MAFS.912.G-MG.1.2Archived Standard

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
General Information
Subject Area: Mathematics
Domain-Subdomain: Geometry: Modeling with Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply geometric concepts in modeling situations. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Items may require the student to use knowledge of other Geometry
standards.
• Calculator :

Neutral

• Clarification :
Students will apply concepts of density based on area in modeling
situations.

Students will apply concepts of density based on volume in modeling
situations.

• Stimulus Attributes :

Items must be set in a real-world context

• Response Attributes :
Items may require the student to apply the basic modeling cycle.

Items may require the student to use or choose the correct unit of
measure.

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

The population of Florida in 2010 was 18,801,310 and the land area was 53,625 square miles. The population increased by 5.8% by 2014.

A. To the nearest whole number, what is the population density, in people per square mile, for Florida in 2014?

B. To the nearest whole number, how much did the population density, in people per square mile, increase from 2010 to 2014?

• Difficulty: N/A
• Type: EE: Equation Editor

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2020910: Astronomy Solar/Galactic Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2000320: Biology 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2000330: Biology 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
2003350: Chemistry 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003360: Chemistry 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2001320: Earth/Space Science Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2000440: Genetics Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002410: Integrated Science 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002430: Integrated Science 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002450: Integrated Science 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002510: Marine Science 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002520: Marine Science 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002530: Marine Science 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2020710: Nuclear Radiation Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003320: Physical Science Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003380: Physics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003390: Physics 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2003410: Physics 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104410: Figure Drawing (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current))
2003385: Physics 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2020 (course terminated))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0102340: Art Collaboration: Designing Solutions for Art, Work, and Life Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))
2003836: Florida's Preinternational Baccalaureate Physics 1 (Specifically in versions: 2015 - 2022, 2022 and beyond (current))
2003838: Florida's Preinternational Baccalaureate Physics 2 (Specifically in versions: 2015 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

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Formative Assessments

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Lesson Plans

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Perspectives Video: Expert

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Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

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In this video, Jim Cox describes a sampling method for estimating the density of dead trees in a forest ecosystem.

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KROS Pacific Ocean Kayak Journey: Food Storage Mass and Volume:

What do you do if you don't have room for all your gear on a solo ocean trek? You're gonna need a bigger boat...or pack smarter with math.

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Perspectives Video: Teaching Ideas

Ecological Sampling Methods and Population Density:

Dr. David McNutt explains how a simple do-it-yourself quadrat and a transect can be used for ecological sampling to estimate population density in a given area.

Type: Perspectives Video: Teaching Idea

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This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can. Multiple solution processes are presented.

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

How many leaves on a tree? (Version 2):

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

How many leaves on a tree?:

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Eratosthenes and the circumference of the earth:

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Teaching Idea

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Type: Teaching Idea

STEM Lessons - Model Eliciting Activity

It’s Not Waste—It’s Matter!:

It's Not Waste—It's Matter is an MEA that gives students an opportunity to review matter, their physical properties, and mixtures. The MEA provides students to work in teams to resolve a real-life scenario creating a design method by which recyclable products are separated in order to further process.

Olympic Snowboard Design:

This MEA requires students to design a custom snowboard for five Olympic athletes, taking into consideration how their height and weight affect the design elements of a snowboard. There are several factors that go into the design of a snowboard, and the students must use reasoning skills to determine which factors are more important and why, as well as what factors to eliminate or add based on the athlete's style and preferences. After the students have designed a board for each athlete, they will report their procedure and reasons for their decisions.

MFAS Formative Assessments

How Many Trees?:

Students are asked to determine an estimate of the density of trees and the total number of trees in a forest.

Mudslide:

Students are asked to create a model to estimate volume and mass.

Population of Utah:

Students are asked to determine the population of the state of Utah given the state’s population density and a diagram of the state’s perimeter with boundary distances labeled in miles.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Type: Perspectives Video: Expert

How thick is a soda can? (Variation II):

This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can. Multiple solution processes are presented.

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

How many leaves on a tree? (Version 2):

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

How many leaves on a tree?:

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

How many cells are in the human body?:

This problem solving task challenges students to apply the concepts of mass, volume, and density in the real-world context to find how many cells are in the human body.

Eratosthenes and the circumference of the earth:

This problem solving task gives an interesting context for implementing ideas from geometry and trigonometry.

Archimedes and the King's Crown:

This problem solving task uses the tale of Archimedes and the King of Syracuse's crown to determine the volume and mass of gold and silver.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

How thick is a soda can? (Variation II):

This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can. Multiple solution processes are presented.

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

How many leaves on a tree? (Version 2):

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

How many leaves on a tree?:

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

How many cells are in the human body?:

This problem solving task challenges students to apply the concepts of mass, volume, and density in the real-world context to find how many cells are in the human body.