These math tasks can be used in algebra classrooms, but are also intended for teacher learning. We include varying amounts of detail for each task. In some cases, only the task is included, but some also contain keys, student work, or multiple documents that include explanations and connections to the mathematical practices and content standards of the SMP, or ways to use them in a PLC or in a large group of teachers.
This document provides a list of the tasks, their math content, and characteristics. It will be updated as more tasks are added to the site:
This task involves student reasoning about time and distance. For students, this task allows them to develop qualitative graphs reflective of their understanding of slope and drawing on their understanding of the Pythagorean Theorem and number sense (what is the meaning of 90 times the square root of 2?). The task requires them to apply SMP 1, 2, 3, 4, 5, and 6, with particular focus on SMP 2 as they decontextualize the context and contextualize the mathematics involved, and on SMP 6 as they use precision in communicating their reasoning and justifying the design of their graph. The activity employs focus and coherence as students delve deeply into their understanding of graphs and slopes, making sense of the problem through connections among multiple geometric concepts. The task can also be used as a formative assessment measure.
For PLCs, this activity has the potential to develop teachers’ MKT and PCK, as well as their understanding of the SMPs and CCSS meaning of focus and coherence. PLCs can also administer the task with students as a means of formative assessment for their classes and program.
Card Sort Equivalent Expressions: Exponents
This card sort contains cards that use rules of exponents and specifically has students confront misconceptions they may have about exponents. Although, the protocol has students sort without talking initially, students will also need time to discuss the reasons for the equivalent expressions. For students, this task draws on SMPs 3, 6, and 7, and emphasizes focus, coherence, and rigor, conceptual progressions, discourse. It can be used as classroom formative assessment. For PLCs, this task can be used as program formative assessment and can contribute to PCK. It can also be used as an introduction to a lesson and thereby part of lesson flow.
Seeing Structure Card Sort
This task engages either students or teachers in changing and comparing forms of a quadratic expression. It can be used to group students or teachers and targets SMP 3 as learners explain and listen to reasoning and SMP 7 as they examine the structures of the expressions. The directions and questions are on the first page and the cards are on the last four pages.
David and Shanna
For students, this task engages them in reasoning about exponential growth and decay (Content Standards F-BF.1a, F-LE.1, and A-SSE.1) and draws on SMP 2, 7 and 8. It can be used for formative assessment purposes and for conceptual progressions. The Representations activity helps students to develop focus, coherence, and rigor in their understanding, and supports seeing structure.
For PLCs, this task can build MKT, PCK, understanding of CP and SMPs, and can be used in an activity of connecting tasks to TPEP criteria, cognitive complexity, and the SMPs.
Equivalent Equations Card Sort and Student Work
In this task for students or PLCs, participants are asked to determine which equations are equivalent. A follow-up activity engages participants in evaluating possible answers and identifying misconceptions associated with incorrect answers while engaging in SMP 3.
This task has students compare linear, exponential, and quadratic growth in a context.
This task addresses F-IF.9 directly. It is also a good task for teachers to work on in a PLC and discuss. The supporting documents provide responses from teachers in the RAMP-A project, and from students so that teachers can discuss student thinking and ways they can support students’ thinking about rates of change and the graphs of the functions
Linear, Exponential, or Quadratic Card Sort
This card sort involves multiple representations and questions for students that has them distinguish among linear, exponential, and quadratic functions, while justifying their reasoning.
This rich task can be used to help students see structure in expressions and build equations that model linear and quadratic growth, so target standards from A-SSE and A-CED, and SMP 2, 3, and 7. The facilitation notes are for use in professional development with teachers, but will also provide ideas for use with students.
Like Urban Sprawl, this task has students notice and represent structure symbolically and graphically from a pattern. Students use SMP 1, 3, 7 and 8. This task was used in a prior MSP project, the Mathematics Content Collaboration Communities.
Another pattern task like Urban Sprawl and Staircase. Students use SMP 1, 3, 7, and 8 to solve the problem.
Win Some Cash! and Motorcycle Race
The two tasks below have students compare linear, exponential, and quadratic functions given as equations and, in Motorcycle Race, compare functions given graphically. Win Some Cash! is an adaptation by one of our teachers of a task we presented in a workshop. Both are good tasks for teachers to work in their PLCs and discuss, have their students work, then bring student work to discuss.
Derby on Marco Hill
This task was written by Peer Teacher, Scott Cooley, and presented in the last workshop. Scott uses it on the first day of Algebra 1 to help students better understand how they will be expected to learn in his class.
Algebraic Reasoning Carousel
This activity consists of a Carousel and can be used either with teachers or students. The goal for teachers it to examine several reasoning problems that can be done in Algebra 1, notice the SMP used, and discuss how to support students’ development of SMPs while doing them. For students, the goal can be similar: after they solve the problems, facilitate discussion about how they used the SMP.
Rotating Triangles and Lines
The goal of this task is to help students logically conclude that the slopes of perpendicular lines are opposite reciprocals. While doing the task, students engage in several SMP: Construct viable arguments and critique the reasoning of others, Look for and make use of structure, and Use appropriate tools strategically.
Systems From Sequences
This task involves students creating their own systems of linear equations to solve and looking for patterns. The mathematics includes understanding arithmetic sequences and solving systems of linear equations. It provides an opportunity for students to engage in and reflect on SMP 1, 2, 3, 7, and 8.
A Comparison Number Game
This task involves students exploring a quadratic situation. They may use SMP 1, 2, 3, 5, 6, 7, and 8. An activity under SMP at this site provides an activity for teachers to consider ways to improve students’ engagement in the practices as they solve this task.
This RAMP-A activity was also presented at the 2013 Northwest Mathematics Conference. The goal of the activity is to give teachers an opportunity to examine student work on a task to determine potential use of SMP and discuss ways to prompt students to use higher levels of the SMP. The task itself could be used in an Algebra 1 class before quadratics are introduced. Teachers could use the task in their classrooms after this activity and practice supporting higher level use of the SMP
A Fair Price?
In this task involving percents, students are given a situation without the numbers. It requires them to see structure in the situation, reason abstractly and quantitatively, and justify their reasoning. They may also engage in SMP 8: look for and express regularity in repeated reasoning.
This is a sequence of tasks involving the graph of a parabola. Students are asked to make conjectures and justify them, using SMP 1, 3, and 7.
This is a rich task we did in the workshop by imagining what students would do, first representing the problem in as many ways as we could (without trying to solve the problem), then writing relationships we saw. We used a monitoring sheet to look at others’ work and think of questions we could ask students, and finally, selecting, sequencing, and connecting to think about how we could plan a lesson with the task.