The Standards for Mathematical Practice (MP) describe the types of thinking and behaviors in which students engage as they do mathematics. Throughout the curriculum, the Teacher Guide identifies lessons and activities in which to observe the different MPs.

Some instructional routines are generally associated with certain MPs. For example:

• The Card Sort routine often asks students to reason abstractly and quantitatively (MP2) and to look for and make use of structure (MP7).
• The Information Gap routine often requires students to make sense of problems and persevere in solving them (MP1) as well as attend to precision (MP6) in their language as they ask questions of their partner.
• The Math Talk routine offers opportunities to look for and make use of structure (MP7) and look for and express regularity in repeated reasoning (MP8) as students explain the strategies they use and apply strategies as they develop fluency.
• The Which Three Go Together? routine also offers opportunities for attending to precision when describing why something doesn’t belong (MP6).

The unit-level Mathematical Practice chart is meant to highlight lessons in each unit that showcase certain MPs. This chart identifies potential opportunities, in the text, to observe students engaging with the different MPs. Students also may exemplify MPs in activities not included here. Some units, due to their size or the nature of their content, have fewer predicted chances for students to engage in a particular MP, indicated in the chart by a dash. For Mathematical Practice 4 (MP4), the modeling prompts that correspond to each unit are indicated by an “M” in front of the number of the prompt.

Integrated Math 1	MP1	MP2	MP3	MP4	MP5	MP6	MP7	MP8
Unit 1 Lessons	4, 5, 8, 11, 12, 14, 18	-	2, 4, 5, 10–12	9   M1, M2	2–7, 9–14, 17–19	1, 2, 7, 9, 11, 12, 14, 16–19	2, 3, 5–7, 15, 17, 19	6
Unit 2 Lessons	4	10	1, 3, 5, 7–10	-	1, 2, 4, 6–9, 11	2, 4, 5, 7, 8	6, 9–10	4
Unit 3 Lessons	13, 16	1, 2, 4, 5, 11, 13–15	4, 11, 15	10, 14–16   M1, M2	2, 9, 10, 12, 16	1, 4, 5, 10, 12, 13, 15, 16	2–4, 7, 8, 10–12	6, 9, 11–12
Unit 4 Lessons	3, 5, 18	2–4, 6, 10–12, 15, 17	3, 7, 11, 14–16	1, 4, 9, 10, 12, 19   M3	1, 9, 11, 12, 15, 17	5, 7, 12, 17, 18	2, 3, 7, 11, 13, 17–19	2, 3, 8, 11, 19
Unit 5 Lessons	7, 11	11	4, 5, 8, 9	11	1, 2, 5, 6, 9, 10	7, 9	1–3, 5, 10	8
Unit 6 Lessons	1, 10	3–9	6–7	3, 4, 8–10   M4	2, 3, 10	1, 2, 4, 7	1, 3, 5–8	2
Unit 7 Lessons	2, 7–9	1–3, 6, 7, 9	-	1, 5, 9	7, 9	8	3, 4	4, 5
Unit 8 Lessons	1, 6, 12, 18, 20	2–11, 17, 18	8, 12	1, 7, 8, 11, 19, 20   M5, M6	5, 10, 13, 17, 20	2, 3, 6–9, 11, 16, 18	4, 9–11, 14	13, 14, 17
Unit 9 Lessons	3, 9, 24	2, 4, 5, 7, 10–14, 16, 17, 19, 20, 22	1, 3, 13, 15, 20, 22	4, 6, 7, 11, 12, 14, 19, 20, 24   M7	1, 3, 4, 7, 9, 11, 14, 15, 21, 24	1, 2, 5, 6, 11, 12, 16, 21, 24	2–4, 6, 8, 9, 17, 21, 23	5, 7, 8, 18, 22, 23

A list of opportunities to use particular MPs is never exhaustive. Some activities lend themselves to the use of a particular MP more than others, Rather than requiring use of the MPs, leave room to be surprised by how students use them to make sense of the mathematics, especially as students become more flexible in making their thinking visible.

