# Movin ‘n Groovin

In the problem Movin ‘n Groovin, students use measurement, rates of change, and algebraic thinking to solve problems involving proportional relationships, metrics, and multiplicative relationships. The mathematical topics that underlie this problem are repeated addition, multiplication, division, unit conversion, linear measurement, proportional reasoning, rates, distance-time-velocity, 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 are presented with a measurement problem. In the problem, students are asked to determine who wins a race between two hamsters running through a maze. The students are given the seconds it takes the hamsters to travel through the maze. Understanding those numbers, they then determine which hamster is faster and who finishes first. They also need to determine how much faster one hamster is than the other by comparing the two finished times.

LEVEL A
In this level, students are presented with a measurement problem. In the problem, students are asked to determine who wins a race between two hamsters running through a maze. The students are given the seconds it takes the hamsters to travel through the maze. Understanding those numbers, they then determine which hamster is faster and who finishes first. They also need to determine how much faster one hamster is than the other by comparing the two finished times.

This level addresses Common Core standard 1.OA.A.1 by having students use addition and subtraction strategies within 20 to solve word problems involving comparisons.

LEVEL B
In this level, students are challenged with a problem involving two runners who run different distances for different times. They will need to reason about the relationship between the two rates to determine who is faster.

This level addresses Common Core standard 5.NF.B.4 by having students divide whole numbers by unit fractions.

LEVEL C
In this level, the students are presented with the challenge of determining the speed of a remote control car. Students must convert measures in feet and seconds to determine the speed of the remote control car in miles per hour and state whether the model car travels faster than a real car.

In this level, students use ratios to convert measurement units (6.RP.A.3d). Students convert inches to miles and seconds to hours and then use these values to find the unit rate in miles per hour. Students then compare the speed of the remote control car to that of a real car traveling on the highway.

LEVEL D
In this level, students analyze a situation involving a speeding car and a policeman on a curvy road. The students create a representation to model the given situation and investigate what average speed the officer must travel in order to overtake the speeder within 3.6 miles.

In this level, students use proportions to solve a rate problem (7.RP.A.2c) and write equations to represent proportional relationships (7.RP.A.3). Students also graph proportional relationships and interpret the slope as the unit rate (8.EE.B5)

LEVEL E
In this level, students are presented with a situation involving airplanes taking off from two different cities at regular intervals of time. Students are asked to determine how many planes originating in one location pass planes originating in the other location.

In this task, students reason recursively to determine the number of airplane passings (F.BF. A.1a). This task also supports the Modeling conceptual category in the Common Core State Standards. Students are asked to solve a non-routine problem, and a model of the situation is the best way to make sense of and solve this problem.

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