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 21^{st} 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
 Select cognitively demanding tasks that are consistent with 21^{st}century 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
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 standalone tool or as a followup 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 13)
 Multiplication and Division of Situation Problems (Grades 35)
 Fractions as Numbers and Operating with Fractions (Grades 35)
 Ratios and Proportional Relationships (Grades 68)
 Expressions and Equations (Grades 68)
INSTRUCTIONAL MATERIALS
Our professional development courses range from short, targeted workshops to courses that are embedded in multiyear school, district, or state partnerships. Our courses are most effective when teachers work sidebyside 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 highlevel 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.
Sets 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 teacherorchestrated 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 performancebased 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 (*).
Sets of Related Lessons
Elementary (K5)
Grade, Focus & Title  Description 

Addition Situations: Solving for the Sum Grade K PURCHASE  This set of related lessons is designed to provide students with multiple opportunities to explore the concepts related to counting and cardinality. Students will

"Add to" Situations: Unknowns in All Positions* Grade 1 PURCHASE  This lesson set provides a study of "adding to" situations that explore solving for unknowns in all positions (whole, change, start). Students will:

The Relationship Between Addition and Subtraction* Grade 1 PURCHASE  This lesson set provides an indepth study of partpartwhole relationships as represented in "take from" and "take apart" situations and subtraction equations. Students will:

Put Together and Compare Situations* Grade 2 PURCHASE  This lesson set provides a study of story situations that explore the partpartwhole relationship, and through it also, the relationship between subtraction and addition with an unknown addend. Students will:

Addition Strategies and Flexible Thinking* Grade 2 PURCHASE  This set of related lessons provides students with an opportunity to develop a deep understanding of addition with twodigit numbers while providing a bridge into addition with threedigit numbers. Students will:

A Focus on Compare Situations Grade 2 PURCHASE  This set of related lessons provides students with an opportunity to grapple with the relationship between subtraction and missing addend addition when using both operations to solve compare situations with an unknown difference. A variety of contexts provide opportunities for students to compare sets of items, heights, lengths, and distances traveled. Students will:

Measurement: Solving for Area of Figures Grade 3 PURCHASE  This set of related lessons provides students with a study of area measurement. Students will learn the meaning of area by tiling figures with square tiles of various sizes and solve for the unknowns in all positions (the area or the unknown length or width). Students will:

Understanding the Associative and Distributive Properties of Multiplication Second Edition * Grade 3 PURCHASE  This lesson set provides a study of the associative and distributive properties of multiplication. Students will:

Comparing Fractions with Common Denominators or Common Numerators* Grade 3 PURCHASE  This lesson set is designed to provide students opportunities to compare and reason about the comparison of fractions with either common denominators or common numerators. Students will:

Exploring Multiplicative Comparisons* Grade 4 PURCHASE  This lesson set provides a study of multiplicative comparisons, problems in which students have to solve for "how many times greater/less." Students will:

Fractions: Relating Repeated Addition to Multiplication* Grade 4 PURCHASE  This set of related lessons provides students with an introduction to addition and subtraction of fractions with like denominators in the same whole. Students will:

Writing and Comparing Decimal Numbers* Grade 4 PURCHASE  This lesson set develops understanding of the relationship between fractions and decimals, decimal number notation and addition, as well as comparison of decimal numbers. Students will:

Addition and Subtraction of Fractions with Unlike Denominators Grade 5 PURCHASE  This lesson set provides students an introduction to fraction addition and subtraction when the denominators of fractions differ; students are given problems in which they have to consider different names for fractions relative to a samesized whole in order to create samesized units to combine or separate quantities. Students will:

Multiplication with Fractions: Finding Portions of Numbers* Grade 5 PURCHASE  This lesson set provides students with a study of multiplication when one or both factors are fractions. Students apply the meaning of factors to numbers less than 1 using visual representations. Students will:

Dividing Fractions: Understanding Division with Numbers Less than 1* Grade 5 PURCHASE  This lesson set provides an introduction to division with numbers less than one, both when the whole number amount is being divided by less than one and when the fraction is being partitioned by a whole number. Students will:

