1st Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 71% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 4 / 8 |
The instructional materials reviewed for Grade 1 Everyday Mathematics partially meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of the grade for Grade 1, but the materials do not always meet the full depth of the standards.
Criterion 1.1: Focus
The Grade 1 Everyday Mathematics materials meet the expectations for not assessing topics before the grade-level in which they should be introduced. Future, grade-level topics are assessed, however those assessments could be removed without affecting the progression of learning for students. The number of above grade-level assessments is limited and could easily be removed by the teacher.
Indicator 1a
The instructional materials reviewed for Grade 1 meet expectations for assessment because above grade-level assessment items could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Probability, statistical distributions, and/or similarity, transformations and congruence do not appear in the Grade 1 materials.
The program allows for a Beginning of the Year, Mid-year, End of the Year Assessment, and Unit Assessments, which mostly assess the Grade 1 standards. There are also nine unit assessments/progress checks. The unit assessments/progress checks have portions for Self Assessment, Unit Assessment, Open Response Assessment, Cumulative Assessment, and a Challenge. Each grade level's standards are broken down into 45 to 80 Goals for Mathematical Content that are listed in the back of the Teacher's Lesson Guide and also in the online Teacher Center. These assessments can be found in the Assessment Handbook. The Individual Profile of Progress for tracking and class progress are present in both paper (pages 101-112 in the Assessment Handbook) and digital formats. Most lessons have an Assessment Check-in that can be used as either formative or summative assessment as stated in the implementation guide.
Assessment check-ins are part of most lessons and mostly assess grade-level content. Examples include:
- Lesson 2-11, (page 201), students solve word problems with unknowns in different positions (1.OA.1).
- Lesson 3-9, (page 277), students count forward and backward and add or subtract 10 from given numbers (1.OA.5, 1.NBT.1, 1.NBT.5).
- Lesson 4-1, (page 312), students directly compare lengths of objects indirectly by using a third object (1.MD.1).
- Lesson 4-11, (page 374), students find 10 more or 10 less than a given number (1.NBT.5).
- Lesson 5-4, (page 417), students compare numbers and use symbols <, >, = to express the relationship (1.NBT.3).
- Lesson 6-10, (page 566), students build numbers with base-ten blocks, identify the tens and ones within a two-digit number and exchange ten ones for a ten stick. (1.NBT.2)
- Lesson 7-3, (page 610), students use addition and subtraction to find missing addends. (1.OA.4, 1.OA.6)
- Lesson 8-2, (page 693), students partition shapes to make two equal shares (1.G.3).
- Lesson 9-1 (page 780), students measure objects using multiple copies of a smaller object (1.MD.2).
The Unit Assessments, the End of the Year Assessment and some of the Assessment Check-Ins do have a few off grade-level problems included. The following off grade-level content is assessed in the Grade 1 Materials:
- In Unit 1 Open response assessment, students count buttons. In the rubric for this assessment, students must group buttons together in consistent groups, which leads to skip-counting, a second-grade skill (2.NBT.A.2), in order to meet or exceed expectations.
- Unit Assessment 3, page 21 in the Assessment Handbook, problem 5 assesses counting by 5's which is a Grade 2 expectation (2.NBT.A.2). Question 7 is skip counting by 2's using odd numbers, which is finding a pattern, Grade 4 standard (4.OA.C.5).
- Unit Assessment 4, page 29 in the Assessment Handbook, problem 3 assesses counting by 5's which is a Grade 2 expectation (2.NBT.A.2).
- Unit Assessment 9, problems 5 and 6, and page 68, problem 7, assess money which is a Grade 2 expectation (2.MD.C.8).
- In the End of the Year Assessment in the Assessment Handbook, page 89, problem 1 and page 90, problem 5, assess counting by 5's which is a Grade 2 expectation (2.NBT.A.2). Page 99, problem 26, assesses defining a larger category of shapes, i.e., polygons, which is a Grade 3 expectation (3.G.A.1).
- The Assessment Check-In for Unit 3, lesson 3-9, page 277, assesses counting by 5's which is a Grade 2 expectation (2.NBT.A.2).
- The Assessment Check-In for Unit 7, lesson 7-7, page 634, assesses defining larger categories of shapes which is a Grade 3 expectation (3.G.A.1).
