Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for the Interactive Mathematics Program series partially meet expectations for alignment to the CCSSM for high school. For focus and coherence, the series showed strength in making meaningful connections in a single course and throughout the series. For rigor and the mathematical practices, the series showed strengths in the following areas: supporting the intentional development of students' conceptual understanding, utilizing mathematical concepts and skills in engaging applications, displaying a balance among the three aspects of rigor, supporting the intentional development of reasoning and explaining, and supporting the intentional development of seeing structure and generalizing. Since the materials partially meet the expectations for Gateways 1 and 2, evidence for usability in Gateway 3 was not collected.

See Rating Scale
Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
10
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
9
14
16
12
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

0
21
30
36
0
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Partially Meets Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
10/18
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Criterion Rating Details

The instructional materials reviewed for the Interactive Mathematics Program series partially meet expectations for focusing on the non-plus standards of the CCSSM and exhibiting coherence within and across courses that is consistent with a logical structure of mathematics. Overall, the instructional materials partially attend to the full intent of the mathematical content contained in the high school standards for all students and partially let students fully learn each non-plus standard. The instructional materials partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards, and they do not spend the majority of time on the CCSSM widely applicable as prerequisites (WAPs). The instructional materials make meaningful connections in a single course and throughout the series, and although the materials regularly use age-appropriate contexts and apply key takeaways from Grades 6-8, they do not vary the types of numbers being used. The materials do not explicitly identify Grade 6-8 standards when addressed in the materials, but there is some evidence that the materials build on knowledge from Grades 6-8 Standards to the high school standards.

Indicator 1a

The materials focus on the high school standards.*
0/0

Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
2/4
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Indicator Rating Details

The instructional materials reviewed for the Interactive Mathematics Program series partially meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. The instructional materials include many instances where all or some aspects of the non-plus standards are not addressed across the courses of the series.

The following standards have at least one aspect of the standard that is not addressed across the series.

  • A-REI.3: Students solve linear equations and inequalities in one variable in Year 1, The Overland Trail, Reaching the Unknown, pages 82, 92, 95-96 as well as in Year 1, Cookies, Cookies and Inequalities, pages 347 and 349; and Year 1, Cookies, Points of Unknown, page 382, but there are no opportunities to solve equations with coefficients represented by letters.
  • G-CO.13: Students construct equilateral triangles, squares, and regular hexagons in Year 2, Geometry by Design, Do It Like the Ancients, page 91, Construction and Deduction, page 123, and Supplemental Activities, page 178, but they do not construct these shapes inscribed in a circle.
  • G-C.3: The materials describe the constructions for the inscribed and circumscribed circles of triangles in Year 3, Orchard Hideout, Supplemental Activities, pages 167-168, but the materials do not include proofs of properties of angles for a quadrilateral inscribed in a circle.
  • S-ID.3: Students interpret differences in the shape, center, and spread of data sets without outliers in several of The Pit and the Pendulum tasks but do not have an opportunity to do so for data sets with outliers.
  • S-IC.5: Students conduct experiments and use simulations in several tasks of Year 1, The Pit and the Pendulum, but do not compare two treatments.
  • S-CP.2: Students find the probability of independent and dependent events in contextual tasks in Year 2, The Game of Pig, Pictures of Probability, page 215 and Year 2, The Game of Pig, In the Long Run, page 219 using area models and tree diagrams. However, no formal definition of independence is included and the products of probabilities are not used to determine if an event is independent.
  • S-CP.4: Students construct two-way tables for numerous contextual tasks in Year 3, A Difference Investigation, but there is no opportunity to determine if events are independent using two-way tables.

The following standards were not addressed across the courses of the series:

  • F-IF.9: Tasks include a single function represented in different ways and two functions represented in the same way, but none compare properties of two functions represented in different ways.
  • G-CO.6: There are no opportunities to use the definition of congruence in terms of rigid motions to decide if two figures are congruent.
  • G-CO.7: There are no opportunities to use the definition of congruence in terms of rigid motions to show that two triangles are congruent.
  • G-CO.8: There are no opportunities to explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions.
  • G-SRT.2: Transformations are not used in relation to similarity.
  • G-SRT.3: Although students use the AA criterion to identify the similarity of two triangles, transformations are not used in relation to the AA criterion.
  • G-GPE.7: Tasks include finding the perimeters of polygons and areas of triangles and rectangles, but the figures are not plotted on the coordinate plane.

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
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Indicator Rating Details

The instructional materials reviewed for the Interactive Mathematics Program series partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. Throughout the series, aspects of the modeling process are present in isolation or combinations, but the full intent of the modeling process is not used to address more than a few of the modeling standards.

Throughout the series, students complete open-ended problems that include defining the variables and selecting methods for solving the problems, but the problems do not ensure that the entire modeling process will occur. Some problems provide significant scaffolding and guidance, which diminishes students’ opportunities to make choices, assumptions, and approximations. Many Problems of the Week (POWs) offer opportunities to formulate models, interpret results, validate conclusions, and report on conclusions, but there are few opportunities for students to improve their first model.

Some examples of standards for which the modeling process is incomplete are:

  • N-Q.1: In Year 1, Overland Trail, The Graph Tells a Story, pages 45-50, students use graphs to describe the relationship between two quantities and supply reasonable units on the axes for such relationships, but the tasks include guiding questions that help students make sense of the relationships rather than having students make their own assumptions.
  • A-SSE.3: In Year 1, Overland Trail, Reaching the Unknown, page 79, students are given the variables to use. Students write their own equation in two variables, solve the equation for one of the variables, graph the solved equation, and use the graph to determine multiple solution possibilities.
  • A-SSE.4: In Year 2, Small World, Isn’t It?, Supplemental Activities, pages 474-475, students are given a definition for a geometric sequence but are not given the term or sum formulas. Students are told to use the variable n to write a term and sum expression following the steps given. Students are told to use and to apply the formulas to “check” with specific terms of the sequence.
  • A-CED.1: In Year 2, Fireworks, A Quadratic Rocket, pages 6-7, students answer questions about population growth for rats using a process they devise. In addition to giving their answer and describing their solution process, students describe attempts that did not work and evaluate how confident they are in the correctness of their answer. Students do not, however, make and test their own assumptions or decide if the results are acceptable.
  • A-REI.11: In Year 4, Meadows or Malls?, Equations, Points, Lines, and Planes, page 33, students write constraints for a system of linear equations based on a cookie-selling scenario, and they represent the given situation with inequalities. In Equations, Points, Lines, and Planes, page 36, students write and solve systems of linear equations for given word problems, but they are told to use substitution to solve.
  • F-IF.4: In Year 3, World of Functions, The What and Why of Functions, page 320, students model and analyze situations involving profit and tickets sold, but they are told to formulate the problem as graphs. In Year 3, World of Functions, Tables, pages 325-334, students model linear, quadratic, cubic, and exponential functions, but are told to use tables.
  • F-BF.1a: In Year 1, The Overland Trail, Reaching the Unknown, pages 81-82, students write functions to model weekly pay rates and time for shifts, choosing rates and checking their functions with the given criteria, but are led through steps for using graphs, words, and equations.
  • F-LE.1c, 2: In Year 1, All About Alice, Who’s Alice?, pages 422-423, students explore exponential growth and decay, as well as give and explain a rule that models a situation from Alice’s Adventures in Wonderland, but the variables are defined for them.
  • S-ID.6a: In Year 1, The Pit and the Pendulum, pages 142-145, 152, and 203, students gather data from an experiment using a pendulum and then graph, analyze, and find a function that fits the data, but the process is scaffolded for students throughout the activities by the information provided and questions asked within the materials.

