrams

How can those quantities be represented?

Part 4: Discuss Diagrams

Display a diagram completed by a pair of students. Have the rest of the class analyze and make sense of the diagram. Have a class discussion about the diagram and how the relationship between quantities was displayed.

Part 5: Reflect

Provide students with sentence starters to help them focus on reflection.

-When looking for quantities, I learned to ________”

-When analyzing a diagram, I now know it is important to ___________”

-Next time I look for quantities, I will _________”

Side note: Sentence frames and starters are a great support during this entire routine.

-The number of _________

-The amount of _________

-(Quantity A)is _________ to (Quantity B)

-I showed/represented _______ by ________

Notice that a question was never asked with the original number story. If you wanted to revisit this number story on a future day, some questions that could be asked include:

-How many pumpkin pies did he bake?

-How many apple pies did he bake?

-How many more pumpkin pies did he bake?

-What fraction of the pies are apple/pumpkin?

Capturing quantities is a proven way to help students understand quantities within a problem and analyze the relationship between them. Routines for Reasoning offers several ways in which educators can provide access for all students to interact with mathematics.