How to Use the Mathematical Practices Chart

No single task is sufficient for assessing students’ engagement with the Standards for Mathematical Practice. Consider these options for assessing students:

• Provide students the list of learning targets to self-assess their use of the MPs.
• Assign students to create and maintain a portfolio of work that highlights their progress in using the MPs throughout the course.
• Monitor collaborative work, and note students’ engagement with the MPs.

Assess the MPs formatively, because students’ use of them is part of a process for engaging with mathematical content. For example, if most students do not use appropriate tools strategically (MP5), then in future lessons, plan to select and highlight work from students who have chosen different tools.

Since the MPs in action take many forms, a list of learning targets for each MP supports teachers and students in recognizing when engagement with a particular MP is happening. The intent of the list is not that students check off every item. Rather, the “I can” statements are examples of the types of actions possible when students engage with a particular MP.

Standards for Mathematical Practice Student-Facing Learning Targets

MP1 I Can Make Sense of Problems and Persevere in Solving Them

• ​​​​​I can ask questions to clarify the problem.
• I can restate the problem in a different way.
• I can keep working when I’m struggling, and try again.
• I can show at least one attempt to investigate or solve the problem.
• I can verify that my solution makes sense, in more than one way.

MP2 I Can Reason Abstractly and Quantitatively

• I can think about and represent numbers in many ways.
• I can define variables and constraints in a problem and connect the appropriate units to each.
• I can think about the meaning of the quantities in a problem as well as how to compute them.
• I can make connections between real-world situations and mathematical representations.

MP3 I Can Construct Viable Arguments and Critique the Reasoning of Others

• I can recognize the information that will contribute to an argument for a problem.
• I can explain my reasoning for why something is true.
• I can listen to and read the work of others and offer feedback to help clarify or improve their work.
• I can make conjectures and build a logical argument that supports a conclusion.

MP4 I Can Model with Mathematics​​​​​

• I can make assumptions and approximations to simplify a complicated situation.
• I can articulate the essential questions to answer in order to solve a problem.
• I can identify and collect or estimate unknown information needed to solve a problem.
• I can relate important quantities, using a mathematical model such as an equation, a table, or a graph.
• I can use a mathematical model to draw conclusions about a situation.
• I can interpret and report on the results of a model, in the context of the situation.
• I can refine or revise the model to more accurately describe the situation.
• I can explain the limitations of my model.

MP5 I Can Use Appropriate Tools Strategically

• I can select a tool that will help me make sense of a problem. These tools might include a protractor, a ruler, tiles, patty paper, a spreadsheet, a computer algebra system, dynamic geometry software, a calculator, a graph, a table, or external resources.
• I can use or experiment with tools to help explain my thinking.
• I can recognize when a tool is producing an unexpected result.
• I know how to use a variety of math tools to solve a problem.

MP6 I Can Attend to Precision

• I can use units or labels appropriately.
• I can communicate my reasoning, using mathematical vocabulary and symbols.
• I can state my assumptions while making a claim to help others understand my thinking.
• I can give an answer, with an appropriate degree of accuracy.

MP7 I Can Look for and Make Use of Structure​​​​

• I can connect problems I have solved to new problems.
• I can compose and decompose numbers, expressions, and figures to make sense of the parts and the whole.
• I can make connections between multiple mathematical representations.
• I can rewrite an expression as an equivalent form, modify a geometric figure, or identify a pattern to make what isn’t pictured visible.
• I can make use of structure to create a different representation to solve a problem.

MP8 I Can Look for and Express Regularity in Repeated Reasoning

• I can identify and describe patterns and regularities.
• I can notice what changes and what stays the same when performing calculations, examining graphs, or interacting with geometric figures.
• I can use patterns and regularities to express a general rule.