Examples of tasks that utilize the full modeling process but do not address non-plus standards from the CCSSM include:

  • In Year 1, The Pit and Pendulum, Statistics and the Pendulum, pages 174-175, students use a pan balance to find the lightest of eight bags of gold, weighing them as few times as possible. This POW does not align to any standards from the CCSSM.
  • In Year 3, Pennant Fever, Play Ball, pages 6-8, students determine on which day of the week a person was born given the date the person was born. This POW does not align to any standards from the CCSSM.

Indicator 1b

The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
0/0

Indicator 1b.i

The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.
1/2
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Indicator Rating Details

The instructional materials reviewed for the Interactive Mathematics Program series partially meet expectations, when used as designed, for spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs, and careers. The instructional materials for the series do not spend a majority of time on the WAPs, and some of the remaining materials address prerequisite or additional topics that are distracting.

The publisher-provided alignment document indicates that each course of the series addresses these standards less frequently as the series progresses. Similarly, in examining each activity of the course independently of the alignment document, reviewers verified the greatest focus on the WAPs is in Years 1 and 2, with less attention to these standards as the series progresses. Overall, the majority of the time across the series is not spent on the WAP standards, and examination of the publisher-provided pacing guide indicated similar findings.

While many of the topics below relate to content in the series, they are distracting topics from the WAPs as either being prerequisite, plus standards, or additional topics that are not a part of the CCSS for high school mathematics. Examples of this include:

  • In Year 1, The Overland Trail focuses on understanding functions (8.F.1) rather than tasks for the related high school standard, F-IF.1 (function notation, domain, and range).
  • In Year 1, the majority of Shadows addresses unit rates (7.RP.1) and proportional relationships (7.RP.2).
  • In Year 2, Do Bees Build It Best?, Area, Geoboards, and Trigonometry, pages 291-299, students spend a majority of the time on tasks involving area, triangles, and geoboards (6.G.1).
  • Year 2, The Game of Pig, Pictures of Probability, pages 209-217 addresses probability (7.SP.C) through area models.
  • In Year 2, Small World, Isn’t it: Beyond Linearity, Speeds, Rates, and Derivatives, page 421, students solve derivatives of functions at given points. This is a topic that does not align to any of the CCSSM.
  • Year 3, Is There Really a Difference?, A Tool for Measuring Differences, pages 460-475 focuses on statistical analyses including chi-square. This is a topic that does not align to any of the CCSSM.
  • In Year 3, Pennant Fever, students use combinatorics (S-CP.9) to develop the binomial distribution (A-APR.5) and find the probability that the team leading in the pennant race will ultimately win the pennant, addressing topics that are not widely-applicable prerequisites for postsecondary work. These are plus standards.

Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.
2/4
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Indicator Rating Details

The instructional materials reviewed for Interactive Mathematics Program series partially meet expectations for letting students fully learn each non-plus standard when used as designed. The following standards are addressed in a way that provides limited opportunities for students to fully learn these standards.

  • N-RN.1: The reviewers found minimal evidence for denoting radicals in terms of rational exponents: Year 1, All About Alice, Curiouser and Curiouser!, pages 442, 443, 449, and 476.
  • N-CN.2: One task (Year 3, High Dive, A Falling Start, page 262, Exercise 3) includes use of the relation i2 = -1 to evaluate higher powers of i and one task that includes addition of complex numbers (Year 3, High Dive, Complex Components, Exercise 3) but no tasks that include subtraction of complex numbers.
  • A-SSE.3c: The reviewers found no tasks related to using the properties of exponents to transform expressions for exponential functions.
  • A-SSE.4: Students derive the formula for the sum of a finite geometric series (Year 1, All About Alice, Supplemental Activities, page 466-467), but reviewers found two tasks that involve using the formula to solve problems: Year 1, All About Alice, Supplemental Activities, pages 466-467 and Year 2, Small World, Isn’t It?, pages 474-475.
  • A-APR.1: Properties of polynomials are described in Year 2, Fireworks, Intercepts and Factoring, page 54, but no tasks address understanding that polynomials form a system that is closed under addition, subtraction, and multiplication.
  • A-APR.3: Students factor quadratics and find x-intercepts in Year 2, Fireworks, Supplemental Activities, pages 75 and 77, but the x-intercepts are not used to draw graphs.
  • A-APR.4: The reviewers found limited opportunities for working with polynomial identities: Year 2, Fireworks, Supplemental Activities, page 74 and Year 3, The World of Functions, Supplemental Activities, pages 417, 421-422.
  • A-APR.6: Students divide polynomial expressions in Year 3, The World of Functions, Supplemental Activities, pages 418-420, but the expression is not presented as a rational function in the form a(x)/b(x).
  • A-REI.4b: In Year 2, Fireworks: Supplemental Activities, page 70, students use the quadratic formula to find x-intercepts of a quadratic equation and compare the number of x-intercepts to the discriminant, but no other problems were found where students recognize when the quadratic formula gives complex solutions and when it doesn’t. The quadratic formula is used to find complex solutions and write them in the form of a + bi for a few exercises in Year 3, High Dive: A Falling Start, page 262.
  • F-IF.7e: In Algebra 1, Supplemental Activity: The Growth of Westville (page 128) and various activities in All About Alice, students graph exponential and logarithmic functions; however, there is little emphasis on intercepts and end behavior.
  • F-BF.2: Students work with arithmetic and geometric sequences recursively and with explicit formulas (Year 1, All About Alice, Supplemental Activities, pages 466-467; Year 2, Small World, Isn’t It?, All in a Row, page 408 and Supplemental Activities, pages 472 and 474; Year 3, High Dive, A Trigonometric Interlude, pages 249-251) but do not translate between the two forms.
  • F-TF.8: Year 3, High Dive, A Trigonometric Interlude, page 242 includes the derivation of the Pythagorean identity, but the reviewers found no tasks addressing use of the Pythagorean identity to calculate trigonometric ratios outside of the first quadrant.
  • G-C.1: Year 2, Geometry by Design, Putting the Pieces together, pages 166-167 notes that all circles are similar but does not include a proof.
  • G-GPE.6: Students find midpoints in Orchard Hideout, Coordinates and Distance, pages 111 but do not partition line segments in other ratios.
  • S-ID.2: Students compare the spread of two data sets in Year 1, The Pit and the Pendulum, Statistics and the Pendulum, pages 163 and 170, but reviewers found limited practice comparing the center of two or more different data sets.
  • S-CP.3: Although students engage in problems related to conditional probability in Year 2, The Game of Pig, In the Long Run, page 225, students do not interpret the independence of events by calculating conditional probabilities.

Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
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Indicator Rating Details

The instructional materials reviewed for Interactive Mathematics Program series partially meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. Tasks are set in relevant contexts and address numerous key takeaways from Grades 6-8, but the materials do not vary the types of real numbers being used.

Scenarios and situations presented are appropriate for high school students and address a variety of interests. For example, the series uses historical scenarios (Overland Trail), literature (Pit & Pendulum, Alice in Wonderland), games (Pig, Pennant Fever) and societal issues (Small World) to engage students.

Key takeaways from Grades 6-8 are addressed. For example:

  • In Year 1, Shadows, Triangles Galore, pages 280-281, students use ratios and proportional relationships (6.RP.A, 7.RP.A, 8.EE.B) to convert recipes, calculate fuel mileage, and plan a dance.
  • In Year 2, Supplemental Activities, Above and Below the Middle, pages 244-246, students build on knowledge of mean and median (6.SP.5c) to analyze results and determine outcomes of rolling a pair of dice until doubles appear.
  • Year 3, The World Of Functions builds on functions (8.F) which is a key takeaway from middle school. Students build on in and out tables and linear functions having features such as “equal spacing” to quadratics, exponential, and cubic tables to examine their spacing and rates of change.

Most problems, however, include only integer values. Students have limited opportunities to work with fractions and decimals. For example:

  • In Year 1, The Graph Tells a Story, page 53, students solve five one-variable equations in which all constants and coefficients are integers, and all solutions are integers.
  • In Year 2, Fireworks, The Form of It All, page 27, completing the square problems is limited to integer values for constants and coefficients.
  • In Year 3, Orchard Hideout, Coordinates and Distance, page 108, students solve problems involving circles on the coordinate plane, but the coordinates contain only integer values.

Indicator 1d

The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for Interactive Mathematics Program series meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. Being an integrated series, major domains, such as Geometry, Algebra, and Functions, are connected throughout the series. Coherence for each unit is built around a unit task, and activities are clearly related in an intentional sequence to support the mathematics of the unit. In some instances, course materials refer to previous units or activities across courses.

Each unit is set in a particular context, such as Year 2, Fireworks which connects quadratic functions and equations to sending up a rocket to create a fireworks display. This feature of the materials makes meaningful connections among topics within each unit as students work to solve the main problem of the unit. In addition, tasks frequently refer back to previous units. For example, Year 3, Pennant Fever, Trees and Baseball, page 12 refers to the use of tree diagrams in Year 2 before beginning a series of tasks about combinatorics and probability.

Examples of meaningful connections within courses include:

  • Year 1: In The Overland Trail, Reaching the Unknown, page 85, students create linear equations in two variables and graph them using a set of values (A-CED.2). In The Pit and The Pendulum, Measuring and Predicting, page 203, students build upon the work from The Overland Trail and create a linear equation in two variables from data they collected (S-ID.6a). Students also create linear equations in two variables and graph in several of the Cookies tasks, including Cookies and the University, A Charity Rock, page 391.
  • Year 2: In Geometry by Design, Isometric Transformations, pages 140-141, students reflect lines over the x-axis, y-axis, and y = x and write the equation of the reflected line (G-GPE.5). Students use this knowledge in Small World, Isn’t It?, Supplemental Activities, page 466 to predict if lines are parallel and investigate lines that are not in the “y =” form to determine if two lines in standard form are parallel.
  • Year 3: In Orchard Hideout: Cable Complications, pages 137-139, students complete the square to find equivalent forms of circles to identify the center and radius of a circle (G-GPE.1). Completing the square is also used to derive the quadratic formula in High Dive: A Falling Start, page 258, and students use the quadratic formula to solve equations (A-REI.4).

Examples of meaningful connections across courses include:

  • F-IF.6 is connected throughout all four courses. In Year 1, The Overland Trail: Traveling at a Constant Rate, pages 74-75, rates are found within real-world contexts, and students write equations using the rates. In Year 2, students further explore average rates in Small World, Isn’t It?, As the World Grows, pages 389-390, by comparing average growth rates in real-world contexts. In Year 3, High Dive: Falling, Falling, Falling, pages 214-215, students find average rates in the context of speed. Lastly, in Year 4, How Much? How Fast?: Rate and Accumulation, pages 255-256, students examine a graph showing the distance a car travels (measured in miles) as a function of time (measured in minutes), and the same graph also shows that the car does not travel at a constant speed for the duration of the trip. Students create a graph that reflects the speed being traveled as a function of time for each segment of the trip.
  • S-ID.6-8: In Year 1, The Overland Trail: Traveling at a Constant Rate, pages 66-68, students find rates and/or interpret them in the real-world context. Also in Year 1, The Pit and the Pendulum: Supplemental Activities, page 213, students are introduced to the idea of correlation coefficient and interpret the meaning of it using a data set. In Year 2, The Game of Pig: Chance and Strategy, page 205, students explore causation.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
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Indicator Rating Details

The instructional materials reviewed for Interactive Mathematics Program series partially meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. The instructional materials do not explicitly identify content from Grades 6-8, but the materials include and build on content from Grades 6-8.

Neither the teacher nor the student materials explicitly identify content aligned to standards from Grades 6-8. Examples of tasks that build on standards from Grades 6-8 to the high school standards that do not identify the standards from Grades 6-8 include:

  • In Year 1, The Overland Trail, Reaching the Unknown, pages 91-93 and 95, students solve equations in one variable (8.EE.7) and explain their solutions (A-REI.1).
  • Year 1, The Pit and the Pendulum, Edgar Allan Poe--Master of Suspense, page 149 connects the mean of a set of data (6.SP.5) with dot plots (S-ID.1).
  • In Year 2, Fireworks, Putting Quadratics to Use, page 34, students use the Pythagorean Theorem (8.G.7) to write a quadratic equation (A-CED.2).
  • In Year 2, Geometry by Design, Isometric Transformations, page 142, students rotate shapes onto themselves (G-CO.3) and state that the new image is the exact same as the original (8.G.2).
  • Year 3, Orchard Hideout, Equidistant Points and Lines, page 113 connects finding the distance between two points in a coordinate system (8.G.8) and using coordinates to determine what type of quadrilateral a figure is (G-GPE.4).
  • In Year 3, High Dive, Sand Castles, page 208, students graph and interpret trigonometric functions (F-IF.7e) and identify inputs and their corresponding outputs (8.F.1) to make sense of a context.

