Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for Carnegie Learning Math Solution (2018) Course 1 meet the expectation for alignment to the CCSS. In Gateway 1, the instructional materials meet the expectations for focus by assessing grade-level content and spending at least 65% of class time on the major clusters of the grade, and they are coherent and consistent with the Standards. In Gateway 2, the instructional materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, and they connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
18
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
33
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for Gateway 1. These materials do not assess above-grade-level content and spend the majority of the time on the major clusters of each grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. These materials are consistent with the mathematical progression in the standards, and students are offered extensive work with grade-level problems. Connections are made between clusters and domains where appropriate. Overall, the materials meet the expectations for focusing on the major work of the grade, and the materials also meet the expectations for coherence.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The materials did not include any assessment questions that were above grade-level.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that they assess grade-level content.

The assessments are aligned to grade-level standards. The instructional materials reviewed for this indicator were the Post-Tests, which are the same assessments as the Pre-Tests, both Form A and Form B End of Topic Tests, Standardized Practice Tests, and the Topic Level Performance Tasks.

For example:

  • Module 5, Topic 2, Performance Task: 6.SP.2, 3, 4, 5c, 5d: Numerical Summaries of Data: Hours Playing Video Games: Students are given a scenario of a student collecting data about video game usage; however, she lost the data set. She still has information such as range, minimum value, median, and interquartile range; the student uses this information to create a data set that could represent the data that was lost. Work is scored on accurate numbers in the data set, summary of the data set, box-and-whisker plot representing the data, explanation of how the data set was generated, and a statement about data sets.
  • Module 1, Topic 1, End of Topic Test-Form A, 6.NS.4: Students find the greatest common factor using the distributive property to rewrite an expression. Questions 15 and 16 state, “Rewrite each sum in the form a(b + c) such that the integers b and c have no common factor: 82 + 30”
  • Module 2, Topic 2, End of Topic Test Form A, 6.RP.3c: Students find a percent of a quantity when completing a fraction-decimal-percent table with survey results. Question 6 states, “One hundred middle school students take a survey that asks them about their food preferences. Complete the table by representing the survey results as a fraction, decimal, and percent. Make sure your fractions are in lowest terms.”
  • Module 3, Topic 3, End of Topic Test Form A, 6.EE.9: Students represent distance and time in an equation. Question 5 states, “A hiker is climbing at a constant rate of 2.4 miles per hour. a. Write an equation to model the relationship between the hiker’s distance climbed and the time in hours.”

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for having students and teachers using the materials as designed, devoting the large majority of class time to the major work of the grade. Overall, the materials devote at least 65 percent of class time to major work.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations for spending a majority of instructional time on major work of the grade.

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days were also included in the evidence.

  • The approximate number of topics devoted to major work of the grade (including supporting work connected to the major work) is nine out of 13, which is approximately 69 percent.
  • The approximate number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 35 out of 50, which is approximately 70 percent.
  • The approximate number of days devoted to major work (including supporting work connected to the major work) is 98 out of 139, which is approximately 70.5 percent.

The approximate number of days is most representative of the instructional materials because it most closely reflects the actual amount of time that students are interacting with major work of the grade. As a result, approximately 70.5 percent of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for being coherent and consistent with the standards. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and fosters coherence between the grades. Content from prior or future grades is clearly identified, and the materials explicitly relate grade-level concepts to prior knowledge from earlier grades. The objectives for the materials are shaped by the CCSSM cluster headings, and they also incorporate natural connections that will prepare a student for upcoming grades.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade.

For example:

  • In Module 1, Topic 3, Lesson 1, Activity 1.2 Volume of Rectangular Prisms: Solving problems involving volume given fractional side lengths (6.G.2) supports the major work of 6.NS.1, dividing fractions.
  • In Module 1, Topic 3, Lesson 1, Activity 1.3 Volume Formulas: Solving problems involving volume using volume formulas (6.G.2c) supports the major work of 6.EE.2, evaluating expressions in which letters stand for numbers.
  • In Module 1, Topic 3, Lesson 3, Activity 3.1 Nets of Rectangular Prisms: Solving problems involving surface area given fractional side lengths (6.G.4) supports the major work of 6.NS.1, dividing fractions.
  • In Module 4, Topic 2, Lesson 2 It’s a Bird, It’s a Plane...It’s a Polygon on the Plane!: Graphing geometric figures and finding their perimeter and area in the coordinate plane (6.G.3) supports the major work of 6.NS.8 involving graphing points in the four quadrants of a coordinate plane.
  • In Module 2, Topic 2, Lesson 1, Activity 1.3 Many Ways to Measure: Students identify equivalent representations between fractions, decimals, and percents. (6.RP.3c,d and 6.NS.3).

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
+
-
Indicator Rating Details

Instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the amount of content designated for one grade-level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications.

Carnegie Learning provides explicit pacing information in several places:

  • The most concise is the Content Map on page FM-15 in the Teacher’s Implementation Guide in both Volumes 1 and 2. There are 139 days of instructional material. This document also provides the information that one day is 50 minutes, facilitator notes offer suggestions for changing the pacing if appropriate, and that allowing 25 assessment days would bring the total to 164 days.
  • The Course 1 Standards Overview on pages FM-18 and 19 in the Teacher Implementation Guide provides a chart of all standards covered in each lesson indicating that students would be able to master all grade-level standards within one school year. All of the standards for each grade-level are taught at least once in the curriculum, and most are addressed more than once.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations for the materials being consistent with the progressions in the Standards.

The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. The content is explicitly related to prior knowledge to help students scaffold new concepts. Content from other grade levels is clearly identified in multiple places throughout the materials.

Examples include:

  • A chart in the Overview shows the sequence of concepts taught within the three grade levels of the series (FM-15).
  • The Family Guide (included in the student book) presents an overview of each Module with sections that look at “Where have we been?" and "Where are we going?” which address the progression of knowledge.
  • The Teacher Guide provides a detailed Module Overview which includes two sections titled, “How is ____ connected to prior learning?” and “When will students use knowledge from ___ in future learning?”
    • Module 5 Overview- How is Describing Variability in Quantities connected to prior learning? (M5-1B): “Describing Variability in Quantities builds on the elementary grades’ Measurement and Data standards, specifically students’ informal work with the statistical process and displaying categorical data (e.g., 1.MD.4, 2.MD.10, 3.MD.3, 4.MD.4, 5.MD.2). Prior to grade 6, students should have a basic understanding of displaying one-variable categorical data and of displaying one-variable quantitative data on a dot plot (called a line plot in grade 5). Students will use their knowledge of these graphs to formalize the statistical process and as an introduction to the formal study of statistics.”
    • Module 5 Overview- When will students use knowledge from Describing Variability in Quantities in future learning? (M5-1C): “This module supports future learning by providing the foundations of the statistical process, data displays, and numerical summaries of data. Students’ understanding of statistical questions and variability will continue to develop as they work with random sampling and drawing inferences about data (7.SP.A), and students will use graphical displays and summary statistics to compare populations (7.SP.B). In high school, students will expand their knowledge of numerical summaries of data and analysis techniques as they learn additional mathematics, including square roots and probability distributions.
  • At the beginning of each Topic in a Module, there is a Topic Overview which includes sections entitled “What is the entry point for students?” and “Why is ____ important?”
    • Module 1, Topic 3- Decimals and Volume (M1-111A) - What is the entry point for students?: “Students began learning about decimals in grades 4 and 5. They have experience in using concrete models and place-value strategies to operate with decimals to the hundredths place. In Decimals and Volume, students formalize the operations with standard algorithms. In grade 5, students learned how to calculate the volume of a right rectangular prism by packing it with unit cubes and using the formulas V = lwh and V = Bh. Decimals and Volume begins by revisiting volume and the terminology associated with solids. From there, students move to determining the volume of right rectangular prisms with fractional edge lengths.”
    • Module 4, Topic 1- Signed Numbers (M4-3B) - Why are Signed Numbers important?: “Signed Numbers provides students with a comprehensive view of the number system with which they will primarily operate in the next few years of their mathematical journey. The focus in grade 6 is on understanding and positioning rational numbers. Students will operate on signed numbers beginning in grade 7. The foundation provided in this topic will enable students to develop strategies for operating with signed numbers. To contrast with rational numbers, students will learn about irrational numbers such as pi in grades 7 and 8. As students enter high school, they will broaden their knowledge of number systems to include complex numbers, including imaginary numbers. Developing a formal understanding of nesting number systems will prepare students to study additional number systems.”
  • The Topic Overview also contains a table called “Learning Together” that identifies the standards reviewed from previous lessons and grades called “Spaced Review.”
  • Each “Lesson Resource” has scaffolded practice for the students to utilize with reminders of concepts taught previously.

