7th Grade Task: Capture-Recapture

7th Grade Task: Capture-Recapture

Standards & Objectives

Academic standards
CCSS.Math.Content.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and...
CCSS.Math.Content.7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a...
CCSS.Math.Content.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
CCSS.Math.Content.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.1
CCSS.Math.Content.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different...
CCSS.Math.Content.7.RP.A.2
Recognize and represent proportional relationships between quantities.
CCSS.Math.Content.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and...
GLE 0706.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0706.1.8
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and...
GLE 0706.2.1
Extend understandings of addition, subtraction, multiplication and division to integers.
GLE 0706.2.2
Understand and work with the properties of and operations on the system of rational numbers.
GLE 0706.2.3
Develop an understanding of and apply proportionality.
GLE 0706.3.5
Understand and graph proportional relationships.
GLE 0706.3.6
Conceptualize the meanings of slope using various interpretations, representations, and contexts.
GLE 0706.4.2
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
GLE 0706.4.4
Understand and use ratios, derived quantities, and indirect measurements.
SPI 0706.1.3
Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
SPI 0706.2.3
Use rational numbers and roots of perfect squares/cubes to solve contextual problems.
SPI 0706.2.5
Solve contextual problems that involve operations with integers.
SPI 0706.2.6
Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
SPI 0706.3.4
Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
SPI 0706.3.5
Represent proportional relationships with equations, tables and graphs.
TSS.Math.7.EE.B.3
Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and...
TSS.Math.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
TSS.Math.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for...
TSS.Math.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For...
TSS.Math.7.RP.A.2
Recognize and represent proportional relationships between quantities.
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Essential and guiding questions: 
  • What role does the constant of proportionality play in helping to relate two quantities?
  • When selecting a representative value for a data set what are some ideas to keep in mind?
  • What key ideas should be remembered when creating a proportion?
  • How can a proportion be rewritten as an equation of the form y = mx (and vice versa)?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can't get started... 

  • What does the 25 tell about the forest? (Question 1a)
  • What is a constant of proportionality?
  • What does the constant of proportionality indicate about a relationship between two quantities?
Extension suggestions: 

If students finish early...
If all the bears in the Smokies are represented by the bowl of black beans in the bowl, describe how to create a capture – recapture situation similar to Question 3 to estimate the bear population. (This would require preparation by placing two one‐pound bags of black beans in a bowl.)