This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

Students investigate the weather from a systems approach, learning how individual parts of a system work together to create a final product. Students learn how a barometer works to measure the Earth's air pressure by building a model using simple materials. Students analyze the changes in barometer measurements over time and compare those to actual weather conditions. They learn how to use a barometer to understand air pressure and predict actual weather changes.

CSDE Model Curricula Quick Start GuideEquitable and Inclusive Curriculum  The CSDE believes in providing a set of conditions where learners are repositioned at the center of curricula planning and design. Curricula, from a culturally responsive perspective, require intentional planning for diversity, equity, and inclusion in the development of units and implementation of lessons. It is critical to develop a learning environment that is relevant to and reflective of students’ social, cultural, and linguistic experiences to effectively connect their culturally and community-based knowledge to the class. Begin by connecting what is known about students’ cognitive and interdisciplinary diversity to the learning of the unit. Opposed to starting instructional planning with gaps in students’ knowledge, plan from an asset-based perspective by starting from students’ strengths. In doing so, curricula’s implementation will be grounded in instruction that engages, motivates, and supports the intellectual capacity of all students.Course Description:  In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.  Upon completion of this course students will have the ability to Analyze proportional relationships and use them to solve real-world and mathematical problems. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models.Aligned Core Resources:  It is critical that curriculum be implemented using high quality instructional materials to ensure all students meet Connecticut’s standards. Ensuring alignment of resources to the standards is critical for success. There are tools that are available to districts to assist in evaluating alignment of resources, such as CCSSO’s Mathematics Curriculum Analysis Project and Student Achievement Partner’s Instructional Materials Evaluation Tool.   In addition, there exist compilations of completed reviews from a variety of resources. Some of these include but are not limited to EdReports, Louisiana Believes, CURATE, and Oregon Adopted Instructional Materials.Aligned Core Programs:  The CSDE in partnership with SERC has engaged with providers of high-quality vetted resources to provide additional alignment guidance to the CSDE model curriculum.  High-quality instructional resources are critical for improving student outcomes. The alignment guidance is intended to clarify content and support understanding for clear implementation and coherence. Materials selection is a local control decision and these documents have been provided from participating publishers to assist districts in implementation. Use of the materials from these publishers is not required. These aligned core programs meet expectations as reported by EdReports. If your resource is not listed below, you are encouraged to review EdReports to ensure the alignment of your resource to the Connecticut Core Standards. Strong alignment of curricula and instructional materials have the potential to support student engagement of meaningful grade level content daily and teacher growth.   Carnegie Learning Math Grade 7EdGems Math Grade 7enVisions Grade 7Eureka Math Grade 7Fishtank Plus Math Grade 7HMH Into Math Grade 7Imagine Learning Illustrative Mathematics Grade 7i-Ready Math Grade 7MidSchoolMath Grade 7Open Up Resouces Math Grade 7Reveal Math Grade 7Additional Course Information:  Major work of Grade 7 mathematics focuses on ratios and proportional relationships and arithmetic of rational numbers. Habits of Mind/SEIH/Transferable Skills Addressed in the Course: The Standards for Mathematical Practice describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics. They describe student behaviors, ensure an understanding of math, and focus on developing reasoning and building mathematical communication. Therefore, the following should be addressed throughout the course: Make sense of problems & persevere in solving them Reason abstractly & quantitatively Construct viable arguments & critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for & make use of structure Look for & express regularity in repeated reasoning 

Unit Overview/Summary - FOCUS: This unit focuses on Ratios and Proportional Relationships and Expressions and Geometry. Learning this unit will enable students to: Analyze proportional relationships and use them to solve real-world and mathematical problems; and Draw, construct, and describe geometrical figures and describe the relationships between them. 

Students explore the densities and viscosities of fluids as they create a colorful 'rainbow' using household liquids. While letting the fluids in the rainbow settle, students conduct 'The Great Viscosity Race,' another short experiment that illustrates the difference between viscosity and density. Later, students record the density rainbow with sketches and/or photography.

In the first part of the activity, each student chews a piece of gum until it loses its sweetness, and then leaves the gum to dry for several days before weighing it to determine the amount of mass lost. This mass corresponds to the amount of sugar in the gum, and can be compared to the amount stated on the package label. In the second part of the activity, students work in groups to design and conduct new experiments based on questions of their own choosing. These questions arise naturally from observations during the first experiment, and from students' own experiences with and knowledge of the many varieties of chewing and bubble gums available.

