In this task students use algebraic methods to determine whether each of the functions is odd, even, or neither.

The task is an introduction to the graphing of exponential functions. The first part asks students to use technology to experiment with the two parameters defining an exponential function, with little guidance. Since it is important for the second part, teachers should encourage students to try a wide range of values, and in particular, values of b both less than and greater than 1. The task includes a Desmos app, in which students can make use of sliders to more viscerally see the effect of changing a and b separately.

This task emphasizes the expectation that students know linear functions grow by constant differences over equal intervals and exponential functions grow by constant factors over equal intervals.

The goal of this task is to get students to focus on the shape of the graph of the equation y=ex and how this changes depending on the sign of the exponent and on whether the exponential is in the numerator or denominator. It is also intended to develop familiarity, in the case of f and k, with the functions which are used in logistic growth models, further examined in ``Logistic Growth Model, Explicit Case'' and ``Logistic Growth Model, Abstract Verson.''

The goal of this task is to work on finding multiples of some whole numbers.

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.

This task has students explore the relationship between the three parameters a, b, and c in the equation f(x)=ax2+bx+c and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part. We outline some of them here (which overlap heavily in places), applied to the top left graph, and then only give the final answers in the solution provided.

This task has students explore the relationship between the three parameters a, h, and k in the equation f(x)=a(x−h)2+k and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part. We outline some of them here (which overlap heavily in places), applied to the top left graph, and then only give the final answers in the solution provided.

This task requires students to determine whether a number is rational or irrational. The task assumes that students are able to express a given repeating decimal as a fraction.

In this task, students use trigonometric functions to model the movement of a point around a wheel and, in the case of part (c), through space (F-TF.5). Students also interpret features of graphs in terms of the given real-world context (F-IF.4).

This is a direct task suitable for the early stages of learning about exponential functions. Students interpret the relevant parameters in terms of the real-world context and describe exponential growth.

M 6–8 Math is a problem-based core curriculum rooted in content and practice standards to foster learning and achievement for all. Students learn by doing math, solving problems in mathematical and real-world contexts, and constructing arguments using precise language. Teachers can shift their instruction and facilitate student learning with high-leverage routines that guide them in understanding and making connections between concepts and procedures.

IM 6–8 Math lessons are designed with a focus on independent, group, and whole-class instruction. This format builds mathematical understanding and fluency for all students. Teachers will also use Warm-ups and Cool-downs to help guide lesson pacing and planning.

IM 6–8 Math, focuses on supporting teachers in the use of research-based instructional routines to successfully facilitate student learning. IM 6-8 Math, authored by Illustrative Mathematics, is highly rated by EdReports for meeting all expectations across all three review gateways. EdReports is an independent nonprofit that reviews K–12 instructional materials for focus, coherence, rigor, mathematical practices, and usability. Read the full analysis here.

IM Algebra 1, Geometry, and Algebra 2 are problem-based core curricula rooted in content and practice standards to foster learning and achievement for all. Students learn by doing math, solving problems in mathematical and real-world contexts, and constructing arguments using precise language. Teachers can shift their instruction and facilitate student learning with high-leverage routines that guide them in understanding and making connections between concepts and procedures.

IM 9-12 Math, authored by Illustrative Mathematics, is highly rated by EdReports for meeting all expectations across all three review gateways.

Students who struggle in Algebra 1 are more likely to struggle in subsequent math courses and experience more adverse outcomes. The Algebra 1 Extra Support Materials are designed to help students who need additional support in their Algebra 1 course. Each Algebra 1 Extra Support Materials lesson is associated with a lesson in the Algebra 1 course. The intention is that students experience each Algebra 1 Extra Support Materials lesson before its associated Algebra 1 lesson. The Algebra 1 Extra Support Materials lesson helps students learn or remember a skill or concept that is needed to access and find success with the associated Algebra 1 lesson.

This task asks students to identify which of the six polygons have the same area. Students may complete the task using a variety of techniques including decomposing shapes, using transformations (rotations, reflections, translations) to move one or more parts of the figure to another part to more easily calculate the area, enclosing the polygon inside a larger rectangle and then subtract the areas of the "extra" pieces, etc.

A comprehensive, standards-aligned, two-course curriculum designed to provide an effective accelerated pathway to Algebra 1.

IM 6–8 Math Accelerated, a compressed version of IM 6–8 Math™ 3.1415, is a thoughtful alternative to conventional accelerated programs because its design eliminates the possibility for unfinished learning as students arrive at Algebra 1. It includes all of the standards in IM 6–8 Math and compacts them into a two-year curriculum meant to be covered during the 6th and 7th grades. The pace is faster than IM 6-8 Math, but no crucial mathematical concepts are missed.

Only IM Certified curriculum is guaranteed to include the rigor, structure, and coherence as developed by our authors. Exclusively available from our IM Certified™ Partners, IM 6–8 Math Accelerated enables deep student learning through a carefully crafted scope and sequence that maintains a balance of conceptual understanding, procedural fluency, and meaningful applications. The IM authors made use of efficiencies in the standards to combine units from IM 6–8 Math and relocated or combined concepts as needed to maintain a thoughtful progression through the standards.

IM K–5 Math is a problem-based core curriculum rooted in content and practice standards to foster learning and achievement for all. Students learn by doing math through solving problems, developing conceptual understanding, and discussing and defending their reasoning. Teachers build confidence with lessons and curriculum guides that help them facilitate learning and help students make connections between concepts and procedures.

Every activity and lesson in IM K–5 Math tells a coherent mathematical story across units and grade levels based on both the standards and research-based learning trajectories. This allows students the opportunity to view mathematics as a connected set of ideas and offers them access to mathematics when developed into the overarching design structure of the curriculum.

The first unit in each grade level provides lesson structures which establish a mathematical community and invite students into the mathematics with accessible content. Each lesson offers opportunities for the teacher and students to learn more about one another, develop mathematical language, and become increasingly familiar with the curriculum routines. The use of authentic contexts and adaptations provides students opportunities to bring their own experiences to the lesson activities and see themselves in the materials and mathematics.

Students are asked to consider the expression that arises in physics as the combined resistance of two resistors in parallel. However, the context is not explicitly considered here. The task is good general preparation for problems more specifically aligned to either A-SSE.1 or A-SSE.2.

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.

The purpose of this task is to probe students' ability to correlate symbolic statements about a function using function notation with a graph of the function, and to interpret their answers in terms of the quantities between which the function describes a relationship

This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.