Illustrative Mathematics Algebra 1 Course Guide - Teachers (2024)

Instructional Routines

Analyze It

Analyze It indicates activities where students have an opportunity touse statistical tools to calculate and display numeric statistics and produce visual representations of one- and two-variable data sets.

Anticipate, Monitor, Select, Sequence, Connect

What: These are the5 Practices for Orchestrating Productive Mathematical Discussions (Smith and Stein, 2011). In this curriculum, much of the work of anticipating, sequencing, and connectingis handled by the materials inthe activity narrative, launch, and synthesis sections. Teachers need to prepare for and conduct whole-class discussions.

Where: Many classroom activities lend themselves to this structure.

Why:In a problem-based curriculum, many activities can be described as “do math and talk about it,” but the 5 Practices lend more structure to these activities so that they more reliably result in students making connections and learning new mathematics.

Aspects of Mathematical Modeling

What: In activities tagged with this routine, students engage in scaled-back modeling scenarios, for which students only need to engage in a part of a full modeling cycle. For example, they may be selecting quantities of interest in a situation or choosing a model from a list.

Why: Mathematical modeling is often new territory for both students and teachers. Opportunities to develop discrete skills in the supported environment of a classroom lesson make success more likely when students engage in more open-ended modeling.

Card Sort

What: A Card Sort uses cards or slips of paper that can be manipulated and moved around (or thesame functionality enacted witha computer interface). It can be done individually or in groups of 2–4. Students putthings into categories or groups based on shared characteristics or connections. This routine can be combined with Take Turns, such that each time a student sorts a card into a category or makes a match, theyareexpected to explain therationale while thegroup listens for understanding. The first few times students engage in these activities, the teacher should demonstrate how the activity is expected to go. Once students are familiar with these structures, less set-up will be necessary. While students are working, the teacher can ask students to restate their question more clearly or paraphrase what their partner said.

Where: Classroom Activities

Why: A Card Sort provides opportunities to attend to mathematical connections using representations that are already created, instead of expending time and effort generating representations. It gives students opportunities toanalyze representations, statements, and structures closely and make connections (MP2, MP7).

Extend It

Extend It indicates activities where students have an opportunity touse a spreadsheet to produce a sequence of numbers to see patterns and make predictions.

Fit It

Fit It indicates activities where students have an opportunity to use a table of points to produce a graph to see patterns and make predictions. Also when appropriate, find a function that best fits the data.

Graph It

Graph It indicates activities where students have an opportunity to usegraphing technology to visualize agraph representingone or more functions with known parameters and usethe tool to find features like intersection points, intercepts, and maximums or minimums. Additionally, theymay use sliders for exploring the effect of changing parameters.

Math Talk

What: In these warm-ups, one problem is displayed at a time. Students are given a few moments to quietly think and give a signal when they have an answer and a strategy. The teacher selects students to share different strategies for each problem, asking, “Who thought about it a different way?” Their explanations are recorded for all to see. Students might be pressed to provide more details about why they decided to approach a problem a certain way. It may not be possible to share every possible strategy in the given time—the teacher may only gather two or three distinctive strategies per problem. Problems are purposefully chosen to elicit different approaches,often in a way that builds from one problem to the next.

Why: Math Talks build fluency by encouraging students to think about the numbers, shapes, or algebraic expressionsand rely on what they know about structure, patterns, and properties of operations to mentally solve a problem. While participating in these activities, students need to be precise in their word choice and use of language (MP6). Additionally a Math Talk often provides opportunities to notice and make use of structure (MP7).

MLR1: Stronger and Clearer Each Time

To provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output. This routine provides a purpose for student conversation as well as fortifies output. The main idea is to have students think or write individually about a response, use a structured pairing strategy to have multiple opportunities to refine and clarify the response through conversation, and then finally revise their original written response. Throughout this process, students should be pressed for details, and encouraged to press each other for details.

MLR2: Collect and Display

To capture students’ oral words and phrases into a stable, collective reference. The intent of this routine is to stabilize the fleeting language that students use during partner, small-group, or whole-class activities in order for student’s own output to be used as a reference in developing their mathematical language. The teacher listens for, and scribes, the student output using written words, diagrams and pictures; this collected output can be organized, revoiced, or explicitly connected to other language in a display for all students to use. This routine provides feedback for students in a way that increases accessibility while simultaneously supporting meta-awareness of language.

MLR3: Clarify, Critique, Correct

To give students a piece of mathematical writing that is not their own to analyze, reflect on, and develop. The intent is to prompt student reflection with an incorrect, incomplete, or ambiguous written argument or explanation, and for students to improve upon the written work by correcting errors and clarifying meaning. This routine fortifies output and engages students in meta-awareness. Teachers can demonstrate with meta-think-alouds and press for details when necessary.

