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Distinguishing Between Surface Area and Volume
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Unit: Area and Surface Area
Lesson 16: Distinguishing Between Surface Area and Volume

In this optional lesson, students distinguish among measures of one-, two-, and three-dimensional attributes and take a closer look at the distinction between surface area and volume (building on students' work in earlier grades). Use this lesson to reinforce the idea that length is a one-dimensional attribute of geometric figures, surface area is a two-dimensional attribute, and volume is a three-dimensional attribute.

By building polyhedra, drawing representations of them, and calculating both surface area and volume, students see that different three-dimensional figures can have the same volume but different surface areas, and vice versa. This is analogous to the fact that two-dimensional figures can have the same area but different perimeters, and vice versa. Students must attend to units of measure throughout the lesson.

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

Subject:
Geometry
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Date Added:
04/07/2021
Does Weight Matter?
Read the Fine Print
Educational Use
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Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct an experiment to determine if weight added incrementally to an object affects the amount of friction encountered when it slides across a flat surface. After graphing the data from their experiments, students can calculate the coefficients of friction between the object and the surface it moved upon, for both static and kinetic friction.

Subject:
Applied Science
Engineering
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mary R. Hebrank
Date Added:
09/26/2008
Dot Plots
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Unit 8: Data Sets and Distributions
Lesson 4: Dot Plots

In this lesson, students continue to choose appropriate representation (MP5) to display categorical and numerical data, reason abstractly and quantitatively (MP2) by interpreting the displays in context, and study and comment on features of data distributions they show. Here they begin to use the everyday meaning of the word “typical” to describe a characteristic of a group. They are also introduced to the idea of using center and spread to describe distributions generally. Planted here are seeds for the idea that values near the center of the distribution can be considered “typical” in some sense. These concepts are explored informally at this stage but will be formalized over time, as students gain more experience in describing distributions and more exposure to different kinds of distributions.

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Date Added:
06/16/2021
Dunk Tank: Venn Diagram
Conditional Remix & Share Permitted
CC BY-NC-SA
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In this activity, Harry covers Venn Diagrams using 2 and 3 circles, plus a circle within a circle. Also included: the mini-game Zoo Mix-Up, a comic video about using a Venn Diagram to solve a problem and quiz-show questions.

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Game
Interactive
Date Added:
08/04/2020
Estimate by Inches and Feet
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CC BY-NC-SA
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This short video and interactive assessment activity is designed to teach fifth graders about estimating the measure of objects by image: feet or inches?.

Subject:
Mathematics
Measurement and Data
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
04/03/2018
Estimating: Counting Trees
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CC BY-NC-ND
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This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

Subject:
Education
Geometry
Mathematics
Measurement and Data
Ratios and Proportions
Material Type:
Assessment
Lecture Notes
Lesson Plan
Teaching/Learning Strategy
Author:
http://map.mathshell.org/
Date Added:
08/06/2020
Estimating the Measure of Items by Description: Inches Feet or Yards
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This short video and interactive assessment activity is designed to teach fifth graders about estimating the measure of items by description: inches, feet, or yards?.

Subject:
Mathematics
Measurement and Data
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
04/03/2018
Finding an   Unknown Angle
Unrestricted Use
CC BY
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The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

Subject:
Geometry
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/12/2012
Finding and Interpreting the Mean as the Balance Point
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CC BY
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Unit 8: Data Sets and Distributions
Lesson 10: Finding and Interpreting the Mean as the Balance Point

In the previous lesson, students interpreted the mean as a fair-share value—i.e., what each group member would have if all the values are distributed such that all members have the same amount. In this lesson, students use the structure of the data (MP7) to interpret the mean as the balance point of a numerical distribution. They calculate how far away each data point is from the mean and study how the distances on either side of the mean compare.

Students connect this interpretation to why we call the mean a measure of the center of a distribution and, through this interpretation, begin to see how the mean is useful in characterizing a “typical” value for the group. Students continue to practice calculating the mean of a data set (MP8) and interpreting it in context (MP2).

Subject:
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Date Added:
06/16/2021
Finding the Amount of Water with Illustrations and Calculations
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CC BY-NC-SA
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This short video and interactive assessment activity is designed to teach second graders about finding the amount of water with illustrations and calculations.

Subject:
Mathematics
Measurement and Data
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
04/03/2018
Finding the Capacity of Water with Illustrations Metric Units
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CC BY-NC-SA
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This short video and interactive assessment activity is designed to teach second graders about finding the capacity of water with illustrations (metric units).

Subject:
Mathematics
Measurement and Data
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
04/03/2018
Finding the Total Amount of Liquid in Liters and Milliliters
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CC BY-NC-SA
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This short video and interactive assessment activity is designed to teach fifth graders about finding the total amount of liquid in liters and milliliters.

Subject:
Mathematics
Measurement and Data
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
Date Added:
04/03/2018
First Grade Elementary Science and Integrates Subjects-Sky Explorers
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CC BY
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The First Grade Elementary Framework for Science and Integrated Subjects, Sky Explorers uses observation of the sun and moon in the sky as a phenomena for exploring patterns of objects in the sky.

Subject:
Astronomy
Education
Elementary Education
English Language Arts
Mathematics
Measurement and Data
Physical Science
Material Type:
Activity/Lab
Module
Reading
Author:
Georgia Boatman
Date Added:
06/13/2021
Formula for the Area of a Triangle
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CC BY
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Unit: Area and Surface Area
Lesson 9: Formula for the Area of a Triangle

In this lesson students begin to reason about area of triangles more methodically: by generalizing their observations up to this point and expressing the area of a triangle in terms of its base and height.

Students first learn about bases and heights in a triangle by studying examples and counterexamples. They then identify base-height measurements of triangles, use them to determine area, and look for a pattern in their reasoning to help them write a general formula for finding area (MP8). Students also have a chance to build an informal argument about why the formula works for any triangle (MP3).

Subject:
Geometry
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Date Added:
04/07/2021