# Measuring Up

In the problem Measuring Up, students use algebraic thinking to solve problems involving proportional relationships, measurement, scale, and multiplicative relationships. The mathematical topics that underlie this problem are repeated addition, multiplication, division, percents, linear measurement, proportional reasoning, scale factors, scale, ratios, variables, functions, 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 read the story “Stone Soup.” In the story, a recipe for the soup is shared. The students are asked to use manipulatives to determine how many carrots, onions, and chunks of meat are needed to feed various numbers of people.

LEVEL A
In this level, students read a version of the story “Stone Soup.” In the story, a recipe for the soup is shared. The students are asked to determine how many carrots, onions, and chunks of meat are needed to feed various numbers of people.

In this level, students must use multiplication to solve word problems in situations involving equal groups by using drawings or skip counting (3.OA.A.3) to determine the number of ingredients for various amounts of people.

LEVEL B
In this level, students are challenged with different proportional relationships between quantities in the Stone Soup recipe. They will need to use inverse relationships to determine some values.

In this level, students must solve multistep word problems having whole-number answers (4.OA.A.3).

LEVEL C
In this level, the students are presented with the challenge of determining a way to enlarge a picture to make a particular size of poster. The copier only has single settings for enlarging and reducing. The students are asked to determine what combinations of enlarging and reducing are required to meet the size specifications of the poster.

In this level, students must apply their knowledge of finding a percent of a quantity (6.RP.A.3c, 7.RP.A.3) to determine what combinations of enlarging and reducing (6.EE.A.1) are required to meet the size specifications of a specific poster size.The copier only has single settings for enlarging and reducing.

LEVEL D
In this level, students analyze the relationship between two different measuring sticks that have different units of measure. The students investigate when the units on the two sticks correspond.

In this level, students recognize and represent proportional relationships by equations (7.RP.A.2b, 7.RP.A.2c). They analyze the relationship between two different measuring sticks that have different units of measure. The students use and solve equations (6.EE.B.7) to investigate when the units on the two sticks correspond.

LEVEL E
In this level, students are presented with a situation that involves three broken rulers with differing unit measures. Students are asked to determine methods for converting between the three measuring sticks and to formalize their findings.

In this level, students use their knowledge of constant of proportionality and proportional relationships (7.RP.A.2b, 2c) to determine methods for converting between three broken rulers with differing unit measures. Students are asked to formalize their findings (7.EE.B.4, A-CED.2).

PROBLEM OF THE MONTH