MLR4: Information Gap Cards

What: Students conduct a dialog in a specific way. In an Info Gap, one partner gets a problem card with a math question that doesn’t have enough given information, and the other partner gets a data card with information relevant to the problem card. Students ask each other questions like “What information do you need?” and are expected to explain what they will do with the information. The first few times students engage in these activities, the teacher should demonstrate, with a partner, how the discussion is expected to go. Once students are familiar with these structures, less set-up will be necessary.

Why: This activity structure is designed to strengthen the opportunities and supports for high-quality mathematical conversations. Mathematical language is learned by using mathematical language for real and engaging purposes. These activities were designed such that students need to communicate in order to bridge information gaps. During effective discussions, students should be supported to do the following: pose and answer questions, clarify what is asked and happening in a problem, build common understandings, and share experiences relevant to the topic.

Illustrative Mathematics Algebra 1 Course Guide - Teachers (1)

MLR5: Co-Craft Questions

To allow students to get inside of a context before feeling pressure to produce answers, and to create space for students to produce the language of mathematical questions themselves. Through this routine, students are able to use conversation skills as well as develop meta-awareness of the language used in mathematical questions and problems. Teachers should push for clarity and revoice oral responses as necessary.

MLR6: Three Reads

To ensure that students know what they are being asked to do, and to create an opportunity for students to reflect on the ways mathematical questions are presented. This routine supports reading comprehension of problems and meta-awareness of mathematical language. It also supports negotiating information in a text with a partner in mathematical conversation.

MLR7: Compare and Connect

To foster students’ meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, and language. Teachers should demonstrate thinking out loud (e.g., exploring why we one might do or say it this way, questioning an idea, wondering how an idea compares or connects to other ideas or language), and students should be prompted to reflect and respond. This routine supports meta-cognitive and meta-linguistic awareness, and also supports mathematical conversation.

MLR8: Discussion Supports

To support rich discussions about mathematical ideas, representations, contexts, and strategies. The examples provided can be combined and used together with any of the other routines. They include multi-modal strategies for helping students comprehend complex language and ideas, and can be used to make classroom communication accessible, to foster meta-awareness of language, and to demonstrate strategies students can use to enhance their own communication and construction of ideas.

Notice and Wonder

What: This routine can appear as a warm-up or in the launch or synthesis of a classroom activity. Students are shown some media or a mathematical representation. The prompt to students is “What do you notice? What do you wonder?” Students are given a few minutes to think ofthings they notice and things they wonder, and share them with a partner. Then, the teacher asks several students to share things they noticed and things they wondered; these are recorded by the teacher for all to see. Sometimes, the teacher steers the conversation to wondering about something mathematical that the class is about to focus on.

Where: Appears frequently in warm-ups but also appears in launches to classroom activities.

Why: The purpose is to make a mathematical task accessible to all students with these two approachable questions. By thinking about them and responding, students gain entry into the context and might get their curiosity piqued. Taking steps to become familiar with a context and the mathematics that might be involved is making sense of problems (MP1).Note: Notice and Wonder and I Notice/I Wonder are trademarks of NCTM and the Math Forum and used in these materials with permission.

Poll the Class

What: This routine is used to register an initial response or an estimate, most often in activity launches or to kick off a discussion. It can also be used when data needs to becollected from each student inclass, for example, "What is the length of your ear in centimeters?" Every student in class reports a response to theprompt. Teachers need to develop a mechanism by which poll results are collected and displayed so that this frequent form of classroom interaction is seamless. Smaller classes might be able to conduct a roll call by voice. For larger classes, students might be given mini-whiteboards or a set of colored index cards to hold up. Free and paid commercial tools are also readily available.

Why: Collecting data from the class to use in an activity makes the outcome of the activity more interesting. In other cases, going on record with an estimate makes people want to know if they were right and increases investment in the outcome. If coming up with an estimate is too daunting, ask students for a guess that they are sure is too low or too high. Putting some boundaries on possible outcomes of a problem is an important skill for mathematical modeling (MP4).

Take Turns

What: Students work with a partner or small group. They take turns in the work of the activity, whether it be spotting matches, explaining, justifying, agreeing ordisagreeing, or asking clarifying questions. If they disagree, they are expected to support their case and listen to their partner’s arguments. The first few times students engage in these activities, the teacher should demonstrate, with a partner, how the discussion is expected to go. Once students are familiar with these structures, less set-up will be necessary. While students are working, the teacher can ask students to restate their question more clearly or paraphrase what their partner said.

Why: Building in an expectation, through the routine, that students explain the rationale for their choices and listen to another's rationale deepens the understanding that can be achieved through these activities. Specifying that students take turns deciding, explaining, and listening limits the phenomenon where one student takes over and the other does not participate. Taking turns can alsogive students more opportunities to construct logical arguments and critiqueothers’ reasoning (MP3).

Think Pair Share

What: Students have quiet time to think about a problem and work on it individually, and then time to share their response or their progress with a partner. Once these partner conversations have taken place, some students are selected to share their thoughts with the class.