The design of the materials concentrates on the mathematics of the grade. Each lesson has three sections (Engage, Develop, and Demonstrate) which contain grade-level problems. Each topic also includes a performance task.

  • In the Engage section, students complete one activity that will “activate student thinking by tapping into prior knowledge and real-world experiences and provide an introduction that generates curiosity and plants the seeds for deeper learning.” For example, Module 3/Topic 3/Lesson 3 (M3-193B) has students work in pairs to determine the values of shapes represented as objects balancing in a mobile. The activity is designed to engage students in thinking about different representations of equality and equations and to stimulate students’ reasoning about solutions to equations. (6.EE.9)
  • In the Develop section, students do multiple activities that “build a deep understanding of mathematics through a variety of activities—real-world problems, sorting activities, worked examples, and peer analysis—in an environment where collaboration, conversations, and questioning are routine practices.” For example, Module 1/Topic 2/Lesson 3/Activity 3.3 (M1-93B) has students explore dividing fractions by dividing across the numerators and denominators and then rewriting the quotient. Students compare different strategies for dividing using analysis of peer work. (6.NS.1)
  • In the Demonstrate section, students “reflect on and evaluate what was learned.” An example of this is Module 2/Topic 2/Lesson 2 (M2-123B), “Talk the Talk: Brain Weights,” where students order the brain weights of different mammals given as percents in relation to the weight of a chimpanzee’s brain. They use benchmark percents to calculate the brain weights. Students also use benchmarks to reason about percents less than one percent and greater than 100 percent. (6.RP.3c)

The end of each lesson in the student book includes Practice, Stretch, and Review problems. These problems engage students with grade-level content. Practice problems address the lesson goals. Stretch problems expand and deepen student thinking. Review problems connect to specific, previously-learned standards. All problems, especially Practice and Review, are expected to be assigned to all students.

After the lessons are complete, the students work individually with the MATHia software and/or on Skills Practice that is included.

  • MATHia - Module 1, Topic 1 (M1-1D): Students spend approximately four days In the MATHia software using the Commutative, Associative, and Distributive Properties to rewrite numeric expressions. Students practice calculating the areas of parallelograms, trapezoids, triangles, and composite figures in mathematical and real-world situations.
  • Skills Practice - Module 1, Topic 2 (M1-67E): Students spend approximately two days expressing fraction multiplication and division relationships represented in bar models.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings, including:

6.RP.A Understand ratio concepts and use ratio reasoning to solve problems.

  • In Module 2, Topic 3, Lesson 3, the Lesson Overview states, “Students use what they know about unit rates to further develop flexible thinking and problem solving with unit rates in different situations using a variety of representations, including tables and graphs. The lesson begins with students investigating a speedometer as a double number line. Students then reason with unit rates in various mathematical and real-world situations, including measuring the diagonals of a Golden Rhombus and investigating the speed of the Duquesne Incline. Finally, students demonstrate their learning by creating a situation of their own to represent the graph of equivalent rates.”

6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions.

  • In Module 3, Topic 1, Lesson 4, the Lesson Overview states, “Students begin by reviewing the properties of arithmetic and algebra that they have formally or informally studied in the past. This allows students to use properties as they rewrite algebraic expressions in equivalent forms. Students analyze pairs of expressions. They use properties, tables, and graphs to show that the expressions are or are not equivalent. Students compare the algebraic expressions and are asked to use tables and graphs to determine if they are equivalent. This opens the discussion that one non-example is necessary to disprove a claim, while an infinite number of examples are necessary to prove a claim.”

6.SP.A Develop understanding of statistical variability.

  • In Module 5, Topic 1, Lesson 1, the Lesson Overview states, “Students consider a variety of questions and determine which are statistical and which are not. They learn about the statistical process: formulating a question, collecting data, analyzing data, and interpreting the results. Students organize data into two types, categorical and quantitative. Then, they determine the best method of data collection to answer each question. Students decide if conducting a survey, performing an experiment, or using an observational study is the best method. Students then conduct a survey in their classroom, interpret bar graphs and circle graphs for categorical data, and create a bar graph or circle graph for their survey data. Finally, students interpret the results, stating conclusions they can make from their data displays. In subsequent lessons, students will interpret histograms and line plots for discrete quantitative data and histograms, stem-and-leaf, and box-and-whisker plots for continuous quantitative data.”

6.SP.B Summarize and describe distributions.

  • In Module 5, Topic 1, Lesson 3, the Lesson Overview states, “Students analyze a histogram. They discuss intervals and interpret information from the histogram. Students then convert information from the histogram to a grouped frequency table and compare the two representations. The process is reversed, and students create two histograms beginning with two tables of information. For each table, they convert the information to a grouped frequency table and finally to a histogram. At the end of each problem, students summarize the data from the data displays.”

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

For example:

  • In Module 1, Topic 3, Lesson 2, students find the volume of a three-dimensional shape with measurements given in decimals, thus connecting clusters 6.G.1 and 6.NS.B.
  • In Module 3, Topic 3, Lesson 4, clusters 6.NS.C and 6.RP.A are connected when students create tables and graph points on a coordinate plane in order to solve real-world problems involving distance and time.
  • In Module 4, Topic 1, Lesson 3, standards 6.NS.5, 6.NS.6 and 6.RP.1 are connected when an understanding of proportional relationships is used to sort and order given rational numbers.
  • In Module 5, Topic 2, Lesson 4, clusters 6.SP.A and 6.SP.B are connected when students determine whether the mean or median most appropriately represents a typical value in a data set and relate the choice of measures of center and variability to the context.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials for Middle School Math Solution Course 1 meet the expectation for aligning with the CCSS expectations for rigor and mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and they also attend to the balance among the three aspects. The instructional materials emphasize mathematical reasoning, identify the Mathematical Practices (MPs), and attend to the full meaning of each practice standard.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and application with a balance of all three aspects of rigor.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Materials include problems and questions that develop conceptual understanding throughout the grade level. Students develop understanding throughout “Engage” and “Develop” activities, which typically activate prior knowledge and use manipulatives to introduce and build understanding of a concept. Students also have the opportunity to independently demonstrate their understanding in the “Demonstrate” questions at the end of each lesson where they attempt to synthesize their learning.

