Volume of 3D figures
Lesson 7 of 8
Objective: SWBAT find the volume of prisms, pyramids, cones, cylinders and spheres.
Students enter silently according to the daily entrance routine. Do Now assignments will be handed upon entry. For the next few days students will follow these procedures completing problems about surface area and volume of 3D figures. On the final day they will take their final math quiz of the year.
Each day, students will be urged to continue showing their work horizontally using algebraic and numeric sentences.
While showing students the work I continuously remind them to notice which part of the numeric expression indicates each face of the geometric figure. The first step students must take before solving is to identify the number of faces to be added together and be able to identify them in their expressions as well.
A mathematical practice we also continue to emphasize is MP6: attention to precision. I introduce a competition at the beginning of the week tracking student mistakes on Do Now assignments. Students will have 5 minutes to complete each assignment. For each problem completed with a visible final answer and work shown, students will receive 5 points. Each mistake will be tallied and subtracted from these 5 points. Like in golf, many scores will be negative. As the score changes each day, students will be celebrated if their change in scores from the beginning to the end of the week is the greatest, in the positive direction, or course. I will be keeping track of student mistakes visible during these 5 minutes. Students making fewer and fewer mistakes each day will be celebrated. This competition encouraged many students to complete the problems, feeling free to make mistakes as long as they returned the next day determined to make fewer mistakes.
To introduce this topic I use some geometric shapes ordered from Learning Resources. I ask the following questions:
- I take out the nets inside the shape: if I wanted to wrap this shape and needed to know how much paper I would use, what would I need to find? Surface area
- What if I wanted to fill this shape with water or rice? What would I need to find?Volume; I have rice to show students filling the shape
- Does anyone know the volume formula? is it the same for all 3D figures?
I use the following Scholastic Formula Sheet to questions and show students the the concept of volume with rice (or water). This activity serves to make this concept sticky. I also collect as much prior knowledge as possible to be aware of the types of problems students are prepared to solve.
The next day we complete a Scholastic activity about volume. This activity includes all resources and steps for completion, but I altered a few things and added some more resources to facilitate the process:
- When drawing rectangular prisms I use graph paper to facilitate the drawing process
- Rather than simply showing students the formula, I ask them to give me the formula if they remember if. I take 5 – 6 minutes to explain WHY we multiply the area of the based times the height using square coasters.
The take home activity is given out for homework.
Each of the first two days students are given the formulas for volume on the board and they must copy them onto a blank sheet of paper, over and over, every time they are used to complete a problem.
On the third day, the day before the final quiz, students are provided with a formula sheet also found on the Scholastic website. It may be necessary to open up some time for questions as students will be looking at unfamiliar formulas. Until this day, students have been creating their own formulas for surface area by considering the shapes that make up the faces. For volume, they’ve explored what volume is, but HAVE been given the formulas. Students will be able to bring this sheet to use during the test.
The class work sheets each day should be completed in pairs. Students will have 10 minutes to complete as many problems as possible in pairs. During this time I will be walking around the room noticing whether there are any students struggling to do the work or having a hard time keeping up with their neighbor. I will also be targeting 5 – 6 students whom I will ask to split up in the following 10 minutes of this section. These will be my undercover student coaches.
After 10 minutes students will be welcome to form groups of 4 to finish the classwork sheet. These will be used for extra credit on their test. Any students whom I noticed struggling will be working with me in a group at the front of no more than 10 students.
The undercover student coaches will have index cards with the following guiding points they need to uphold with each of their teammates. The goal: Everyone in the group they choose to work with completes the classwork earning an 80% or above. The reward: They get to skip any ONE question on the final test and automatically earn points for it.
Students are given an exit ticket each day which is returned within the same day with feedback for students. For homework, students are asked to write a paragraph summary of the feedback given and how they are going to use this feedback to study for their quiz. Even kids who get everything correct are given feedback in the form of an additional problem including composite 3D figures.