This paper makes recommendations for developing mathematics instruction for English Language Learners (ELLs) aligned with the Common Core State Standards. The recommendations can guide teachers, curriculum developers, and teacher educators as they develop their own ways of supporting mathematical reasoning and sense-making for ELLs.Some instructional recommendations discussed in the paper include: Focus on ELL students' mathematical reasoning, not the correctness of their mathematical language use. Shift to a focus on mathematical discourse practices; move away from simplified views of language. Support ELL students as they engage in complex mathematical language. Use ELL students' language and experiences as resources. Provide professional development to enhance teachers' awareness of ways to support ELs as they develop both language and mathematical knowledge.

This lesson unit is intended to help you assess how well students are able to: Interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant; interpret and evaluate the data generated and identify the optimum case; and communicate their reasoning clearly.

The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

In this task students work with partners to measure themselves by laying multiple copies of a shorter object that represents the length unit end to end. It gives students the opportunity to discuss the need to be careful when measuring.

In this Cyberchase video segment, the CyberSquad helps resolve a dispute about the squares on the Gollywood Walk of Fame.

In this unit, students will read and interpret primary sources to address the question “How do we measure the attainment of human rights?” By exploring the Universal Declaration of Human Rights, the UN’s Guide to Indicators of Human Rights, and data about development indicators from multiple databases, students will unpack the complexities of using indicators to measure human rights.

In this Cyberchase video segment, the CyberSquad must measure the length of the rope that will lower Digit from the ceiling to remove the voice box from a statue of Hacker.

Rating: Examples of High Quality NGSS Design if Improved

Science Discipline: Life Science

Length: Unit

This middle school unit was designed to support the middle school NGSS related to Ecosystems: Interactions, Energy, and Dynamics integrated with elements of related Earth science NGSS (Human Impact). The unit includes five chapters, each focused on a specific phenomenon related to ecosystem disruption, including questions around the reintroduction of wolves into Yellowstone and the invasion of zebra mussels in the Great Lakes and the Hudson River. © Regents of the University of California

Rating: Example of High Quality NGSS Design if Improved

Science Discipline: Earth & Space Sciences, Physical Sciences

Length: Unit

In Investigating Life on the Third Rock, middle school students work to generate and explore the overarching question of “How does the solar system and its objects affect life on Earth?” Students use modeling and argumentation to explore the lesson-level questions: “What properties of the solar system and its objects help explain why Earth can sustain life?” “Does the Moon affect life on Earth?” and “Why do the solar system and its objects move like they do?”

Rating: Example of High Quality NGSS Design

Awarded the NGSS Design Badge

Science Discipline: Life Science, Earth and Space Science, Physical Science

Length: Unit

Numerous reports suggest an increase in white shark encounters in the United States in recent years and the public is worried. In this integrated middle school unit, students engage in three-dimensional learning that enables them to explain the phenomenon. White sharks in the coastal waters of Southern California serve as a case study for students to ask questions and build understanding. Students initially question if white shark encounters are in fact increasing and investigate reports of sightings. They wonder if we know whether or not the population is on the rise, leading students to next explore past evidence from fossils and data from historic fishers logs. Students then question how scientists today are monitoring white sharks, setting the stage to explore the use of modern tracking devices (digging deep into waves and signals) and what researchers know about white sharks because of the application of this technology. This opens up the opportunity for students to question and consider what the science community has learned about white shark life history, how humans have impacted the white shark population off Southern California, and to devise a way to address public concerns.

This module is centered on the driving question, “How can we as engineers design a concert experience for others to enjoy?” In order to answer this question, students will consider what a wave is, and how waves are modeled. They will explore sound and light waves, and how these waves interact with various media. The culminating performance task requires students to synthesize this information, and apply it to the design of a concert experience.

The materials below are shared via a google drive folder and can be viewed and downloaded for use.

Students simulate operating an iron mine, from choosing property to writing an environmental impact statement to setting up the mining operation. Chocolate chip cookies (with the chocolate chips representing iron ore) are used for this experiment. Students are challenged to operate the most profitable and environmentally sound mine they can.

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

In this activity, student teams design small-scale physical models of hot and cold planets, (Venus and Mars), and learn that small scale models allow researchers to determine how much larger systems function. There is both a team challenge and competition built into this activity. Experimental findings are then used to support a discussion of human outposts on Mars. The resource includes an experimental design guide for students as well as a handout outlining a method for the design of controlled experiments, and student data sheets. Student questions and an essay assignment are provided as classroom assessments. This is Activity A in the second module, titled "Modeling hot and cold planets," of the resource, "Earth Climate Course: What Determines a Planet's Climate?" The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

This lesson unit is intended to help you assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods; interpret and evaluate the data generated; and communicate their reasoning clearly.

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Students will breed fruit flies through several generations and record their data using mathematical models in order to demonstrate the inheritance of trait variations.