For example:

  • In Module 2, Topic 1, Lesson 6, students develop an understanding of ratios by using various mathematical models to solve real-world problems. In Talk the Talk - “In Goes the Kitchen Sink,” students are given a ratio and use multiple representations (scale up/scale down, table, graph, double number line) to show equivalent ratios. (6.RP.A)
  • In Module 2, Topic 1, Lessons 5, students develop an understanding of the proportional relationship needed to solve a problem by using a table and a coordinate graph. In Activity 5.1 Analyzing Rectangle Ratios, students cut out and sort rectangles. They group and stack the rectangles according to the ratio of the side lengths. Then, they attach their rectangles to a coordinate grid. Students learn that graphs of equivalent ratios form a straight line that passes through the origin. (6.RP.3a, 6.RP.3b)
  • In Module 3, Topic 1, Lesson 3, students explore the use of properties of arithmetic in expressions and understand that these properties apply to expressions with variables. In Activity 3.2 Algebra Tiles and the Distributive Property, students use algebra tiles to multiply expressions using the Distributive Property, Order of Operations, and combining like terms. (6.EE.3)
  • In Module 4, Topic 1, Lesson 1, students develop an understanding of positive and negative numbers through the use of number lines to solve real-world problems. In Activity 1.1 Investigating Time on a Number Line - Human Number Line, students create a human number line and use it to show locations of time in the past, present, and future. Students analyze number lines and discuss the meaning of zero in the context of their number line. Negative numbers are described as the numbers to the left of zero on the number line. (6.NS.C)
  • In Module 4, Topic 1, Lesson 1, students engage in the application of mathematical skills when explaining how two integers are compared. In Talk the Talk, students communicate understanding through a situation: “Your sixth grade cousin goes to school in a different state. His math class has not yet started comparing integers. Write him an email explaining how to compare any two numbers. Be sure to include one or two examples and enough details that he will be able to explain it to his class.” (6.NS.7)

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade.

  • In Module 1, Topic 3, Lesson 2, students show conceptual understanding of ratio reasoning and relationships when solving real-world unit rate problems. In Activity 2.2 Writing Unit Rates, students write unit rates that compare the unit rates in two ways: the number of objects per dollar and the number of dollars per one object. Then students write two different unit rates for situations that do not involve money. They decide which unit rates are useful, both in general and to answer specific questions. (6.RP.3b)
  • In Module 2, Topic 1, Lessons 4, students demonstrate an understanding of ratios by creating and using ratio tables to solve real-world problems. In Activity 4.3 Parts and Wholes in Ratio Tables, students use ratio tables to answer questions about mixing paint. Five pints of bluish green paint is made by using two pints of yellow paint and three pints of blue paint. Students use a ratio table to analyze student thinking about mixing paint and to determine various amounts of paint needed. (6.RP.3)
  • In Module 2, Topic 1, Lessons 5, students demonstrate an understanding of ratios by using various mathematical models to solve real-world problems. In Activity 5.2 Graphing Equivalent Ratios, students analyze a time-to-distance rate scenario: Stephanie drives her car at a constant rate of 50 miles per hour. Students use a table, double number line, and the coordinate plane to determine the number of miles Stephanie drives over a period of time, and then they compare these different representations. (6.RP.3a, 6.RP.3b)

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade level. They also provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level. This is primarily found in two aspects of the materials: first, in the “Develop” portion of the lesson where students work through activities that help them deepen understanding and practice procedural skill and fluency; second, in the MATHia Software, which targets each student’s area of need until they demonstrate proficiency.

The instructional materials develop procedural skill and fluency throughout the grade-level.

  • In Module 1, Topic 2, Lesson 3, students develop fluency with multiplication and division of fractions. In Activity 3.1, Fractional Fact Families, students investigate area models that show fraction-by-fraction, multiplication-division fact families. Students use cut-out diagrams from Lesson 1 to write multiplication-division fact families involving fractions. (6.NS.1)
  • In Module 1, Topic 3, Lesson 4, students develop fluency when computing volume and surface area. Students learn and practice the standard algorithm for division, including division of decimals, in the context of volume and surface area. (6.NS.2, 6.NS.3)
  • In Module 3, Topic 1, Lesson 2, students develop procedural skill and fluency when evaluating algebraic expressions. In Activity 2.2, Matching Algebraic and Verbal Expressions, students play Expression Explosion to practice matching verbal and algebraic expressions. (6.EE.2)
  • In Module 3, Topic 2, Lesson 1, students develop procedural skill and fluency as they determine whether a number makes an equation or inequality true. In Activity 1.2, Solutions from a Set, students create equations from a list of given expressions. Then students decide which values from a set make each equation true. They investigate true and false equations and equations with no solutions and infinite solutions. (6.EE.5)

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level.

  • In Module 1, Topic 2, students independently demonstrate fluency and procedural skill with multiplication and division of fractions through technology. In the MATHia Software, students calculate products and quotients of fractions, including mixed numbers and improper fractions. (6.NS.1)
  • In Module 1, Topic 3, students independently demonstrate fluency and procedural skill with addition, subtraction, multiplication, and division of decimals through technology. In the MATHia Software, students review Adding and Subtracting Decimals, Decimal Sums and Differences, Exploring Decimal Facts, Multiplying and Dividing Decimals, and Decimal Products and Quotients. (6.NS.3)
  • In Module 4, Topic 1, students independently demonstrate fluency with addition, subtraction, multiplication, and division of multi-digit decimals. In Skills Practice Section A, problems 1-8, students are provided with a number line that has determined points and answer a series of questions on which point is greater or less than a given value. (6.NS.3)
  • In Module 4, Topic 1, Lesson 2, students independently demonstrate fluency in solving mathematical problems involving absolute value. In Activity 2.2, Interpreting Absolute Value Statements, students complete tables of situations, absolute value statements, and numeric values described in given and student-generated situations. The tables include statements of equality and inequality. (6.NS.7)
  • In Module 5, Topic 2, students independently demonstrate the procedural skill of calculating Mean Absolute Deviation through technology. The MATHia Software provides multiple opportunities for the students to calculate and compare the mean absolute deviations with the spread of similar data sets. (6.SP.5c,d)

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level. The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. This is primarily found in two aspects of the materials: first, in the “Demonstrate” portion of the lesson where students apply what they have learned in a variety of activities, often in the “Talk the Talk” section of the lesson; second, in the Topic Performance Tasks where students apply and extend learning in more non-routine situations.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level.

  • In Module 2, Topic 1, Lesson 6, students engage in the application of mathematical skills when analyzing ratios to solve real-world problems. In Activity 6.2, Choosing a Strategy to Solve Ratio Problems, students are given ratio situations and choose a strategy such as graph, scaling, or addition to solve the problem and analyze how their strategy worked. (6.RP.3)
  • In Module 5, Topic 1, Lesson 2, students engage in the application of mathematical skills when analyzing and writing equations to solve real-world problems. In Activity 2.1, Creating and Analyzing Dot Plots, students are given information about the medals won at the 2014 Winter Olympics and analyze the data, create a dot plot and a stem and leaf plot, as well as describe the distribution. Students take skills they’ve practiced and apply them to real data in order to analyze and report out on the questions that were generated such as, “What is the typical number of gold medals won by a country?” (6.SP.B)

The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts.

