## Saxon Math

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
9780547729169
9781600325342
9780547746951
9781600327216
9780547729183
9781600325465
9780547746975
9781600327179
9780547746937
9781600327193
9780547729176
9781600325403
Showing:

### Overall Summary

The instructional materials reviewed for Grade 1 do not meet expectations for alignment. The materials do not spend the majority of time on the major clusters in the grade and assess math content from standards in grades above Grade 1. The materials do not foster coherence within the clusters of the grade and do not support the full intent and connections that naturally occur between the standards. In the instances where more than one cluster was identified in a lesson, they were generally addressed separately. Since the materials do not meet the expectations for focus and coherence in Gateway 1, they were not reviewed for Gateway 2.

###### Alignment
Does Not Meet Expectations
Not Rated

### Focus & Coherence

The instructional materials reviewed for Grade 1 do not meet the expectations for alignment to focus on major work of the grade and coherence. The instructional materials do not meet expectations for each of the two focus criterions because they assess above grade-level standards and allocate too large of a percentage of lessons to clusters of standards that are either from prior grade levels or grade levels above Grade 1. Overall, the instructional materials need to eliminate the assessment of above grade-level standards and more clearly define the amount of time to be spent on major clusters of Grade 1, supporting focus and coherence simultaneously.

##### Gateway 1
Does Not Meet Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 1 do not meet expectations for assessment. The instructional materials for Grade 1 assess several topics that are beyond the expectations for Grade 1 repeatedly in their assessments. Overall, the number of modifications or omissions needed significantly impacts the underlying structure of the instructional materials. A list of the topics that align to expectations beyond Grade 1, the standards or clusters to which they actually align and the assessments in which the topics appear is provided in the evidence section of the report for this indicator.

##### Indicator {{'1a' | indicatorName}}
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.

The instructional materials reviewed for Grade 1 do not meet expectations for assessment. For this indicator, the review team examined all written assessments. The instructional materials for Grade 1 repeatedly assess several topics that are beyond the expectations for Grade 1. Some of the assessments could have items modified or omitted so as to align to Grade 1 expectations, and in other cases, the inclusion of the above grade-level expectations is Mathematically reasonable. Overall, the number of modifications or omissions needed, however, significantly impacts the underlying structure of the instructional materials. Following is a list of the topics that align to expectations beyond Grade 1, the standards or clusters to which they actually align and the assessments in which the topics appear.

• Continuing patterns aligns to 3.OA.D.9 “Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends”, and 4.OA.C.5, “Generate and analyze patterns,” and it appears in written assessment 7 after lesson 40-2, written assessment 13 after lesson 70-2 and written assessment 26 after lesson 135. The teaching of this topic is found in nine lessons.
• The identification of pieces of money and determining the value of a collection of coins align to 2.MD.C.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?”, and they appear in the following written assessments: 10 after lesson 55-2, 12 after lesson 65-2, 15 after lesson 80-2, 19 after lesson 100-2, 21 after lesson 110-2, 22 after lesson 115-2, 24 after lesson 125-2 and 26 after lesson 135. The teaching of these topics is found in 16 lessons. • Addition and subtraction with money aligns to MD.C.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?”, and it appears in the following written assessments: 17 after lesson 90-2, 18 after lesson 95-2, 20 after lesson 105-2 and 26 after lesson 135. The teaching of this topic is found in 16 lessons.
• Determining if a number is even or odd aligns to 2.OA.C.3 and it appears in the following Written Assessments: 12 after lesson 65-2, 15 after lesson 80-2 and 20 after lesson 105-2. The teaching of this topic is found in six lessons.
• Lines of symmetry is a topic that aligns to G.A.3,, “Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry”, and this topic appears in written assessment 14 after lesson 75-2. The teaching of this topic is found in two lessons.
• Measurement with inches and centimeters aligns to standards in 2.MD.A, “Measure and estimate lengths in standard units,” and this topic appears in the following written assessments: 21 after lesson 110-2, 22 after lesson 115-2, 25 after lesson 130-2 and 26 after lesson 135. The teaching of this topic appears in 16 lessons.
• Division is a topic that aligns to standards in 3.OA.A,, “Represent and solve problems involving multiplication and division,” and this topic appears in written assessment 22 after lesson 115-2. The teaching of this topic appears in one lesson.
• Fractions with a denominator of three or six is a topic that aligns to standards in 3.G.A, “Reason with shapes and their attributes,” and this topic appears in written assessment 23 after lesson 120-02. The teaching of this topic appears in three lessons.

*Evidence updated 10/27/15

#### Criterion 1.2: Coherence

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.

