# Measuring Mammals

In the problem Measuring Mammals, students use algebraic thinking to solve problems involving proportional relationships, measurement, variables, and simultaneous equations. The mathematical topics that underlie this problem are linear measurement, proportional reasoning, scale factors, scale, ratios, variables, functions, inverse variation, and algebraic reasoning.In each level, students must make sense of the problem and persevere in solving it (MP.1). Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.

PRE-K
In this task, students view three drawings of giraffes. Their task is to determine the relational size of one giraffe to another.

LEVEL A
In this level, students view three drawings of giraffes. Their task is to determine the relational size of one giraffe to another.

This level addresses Common Core standard 1.MD.A.1 by having students compare the lengths of the two giraffes using a third object.

LEVEL B
In this level, students are given a picture and must use proportional reasoning to determine the linear dimension of an enlarged picture. Then the students are asked to find the inverse relationship: given an enlarged measurement, what was the original size?

This level addresses Common Core standard 4.OA.A.2 by having students multiply or divide to solve word problems involving multiplicative comparisons.

LEVEL C
In this level, the students are presented with view tubes. Students create and analyze tables (7.RP.A.2a, b, c) to determine the relationship between the tubes and the size of the objects they view.

This level addresses Common Core State Standard 7.RP.A.2a-c by having students create a table to represent a relationship. From this table, students can graph the data to determine that there is a proportional relationship between the quantities. They then find the constant of proportionality and write an equation to represent the relationship. Students find the ratio of the diameter of a scope to its length (7.RP.A.1) and use this ratio to find how tall a giraffe is.

LEVEL D
In this level, students analyze the relationship between different-sized view tubes. The students investigate the relationship of objects viewed when a dimension of a tube is altered.

This level addresses Common Core State Standard G-SRT.B.5 because students use similar triangles to formulate equations. A-CED.A.2 is also addressed because students create equations that show the relationships between the height of an object, the distance from it, and the dimensions of a tube. Students then create a system of equations and solve it to determine different relationships (A-REI.C.6).

LEVEL E
In this level, students are presented with a situation in the wild where they need to use their developed knowledge of proportional reasoning and algebraic thinking in order to find the height of an animal in the field.

This level addresses Common Core State Standard G-SRT.B.5 because students use similar triangles to formulate equations. A-CED.A.2 is also addressed because students create equations that show the relationships between the height of an object, the distance from it, and the dimensions of a tube. Students then solve these equations to determine different relationships (A-REI.B.3).

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