  • In Module 2, Topic 2, Lesson 3, students independently demonstrate the use of mathematics when solving real-world problems involving percent. In Talk the Talk, students demonstrate two different ways to determine the answer to questions given such as, “Leah’s goal is to score a 90 percent on the upcoming science test. If there are 40 questions on the test, how many does Leah need to answer correctly?” They then plan a presentation of the two solutions, making sure to talk about how they are the same and how they’re different. (6.RP.3)
  • In Module 3, Topic 3, students independently demonstrate the use of mathematics when analyzing and writing equations to solve real-world problems. In Performance task, Graphing Quantitative Relationships - Throw it in Reverse, students reverse the dependent and independent variables on a graph and analyze the impact that has. They discuss proportionality, rate of change, and generate questions that the new graph could answer. They also create tables and equations for both graphs. Finally, they compare and contrast the two versions of the data. (6.EE.9)

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Within each topic, students develop conceptual understanding by building upon prior knowledge and completing activities that demonstrate the underlying mathematics. Throughout the series of lessons in the topic, students have ample opportunity to practice new skills in relevant problems, both with teacher guidance and independently. Students also have opportunities to apply their knowledge in a variety of ways that let them show their understanding (graphic organizers, error analysis, real-world application, etc.). In general, the three aspects of rigor are fluidly interwoven.

For example:

In Module 4, Topic 2 Overview: “In The Four Quadrants, students explore the four quadrant coordinate plane. They use reflections of the first quadrant on patty paper and their knowledge of the rational number line to build their own four quadrant coordinate plane. They look for patterns in the signs of the ordered pairs in each quadrant and for ordered pairs that lie along the vertical and horizontal axes. After developing a strong foundation for plotting points and determining distances on the coordinate plane, students analyze and solve problems involving geometric shapes on the coordinate plane. They identify geometric shapes defined by given coordinates and determine perimeters and areas of geometric shapes in mathematical and real-world situations. Finally, students use the knowledge gained throughout the course to solve a wide range of problems on the coordinate plane, using scenarios, graphs, equations, and tables. Throughout this topic, students continue to develop their fluency with whole numbers, fractions, and decimals.”

There are areas where an aspect of rigor is treated more independently, such as developing procedural skill and fluency in the MATHia software and Skills Practice or in the Performance Task where students work primarily with Application.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
10/10
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for practice–content connections. The materials identify and use the MPs to enrich the content, attend to the full meaning of each MP, support the Standards' emphasis on mathematical reasoning, and attend to the specialized language of mathematics.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

Standards for Mathematical Practice are referred to as Habits of Mind in this program. The Habits of Mind are identified in all lessons in both the teacher and student workbooks using an icon. There are four icons, only one represents a single MP, “attend to precision,” while the other three represent pairs of MPs, though generally one MP is the focus of the lesson. No icon is used for MP1, and it is stated in the Teacher’s Implementation Guide (TIG): “This practice is evident every day in every lesson. No icon used.” Each activity shows the practice or pair of practices being developed. Questions to facilitate the development of Habits of Mind are listed for both students and teachers throughout the program. The Habits are identified in the Overview in the Student and Teacher Editions, but not in the Family Guide that comes with the Topics. The icon appears within each lesson with questions listed in the Teacher Guide to facilitate the learning where they occur. Generally, lessons are developed with activities that require students to make sense of mathematics and to demonstrate their reasoning through problem solving, writing, discussing, and presenting. (Side note: persevere is spelled incorrectly throughout the program.) Overall, the materials clearly identify the MPs and incorporate them into the lessons. All the MPs are represented and attended to multiple times throughout the year. With the inclusion of the “Questions to Ask” in the Teacher Guide and the corresponding Facilitation Notes in each lesson, MPs are used to enrich the content and are not taught as a separate lesson.

MP2 - Reason abstractly and quantitatively.

  • In Module 2, Topic 3, Lesson 3, students reason abstractly when completing a table and constructing a graph to represent a unit rate. Using the graph, two unit rates are identified, one in which the x-value is 1 and one in which the y-value is 1, and the student explains the meanings of the unit rate in terms of the situation.

MP4 - Model with mathematics.

  • In Module 4, Topic 2, Lesson 3, students model with mathematics when creating a presentation of their solution. In Activity 3.8 The Diver, students “train” as a freediver to beat William Trubridge’s record from 2016 of freediving almost 407 feet into the ocean. Students decide what type of questions they would ask Trubridge, how long they would need to hold their breath in order to beat Trubridge, and then make a presentation for a similar problem.

MP6 - Attend to precision.

  • In Module 2, Topic 2, Lesson 1, students attend to precision when completing several columns within a table involving ratios, fractions, and decimals. “The sixth grade class is planning a field trip to Philadelphia. To decide which historical site they will visit, the 100 sixth-graders completed a survey. The results of the survey are provided in the table. Complete the Ratio, Fraction, Decimal, and Grid columns with these representations of the survey results: a ratio using colon notation, a fraction in lowest terms, a decimal, a shaded grid, an equivalent percent.”

MP7 - Look for and make use of structure.

  • In Module 1, Topic 1, Lesson 1, students make use of structure when writing equivalent equations. “Rewrite the original equation 5 x 27 = 135 with an equivalent equation to represent the model you drew. a. How can you rewrite the original product by substituting the sum of the two lengths making up the split side?”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

Each activity asserts that a pair of practices are being developed, so there is some interpretation on the teacher’s part about which is the focus. In addition, what is labeled may not be the best example; i.e., using appropriate tools strategically (MP5) is sometimes weak where it’s labeled, but student choice is evident in Talk the Talk and Performance Tasks, which are not identified as MP5. Over the course of the year, the materials do attend to the full meaning of each mathematical practice.

MP1 - Make sense of problems and persevere in solving them.

  • In Module 4, Topic 1, Lesson 3, students sort and classify rational numbers. They investigate how many rational numbers can fit between between two other rational numbers on a numberline.

MP2 - Reason abstractly and quantitatively.

  • In Module 4, Topic 1, Lesson 1, students explain the meaning of zero, positive numbers, and negative numbers in a variety of contexts. The teacher is directed to ask: “What representation can I use to solve this problem?; How can this problem be represented with symbols and numbers?”

MP4 - Model with mathematics.

  • In Module 2, Topic 3, Lesson 3, students identify statements that are true from a given set of information about the Duquesne Incline as commuter transportation. The teacher is directed to ask: “What expression or equation could represent this situation?; What representations best show my thinking?; How does this answer make sense in the context of the original problem?”
  • In Module 3, Topic 3, Lesson 3, students create graphs, tables of values, and write algebraic equations to describe the relationship between two quantities. They also answer relevant questions about two real-world scenarios.

MP5 - Use appropriate tools strategically.

  • In Module 2, Topic 1, Lesson 6, given a scenario, students choose to solve problems by using the graph, by scaling, or by using an addition strategy.
  • In Module 3, Topic 3, Lesson 3, students choose standard and non-standard tools to measure length. “Use standard and non-standard tools to measure the lengths of the diagonals using six different units of measure and record them in the table. Be sure to include inches and centimeters as two of your units.” The teacher is directed to ask: “What tools would help me solve this problem?”

MP6 - Attend to precision.