Decimal Operations: Multiplication and Division* Grade 5 PURCHASE  This lesson set provides an introduction to decimal multiplication and division problems in which students have to consider how many groups of a fixed size comprise a total. Students will:

Middle (68)
Grade, Focus & Title  Description 

Integers: Equivalent Expressions* Grade 6 PURCHASE 
This lesson set provides students with an introduction to the equivalence of expressions and to generating equivalent expressions. Students will:
Approximately 815 days of instruction. 
Solving OneVariable Equations and Inequalities* Grade 6 PURCHASE 
This lesson set provides an introduction to onevariable equations and inequalities. The set of lessons allows students to work on writing and solving onevariable equations then transition from equations to inequalities. Students will:
Approximately 815 days of instruction. 
Ratios: A Focus on PartPart and PartWhole Relationships Grade 6 PURCHASE 
Learning to reason proportionally is one of the key mathematical studies of the middle school grades. In this lesson set for grade 6, students use a variety of representations to explore ratio thinking. Students will:
Approximately 815 days of instruction. 
Proportional Relationships Second Edition* Grade 7 PURCHASE 
This lesson set provides a study of Proportional Relationships. Students will learn to move from the grade 6 study of ratios and equations of the form px = q to the study of proportional relationships. They combine their previous understanding of the topics of both ratio and equation to examine tests that establish or refute the presence of a proportional relationship between two variables. Students will:
Approximately 815 days of instruction. 
Solving Linear Equations in OneVariable* Grade 8 PURCHASE 
This lesson set provides students with the opportunity to write and solve linear equations in one variable, focusing particular attention on what it means for a value to be in the solution set of a linear equation in one variable. Students will:
Approximately 815 days of instruction. 
Understanding and Solving Systems of Linear Equations* Grade 8 PURCHASE 
This lesson set provides the opportunity for students to extend their previous understanding of linear equations to include systems of linear equations. Students will:
Approximately 815 days of instruction

Understanding Congruence and Similarity* Grade 8 PURCHASE 
This lesson set provides the opportunity for students to explore congruence and similarity as a result of transformations in the plane. Students will:
Approximately 815 days of instruction. 
Algebra I, Algebra II, and Geometry
Grade, Focus & Title  Description 

Creating and Interpreting Functions* Algebra I PURCHASE  This set of related lessons provides the opportunity for students to create and integrate functions, rate of change, and average rate of change of the function. Students will

Developing and Understanding Quadratics* Algebra 1 PURCHASE  This set of related lessons examines the graphs of quadratic functions and differentiates characteristics of quadratic functions from those of linear functions. Students will

Solving Problems Using Linear and Exponential Models Algebra I PURCHASE  This set of related lessons provides students the opportunity to extend their previous understanding of functions to include exponential functions. Students will

Building Polynomial Functions Algebra II PURCHASE  This set of related lessons provides students the opportunity to use arithmetic to combine polynomial functions and explore the relationship between the original and new functions. Students will

Investigating Rational Exponents Algebra II PURCHASE  This set of related lessons provides students the opportunity to investigate the characteristics of expressions and equations with rational exponents. Students will

Reasoning with Rational Equations Algebra II Coming Soon  COMING SOON! 
Investigating Coordinate Geometry and Its Use in Solving Mathematical Problems Geometry PURCHASE  This set of related lessons provides students the opportunity to explore coordinate geometry as a mechanism for proving simple geometric theorems and solving problems. Students will

Investigating Congruence in Terms of Rigid Motion Geometry PURCHASE  This set of related lessons provides students the opportunity to formalize their understanding of the rigid motions: translation, rotation, and reflection. Students will

Trigonometric Ratios: Solving the Mystery of Similar Right Triangles Geometry Coming Soon  COMING SOON! 
PERFORMANCE BASED ASSESSMENTS
The IFL's math performancebased assessments (PBAs) are comprised of an openended, highlevel 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.