2015

Math Trailblazers

Publisher
Kendall Hunt Publishing Company
Subject
Math
Grades
K-5
Report Release
02/13/2015
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Does Not Meet Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
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Additional Publication Details

Title ISBN
International Standard Book Number
Edition Publisher Year
9781465224101
9781465224279
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About This Report

Report for 1st Grade

Alignment Summary

The instructional materials reviewed for Grade 1 do not meet the expectations for alignment to the CCSSM.

The materials do not devote the large majority of class time to major standards of the grade, but the materials can be utilized to appropriately assess grade-level content. One partial strength was noted in the coherence criterion, but too many areas of weakness mean the instructional materials do not meet quality expectations for coherence. Due to the materials not meeting expectations for focusing on major work and coherence, they were not reviewed for rigor and Mathematical practices.

1st Grade
Gateway 2

Rigor & Mathematical Practices

NE = Not Eligible. Product did not meet the threshold for review.
NE
0
10
16
18
Alignment (Gateway 1 & 2)
Does Not Meet Expectations
Usability (Gateway 3)
Not Rated
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 1 do not meet expectations for alignment to focusing on major work of the grade and coherence. The instructional materials do not allocate a large percentage of class time to major standards of the grade, but the materials can be utilized to appropriately assess grade-level content. One partial strength was noted in the coherence criterion, but too many areas of weakness lead to the instructional materials not meeting quality expectations for coherence.

Criterion 1.1: Focus

02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 1 meet the expectations for assessing material at the grade level. Although there are multiple units and lessons noted that align to and/or assess standards that are beyond Grade 1, the inclusion of these lessons and units is either Mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.

Indicator 1A
02/02
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 meet expectations for assessment because above grade-level assessment items, and their accompanying lessons or units, could be modified or omitted without significantly impacting the underlying structure of the instructional materials. For this indicator, all of the identified assessments and end-of-unit assessments for the 17 units were reviewed. Units and lessons accompanying above grade-level assessment items are noted in the following list.

  • In unit 3, lesson 7 has assessment items that 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?”. The Key Assessment Opportunities Chart shows the expectation that students be able to solve addition word problems involving two or three whole numbers whose sum is less than or equal to 20 using counters and ten frames. The expectation for students does align to standards in 1.OA.A, “Represent and solve problems involving addition and subtraction,”, but given that the problems in lesson 7 have students use the ¢ symbol appropriately, the problems more closely align to 2.MD.C.8. This lesson accounts for two class sessions of unit 3, which encompasses 13 to 14 class sessions total, so the omission or modification of this lesson would not significantly impact the structure of this unit.
  • In unit 5, lessons 2, 3, and 4 have assessment items that align 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 2.NBT.A.2., “Count within 1000; skip-count by 5s, 10s, and 100s.” The Key Assessment Opportunities Chart shows the expectation that students be able to skip count by 5s and count on to find the value of a set of coins. These lessons account for six to seven class sessions of unit 5, which encompasses 10 to 12 class sessions total, so the omission or modification of these lessons would have an impact on the structure of this unit.
  • In unit 7, lessons 1 and 3 have assessment items that align 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?”, 2.NBT.A.2, “Count within 1000; skip-count by 5s, 10s, and 100s,”, and 2.MD.D.10, “…Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. The Key Assessment Opportunities Chart shows the expectation that students be able to represent and identify quantities using connecting links, coins, and symbols; connect representations of quantities; skip count by 5s and 10s and count on to find the value of a set of coins; and read a table or bar graph to find information about a data set. These lessons account for five to seven class sessions of unit 7, which encompasses 12 to 16 class sessions total, so the omission or modification of these lessons would have a minor impact on the structure of this unit.
  • In unit 8, lessons 1 – 4 have assessment items that align to standards from 3.MD.C., “Geometric measurement: understand concepts of area and relate area to multiplication and addition.” The Key Assessment Opportunities Chart shows the expectation that students be able to recognize that different shapes can have the same area and find the area of a shape by counting square units and nonstandard units using efficient counting strategies. These lessons account for four to six class sessions of unit 8, which encompasses five to seven class sessions total, so the omission or modification of these lessons would have a significant impact on the structure of this unit. Given the size of this unit, though, its omission or modification would not have a significant impact on the entirety of the materials for the grade.
  • In unit 11, lessons 4, 6, and 7 have assessment items that align 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?” The Key Assessment Opportunities Chart shows the expectation that students be able to use skip counting to find the value of a collection of pennies, nickels, dimes, and quarters and recognize the relationship between larger and smaller units (i.e., one dime is two nickels). These lessons account for five class sessions of unit 11, which encompasses 11 to 13 class sessions total, so the omission or modification of these lessons would have a minor impact on the structure of this unit.
  • In Unit 13, Lessons 1 through 4 have assessment items that align to standards from 5.MD.C, “Geometric measurement: understand concepts of volume”. The Key Assessment Opportunities Chart shows the expectation that students be able to solve problems involving volume using repeated addition and skip counting; represent the volume of an object using symbols, connecting cubes, and number sentences; measure and estimate volume by building models and counting cubic units; and recognize that different shapes can have the same volume. These lessons account for seven to 10 class sessions of unit 13, which encompasses 9 to 12 class sessions total, so the omission or modification of these lessons would have a significant impact on the structure of this unit.
  • In unit 14, lesson 2 has assessment items that align to 3.MD.B.3., “Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.” The Key Assessment Opportunities Chart shows the expectation that students be able to read a table or bar graph to make predictions and solve problems about a data set. This lesson accounts for two to three class sessions of unit 14, which encompasses 11 to 14 class sessions total, so the omission or modification of this lesson would not have a significant impact on the structure of this unit.