  • In Module 3, Topic 3, Lesson 1, students solve a real-world problem based on a pool party involving variables. “a. What two quantities are changing in this situation? b. Which quantity depends on the other? c. Define variables for each quantity and label them appropriately as the independent and dependent variables.”

MP7 - Look for and make use of structure.

  • In Module 1, Topic 2, Lesson 1, students are given two strategies to order rational numbers, then look for and make use of structure to identify and evaluate the most efficient strategies for a solution.
  • In Module 2, Topic 1, Lesson 2, students decompose a parallelogram to create a rectangle and conclude the two shapes have the same area. The same formula can be used to determine the area of either figure. In the process of reconstructing the rectangle from the parallelogram, students make use of the structure of rectangles to discover the relationship between the parallelogram and rectangle.
  • In Module 3, Topic 2, Lesson 3, students use bar models and formal properties to solve equations. The teacher is directed to ask: ”What characteristics of this expression or equation are made clear through this representation?; How can I use what I know to explain why this works?”

MP8 - Look for and express regularity in repeated reasoning.

  • In Module 3, Topic 1, Lesson 3, students use the Distributive Property to factor algebraic expressions, rewriting expressions as a product of two factors, including expressions where the coefficients of the original terms do not have common factors. Students answer questions such as: “Use your example to explain what is meant by the phrase, 'multiply or divide an expression by a given value.' Use your example to explain what is meant by the phrase, 'product of two factors.' The teacher is directed to ask: How can I use what I know to explain why this works?; Can I develop a more efficient method?; How could this problem help me to solve another problem?”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Students are consistently asked to verify their work, find mistakes, and look for patterns or similarities. The materials use a thumbs up and thumbs down icon on their “Who’s Correct” activities, where students question the strategy or determine if the solution is correct or incorrect and explain why. These situations have students critique work or answers that are presented to them.

Examples of students constructing viable arguments and/or analyzing the arguments of others include:

  • In Module 2, Topic 2, Lesson 2, “Noah and Dylan were assigned the numbers 0.06 repeating and 0.1 percent, but they disagreed on which was larger. Noah says that 0.06 repeating is less than 0.1, so 0.06 repeating is less than 0.1 percent. Dylan says that since 0.1 percent is the same as as 0.001 and 0.001 is less than 0.06 repeating, 0.1 percent is less than 0.06 repeating. Who is correct? Explain your reasoning.”
  • In Module 3, Topic 2, Lesson 1, “Identify your equations that are always true, never true, and those equations where you don’t yet know whether they are true or false. Explain your reasoning.” and “Write an equation with variables that has no possible solution. Explain why the equation has no solution.”
  • In Module 5, Topic 1, Lesson 2, “Jessica asked, 'How many medals did the United States win? How many of those were gold?' Maurice thought a better set of questions would be, 'What is the typical number of medals won? What is the typical number of gold medals won by a country?' Who’s correct? Explain your reasoning.”
  • In Module 5, Topic 1, Lesson 3, “Bella says, 'There are 5 buildings represented in the histogram since there are 5 bars.' Do you agree or disagree with Bella’s statement? If you do not agree with Bella, estimate how many buildings are represented in the histogram.”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Throughout the teacher materials, there is extensive guidance with question prompts, especially for constructing viable arguments.

  • In Module 1, Topic 3, Lesson 3, the teacher is prompted to ask, “How is the area of a face of a cube measured? Analyze the two responses and explain why Leticia is incorrect in her reasoning.”
  • In Module 2, Topic 1, Lesson 1, students critique the reasoning of others when analyzing two predictions of a solution to a problem. “Robena and Eryn each predicted the final score of a basketball game between the Crusaders and the Blue Jays. Analyze each prediction. Describe the reasoning that Robena and Eryn used to make each statement.” Teachers are provided questions to ask, such as: "How can both of these be thumbs up if their predictions are different? How is Robena’s reasoning different than Eryn’s reasoning?”
  • In Module 3, Topic 2, Lesson 1, the teacher is prompted to ask, “Why is Rylee’s work incorrect? What feedback would you give Rylee about her strategy? What property did Clover use? Did anyone use the Reflexive Property of Equality as part of their strategy? Did Clover and Fiona use the same strategy? Is there more than one solution completing this equation?”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 meet expectations that materials attend to the specialized language of mathematics.

Each Topic has a “Topic Summary” with vocabulary given with both definitions and examples (problems, pictures, etc.) for each lesson. There is consistency with meaning, examples, and accuracy of the terms.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols.

  • In Module 3, Topic 3, Lesson 3, Talk the Talk, students complete a graphic organizer describing the advantages of using verbal, tabular, graphical, and equation representation.
  • In Module 4, Topic 2, Lesson 3, students accurately represent absolute value equations to calculate temperature changes, for example, calculating the temperature change between two points: |15.6| + |-10.6| = 26.2 degree drop.

The materials use precise and accurate terminology and definitions when describing mathematics and include support for students to use them.

  • In Module 1, Topic 1, Lesson 1, key terms are identified as numeric expression, equation, and Distributive Property. Students describe the expression 4(2+15) in different ways. Teachers are prompted to ask, “What is the difference between an expression and an equation?” A tip for helping ELLs differentiate expression and equation can be used as part of the lesson.
  • In Module 2, Topic 3, Lesson 3, the Topic Overview describes how students deepen their understanding of converting units of measurement using ratio reasoning and strategies for determining equivalent ratios. The term convert is defined, and students use approximate conversion rates to estimate measurement conversions before engaging with formal methods of converting. Converting among units of measurement in the same system is recast in terms of conversion ratios, which can also be called conversion rates.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

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.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

The course has five modules with each module broken into topics. Each topic has a set of three to six lessons/activities. Each lesson consists of several sections, which may include Warm Up, Getting Started, Activities, Talk the Talk, and an Assignment. The Warm Up and Getting Started sections activate students’ prior knowledge and engage students in non-routine problem solving. The Activities develop students' understanding of concepts by exploring problems through both individual and whole group instruction. The students demonstrate their understanding of concepts by applying their knowledge to real-world problems in the Talk the Talk section. The Assignment includes five mini-sections that reinforce understanding of the new mathematical concept. Each lesson has a coordinating practice set called Skills Practice with exercises for students to solve using their new learning. MATHia (online) provides additional personalized exercises for students to show their understanding of the activity/lesson.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.

Lessons follow a consistent format that intentionally sequences assignments:

  • “Warm Up” - exercises that activate students’ prior knowledge.
  • “Getting Started/Engage” - students solve/think/share and notice others' work/thinking, usually for a non-routine problem.
  • “Develop/Activities” - new learning takes place; students explore problems that engage them with examples and explanations of the targeted skill in a whole-class setting. Each Activity includes verbiage describing how the new knowledge relates to previous understanding.
  • “Demonstrate/Talk the Talk” - students reflect on and connect what was learned.
  • “Assignment” - five sections that review the lesson: Write - reviewing rules or vocabulary, Remember - summary of one or two key points, Practice - problems related to the activities, Stretch - an extension, and Review - looping in previous skills.

Students practice with “Learn Individually” lessons using the MATHia software or, if technology is not accessible, students use the Skills Practice workbooks.

Overall, each topic is sequenced to begin with prior knowledge and build upon that knowledge to develop conceptual understanding and procedural skill.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that there is a variety in what students are asked to produce. Students are asked to produce a variety of products in both digital and written form.