Indicator 1f

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.
0/0
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Indicator Rating Details

Generally, the instructional materials reviewed for Interactive Mathematics Program series explicitly identify the plus standards in the teacher materials but not in the student materials. Plus standards coherently support the mathematics which all students should study in order to be college and career ready. Tasks addressing plus standards are generally integrated into the units seamlessly, so they could not be omitted easily without interfering with the flow of the content within the series.

The following plus standards are fully addressed:

  • N-CN.3: This standard is not explicitly identified by the publisher, but the reviewers found evidence of this standard in Year 3, High Dive: Supplemental Activities, page 300, when students are introduced to complex conjugates and find the quotient of complex conjugates. In Supplemental Activities, page 301, students find the moduli of complex numbers.
  • N-CN.4: In Year 3, High Dive, Complex Components, page 263, students graph complex numbers in rectangular form, find the sum of two complex numbers, and represent the sum as a vector. In Year 3, High Dive, Supplemental Activities, pages 302-303, students graph complex numbers as polar coordinates, find the rectangular form of complex numbers, and compare the rectangular and polar forms of complex numbers.
  • N-CN.9: In Year 3, High Dive: Supplemental Activities, pages 306-307, the materials state the Fundamental Theorem of Algebra. In Exercises 2 and 3, students work with quadratic polynomials as they find roots and explain the meaning of a double root for a given quadratic equation.
  • N-VM.3: In Year 3, High Dive, A Falling Start, page 263; Year 3, High Dive, Components of Velocity, pages 274; and Year 3, High Dive, Supplemental Activities, pages 312-314, students solve problems that can be represented with vectors.
  • N-VM.4a: In Year 3, High Dive, A Falling Start, page 263; Year 3, High Dive, Components of Velocity, pages 273-277; and Year 3, High Dive, Supplemental Activities, pages 312-314, students add vectors.
  • N-VM.4b: In Year 3, High Dive, Components of Velocity, page 275 and Year 3, High Dive, Supplemental Activities, page 312, students find the magnitude and direction of the sum of two vectors given in magnitude and direction form.
  • N-VM.5: In Year 3, High Dive, Supplemental Activities, page 306, students multiply vectors by scalar values.
  • N-VM.6: In Year 4, Meadows or Malls?, Saved by the Matrices!, pages 70-72 and 75-81, students use matrices to represent and use data to solve problems.
  • N-VM.7: In Year 3, High Dive: Supplemental Activities, page 314, students multiply 2 x 1 column matrices to produce new matrices.
  • N-VM.8: In Year 4, Meadows or Malls?, Saved by the Matrices!, pages 70-72 and 77-84, students compute with matrices.
  • N-VM.9: In Year 4, Meadows or Malls?, Saved by the Matrices!, page 87, students determine if multiplication for square matrices is commutative, associative, or distributive.
  • A-APR.5: Year 3, Pennant Fever, Supplemental Activities, pages 91-92 defines the Binomial Theorem using Pascal’s triangle and connects to combinatorial coefficients. Year 3, The World of Functions, Supplemental Activities, page 423 includes problems using the Binomial Theorem.
  • A-REI.8,9: In Year 4, Meadows or Malls?, Saved by the Matrices!, page 90, students write systems of linear equations as matrix equations, find inverse matrices (if possible), and use inverse matrices to solve matrix equations.
  • F-BF.1c: In Year 3, The World of Functions, Composing Functions, pages 373-379 and Year 3, The World of Functions, Supplemental Activities, pages 411-412, students compose functions and examine properties of composite functions.
  • F-BF.4b: In Year 3, The World of Functions, Composing Functions, page 386, students show that one function is the inverse of the other through composition of the functions.
  • F-BF.4c: In Year 3, The World of Functions: Composing Functions, pages 382-383, students complete an in and out table for a function and its inverse function in several exercises before reaching conclusions regarding the relationship between the table of values for a function and the table of values for its inverse function. Additionally, students graph a function and its inverse on the same x and y axes in several exercises before reaching conclusions regarding the relationship between the graph of a function and the graph of its inverse.
  • F-BF.5: In Year 2, Small World, Isn’t It?, A Model for Population Growth, pages 431-432, students explore the connection between exponential and logarithmic equations. In Year 2, Small World, Isn’t It?, Supplemental Activities, page 477, students connect the domain of an exponential function to the range of a logarithmic function and the range of an exponential function to the domain of a logarithmic function in Exercises 3 and 4.
  • G-SRT.9: In Year 2, Do Bees Build It Best?, Supplemental Activities, page 374, students derive the formula for the area of a triangle using sine and then use the formula to find the area of a given triangle.
  • G-C.4: In Year 3, Orchard Hideout, Equidistant Points and Lines, page 115, students construct a tangent line from an external point to a circle.
  • S-MD.5: In Year 2, The Game of Pig, In the Long Run, pages 219-230, students examine expected payoffs and expected values, mostly in the context of basketball games.
  • S-MD.6,7: In Year 2, The Game of Pig, students frequently use probability to analyze situations and make decisions.

Parts of the following plus standards were addressed:

  • N-VM.1: In Year 3, High Dive: Supplemental Activities, page 314, students find the magnitude of vectors, but students do not use appropriate symbols to represent the magnitude.
  • N-VM.10: In Year 3, The World of Functions, Composing Functions, pages 385-386, students identify zero and identity matrices for 2 x 2 and 3 x 3 matrices while examining inverses of functions. In Year 4, Meadows or Malls?, Saved by the Matrices!, pages 86 and 88-89, students work with identity matrices, but students do not have the opportunity to understand that the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
  • N-VM.11,12: In Year 4, As the Cube Turns, Translation in Two Dimensions, pages 316-318 and Year 4, As the Cube Turns, Rotation in Two Dimensions, pages 329-330 and 336, students use matrices in problems involving transformations, but they do not work with determinants.
  • F-IF.7d: In Year 3, The World of Functions, Going to the Limit, pages 343-344, students graph rational functions, accounting for asymptotes and values of x that make the denominator equal to zero. In The World of Functions: Going to the Limit, page 348, students explore the end behavior of several function families, including rational functions. No emphasis, however, is given to zeros of the functions.
  • F-BF.4d: In Year 3, The World of Functions, Supplemental Activities, page 416, students investigate inverse trigonometric functions with restricted domains, but students do not produce an invertible function from a non-invertible function by restricting the domain.
  • F-TF.4: This standard is not explicitly identified by the publisher, but the review found evidence of this standard in Year 3, High Dive: Trigonometric Interlude, pages 244-247. Students use the unit circle to explore the periodicity of the sine and cosine functions. In Year 3, The World of Functions: Supplemental Activities, pages 406-407, students recognize the sine function as an odd function by showing sin(30)= sin(-30), but students do not directly explain symmetry using the unit circle.
  • F-TF.6: Year 3, The World of Functions, Composing Functions, page 384 notes that the sine function cannot have an inverse since the sine of 30 degrees and 150 degrees are the same. Year 3, The World of Functions, Supplemental Activities, page 416 builds on this observation by explaining that a calculator gives one value because it works with a restricted range (rather than restricted domain as in the standard).
  • F-TF.7: In Year 3, High Dive: The Height and the Sine, page 212, students solve a trigonometric equation using trigonometric inverses with technology and interpret their solution in terms of the context provided. The modeling context is not present as the quantities are defined for the students and the trigonometric equation is provided.
  • G-SRT.10: In Year 2, Do Bees Build It Best?, Supplemental Activities, pages 370-371, students derive the Law of Sines and Law of Cosines. Students solve problems using the Law of Cosines in Do Bees Build it Best?: Supplemental Activities, page 370, and Geometry by Design: Supplemental Activities, page 186. Students do not use the Law of Sines to solve problems.
  • G-SRT.11: In Year 2, Geometry by Design, Supplemental Activities, page 186 and Do Bees Build It Best?, Supplemental Activities, page 370, students apply the Law of Cosines. Students do not solve problems to find the unknown measurements in right and non-right triangles using the Law of Sines.
  • G-GPE.3: In Year 3, Orchard Hideout, Supplemental Activities, pages 183-185, students derive a general equation of an ellipse and an equation of a hyperbola when the difference of the distances from the foci is 8 and 2. Students generalize their results for the equation of an ellipse in “standard position” with its center at the origin and its foci on the x-axis at (c, 0) and (-c, 0). Students do not generalize their results to derive the general equation of a hyperbola.
  • G-GMD.2: In Year 3, Orchard Hideout: Supplemental activities, pages 172-173, students solve a problem involving the volumes of a sphere and a cone in Exercise 2. However, there is no informal argument provided relating to the formula for the volume of a sphere using Cavalieri’s principle.
  • S-CP.8: In Year 3, Pennant Fever, Trees and Baseball, pages 13, 17, and 20, the Multiplication Rule of Probability is one possible approach for solving the given problems.
  • S-CP.9: In Year 3, Pennant Fever, Baseball and Counting, pages 46-47, using combinations to find probabilities is one possible approach for solving the given problems.
  • S-MD.1: In Year 2, The Game of Pig, students perform several simulations to collect data and display the results, though they represent probabilities with a rectangular area model rather than a graph of the probability distribution.
  • S-MD.2-4: In Year 2, The Game of Pig, Chance and Strategy, pages 196, 201, and 204; Pictures of Probability, page 217; Analyzing a Game of Chance, page 233; and Supplemental Activities, page 278, as well as in Year 3, Is There Really a Difference?, Coins and Dice, pages 446-447 and Comparing Populations, pages 483, 485, and 487, students calculate expected values but do not connect them to probability distributions.

The review found no evidence that the following plus standards were addressed:

  • N-CN.5
  • N-CN.6
  • N-CN.8
  • N-VM.2
  • N-VM.4c
  • A-APR.7
  • F-TF.3
  • F-TF.9

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for the Interactive Mathematics Program series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately. Overall, conceptual understanding and application are thoroughly attended to, but students are provided limited opportunities to develop procedural skills and fluencies.

Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
2/2
+
-
Indicator Rating Details

The instructional materials for the Interactive Mathematics Program series meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The instructional materials develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the series.

Examples of the materials developing conceptual understanding and providing opportunities for students to independently demonstrate conceptual understanding are highlighted below:

  • A-APR.B: In Year 2, Fireworks, A Quadratic Rocket, page 17, the Group Activity connects the number of x-intercepts with the shape of the parabola. Quadratic functions are given in vertex form, and students determine where the vertex lies, whether the parabola is concave up or concave down, and use these facts to determine how many x-intercepts it has. In the Glossary on page 504 in Year 2, the zero product rule is defined. This is explored in Year 2, Fireworks, Intercepts and Factoring, page 47, Group Activity, where students factor to find zeros and make a statement that connects the idea of x intercepts to “the values of x that make y = 0.” There are subsequent activities in Year 2, Fireworks that students independently engage in factoring expressions, graphing parabolas, and solving a cattle pen application using the factored form and the x-intercepts. Year 3, The World of Functions, Supplemental Activities, page 423 connects the idea between roots, equations, and graphs of polynomial functions. Note the term roots is used rather than zeros.
  • A-REI.A: In Year 1, The Overland Trail, pages 92-96, students build understanding around balancing equations and explain what they are doing, which is pertinent in the conceptual development for this cluster of standards. In Year 2, Fireworks, Supplemental Activities, pages 68-69, students are exposed to extraneous solutions. Students are asked “See if you can find a rule for determining when an extraneous solution will occur.”
  • A-REI.10: In Year 1, The Overland Trail, The Graph Tells a Story, page 51, students are given in-out relationships to make a table, plot the ordered pairs, and sketch a graph. Students connect “in and out” to independent and dependent variables on a graph and then graph equations on a coordinate plane. In the same year, All About Alice, Curiouser and Curiouser!, page 443, students use a similar method to graph y=2x. In Year 3, The World of Functions, Going to the Limit, pages 343-344, students investigate rational function graphs.
  • F-IF.A: In Year 1, The Overland Trail, The Importance of Patterns, page 12 and The Graph Tells a Story, pages 49-51, students use in and out tables and real-world context to develop the idea of functions. Students extend their idea of functions using sequences later on in The Overland Trail, Supplemental Activities, page 104 where students find next terms and write equations for the sequences.
  • G-SRT.6: Year 1, Shadows, pages 305-309 provide students a task to draw a right triangle and investigate the idea of the ratios that lead to defining sine, cosine, and tangent. Students are asked if their classmates will get similar results for their ratios and have to “Explain in detail why or why not.”
  • S-ID.7: Year 1, The Overland Trail, page 66 begins to develop the idea of slope by giving real-world scenarios, and students write linear equations and answer questions. Pages 74 and 75 extend the conceptual development of slope by providing opportunities for students to find equations of real-world scenarios and answer questions related to the rate and the starting point (y-intercept). It should be noted that rate of change, slope, and y-intercept are not used.

Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
1/2
+
-
Indicator Rating Details

The instructional materials for the Interactive Mathematics Program series partially meet expectations that the materials provide intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters.

Students’ independent demonstration of procedural skills is often limited to a few problems. The following are examples of how the instructional materials provide students with limited opportunities to independently demonstrate procedural skills throughout the series.

  • N-RN.2: Students work with rational exponents in Year 1, All About Exponents, pages 434-435 and Year 1, All About Alice: Curiouser and Curiouser!, pages 443-444 and 447-448. However, Year 1, All About Alice: Curiouser and Curiouser!, pages 449-450 has limited practice for students to rewrite expressions involving radicals using the properties of exponents.
  • N-CN.7 and A-REI.4b: Quadratic equations with complex solutions are introduced in Year 3, High Dive: A Falling Start, page 262. There are three problems where students develop and independently demonstrate solving quadratic equations with complex solutions. Overall, students have limited practice at recognizing when the quadratic formula will result in complex solutions.
  • A-APR.6: Year 3, The World of Functions: Supplemental Activities, page 418, includes two examples of long division. Students are given three problems to practice polynomial division.
  • F-BF.3: Year 2, Fireworks, A Quadratic Rocket, pages 11-14 introduces the idea of transformations of quadratic functions and includes limited problems for students to independently demonstrate transforming functions on their own. Also, f(kx) is not included in these pages. Year 3, The World of Functions: Transforming Functions, pages 388 - 392 does include f(kx) for sine functions. Students have minimal practice in looking at functions and determining the transformation of the graph. They are given a graph to complete four different transformations. Later they complete four single transformations using a table. Students are not given practice looking at graphs to find the value of k.
  • F-TF.2: Reviewers found few tasks related to radian measures of angles on the unit circle. They are located in Year 3, High Dive, Supplemental Activities, pages 308-310.
  • G-GPE.5: There is minimal evidence students develop procedural skills in using the criteria for perpendicular and parallel lines to solve problems. In Year 2, Geometry by Design: Isometric Transformations, page 149, the slope criteria for perpendicular lines is used to find the equation of the line that passes through a given point and is perpendicular to a line for two exercises. In a Group Activity in Year 2, Small World, Isn’t It?: All in a Row, page 404 and Small World Isn’t It?: Supplemental Activities, page 466, students develop the concept that parallel lines have the same slope.

Indicator 2c

Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
2/2
+
-
Indicator Rating Details

The instructional materials for Interactive Mathematics Program series meet expectations that the materials support the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.

Students engage in and practice problem solving, solve non-routine problems, and apply math in contextual situations with increasing sophistication across the courses.

Examples of engaging high school applications in real-world contexts are shown below:

  • N-Q.1: Students choose and interpret the scale and origin in graphs and data displays frequently, including choosing axes for various real-world situations in Year 1, The Overland Trail, The Graph Tells a Story, pages 46-47. Students also use an appropriate scale as they graph data on supplies settlers used while travelling by wagon train in Year 1, The Overland Trial, pages 55 and 59. In Year 1, Cookies, Cookies and the University, page 389, students make an appropriate graph to decide how many cookies to produce for maximum profit.
  • A-SSE.3: In Year 2, students use equivalent forms of expressions to show properties of quantities represented by those expressions as they learn about relationships between equations and graphs of quadratic functions. In Fireworks, A Quadratic Rocket, pages 4-5, 11-12, and 14-17; The Form of It All, pages 21-27 and 29-30; Putting Quadratics to Use, pages 36-38 and 41; and Back to Bayside High, page 45, students also use completing the square to rewrite quadratic equations to solve problems involving rockets.
  • G-SRT.5: Students apply triangle congruence and similarity to solve problems through indirect measurement in various contexts for Year 1, Shadows, The Lamp Shadow, pages 294-298 and 302 and then use this idea to develop and use trigonometric ratios for Year 1, Shadows, The Sun Shadow, pages 305-313.
  • F-IF.4: Students sketch graphs showing key features of the relationship between two quantities for given stories in Year 3, The World of Functions, The What and Why of Functions, pages 320-321 and 326.
  • F-IF.6: Students calculate and interpret the average rate of change in a number of contexts, including graphs showing distance travelled each day in Year 2, Small World, Isn’t It?, Average Growth, page 392 and 396; a graph showing population growth in Year 2, Small World, Isn’t It?, page 398; and a graph of an equation representing the height of a falling object in Small World, Isn’t It?, Beyond Linearity, page 415.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
2/2
+
-
Indicator Rating Details

The instructional materials for Interactive Mathematics Program series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

All units emphasize applications. In general, tasks use a real-world context, and units are organized around an overarching real-world problem. Conceptual understanding is developed through the applications by teaching through problem solving. Units often feature limited opportunities for practicing procedural skills, but when present, procedural skills are integrated into the problem-solving scenarios.

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples of this include:

  • In Year 1, Overland Trail, Setting Out with Variables, pages 33-39, procedural skills and applications are integrated. Students find the value of algebraic expressions and solve algebraic equations in the context of planning a trip by wagon train.
  • In Year 2, Fireworks, The Form of It All, pages 19-32, students build a conceptual understanding of completing the square by working with area models of multiplication, applying those area models to the distributive property of multiplication over addition and the multiplication of binomial expressions, and using those ideas to derive the process of completing the square. In Putting Quadratics to Use, pages 33-41, students use completing the square to solve maximization problems involving quadratic functions, with practice of this procedural skill distributed throughout the unit and included in Supplemental Activities, pages 72, 73, and 77.
  • In Year 3, The World of Functions, page 318, students reason about the relationship between speed and stopping distance using multiple representations as they are introduced to the unit problem. Students continue to make connections between a verbal description and an appropriate graph on pages 320-323 and 326. Continuing in World of Functions, Tables, students use tables to explore patterns and properties of linear, quadratic, cubic, and exponential functions, pages 325, 327, 330-334, 339, then assign functions to tables in Who’s Who?, page 353. The unit concludes with students returning to the unit problem to explain what function family they think best represents data given in a table.

