To begin this lesson, I take time reviewing the "rules" that students discovered during the previous lesson.
Through solving problems involving nonsense units of measurement, they discovered:
• When converting from a small unit to a large unit - use division
• When converting from a large unit to a small unit - use multiplication.
We did not have time yesterday to discuss WHY these rules make sense. This will be focus of the introduction to todays lesson.
Students compare converting from a small unit to a large unit to working with fractions. When you are changing a lot of small units into larger units, you have to see how many of the small units fit together to make one of the large units. You multiply because you need more of the small to make the same size as a large unit.
When converting from a large unit to a small unit, you are grouping small units together to make the size of the larger unit. Small unit x ? = large unit. This is division.
Next, students will be provided with conversion chart for standard units of metic and US measurement of length, weight, and capacity. We will take time to make sense of each of these charts and allow students to ask questions before they begin solving problems with these standard units.
Students work in pairs to practice solving conversion problems. These problems include both metric and US systems for measuring length, weight, and capacity.
The students are encouraged to use a conversion chart and the "rules" they discovered about converting within a system of measurement.
I allow students to use these resources because I don't want to have them focusing on memorizing the relative size of each unit with in these systems. I explain that even as adults, we look to conversion charts as resources all the time. What I do want the students to know is HOW to solve conversion problems in ANY system of measurement. And to understand that the same rules apply to each system.
Providing time for students to process the conversion chart is important. I allow them to make statements as ask questions about any of the units or measurement systems.
One student asked about measuring the amount of air in a balloon, "How can you measure the amount of gas used in a hot air balloon? or the Macys' balloon?" This question leads to an interesting discussion between the students.
"I remember when we did the Macys' Parade math problems, my group wanted to know how much helium was in each balloon. I think we found the answer was in gallons."
"When we get gas for the cookout grill, we buy a 5 gallon tank."
(I looked these up to confirm the students thoughts. The helium for the balloons is measured in galloons, (each requires millions of gallons). Propane tanks are often sold by the pound.) It is important to follow up with students when they think about math outside of the text book. I want to let them know that predictions are excellent, and follow up is essential.
Students work in pairs to solve problems on the measurement conversion hand out. I choose to start with problems from the metric system because these problems reflect student learning about multiplying and dividing by multiples of 10. These problems are easy to solve once an equation is created. Even though the students were able to come up with the answers rather easily, I emphasized the importance of writing an equation for each one. This practice helps students when they solve more complex conversion problems.
While students are working, I circulate to make sure the students are using the clues they developed to help write equations.
In order to assess student progress, I wrap up this lesson with a "mini-quiz". Most ticket outs that I use consist of one short reflection or one math problem. I call this a quiz because it is a little more elaborate.
Students work on their own to solve problems about converting between units. For each problem, students must show their thinking with an equation.