Two diagrams are posted on the board. One representing 54 x 5, the other representing 25 divided by 5. Students use collaboration and prior knowledge to write an expression that represents each of these diagrams.
The purpose of this warm-up is to bring the part/part/whole model for multiplying and dividing to the front of students minds. These diagrams will be helpful throughout the lesson.
The purpose of this introduction is to set the context for the lesson. Students have previously worked with measurement terminology to sort words into categories of US Customary and Metric. They have developed an understanding of the relative size of units within a system in 4th grade.
Today, students will develop an understanding of why converting within a system of measurement is important and how to change from one unit to another.
To begin this lesson, I show the Systems of Measurement: Thinking Board from the previous lesson. It outlines the systems of measurement used for measuring length, weight, and capacity as well as the tools used for measuring each. Then, I introduce the term “convert”, and explain that we convert within a system of measurement - inches to feet for example - and we can also convert to another system of measurement - say inches to centimeters
This lesson is designed to help students develop the understanding that converting from a smaller unit of measurement to a larger unit you divide and when converting from a larger unit to a smaller you multiply.
This makes sense because when you are changing a smaller unit (inches) into a larger unit (feet) you will need fewer feet to measure the same size length. When converting from a larger unit (feet) to a smaller unit (inches) you multiply because it takes more of the smaller unit to make the same size.
I could just tell the student this, but I have chosen to design an activity that helps them discover it on their own. In this lesson, students rely on MP7 and MP8 as the look for and make sense of structure and repeated reasoning. Each problem is not a unique problem when converting within a system of measurement. Once a pattern is established, each problem, no matter what system of measurement is used, can be solved using the same system.
Students are presented with a non-sense measurement system that I have developed to measure happiness. This Happiness Conversions Chart shows the relationship between these made up units.
6 smirks = 1 smile
2 smiles = 1 giggle
3 giggles = 1 laugh
Students are given time to make sense of this measurement system. They ask questions for clarification and to increase interest.
Next, I explain the challenge. Today, we will be converting between different units of measuring happiness. The lessons that you learn from this non-sense system of measurement will help you when converting in any standard system.
When you are converting, there are some focus questions that you should ask yourself and your group each time. These Focus Questions & Thinking Examples help students progress through the lesson.
• Am I changing to a smaller unit?
• Am I changing to larger unit?
• Are there any leftovers?
• How can I use a picture/diagram to represent this conversion?
Students are provided with a "Nonsense" Conversions Handout handout. They work in pairs to solve the problems. Creating a diagram for each problem and making note of the type of conversion they used (small unit to large unit or large unit to small unit).
These notes will become the focus of the group discussion to help students recognize the "rule for conversions".
Students gather at the carpet with the Measuring Happiness handout and their classwork.
I present a t-chart to help students organize their thinking. One column is labeled small units to large units and the other is labeled large units to small units. I ask the students to review their work and find the examples that would fit in each column.
Then, we focus on the small to large units column first.
If I am changing small units into large units what does that mean? (You have a lot of little parts that you are putting together into groups. You will not have has many groups as you had little parts)
What operation helps me group all of these small parts? (division)
How can this be modeled using a diagram?
The same questions are used to discuss converting from a large unit to a small unit.
Students work in small groups to write a generalized statement about converting.
These statements will be tested with standard units in the following days.