There are some instances where procedural skills activities are not presented simultaneously with other aspects of rigor. Examples of this include:

  • In Year 1, Overland Trail, Reaching the Unknown, page 92, students solve one-step, two-step and multi-step equations containing variables on both sides of the equal sign.
  • In Year 1, Shadows, The Shape of It, pages 269, 270, and 272, students create proportions based on similar figures and solve the proportions to find the lengths of missing sides.
  • In Year 1, Cookies, Points of Intersection, page 387, students solve linear equations and linear systems.
  • In Year 2, Fireworks, Intercepts and Factoring, page 48, students factor quadratic equations.
  • In Year 2, Small World, Isn’t It?, All in a Row, page 410, students find the equation of a line, given specific information.

The instructional materials embed conceptual understanding and application in contexts such that these two aspects of rigor are simultaneously being addressed. For example:

  • In Year 2, Small World, Isn’t It?, All in a Row, page 404, students make a connection between the slope of parallel lines and the graph of parallel lines within the context of teammates saving money to help buy new basketball uniforms. They develop formulas to describe the amount of money each of the friends has at any time and consider how these formulas relate to their respective slopes and graphs.
  • In Year 3, The World of Functions, Composing Functions, page 373, students develop their conceptual understanding of composition within the context of a student who is trying to save enough money to travel across the country. Students can either make a graph or a table to show student earnings as they apply one function to another function.

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
5/8
+
-
Criterion Rating Details

The instructional materials for the Interactive Mathematics Program series partially meet expectations that the materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials develop each of the Mathematical Practices, except for MP5 and MP6. For MP5, students do not have opportunities to choose an appropriate tool to use to solve a problem because the materials include directions that specify which tool(s) to use, and for MP6, the materials do not always use precise mathematical vocabulary and definitions.

The instructional materials do not identify the MPs in the units or activities for teachers or students. At the beginning of each unit, there is a document titled "(Unit Name) and the Common Core State Standards for Mathematics," and in each of these documents, there is the following general statement, "The eight Standards for Mathematical Practice are addressed exceptionally well throughout the IMP curriculum." A publisher-provided document, that is separate from the digital materials, entitled "Correlation of Interactive Mathematics Program (IMP), Years 1-4, Common Core Edition (2014) to Common Core State Standards (June 2010)", lists activities within courses for each MP that are representative of the MP, but other than a description of the activity, there is no identification of the MPs for those activities. The lack of identification of the MPs is reflected in the scoring of indicator 2e, and does not affect the scoring of indicators 2f, 2g, or 2h.

Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
0/2
+
-
Indicator Rating Details

The instructional materials for Interactive Mathematics Program series do not meet expectations that the materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards. In addition to not developing MP6 to its full intent, the materials do not identify the MPs for teachers or students as evidenced in the EdReports.org Criterion Summary for the MPs.

Students often make sense of problems and persevere in solving them (MP1), and several tasks address a general problem-solving process and are not connected to the high school content standards. There is intentional development of MP1 across the series, but MP6 is not developed to its full intent as the materials do not always use precise mathematical vocabulary and definitions.

Problems of the Week (POW) provide opportunities to make sense of problems and persevere in solving them (MP1). Examples include:

  • In Year 1, The Pit and the Pendulum, Edgar Allan Poe - Master of Suspense, POW 5, pages 140-141, the materials present a modified chess board and explain how a knight moves. Students determine if it is possible to move each knight from one spot on the board to another spot on the modified board. In order to determine if the movements are possible, students make sense of how a knight moves, and they also make sense of how to record the movements of the knights. Students persevere in the task as they record multiple combinations of moves in order to determine if the knights can land in the desired spaces on the modified board.
  • In Year 2, The Game of Pig, Pictures of Probability, POW 7, pages 213-214, pairs of students play a game in which each can remove a limited number of objects from a group (e.g., remove one, two, or three objects from a group of ten). The winner is the player who takes out the last object. After playing several variations of the game, students describe their best strategies, make generalizations about the structure of the game, and give justification for their findings.
  • In Year 3, Pennant Fever, The Birthday Problem, POW 2, pages 20-21, students examine the Monty Hall problem where a contestant is presented with three doors. Behind two of the doors are worthless prizes, and behind the third door is a new car. The contestant picks a door, and a worthless prize is revealed behind one of the two doors that were not picked. The contestant then decides whether to keep the original door selected or switch to the door that was not revealed. Students make sense of how to simulate the game in order to determine a strategy that produces the best chance for winning the car. The strategy is supported by an explanation that includes the probabilities involved in the problem.

The materials do not develop MP6 to its full intent as they do not always use precise mathematical vocabulary and definitions. Examples of how the materials do not use precise mathematical vocabulary and definitions include:

  • Functions are introduced in Year 1, The Overland Trail, within the context of in-out tables and are defined in the Glossary on page 482 as “a process or rule for determining the numerical value of one variable in terms of another. A function is often represented as a set of number pairs in which the second number is determined by the first, according to the function rule.” The materials do not use the definition of a function as assigning each element of the domain exactly one element of the range (F-IF.1).
  • In Year 1, The Pit and the Pendulum, Supplemental Activities, page 234, the term domain is defined as “intervals on the x-axis” and used in relationship to piecewise functions, and the term range is not defined or used in relationship to functions in Year 1. In Year 2, Small World, Isn’t It?, Supplemental Activities, pages 476-477, the terms domain and range are examined in the context of the relationship between exponential and logarithmic functions. In Year 3, The World of Functions, Supplemental Activities, pages 400-401, students determine the domains of rational and radical expressions. The terms domain and range are not used or defined for other types of functions, including polynomial functions, in the series.
  • In Year 2, Geometry by Design, Do It Like the Ancients, page 104, the definition of congruent is written as, “Two figures are congruent if they can be placed one on top of the other, and they match up perfectly.” The materials do not define congruence in terms of rigid motions.
  • In Year 3, High Dive, The Height and the Sine, page 205, students model the movement of a Ferris Wheel using a trigonometric function and examine how the amplitude, period, and frequency affect the graph and equation modeling the Ferris Wheel. The materials do not use the term frequency when referring to trigonometric functions, but in Exercise 1, students modify the frequency by changing the period of the trigonometric graph.
  • The term zeros is used in Year 3, High Dive, Supplemental Activities, page 306, but there is no other evidence for the use of this term. The term is also not used in any of the problems that are a part of the Supplemental Activity on page 306.
  • The review did not find any evidence of the use of the term interquartile range (S-ID.2).

Indicator 2f

The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.
2/2
+
-
Indicator Rating Details

The instructional materials for Interactive Mathematics Program series meet expectations that the materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. MP2 and MP3 are used to enrich the mathematical content throughout the series, and there is intentional development of MP2 and MP3 that reaches the full intent of the MPs.

