How Much Does It Take?
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This learning activity provided by:
Author:
Kimberly Dockery
System: Alabama Department of Education School: Alabama Department of Education
General Activity Information
Activity ID:
2703
Title: How Much Does It Take?
Digital Tool/Resource: Dooley's Calculator Rectangular Prisms
Web Address – URL:
Overview: In this activity, students will compute real-world problems involving the volume of rectangular prisms. Students are provided models of rectangular prisms with fractional edge lengths and asked to compute how many smaller prims with a given measure are needed to pack the model. They will compute volume measurements using two different methods. Students are provided a link to an online rectangular prism calculator to check their calculations. An answer key with detailed explanations is provided for this activity.
How Much Does It Take? Student Response Page
Associated Standards and Objectives
Content Standard(s):
Digital Literacy and Computer Science 6) Identify steps in developing solutions to complex problems using computational thinking.
Unpacked Content
Evidence Of Student Attainment:
Students will:
use the problem solving or design thinking process to think logically through a previously solved complex problem. Teacher Vocabulary:
Knowledge:
Students know:
how to define the problem.
how to plan solutions.
how to implement a plan.
how to reflect on the results and process.
how to iterate through the process again. Skills:
Students are able to:
identify the steps involved with formulating problems and solutions in a way that can be represented or carried with or without a computer. Understanding:
Students understand that:
computational thinking is formulating problems and solutions in a way that can be represented or carried out with or without a computer.
Mathematics 28. Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.
a. Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh ) to find and compare volumes of right rectangular prisms.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a right rectangular prism with fractional edge lengths within a real-world or mathematical problem context,
Find and justify the volume of the prism as part or all of the problem's solution by relating a cube filled model to the corresponding multiplication problem(s).
Given cubes with appropriate unit fraction edge lengths,
Create and explain rectangular prism models to show that the volume of a right rectangular prism with fractional edge lengths l, w, and h is represented by the formulas V = l w h and V = b h. Teacher Vocabulary:
Right rectangular prism
V = b h (Volume of a right rectangular prism = the area of the base x the height) Knowledge:
Students know:
Measurable attributes of objects, specifically volume.
Units of measurement, specifically unit cubes.
Relationships between unit cubes and corresponding cubes with unit fraction edge lengths.
Strategies for determining volume.
Strategies for finding products of fractions. Skills:
Students are able to:
Communicate the relationships between rectangular models of volume and multiplication problems.
Model the volume of rectangles using manipulatives.
Accurately measure volume using cubes with unit fraction edge lengths.
Strategically and fluently choose and apply strategies for finding products of fractions.
Accurately compute products of fractions. Understanding:
Students understand that:
The volume of a solid object is measured by the number of same-size cubes that exactly fill the interior space of the object.
Generalized formulas for determining area and volume of shapes can be applied regardless of the level of accuracy of the shape's measurements (in this case, side lengths). Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.6.28.1: Define volume, rectangular prism, edge, and formula.
M.6.28.2: Recall how to multiply fractional numbers.
M.6.28.3: Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
M.6.28.4: Use models and volume formulas (V=lwh and V=Bh) to find volumes in the context of solving real-world and mathematical problems.
M.6.28.5: Calculate the volume of a rectangular prism using fractional lengths.
M.6.28.6: Test the formula V= lwh and V=Bh with the experimental findings.
M.6.28.7: Experiment with finding the volume using a variety of sizes of rectangular prisms manipulatives.
Prior Knowledge Skills:
Define volume.
Recognize the formula for volume.
Recall the attributes of three-dimensional solids.
Compare the unit size of volume/capacity in the metric system including milliliters and liters.
Measure and estimate liquid volumes.
Describe attributes of three-dimensional figures.
Describe attributes of two-dimensional figures.
Define volume including the formulas V = L × W × h, and V = B × h.
Define solid figures.
Define unit cube.
Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Describe attributes of three-dimensional figures.
Describe attributes of two-dimensional figures.
Compare the unit size of volume/capacity in the metric system including milliliters and liters.
Alabama Alternate Achievement Standards
AAS Standard:
Learning Objectives: Students will solve volume problems of rectangular prisms with fractional edge lengths.
Students will develop steps to solve complex problems using multiple methods.
Strategies, Preparations and Variations
Phase: During/Explore/Explain
Activity: Students will explore packing three-dimensional rectangular prisms with fractional edge lengths. They will also calculate the volume of rectangular prisms using multiple methods. The link to an online rectangular prism calculator is available for students to check their calculations. Students are provided three real-world context problems and asked to solve how many smaller rectangular prisms of a given size can be packed into the larger rectangular prism model. Then students are challenged to solve the volume of the larger rectangular prism using two different methods. Most students will solve using the most common method V=lwh. At this point, the teacher should conduct a Think-Pair-Share with the class. Ask the students how there is another way they could solve for the volume of the larger rectangular prism using how many smaller prisms are needed to pack the larger prism. Have the students compare their results with a partner and decide what they would like to share back with the class. All students should have the same answers. An answer key is provided with detailed explanations of how to solve each step. Another variation of the lesson could be the teacher modeling problems 1 and 2, students work in pairs on problems 3 and 4, and students work independently on problems 5 and 6. Problems 3 and 4 are more difficult due to some conversion calculations needed to complete the problems. Students are also provided the link to an online rectangular prism calculator where they can check their calculations along the way.
Assessment Strategies: Students will complete an exit ticket explaining which method they preferred to use when finding the volume of the larger rectangular prism.
Review the student response page to ensure the student identified the proper steps needed to solve the problem and mathematically solved the problem correctly.
Advanced Preparation: Students will need to know how to compute the volume of rectangular prisms.
Visit the digital tool rectangular prism calculator to become familiar with how to use the tool.
Students will need online access to the digital tool rectangular prisms calculator.
Copy the “How Much Does It Take?” student response page.
Variation Tips (optional): To expand student’s understanding, have students work in groups to write their own word problems including fractional edge lengths. They can exchange problems with classmates to solve.
Notes or Recommendations (optional): The lesson can also be scaffolded for the students. The teacher can work through problems 1 and 2 with the students, students can work in groups on problems 3 and 4, and students can work independently on problems 5 and 6.
If students do not have access to the internet to use the rectangular prisms calculator, the students can compare answers with a classmate and work through any differences with that classmate. The teacher can also provide the students with answers in the place of the rectangular prisms calculator.
Keywords and Search Tags
Keywords and Search Tags:
complex problem, conversions, fractional edge length, geometry, packing, packing rectangular prisms, rectangular prism, sixth grade math, solve using multiple methods, volume