Some of these products include:

  • Multiple representations including expressions and equations, models, arrays, number lines, etc.
  • In Module 4, Topic 2, Lesson 2.2, students are given parts of quadrilaterals on a coordinate plane and use their knowledge of polygons and horizontal or vertical distances to complete the missing parts, then determine the area of the polygons.
  • Justification of their thinking and others', critiquing others’ work, explaining why answers given are correct.
  • Writing, reviewing, practicing, and stretching activities at the end of each lesson, for example, writing their own situations to model a given expression. (Module 1, Topic 2, Lesson 3.5)

Finally, each module includes a real-world connection where students produce solutions in a variety of ways to demonstrate their mathematical knowledge, such as plotting band member locations on a coordinate plane.

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that manipulatives are faithful representations of the mathematical objects they represent and are appropriately connected to written methods.

Manipulatives are embedded in activities and the MATHia Independent Digital Lessons. Number lines, patty paper, equivalency cards, etc. are used throughout the year in connection to the mathematics being presented and are faithful representations. For example, students cut, fold, and tape a cube net and answer questions about the net, then make conjectures on different nets based on creating this one. (Module 1, Topic 3, Lesson 3, Getting Started: Breaking Down a Cube)

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that the visual design is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The student materials are clear and consistent between modules within a grade level as well as across grade levels. The black and white design of the program is not distracting or chaotic. The text is supported by graphic elements that enhance the lesson, such as a highlighted worked example or various visual models to help with conceptual understanding. Both the textual and graphic elements complement each other and do not crowd the page or overwhelm the student with too much information.

Side bars complement the lesson and highlight important information. The informational side bars can include reminders of procedural steps, hints as to what strategies may need to be used to solve a problem, new vocabulary definitions, as well as reflective questions to students about their thinking. The program is logically organized with appropriate readability levels. Lesson numbers and activities are labeled in a consistent and orderly fashion. Each question in the student book is followed with a large open space for the student to write in, making the appearance uncluttered and easy to read and write.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 partially meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials support: planning and providing learning experiences with quality questions; contain ample and useful notations and suggestions on how to present the content; and contain explanations of the grade-level mathematics in the context of the overall mathematics curriculum. However, the materials do not contain full, adult-level explanations and examples of the more advanced mathematics concepts.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that the materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

In the Teacher Edition, facilitator notes for each activity include questions for the teacher to guide students' mathematical development and to elicit students' understanding. The material indicates that questions provided are intended to provoke thinking and provide facilitation through the mathematical practices as well as getting the students to think through their work. The Note provided on page FM-21 of the Teacher’s Implementation Guide Volume 1 reads, “When you are facilitating each lesson, listen carefully and value diversity of thought, redirect students’ questions with guiding questions, provide additional support with those struggling with a task, and hold students accountable for an end product. When students share their work, make your expectations clear, require that students defend and talk about their solutions, and monitor student progress by checking for understanding.”

Each lesson guide in the Teacher Edition provides quality questions to help guide students' mathematical development.

For example:

  • “Did you calculate the area of both figures, or did you take a shortcut? If you took a shortcut, what was it?”
  • “If you didn’t have a rectangle with the same dimensions as a parallelogram, how could you determine the area of the parallelogram?”
  • “Which formula did you learn first, the area of a parallelogram or the area of a rectangle?”
  • “Explain how knowing the area formula for a rectangle helped you derive the area formula for a parallelogram.”

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.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that the materials contain a teacher 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 such as how to use and read data in the MATHia software.

In the Lesson Resources, the teacher guide provides information including a lesson overview, lesson structure and pacing facilitation notes, questions to ask, connections to standards, a materials list, essential ideas, facilitation notes, what to look for when students are working, and a summary of the lesson.

As part of the blended learning approach, there is Learning Individually with MATHia software. There is ample support for students and teachers to engage with this software such as the Getting Started guide, a table of contents, an RTI table of contents, and MATHia system requirements.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 do not meet the expectation that materials contain a teacher edition (in print or clearly distinguished/accessible as a teacher edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

  • There are no adult-level explanations or examples for teachers to enhance their own knowledge of the content.
  • Teachers are not provided any content beyond what the student sees in the student resources.
  • The materials provide extensive information about how the content fits into the curriculum, but do not provide adult-level explanations or examples for teachers to understand the mathematics.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that materials contain a teacher edition (in print or clearly distinguished/accessible as a teacher edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.

  • The Module Overview includes information for the teacher with explanations that build the teacher’s understanding of how the lesson content fits into the curriculum. It tells what mathematics is in the module and how the module connects to prior and future learning.
  • Each Topic Overview provides information on the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Knowledge required from prior chapters and/or grades is explicitly called out in this section.
  • The Topic Overview also connects each lesson to standards from a previous grade. These previous grade standards are embedded into each lesson through the Warm Up and Getting Started sections as well as the Activity sections.
  • The Topic Overview describes the entry point or prior experience with the mathematical concept for students, why what is being learned is important, and how the activities in the topic promote student expertise in the MPs.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 provide a list of lessons in the teacher edition (in print or clearly distinguished/accessible as a teacher edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter, and unit (i.e., pacing guide).

  • Each course in this series contains a Scope and Sequence/Table of Contents categorized by Module, Topic, and Lesson and includes the standard, pacing, summary, and the essential ideas of the mathematics.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

  • The Family Guide for each topic is available in a PDF file that can be downloaded. The manual contains general topic information, what the students have learned in the past, what they will be learning, talking points, myths about math, keys for student success, vocabulary, content explanations, examples, and practice problems with answers aligned by topic and chapter.
  • Families are also provided with generic tips about how to facilitate success:
    • “To further nurture your child’s mathematical growth, attend to the learning environment. You can think of it as providing a nutritious mathematical diet that includes: discussing math in the real world, offering encouragement, being available to answer questions, allowing your student to struggle with difficult concepts, and providing space for plenty of practice.”
    • “You can further support your student’s learning by asking questions about the work they do in class or at home.”
      • How does this problem look like something you did in class?
      • Can you show me the strategy you used to solve this problem?
      • Do you know another way to solve it?
      • Does your answer make sense? Why?
      • Is there anything you don’t understand?
      • How can you use today’s lesson to help?

Indicator 3l

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

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Middle School Math Solution Teacher’s Implementation Guide contains both the research-based strategies and the instructional approaches for the program.

  • The instructional approach to learning is described as: “Carnegie Learning’s instructional approach is based upon the collective knowledge of our researchers, instructional designers, cognitive learning scientists, and master practitioners. It is based on a scientific understanding of how people learn and a real-world understanding of how to apply that science to mathematics instructional materials. At its core, our instructional approach is based on three simple yet critical components: Engage, Develop, and Demonstrate.” Each of these components is provided in detail. (FM-11,12)
  • The components of the blended learning program are described in detail as well as giving a website to learn more about the approach. (FM-12)

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
8/10
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities to collect information about students’ prior knowledge but lack strategies for about how to utilize the information in the classroom. The materials provide opportunities for identifying and addressing common student errors and misconceptions, ongoing review and practice with feedback, and assessments with standards clearly noted in most cases. The assessments contain detailed rubrics and answer keys, but there is no guidance for interpreting student performance or suggestions for follow-up.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 partially meet the expectation that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

  • There is a pretest for every topic in each module that addresses standards that will be taught. The post-test for the topic is the same test.
  • The Topic Overview provides a list of Prerequisite Skills needed for the topic, which creates an indirect opportunity for teachers to gather information about students’ prior knowledge although there is no direct guidance provided to the teacher about how to use the information.
  • The MATHia software is used as an assessment and progress monitoring tool, providing personalized data about where a student stands on various skills.
  • In every assignment in the textbook, there is a Review section. Students practice two questions from the previous lesson, two questions from the previous topic, and two questions that address the fluency standards outlined in the Standards. This provides teachers information about students' learning gaps as they work through the instructional materials.