Student groups are provided with a generic car base on which to design a device/enclosure to protect an egg on or in the car as it rolls down a ramp at increasing slopes. During this in-depth physics/science/technology activity, student teams design, build and test their creations to meet the design challenge, and are expected to perform basic mathematical calculations using collected data, including a summative cost to benefit ratio.

Based on what they have already learned about friction, students formulate hypotheses concerning the effects of weight and contact area on the amount of friction between two surfaces. In the Associated Activities (Does Weight Matter? and Does Area Matter?), students design and conduct simple experiments to test their hypotheses, using procedures similar to those used in the previous lesson (Discovering Friction). An analysis of their data will reveal the importance of weight to normal friction (the friction that occurs as a result of surface roughness) and the importance of surface area to the friction that occurs between smooth surfaces due to molecular attraction. Based on their data, students will also be able to calculate coefficients of friction for the materials tested, and compare these to published values for various materials.

In this lesson and its associated activity, students conduct a simple test to determine how many drops of each of three liquids can be placed on a penny before spilling over. The three liquids are water, rubbing alcohol, and vegetable oil; because of their different surface tensions, more water can be piled on top of a penny than either of the other two liquids. However, this is not the main point of the activity. Instead, students are asked to come up with an explanation for their observations about the different amounts of liquids a penny can hold. In other words, they are asked to make hypotheses that explain their observations, and because middle school students are not likely to have prior knowledge of the property of surface tension, their hypotheses are not likely to include this idea. Then they are asked to come up with ways to test their hypotheses, although they do not need to actually test their hypotheses. The important points for students to realize are that 1) the tests they devise must fit their hypotheses, and 2) the hypotheses they come up with must be testable in order to be useful.

Most of the flavoring in gum is due to the sugar or other sweetener it contains. As gum is chewed, the sugar dissolves and is swallowed. After a piece of gum loses its flavor, it can be left to dry at room temperature and then the difference between its initial (unchewed) mass and its chewed mass can be used to calculate the percentage of sugar in the gum. This demonstration experiment is used to generate new questions about gums and their ingredients, and students can then design and execute new experiments based on their own questions.

Students learn about radar imaging and its various military and civilian applications that include recognition and detection of human-made targets, and the monitoring of space, deforestation and oil spills. They learn how the concepts of similarity and scaling are used in radar imaging to create three-dimensional models of various targets. Students apply the critical attributes of similar figures to create scale models of a radar imaging scenario using infrared range sensors (to emulate radar functions) and toy airplanes (to emulate targets). They use technology tools to measure angles and distances, and relate the concept of similar figures to real-world applications.

Students explore whether rooftop gardens are a viable option for combating the urban heat island effect. Can rooftop gardens reduce the temperature inside and outside houses? Teams each design and construct two model buildings using foam core board, one with a "green roof" and the other with a black tar paper roof. They measure and graph the ambient and inside building temperatures while under heat lamps and fans. Then students analyze the data and determine whether the rooftop gardens are beneficial to the inhabitants.

The purpose of this task is to engage students in Standard for Mathematical Practice 4, Model with mathematics and as such, the question as it is worded cannot be answered without making some assumptions. For example, if the items that are purchased do not have the same value, then the price reduction depends on the cost of the items.

This problem can be solved in more than one way. The choice in solution method may reflect the comfort and mathematical sophistication of the student.

This is a multi-step problem since it requires more than two steps no matter how it is solved. The problem is not scaffolded for the student, but each step is straightforward and should follow from the previous with a careful reading of the problem.

Through two lessons and their associated activities, students do the work of scientists by designing their own experiments to answer questions they generate. Through a simple activity involving surface tension, students learn what a hypothesis is—and isn't—and why generating a hypothesis is an important aspect of the scientific method. In the second activity, with bubble gum to capture their interest, students learn to design and conduct controlled experiments to answer their own questions about the amounts of sugar (or artificial sweetener) in bubble or chewing gum.

Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.

Students conduct a simple test to determine how many drops of each of three liquids water, rubbing alcohol, vegetable oil can be placed on a penny before spilling over. Because of their different surface tensions, more water can be piled on top of a penny than either of the other two liquids. However, the main point of the activity is for students to come up with an explanation for their observations about the different amounts of liquids a penny can hold. To do this, they create hypotheses that explain their observations, and because middle school students are not likely to have prior knowledge of the property of surface tension, their hypotheses are not likely to include this idea. Then they are asked to come up with ways to test their hypotheses, although they do not need to actually conduct these tests as part of this activity.