# Digging Dinosaurs

In the problem Digging Dinosaurs, students use algebraic thinking to solve problems involving multiple answers, optimum solutions, variables, and functions. The mathematical topics that underlie this problem are equations, optimization, variables, functions, and linear and non-linear patterns.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 a drawing of eight dinosaur feet underwater. They discuss multiple solutions for answering the question of how many dinosaurs are standing in the water.

LEVEL A
In this level, students view a drawing of eight dinosaur feet under the water. Their task is to determine multiple solutions for answering the question of how many dinosaurs are standing in the water.

Students will use reasoning to determine the number of dinosaurs they think are represented in the picture. They will then use addition concepts found in Common Core standard K.OA.A.2 to check their reasoning.

LEVEL B
In this level, students analyze different rate plans in order to visit a museum. The purpose is to determine the least expensive plan for a particular group given the frequency of their visits.

Students can use operations involving money to solve this task. Common Core standard 2.MD.C.8 would involve the students using addition concepts with money, while standard 4.MD.A.2 would involve the students using some multiplication concepts with money.

LEVEL C
In this level, students analyze different rate plans, which include decimals and cents. The purpose is to determine the least expensive plan for a particular group given the frequency of their visits.

Students will use the concepts found in Common Core standard 5.NBT.B.7 to multiply money with decimals.

LEVEL D
In this level, students examine a table of data that involves a linear relationship. Students are asked to write a function rule (8.F.B.4, 8.EE.C.7b) to determine the number of feet to dig when given the number of years. Students decide if the function rule is reasonable when applied to a different time period.  In the context of the situation, students focus on algebra and functions (SMP 3).

LEVEL E
In this level, students examine a table of data that is non-linear. Students are asked to write a function rule that describes the data and use the function to predict a value. Students choose from different function families and decide which model is most reasonable given the context of the problem situation.

In this level, students are given a table of non-linear data and write an equation to model the situation, supporting Common Core standard A-CED.A.2. Students must decide what function best models the data and may choose from a square root function or a logarithmic function (F-IF.C.7b, F-IF.C.7e) They use the function rules to predict a value of the function not given in the data (S-ID.6.a) and consider the reasonableness of their prediction. Analyzing the data and deciding on the best function rule requires students to look for a pattern in the data and the graph, supporting the mathematical practice of looking for and making using of structure (SMP.7).

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