Why: This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking. First they have an opportunity to share their thinking in a low-stakes way with one partner, so that when they share with the class they can feel calm and confident, as well as say something meaningful that might advance everyone’s understanding. Additionally, the teacher has an opportunity to eavesdrop on the partner conversations so that they can purposefully select students to share with the class.

Which One Doesn’t Belong?

What: Students are presented with four figures, diagrams, graphs, or expressions with the prompt “Which one doesn’t belong?” Typically, each of the four options “doesn’t belong” for a different reason, and the similarities and differences are mathematically significant. Students are prompted to explain their rationale for deciding that one option doesn’t belong and given opportunities to make their rationale more precise.

Where: Warm-ups

Why: Which One Doesn’t Belong fosters a need to define terms carefully and use words precisely (MP6) in order to compare and contrast a group of geometric figures or other mathematical representations.

Glossary ›

Illustrative Mathematics Algebra 1 Course Guide - Teachers (2024)

FAQs

What makes illustrative math different? ›

Problem-based with real-world connections: Students discover, understand, and internalize key math concepts and apply their learning to various real-world problems and scenarios, simultaneously building procedural fluency and conceptual understanding.

How long is an illustrative math lesson? ›

Each lesson is designed for a 50-minute class period. For educators with different class period lengths, IM provides guidance of where material can be safely added or removed to support the individual needs of teachers.

What do you teach in algebra 1? ›

Algebra 1 typically includes evaluating expressions, writing equations, graphing functions, solving quadratics, and understanding inequalities.

Is the illustrative math curriculum free? ›

Free & Digital Curriculum based on the IM K–12 Math authored by Illustrative Mathematics® GeoGebra makes this open educational resource available to you digitally for free!

What are the cons of illustrative math? ›

SEVERE lack of practice for each skill. Lessons generally have 2-3 "activities" to introduce concepts with only 4-5 problems per lesson. As with many other options, you cover a lot of topics but do not get very deep into any of them really.

Is Illustrative Mathematics a good curriculum? ›

IM K–5 Math has earned top ratings from EdReports in every review category. See why educators love IM K–5 Math. This curriculum has taken all of the fantastic instructional routines teachers were pulling from multiple sources and tied them up with a great big bow into a rigorous, coherent curriculum resource!

Does illustrative math have homework? ›

Each lesson includes an associated set of practice problems. Teachers may decide to assign practice problems for homework or for extra practice in class. They may decide to collect and score it or to provide students with answers ahead of time for self-assessment.

Is illustrative math common core? ›

This site organizes the standards across grade levels and provides example content, activities, or assessment items for some of the common core standards.

How much does illustrative math cost? ›

Kendall Hunt's Illustrative Mathematics 6-8 Mathematics curriculum is an Open Educational Resources (OER) and are free to download and use with a CC-BY license.

What grade is algebra 1 usually taught? ›

Typically, algebra is taught to strong math students in 8th grade and to mainstream math students in 9th grade. In fact, some students are ready for algebra earlier.

What is the most important topic in algebra 1? ›

Some of the overarching elements of the Algebra I course include the notion of function, solving equations, rates of change and growth patterns, graphs as representations of functions, and modeling.

Is algebra 1 harder than geometry? ›

So if you want to look at these three courses in order of difficulty, it would be algebra 1, geometry, then algebra 2. Geometry does not use any math more complicated than the concepts learned in algebra 1.

Who funds Illustrative Mathematics? ›

Illustrative Mathematics is funded by The W.K. Kellogg Foundation . When was the last funding round for Illustrative Mathematics ?

Is Zearn aligned with illustrative math? ›

Zearn Math Grade 6–8 materials are directly aligned to Illustrative Math's scope and sequence. All K–5 lessons align with Illustrative Math on the unit level.

What does PLC mean in illustrative math? ›

Professional Learning Community. Teaching mathematics is complex work. It requires teachers to plan lessons that offer each student access, elicit students' ideas during these lessons, find ways in which to respond to those ideas, and build a classroom community where students feel known, heard, and seen.

What makes illustration different? ›

An illustration is different from a typical piece of art. While an illustration's purpose is to explain something visually, art pieces, such as paintings, are not necessarily always connected to specific information and are a subject to interpretation.

Is illustrative math aligned to common core standards? ›

The curriculum was aligned to the shifts of the Common Core Standards of Focus, Coherence, and Rigor.

What is illustrative method of teaching? ›

The Illustration method involves the use of various. visual aids such as posters, maps, sketches, paintings, and. digital media to support the learning process[2]. These visual.

Why are schools teaching math differently? ›

This can be especially empowering for kids with learning and thinking differences. It prepares them to solve the real-world problems they will face in the future. Yes, math is being taught differently today. It may be a little more difficult for parents at times, but it definitely can be better for kids.

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