The instructional materials reviewed for Grade 1 do not meet expectations for focus. The material did not spend the majority of time on the major clusters in the grade. There is little work with addition and subtraction problems in context. There was evidence found where actual student activities do not align with the standards labeled in the materials and where students are engaging in work above the grade level, thus diminishing the focus.

##### Indicator {{'1b' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 1 do not meet expectations for focus. The majority of class time is not spent on the major clusters of the grade. At first glance, according to the author's alignment, 95 of the 139 lessons are aligned to the major work of the grade level (~68%). However, upon closer study of the material within each lesson, a number of lessons deal with concepts not considered major work. For example, money, odd and even numbers, and addition and subtraction involving money is presented. Some examples of misalignment can be found in:

• Lesson 39; weight;
• Lesson 41; the calendar, pattern, weather and lunch graph, clock, coin cup mental math and problem solving, and right/left sections;
• Lesson 53: counting dimes and pennies;
• Lesson 56: odd and even numbers;
• Lesson 86: adding 2-digit numbers with regrouping using dimes and pennies;
• And lesson 127: subtracting 2-digit numbers.

In actuality, only 62 of the 139 lessons (44.6%) are major work of Grade 1. It is also noteworthy that according to the program overview, the daily instructional time consists of two blocks of instructional time-first 15-20 minutes are "meeting time" and the second 40-45 minutes of "new concept lesson/fact practice/guided practice." Roughly 25% of the daily instructional time is meeting time. It should be noted that some of the activities within the meeting time also are outside of the major work, and only the counting, graphing and math fact pieces are sometimes aligned. At times, the counting activities go beyond the scope as the year progresses, and the math facts addressed go beyond the "sums to 10." Therefore, the amount of minutes spent in major work is further diluted, lessening the amount of time spent on major work, subsequently earning a rating of zero.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The review team found that the coherence between the standards at the Grade 1 level fall short of meeting expectations for these criteria. A few examples as evidence for the rating are as follows:

• Lesson 121 focuses on subtraction and could be connected to Grade 1 clusters, but the opportunity was missed.
• Lessons 73-75 involve 2-digit computation with money, which should not be introduced until Grade 5, but is aligned to 1.NBT.C.
##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 1 do not meet expectations for coherence in that the content addressed in the materials does not support focus and coherence. Overall, very few lessons address supporting/additional clusters that substantially support the major work. The reviewers felt that this was due in large part to the low percentage of lessons that were actually focused on the major work of the grade level. Examples of supporting work that does not enhance focus includes:

• In lesson 24, geometry is taught in isolation, therefore it does not support major work of this grade level.
• In lesson 26, shapes are used to create AB patterns which is not consistent with geometry standards and is taught in isolation.
• In lessons 65-1 and 67, students are asked to make a graph (above grade level) by covering a design with pattern blocks.
• In lesson 67, students are asked to partition rectangles into halves and to know the numeric representation of ½, which exceeds the standards and is appropriate for Grade 3.
• In lesson 96, students are drawing congruent shapes. This does not support the major work of the grade and it exceeds the expectations of this grade.

While students routinely answer questions such as "How many?" and "How many more?" about the class weather and classroom lunch /attendance graphs in the "meetings," there is not enough evidence that supporting content enhances focus in the Grade 1 instructional materials.

##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

##### Indicator {{'1e' | indicatorName}}
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.

The instructional materials reviewed for Grade 1 do not meet expectations for consistency with the progressions in the standards. This is evidenced through examples below which were found in materials around the progression of grade-by-grade content, the access in materials to grade level problems and the connections to concepts from prior grades. The materials address a great deal of off-grade level content not clearly identified as such, other than identifying the CCSSM focus of the lesson as a MP rather than a Content Standard.

• Lessons 46, 53 and 66 focus on money, which is the major work of Grade 2, yet they are aligned to 1.NBT.B.
• Lessons 73-75 involve 2-digit computation with money, which should not be introduced until Grade 5, but is aligned to 1.NBT.C.

Prior work in Kindergarten is not identified as it relates to Grade 1 work. In no instances did the review team find evidence that the author explicitly made these connections to prior knowledge. Although the lessons aligned to 1.NBT.A (extending the counting sequence) relate to prior work with numbers to 20 in Kindergarten, no explicit connection is made in the teaching materials. In fact, a great number of lessons seem to still be stuck at the Kindergarten level while revisiting reading, writing and counting to 20. Examples of this are lessons 2, 3, 4 and 8.