*Evidence updated 10/27/15

Criterion 1.2: Coherence

00/04
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 the expectations for spending the large majority of class time on the major clusters of the grade. Too much time is focused on non-major work of the grade. Major work of Grade 1 includes addition and subtraction within 20 with only two units out of 17 units covering this work. For Grade 1, close to 85% of instructional time should be focused on major work of the grade, and with the amount of above-grade level instruction and assessment, these instructional materials do not approach 85%. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 1 or on standards that are above Grade 1.

Indicator 1B
00/04
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 the expectations for spending the large majority of class time on the major clusters of the grade. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 1 or on standards that are above Grade 1.

  • Major work of Grade 1 includes addition and subtraction within 20. Only two units out of 17 (12%) units cover this work.
  • Too much time is focused on non-major work of the grade.
  • For Grade 1, close to 85% of instructional time should be focused on major work of the grade, and with the amount of above-grade level instruction and assessment, these instructional materials do not approach 85%.

Criterion 1.3: Coherence

01/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 1 do not meet the expectations for being coherent and consistent with the CCSSM. The instructional materials have some instances of supporting work fostering coherence by engaging students in major work of the grade as addressed in indicator 1C, but the amount of content designated for Grade 1 is not viable for one school year. Also, the instructional materials are not consistent with the progressions in the CCSSM, and they do not foster coherence through connections at a single grade. Overall, the instructional materials for Grade 1 exhibit some characteristics of coherence as noted in indicator 1C, but for the entire criterion, there are too many weaknesses for the materials to even partially meet the expectations.

Indicator 1C
01/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 1 partially meet the expectations for having the supporting content enhancing focus and coherence simultaneously. Overall, the instructional materials miss opportunities to connect non-major clusters of standards to major clusters, and as a result, the supporting content does not engage students in the major work of Grade 1.

  • Time and shapes are presented separately and do not engage students in the major work of the grade.
  • Representing and interpreting data is not presented in a way so that students are engaged in the major work as evidenced in lesson 6, unit 1, and lesson 5, unit 5.
  • The supporting work of representing and interpreting data is present in unit 14.
  • Unit 2, lesson 2 describes and compares shapes.
  • Unit 15, lesson 1 folds shapes and partitions them into halves and fourths.
Indicator 1D
00/02
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Grade 1 do not meet the expectations for having an amount of content designated for one grade level as viable for one school year. Overall, the amount of time needed to complete the lessons is not appropriate for a school year of approximately 170-190 days.

  • The content is designed for 220 days, which far exceeds the amount of content which could be taught/learned in a school year.
  • The instructional materials contain 17 units with five to six lessons in a unit.
  • The instructional materials contain 109 lessons with up to five activities per lesson.
Indicator 1E
00/02
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 the expectations for having materials that are consistent with the progressions in the CCSSM. Overall, the materials do not give students extensive work with grade-level problems, and grade-level concepts are not always explicitly related to prior knowledge from earlier grades. Also, the materials do not develop according to the grade-by-grade progressions, with non grade-level content not being clearly identified.

  • The content is somewhat connected to the major work of the grade, but because the mastery of the off-grade content must occur before the problems can make sense, this becomes a problem as evidenced by lesson 7, unit 3; lesson 2, unit 5; lesson 1, unit 7; lesson 5, unit 5; and lesson 3, unit 7.
  • Work from prior grades is identified at the beginning of each unit in the "unit overview."
  • Content does not progress appropriately within the major work of each grade as addressed in 1a, 1b and 1c.
  • No mention of work in preparation for future grades is identified.
  • All units except unit 1 and unit 2 have future grade content.
  • The amount of time spent off grade level does not allow for students to spend enough time with grade-level work.
  • Daily practice problems and problems of the week are present, but there is no evidence of differentiation for below- or above-level students.
  • There are no explanations provided for the teacher or student linking prior knowledge from prior grades.
Indicator 1F
00/02
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 instructional materials reviewed for Grade 1 do not meet the expectations for having materials foster coherence through connections at a single grade. Overall, the materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings, and the materials do not always connect two or more clusters in a domain or two or more domains in a grade when appropriate.

  • It is not clear the learning objectives have been shaped by the cluster headings due to the amount of off grade-level objectives.
  • Unit 4, lesson 3, aligns to 1.OA.A.1 and 1.OA.A.2 (add and subtract within 20), but there is no evidence in the unit of going beyond 10. Other examples include unit 4, lesson 4; unit 12 lesson 2; and unit 6, lesson 6.
  • Units are departmentalized. For example, unit 2 explores shapes, but then it is not until unit 16 that 3-dimensional shapes are introduced.
  • Lesson 1, unit 3, is the only lesson in the series that connects two clusters appropriately. There are some other instances where clusters are connected, but those involve future grade level content.
  • In unit 2, lesson 2, there is no connection between describing and comparing shapes with place value and 10s, for 1.NBT.
  • In unit 7, lesson 5, there is no connection between measuring in inches and adding and subtracting when solving word problems.
Overview of Gateway 2

Rigor & Mathematical Practices

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

Criterion 2.1: Rigor

NE = Not Eligible. Product did not meet the threshold for review.
NE
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
00/02
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
00/02
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
00/02
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
00/02
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

NE = Not Eligible. Product did not meet the threshold for review.
NE
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
Indicator 2E
00/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
Indicator 2F
00/02
Materials carefully attend to the full meaning of each practice standard
Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
00/02
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
00/02
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
00/02
Materials explicitly attend to the specialized language of mathematics.

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
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
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
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
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
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

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
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
00/02
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
00/02
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
Read
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
Read
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
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
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
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
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
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
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.
Indicator 3AD
Read
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
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.