While there are opportunities to collect information about students’ prior knowledge, the materials do not provide strategies about how to utilize the information in the classroom.

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that materials provide strategies for teachers to identify and address common student errors and misconceptions.

  • In the Topic Guide, lessons regularly have a section titled “Misconceptions” with suggestions for teachers to identify and address common student errors and misconceptions.
    • Example: “Students may get confused over the varied uses of the term scale—such as scaling up, scaling down, scale on a number line, even bathroom scale. Take the time to explain how all the uses of the term are related.” (M2-37J)
  • Teachers are encouraged to engage students in mathematical conversations to address student errors and misconceptions with phrases such as, “Remind the students…, Discuss with students…, Point out that….”
  • MATHia software provides a solution pathway to common student misconceptions. “Like a human tutor, MATHia re-phrases questions, re-directs the student, and hones in on the parts of the problem that are proving difficult for the student. Hints are customized to address the individual student, understanding that there are often multiple ways to do the math correctly.”

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials provide several opportunities for ongoing review and practice:

  • Students practice with “Learn Individually” lessons using the MATHia software or, if technology is not accessible, the Skills Practice workbooks. In the Skills Practice book, odd number answers are provided, so students know if they’re solving problems correctly; and in the MATHia software, feedback is continually given for both correct and incorrect answers.
  • The MATHia software includes “Hints” which students can select while reviewing and practicing skills. There are three types of “Hints”:
    • Just-in-Time Hints automatically appear when a student makes a common error.
    • On-Demand Hints are hints that a student can ask for at any time while working on a problem.
    • Step-by-Step demonstrates how to use the tools in a lesson by guiding step-by-step through a sample math problem.
  • Each lesson ends with Talk the Talk, a few questions that capture the learning of all of the activities the students have engaged in with the lesson.
  • Each lesson also has a short review section that provides a spiral review of previous concepts.
  • Standardized Practice Test that the teacher can use at any time to review and practice concepts and skills learned throughout the course.
  • Prior to each lesson there is a Warm-Up that reviews previous topics.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 partially meet the expectation for assessments clearly denoting which standards are being emphasized.

  • The series provides five options for assessment for every topic: Pretest, Post test, End of Topic test, Standardized Practice test, and a Performance Task. The Performance Task clearly notes which standards are being assessed.
  • The other assessment options address the set of standards included in each topic, but there are no standards specifically attached to the questions or the assessments.
  • It is stated in the materials that an assessment bank is also available through Edulastic, which is an optional tool that offers technology-enhanced items that can be used as-is or modified. However, reviewers did not evaluate this assessment bank.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 1 partially meet the expectation for assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

  • The Performance Task includes a detailed scoring rubric.
  • All other assessments provide an answer key, but no guidance about scoring.
  • MATHia reports provide teachers with detailed information about student performance in relation to progress on standards.
  • None of the assessment options provide guidance for teachers to interpret students performance and suggestions for follow-up.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 encourage students to monitor their own progress.

  • MATHia software encourages students to monitor their own progress using strategies such as: Just-in-time hints, On-demand hints, a Progress Bar showing a summary of major skills, and Skill Tracking Behavior.
  • There is a review for students at the end of every lesson which includes some spiral review of previous concepts.
  • The Family Guide suggests questions for students such as, “Is there anything you don’t understand? How can you use today’s lesson to help?”
  • Within the lessons, students do not monitor their own personal learning growth.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
11/12
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. The instructional materials provide a balanced portrayal of various demographic and personal characteristics. The instructional materials also consistently provide: tasks with multiple entry-points; support, accommodations, and modifications for English Language Learners and other special populations; and opportunities for teachers to use a variety of grouping strategies. There are opportunities for students to investigate mathematics content at greater depth, but they are intended for all students over the course of the school year, and there are very few tips for teachers to expand or deepen lessons.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials include a detailed Scope and Sequence of the course, including pacing. The lesson summary and the essential ideas provide further information on sequencing of the lessons. There is a chart in the Teacher’s Implementation Guide that includes a table with a column entitled, “Connections to Prior Learning,” which enhances the opportunity to scaffold instruction by identifying prerequisite skills that students should have.

All lessons include instructional notes and classroom strategies that provide teachers with key math concepts, sample questions, differentiation strategies, discussion questions, possible misconceptions, what to look for from students, and summary points providing structure for the teacher in making content accessible to all learners.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 partially meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

A primary strategy for meeting the needs of all learners in this program is MATHia software. MATHia provides differentiation, providing varying levels of support based on how students solve the problems. The software adapts to the specific responses and “tutors” each student to meet their needs.

Most lessons provide “Differentiation strategies,” “Questions to ask,” and a “Misconception” section. Most of the suggestions and the questions included in the “Questions to ask” section are intended for all students rather than geared toward helping students who struggle or challenging students ready to go deeper. For example, in Module 4, Topic 2, Lesson 3.1, Questions to ask: “What quantities are being compared? Which quantity depends on the other? How did you decide which quadrants you will need in order to graph the data? How did the signs of the numbers in the table help you decide which quadrants are needed in order to graph the data? How did you determine the weight differentials in Question 2?”

However, in the “Differentiation strategies” section, suggestions are limited but more specific. For example, in Module 1, Topic 2, Lesson 3.1: “For students who struggle, reduce the number of diagrams for which they must create fact families.”

Indicator 3t

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

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

  • Each Topic Overview includes a section called, “What is the entry point for students?” For example, in Module 1, Topic 1, the Factors and Area overview states: “Students enter Grade 6 with a conceptual understanding of area and fluency in computing the perimeter and area of rectangles. They have used tiling to relate area to multiplication and addition, and they have used informal statements of the number properties. Students have also used area models to represent multiplication. Factors and Area draws on this prior knowledge to formalize the Distributive Property, to reinforce connections between area models and multiplication, and to determine the area of new shapes.”
  • Some application tasks, particularly the Performance Task, allow for multiple solution strategies or representations. For example, in Module 5, Topic 1, “The Statistical Process,” students create a histogram for each display given and then describe how they selected the size of the bin. Students make a conclusion about the amount of sleep that children, teenagers, and adults get.
  • Some assessment questions allow for multiple entry points. For example, in Module 3, Topic 3, Post-test question 5, students write a story that matches a graph shown, allowing answers to vary.
  • Lesson activities provide limited opportunities for students to create their own solution paths since strategies are often provided.

Indicator 3u

Materials suggest 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).
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 partially meet expectations for suggesting 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).

ELL Tips are specifically cited throughout the materials. For example, “ELL Tip: In the first sentence, there are several words that may be challenging for English Language Learners (analyze, situation, corresponding). Have students read the paragraph independently and circle words that they do not know. Then have students find people in the class that have different circles. The students should help each other define words that they have circled. If numerous students are circling the same words, define these as a class.” (M3-197)

Additional differentiation strategies included in the materials are often general, such as providing additional examples, using manipulatives, or using a graphic organizer.