##### Indicator {{'1f' | indicatorName}}
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.

The materials reviewed for Grade 1 do not meet expectations for coherence through connections at the grade level. This is evidenced through the absence of CCSSM aligned learning objectives. For example:

• Section 10, lessons 96-99 identified goals such as to draw congruent shapes and designs, measure and draw line segments to the nearest inch, count nickels, count nickels and pennies and order events by time. None of these lessons are shaped by the CCSSM cluster headings for this grade.
• Lessons aligned to 1.OA.B, specifically 41, 61 and 76 have titles that imply standards alignment but are very vague and inaccurate when examining individual problems. Even though the objective is not specific, the commutative property is addressed when reversing the order of the addends.

Additionally, a lack of connections in math problems made between and among clusters in a domain and domains in a grade informed the evaluation of instructional materials for this criteria. Examples of missing connections include:

• The connections between 1.NBT.A and 1.NBT.B (understanding place value) should connect to and support students as they work in cluster 1.NBT.C to add and subtract two-digit numbers using strategies and mental math. However, all of the 2-digit computation uses a money (dimes and pennies) context as a place value connection. Examples can be found in lessons 73-75.
• Lesson 81 approaches computation in a procedural way and this continues throughout the rest of the opportunities (lessons 123 and 127). As mentioned, the connection to money is not true coherence in Grade 1 since money is not a grade level expectation.
• The connections between 1.OA.A. (addition and subtraction within 20 to solve word problems) and 1.OA.B (understand and apply properties of operations and relationship between addition and subtraction) and 1.NBT.C (multi-digit addition and subtraction) are limited in that in many lessons, only single-digit computation is involved, and therefore, no real place value connection is made. Examples can be found in lessons 15-1, 25-1 and 33.
• In lesson 95-1, sums of 10 and extension activity solving word problems could be connected as both address Grade 1 clusters but are treated separately. The extension may be completed with some students, not all.
• Lesson 114 focuses on adding three one-digit numbers and could be connected to Grade 1 clusters, but the opportunity was missed.
• Lesson 121 focuses on subtraction and could be connected to Grade 1 clusters, but the opportunity was missed.

### Rigor & Mathematical Practices

Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One
Not Rated

#### Criterion 2.1: Rigor

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.
##### Indicator {{'2a' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
##### Indicator {{'2c' | indicatorName}}
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
##### Indicator {{'2d' | indicatorName}}
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.

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
##### Indicator {{'2e' | indicatorName}}
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
##### Indicator {{'2g.ii' | indicatorName}}
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.
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

### Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Not Rated

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
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.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
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.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
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.
##### Indicator {{'3h' | indicatorName}}
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.
##### Indicator {{'3i' | indicatorName}}
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.
##### Indicator {{'3j' | indicatorName}}
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).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
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).
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
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.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
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.
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.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

## Report Overview

### Summary of Alignment & Usability for Saxon Math | Math

#### Product Notes

The assessment materials were not provided with this series. The lack of the assessment resources for the Grades 3 to 5 band made it difficult to review for focus. Reviewers could only review the assessments as they appeared in the teacher guide. It is important to note that there are two different versions of the third grade curriculum materials, and the team reviewed the version consistent with the Grades 4 and 5 materials. The Grade 3 version that is consistent with the Kindergarten to Grade 2 materials was not reviewed.

#### Math K-2

The structure of the instructional time creates a situation in which the time actually allotted for the major work of the grade level is limited and extremely difficult to determine. Depending upon the grade level, between 25 and 40% of the daily math time is spent in meetings and many of the meeting concepts are not aligned to the grade level expectations. The amount of time devoted to new concept introduction is reduced to approximately 15 minutes, followed by practice that is not focused on the new concept of the day, but rather a compilation of skills and concepts introduced thus far, many of which are not grade level work. This structure makes it virtually impossible for a teacher to adjust the curriculum in order to meet the grade level expectations.

The incorporation of different games and workstations was a positive part of the series. This allows for students to engage in hands on mathematics and discourse with peers on the mathematics they are working through in games.

##### Kindergarten
###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated

#### Math 3-5

The structure of the daily instructional time creates a situation in which the time actually allotted for the major work of the grade level is limited and extremely difficult to determine. Of the suggested 60-minute class period, 15 minutes is devoted to power up activities that includes ongoing practice involving some concepts not pertinent to the grade level. This is followed by a 15-minute new concept introduction and a 30-minute distributed practice session which involves very little practice with the new concept and ongoing practice in unaligned concepts. Therefore, even on days when the new concept is considered major work of the grade level, very little time is actually devoted to it. By the time students are in Grade 5, more than half of the lessons are not aligned to Grade 5 expectations. This structure and the large number of unaligned concepts make it extremely difficult for a teacher to adjust the curriculum in order to address the CCSSM expectations for the grade level.

###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated
###### Alignment
Does Not Meet Expectations
Not Rated

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### Overall Summary

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###### Usability
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