Mathematics

We help teachers, coaches, and administrators to define and work towards a common vision of what it means to know, learn, and teach mathematics.

We provide teachers with the knowledge and tools to engage all students in rigorous mathematics instruction and implement the kinds of cognitively demanding tasks that are called for by the National Council of Teachers of Mathematics and 21st century standards.

We understand the power of shared experiences. We ask participants to implement common tasks, lessons, or units with their students and bring back artifacts of practice for discussion, reflection, and further planning.

Professional Development

Shapes discussion elementary girls

Our professional development courses help mathematics educators

  • Select cognitively demanding tasks that are consistent with 21stcentury standards
  • Modify tasks to increase the cognitive demand
  • Engage students in cognitively demanding tasks in ways that maintain the cognitive demand
  • Use targeted questions to assess and advance student learning so that all students have the opportunity to advance in their thinking
  • Engage students in discussions to make sense of mathematical concepts and make connections between and among mathematical representations in order to form mathematical generalizations
  • Use quick writes to formatively assess student growth
  • Study student work to identify what students know and can do and determine instructional next steps

Supporting Ongoing Achievement Responsively

Mathematics materials
SOAR tools and activities are designed to identify and support students' mathematical understanding that is in need of further inquiry and development

SOAR Survey Tools

The survey tools are comprised of three parts: a set of survey questions, a monitoring checklist, and a tiered survey summary. The survey can be used as a stand-alone tool or as a follow-up to universal screeners that give only broad areas of need. Teachers gain valuable data on their students' ability to make send of, represent, solve, and explain mathematical concepts.

SOAR Activities

The intervention activities are designed and sequenced to support students across tiers of intervention. These activities are aligned to the survey tool and are designed to support student learning in making sense, creating and using representations, using strategies, and providing explanations. Each activity has teacher facing materials that outline the mathematical foci, identify the essential mathematical understandings, as well as provide questions to target those understandings.

SOAR tools and activities are available for the following concepts:

  • Adding and Subtracting Situation Problems (Grades 1-3)
  • Multiplication and Division of Situation Problems (Grades 3-5)
  • Fractions as Numbers and Operating with Fractions (Grades 3-5)
  • Ratios and Proportional Relationships (Grades 6-8)
  • Expressions and Equations (Grades 6-8)
  Download SOAR Workshop flyer Register for a SOAR Workshop

Instructional Materials

Our professional development courses range from short, targeted workshops to courses that are embedded in multi-year school, district, or state partnerships. Our courses are most effective when teachers work side-by-side with professionals who support classroom instruction, such as coaches, administrators, and central office educators. Additional courses are available for leaders to support mathematics teaching and learning.

The IFL's Sets of Related Lessons include eight high-level tasks designed around key mathematics concept, and accompanying lesson guides. Sets of Related Lessons can be strategically integrated into existing curricula.

A Set of Related Lessons has two types of tasks: developing understanding tasks and solidifying understanding tasks. Tasks are sequenced to provide students with opportunities to investigate concepts and skills in a coherent way. First, to make discoveries and then to form mathematical generalizations related to the concepts under study.

Math SOAR bookletsSets of Related Lessons include:

  • an outline of the concepts students will study;
  • an articulation of strategies and representations for students to learn and/or use;
  • multiple and varied forms of formative assessment, including opportunities for students to write about their mathematical understanding; and
  • structures and routines to support students' engagement with tasks, including information about:
    • setting up the task so students have an entry point;
    • supporting students in exploring the mathematical ideas developed in the task both individually and in small groups; and
    • engaging students in teacher-orchestrated discussions to deepen and solidify their understanding of the key mathematical ideas.

A unique aspect of the Sets of Related Lessons is the identification of essential understandings (EUs)-underlying mathematical truths-within the lessons. EUs drive the sequence of the solution paths and the discussion questions outlined in the lesson guides.

The IFL also offers performance-based assessments (PBAs) to assess students' learning of concepts and practices in specific Sets of Related Lessons. Sets of Related Lessons with associated PBAs are marked with an asterisk (*).

Visit our store ShopIFL

Performance Based Assessments

The IFL's math performance-based assessments (PBAs) are comprised of an open-ended, high-level tasks designed to assess students' learning of Standards for Mathematical Content and Standards for Mathematical Practice as outlined in the Common Core State Standards. PBAs require students to apply what they have learned related to a CCSS concept or domain.

The IFL math PBAs can be flexibly inserted into existing curricula, or they can be used in conjunction with the IFL's Sets of Related Lessons. Because the IFL's PBAs assess students' learning of concepts and practices specific to IFL math Sets of Related Lessons, assessments can be used strategically during the implementation to make sure learning is on target. Each PBA comes with a scoring guide and annotated student work. PBAs that are related to a Set of Related Lessons are indicated in the description. View the PBAs in Mathematics.