Some suggestions are specific to the lesson, but don’t necessarily further knowledge, such as in Module 2, Topic 2, Lesson 1.3: “Differentiation strategy: To support students who struggle, provide a hint sheet to support their learning while they play the game with peers who may think faster than they do."

There are differentiation suggestions that do not include a rationale as to how they would provide support. For example, in Module 2, Topic 1, Lesson 1.1: “For students who struggle, provide another example to compare/contrast. For example, scores for two games are 99-100 and 1-2. Which game was probably 'closer'?” It is unclear how this suggestion would support a student's development of additive and multiplicative reasoning.

However, there are numerous examples that do support accommodations for special populations such as:

  • “For students who struggle with base and height, it may be helpful to have them cut out figures. That way, they can turn the paper to see different sides can be the base. They can then use folds to determine the height.” (M1-15E)
  • “For students who struggle, transferring measurements from Question 2 into the diagram may be confusing. You may want to have pre-labeled diagrams available in those cases.” (M1-29D)
  • “For students who struggle, using the terms greatest and least may sound counter-intuitive compared to their answers. Stress that they should concentrate on key terms. In GCF, factor is the key term, and common factors cannot be larger than both values. In LCM, multiple is the key term and multiples may be larger than both values.” (M1-39G)
  • “Questions 1 through 4 and Questions 5 through 6 require the same knowledge; however, Questions 5 through 6 are less scaffolded and different information is provided. Assign Questions 1 through 4 to students who struggle and assign Questions 5 through 6 to students who need a challenge.” (M4-73H)
  • “For students who struggle, the use of inequality symbols often adds more confusion. You may want to adjust the directions so that students circle the larger number or label the values on a number line.” (M1-71G)
  • “To support students who struggle, it may be difficult to draw tape diagrams with rectangles of the same size. For this reason, you may want to provide a rectangle stencil or pre-drawn tape diagrams.” (M2-37E)

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The problems provided are grade-level work and are intended for all students over the course of the school year. There are very few tips for teachers to expand or deepen the lesson.

  • There are “Stretch” questions at the end of a lesson, but they are also designed for all students.
  • Some of the differentiation suggestions are for extension but benefit all students such as: “Differentiation strategy: To extend the activity, have students write each fraction in lowest terms and connect their response to the diagram.” (M2-7I) It is not clear whether these are generic lesson extensions or geared toward advanced students.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.

  • No examples of bias were found.
  • Pictures, names, and situations present a variety of ethnicities and interests.
    • The text is black and white with green as the only color. The people are gray with black hair, but still appear to represent many ethnicities.
    • Problems include a wide span of international settings, as well as situations in urban, suburban, and rural settings.
    • There is a wide variety of names in the problems, from James, Ben, and Haley to Keirstin, Miguel, and Miko, representing a variety of cultures.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 provide opportunities for teachers to use a variety of grouping strategies. The Blended Learning Model is explained in the Teacher’s Implementation Guide (FM-11). “Carnegie Learning delivers a different brand of blended learning: it combines collaborative group learning with focused individual learning. The two components are Learning Together and Learning Individually. Carnegie believes students “learn together” in a collaborative classroom model where they can think critically, reason mathematically, and learn from each other. Consumable textbooks and manipulatives allow them to engage directly with the mathematics as they learn. “Learning individually” offers two models: with or without technology. With MATHia, students learn independently using powerful 1-to-1 tutoring technology that adapts to give them exactly what they need at any given moment. With Skills Practice, students practice the important concepts of each topic to improve their problem-solving abilities and to gain fluency.”

Throughout the program, the facilitation guide instructs the teacher to, “Have students work individually to answer,” or “Have students work in groups or partners to answer question 2 and 3.” There is no explanation of how to form groups based on a skill or topic and/or why certain questions are given to groups or individuals.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 partially encourage teachers to draw upon home language and culture to facilitate learning.

  • There is no evidence of teachers drawing upon home language and culture to facilitate learning.
  • There is a Family Guide with each Topic that explains the mathematics and provides tips to support learning, but it does not utilize aspects of language and culture.
  • Materials are available in Spanish.

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
+
-
Criterion Rating Details

The instructional materials for Middle School Math Solution Course 1 integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, and they include opportunities to assess students' mathematical understandings and knowledge of procedural skills. The instructional materials include opportunities for teachers to personalize learning for all students, and the materials offer opportunities for customized, local use. However, the instructional materials do not include opportunities for teachers and/or students to collaborate with each other.

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 Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
+
-
Indicator Rating Details

Carnegie Learning Middle School Math Solution Course 1 claims that MATHia software will run on:

  • Windows Computers with operating systems Windows 7 and 10
  • Apple Computers with operating systems Mac OS X 10.11 or higher
  • Apple iPads with iOS 10 or higher
  • Windows Tablets with operating systems Window 8 or higher
  • Android Tablets with Android 4.1 and above
  • Chromebooks with ChromeOS 52 or higher
  • It is not recommended for phones or small devices.

All of these, except Android tablets, were tested, and all access was successful.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
+
-
Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 include opportunities to assess student mathematical understandings and knowledge of procedural skills using MATHia’s Adaptive Personalized Learning Reports. These reports provide information used for assessing students' learning and adjusting instruction.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. 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 Rating Details

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. The MATHia software for Carnegie Learning Middle School Math Solution Course 2 is customizable for individual learners users. Teachers can select specific skills and levels for individuals, and it adapts to the learners' needs as they progress.

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic. Within the lessons and assessment sections, the teacher chooses which exercises to assign students. Teachers can assign the lessons in any order; however, the lesson must be completed as provided before moving on. Additionally, these exercises cannot be modified for content or wording from the way in which they are given.

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 Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 1 do not provide opportunities for teachers and/or students to collaborate with each other online or in any technology-based environment.

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
+
-
Indicator Rating Details

Online materials for Carnegie Learning Middle School Math Solution Course 1 (MATHia) integrate technology incorporating Mathematical Practices that include:

  • Explore Tools to investigate different mathematical concepts, search for patterns, and look for structure
  • Animations to watch, pause, and re-watch demonstrations of various mathematical concepts
  • Classification Tools to categorize answers based on similarities
  • Problem Solving Tools provide students with individualized and self-paced instruction that adapts to their needs
  • Worked Examples to allow students to identify their own misconceptions

In MATHia, “Unit goals, based on CCSS and mathematical practices as well as aligned with the print materials, are listed at the beginning of the unit. Students are doing math by being engaged with sample problems and hints (just-in-time and on-demand), system help, a glossary, and a progress bar. Features are included to motivate and engage students like the creation of a personal avatar and tools such as 3D Geometry, Algebra Tiles, Fraction Shapes, and Pattern Blocks.”

Additional Publication Details

Report Published Date: Tue Mar 06 00:00:00 UTC 2018

Report Edition: 2018

Title ISBN Edition Publisher Year
Course 1: Student Edition 978-1-60972-889-2 Carnegie Learning 2017
Course 1 Blended: Student Edition and MATHia 978-1-60972-893-9 Carnegie Learning 2017
Course 1: Teacher Implementation Guide 978-60972-877-9 Carnegie Learning 2017

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.

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 K-8 Rubric and Evidence Guides

The K-8 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 K-8 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.

X