Students often reason abstractly and quantitatively (MP2). Examples include:

  • In Year 1, The Overland Trail, The Graph Tells a Story, pages 49-50, students answer a series of questions that lead them to analyze graphs, create corresponding tables, and write rules based on the information.
  • In Year 2, Geometry by Design, Isometric Transformations, page 148, students solve a problem about a right triangle with a given slope and then describe a general solution for any slope.
  • In Year 3, High Dive, Falling, Falling, Falling, pages 217-218, students are given a particular example of the distance travelled by a falling object and develop a general formula for the height of a falling object after a given number of seconds.

Students often construct viable arguments and critique the reasoning of others (MP3). Examples include:

  • In Year 1, All About Alice, Curiouser and Curiouser, pages 447-448, three students share their strategy for shrinking the size of a house while keeping the shape exactly the same. Students critique the reasoning of others as they determine whether each strategy works and explain why the method does or does not work.
  • In Year 2, Geometry by Design, Dilation, page 161, a student seeks advice from five friends about how to enlarge a figure on a copier. Students critique each friend’s response as to whether it produces the desired enlargement and if it doesn’t then students determine what size enlargement was made.
  • In Year 3, Is There Really a Difference?, Data, Data, Data, page 431, a scenario is given where students are constructing a mathematical argument for a jury. The student then becomes a member of the jury to see if there is enough evidence. This scenario develops further by having students include an explanation of additional evidence that might be needed to win the case.

Indicator 2g

The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
1/2
+
-
Indicator Rating Details

The instructional materials for Interactive Mathematics Program series partially meet expectations that the materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. Students make numerous models and use tools to solve real-world problems, but they are typically told which tool to use.

Students often model with mathematics (MP4). Examples include:

  • In Year 1, The Overland Trail, The Graph Tells a Story, page 43, students use a graph to answer questions about situations and sketch a graph to represent situations.
  • In Year 2, Fireworks, The Form of It All, pages 31-32, students write an equation to represent a real-world situation involving the volume of a rectangular figure.
  • In Year 3, Is There Really a Difference?, Data, Data, Data, page 428, students use diagrams or organized lists to develop a plan to maximize the number of phone calls that can be made under given conditions.

In the series, students often use tools, but students generally do not choose which tool to use. Some examples of not choosing a tool include:

  • In Year 1, The Overland Trail, Traveling at a Constant Rate, page 67, students are directed to use a graphing calculator to plot data and find a linear function that approximates the data. Students do not have the opportunity to make decisions about whether to construct a graph by hand or use a calculator nor do they consider the advantages/limitations of finding possible linear functions by guess and check or using the calculator.
  • In Year 2, Do Bees Build It Best?, Area, Geoboards, and Trigonometry, pages 298-299, the materials explicitly use geoboards to derive the formula for the area of a triangle. By explicitly using geoboards, the materials take away the opportunities for students to determine what tool(s) would be helpful to derive the formula for the area of a triangle, as well as identify the strength and limitations of the tool(s).
  • In Year 3, Pennant Fever, Trees and Baseball, page 12, the materials state that “one of the best techniques for analyzing situations like the baseball problem is the tree diagram,” and students read that “over the next several days, you’ll apply this technique to several situations.” These directions restrict the students’ opportunity to choose and use appropriate tools strategically.

Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
2/2
+
-
Indicator Rating Details

The instructional materials for Interactive Mathematics Program series meet expectations that the materials support the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. In the instructional materials, students find and use patterns and generalize findings from regularity in repeated reasoning.

Students often look for and make use of structure (MP7). Examples include:

  • In Year 1, All About Alice, Extending Exponentiation, pages 152-153, students examine a list of integer powers of 2 from -4 to 5, describe the structure they see, and use their results to find other powers of 2 with negative exponents.
  • In Year 2, Fireworks, The Form of It All, pages 22-23, students consider the multiplication of two two-digit numbers using an area model. The structure of an area model is built upon in pages 24-25 as students multiply algebraic expressions using the same format. Factoring is informally introduced using the area model in Exercise 4 on page 25 when students are given the total area and seek to find the length and width to set the stage for factoring quadratic expressions using this model later in Fireworks, Intercepts and Factoring, page 47.
  • In Year 3, Pennant Fever, Baseball and Counting, students write formulas for combinations and permutations by looking for structure in their work with specific examples from previous activities.

Students often look for and express regularity in repeated reasoning (MP8). Examples include:

  • In Year 1, Shadows, The Shape of It, page 254, students use protractors to discover the angle sums of triangles and quadrilaterals. Students build upon this knowledge in the following activity on page 255 as they consider other polygons. During this activity, students generalize their findings for a few specific polygons to find an expression for the sum of the angles in a polygon as a function of the number of its sides.
  • In Year 2, Small World, Isn’t It?, Average Growth, pages 398-399, students find the rate of change of a function from several graphs of real-world situations and use these repeated examples to determine a general expression for rate of change of a linear function given any two ordered pairs.
  • In Year 3, The World of Functions, Tables, page 325, students consider f(x) = 4x + 7 and look for a pattern using equally-spaced inputs. Students then consider other linear functions of their own choosing and reach a generalized statement regarding the pattern in constant differences in outputs within a table for all linear functions. On page 338, students work with concrete examples and then generalize to reach a conclusion regarding constant, second differences in outputs with constant changes in x within a table for all quadratic functions.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
0/2

Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
0/2

Indicator 3h

Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
0/2

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
0/2

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3aa - 3z3ad

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/10

Indicator 3aa

0/

Indicator 3ab

0/

Indicator 3ac

0/

Indicator 3ac.i

0/

Indicator 3ac.ii

0/

Indicator 3ad

0/

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

Materials provide support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
0/2

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/0

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Indicator 3z

0/

Indicator 3z3ad

0/

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

Materials can be easily customized for individual learners.
0/0

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
0/0

Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Tue Apr 03 00:00:00 UTC 2018

Report Edition: 2015

Title ISBN Edition Publisher Year
IMP 2015 Year 4 Student Edition 978-1-60720- 2015 Activate Learning 2015
IMP 2015 Year 1 Student Edition 978-1-60720-727-6 2015 Activate Learning 2015
IMP 2015 Year 2 Student Edition 978-1-60720-731-3 2015 Activate Learning 2015
IMP 2015 Year 3 Student Edition 978-1-60720-735-1 2015 Activate Learning 2015
IMP 2015 Year 1 ebook 978-1-68231-208-7 2015 Activate Learning 2015
IMP 2015 Year 2 ebook 978-1-68231-210-0 2015 Activate Learning 2015
IMP 2015 Year 3 ebook 978-1-68231-212-4 2015 Activate Learning 2015
IMP 2015 Year 4 ebook 978-1-68231-214-8 2015 Activate Learning 2015

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

The publisher has not submitted a response.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Math HS Rubric and Evidence Guides

The High School review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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