- Four Assessment Check-Ins for Unit 9 assess money, which is a Grade 2 expectation (2.MD.C.8). Lesson 9-2, page 786, lesson 9-3, page 794, lesson 9-6, page 813, and lesson 9-8, page 824, all assess money (2.MD.C.8).
Most of the off grade-level assessments could be removed by the teacher without affecting the sequence of learning for students. The assessments of money would need to be modified since those assessments are also assessing addition and subtraction. In Units 1, 3, 6 and 9, the teacher will need to supplement in order to assess all skills and concepts.
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 Grade 1 Everyday Mathematics materials meet expectations for devoting the large majority of class time to the major work of the grade level. The Grade 1 Everyday Mathematics engages students in the major work of the grade about 65 percent of the time.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Grade 1 meet the expectations for focus by spending the majority of the time on the major clusters of the grade. This includes all the clusters in 1.OA and 1.NBT and cluster 1.MD.A.
The Grade 1 materials do spend the majority of class time on the major clusters of the grade. Work was not calculated by units since the units spiral and are not clustered by groups of standards. Grade 1 Everyday Math includes 109 lessons, 100 of which are expected to be completed within one day. Each of the nine units includes an Open Response and Reengagement lesson which is designed to be done over two days. Progress checks are also allotted two days worth of instructional time at the end of each unit. At the lesson level, the lessons are divided into Daily Routines, Core Activities, and Practice. Each day consists of 15-20 minutes on routines, 30-45 minutes of a core activity, and 15-20 minutes of practice. Assessment days were not included in these calculations.
The following calculations were derived from the core activities of the lesson.
- Sixty-eight lessons out of the 109 are focused on the major work. This represents approximately 62 percent of the lessons. Additionally, another three lessons, or approximately 3 percent, are supporting work which truly supported the major work of the grade bringing the time spent on major work to approximately 65 percent.
- Thirty-one lessons out of the 109 are focused solely on the supporting work of the grade. This work was treated separately from the major work of the grade. This represents approximately 27 percent of the lessons.
- Ten lessons out of the 109 are focused on off grade-level work. This represents approximately 8 percent of the lessons. This includes: lessons 3-5 and 3-8, on counting by 5's, a Grade 2 standard; lesson 3-9, page 275, on counting by 2's, a Grade 2 expectation; lesson 3-11 on counting by 2's and 5's, a Grade 2 expectation; lesson 6-11 on exchanging money, a Grade 2 standard; and lessons 9-2, page 784, 9-3, page 788, 9-5, page 802, 9-6, page 808, and 9-8, page 823, on money, which is a Grade 2 standard.
Notes: Lesson 2-5 includes finding the missing day of the week which is not a mathematics standard. Lesson 5-3, focusing on exchanging ones for tens, comes very close to the Grade 2 standard of exchanging money. Lesson 6-7 is on the reference book; however, it is not introduced until the 6th chapter, or almost the end of the year.
Criterion 1.3: Coherence
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 CCSSM. The instructional materials have enough materials to be viable for a school year, but they do not always meet the depth of the standards. The majority of instructional materials do not have supporting content enhancing focus and coherence simultaneously, but they do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 1 do not exhibit enough characteristics of coherence.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials partially meet the expectations for having the supporting content enhance focus and coherence by engaging students in the major work of the grade. The majority of supporting work is mostly treated separately and does not always support the major work of the grade. The following details the lessons and practices with supporting work.
- Unit one has three lessons and five practices which are supporting work, and only one lesson, 1-8, supports major work. Lesson 1-8 connects supporting work with tally charts (1.MD.4) with addition and subtraction and counting. In Lesson 1-7, tally marks for data, tally marks are treated mainly as a means to represent data with little support for using tally marks as a counting tool. In Lesson 1-9, Building with base 10 blocks, blocks are used to build structures with no support for the base-10 numbering system which they represent.
- Unit two has two lessons and two practices which are supporting work, and only one practice, 2-2, supports major work.
- Unit three has one lesson which is supporting work, and it does not support the major work.
- Unit four has two lessons which are supporting work, and both lessons, 4-5 and 4-6, support major work. Lesson 4-5 connects supporting work with tally charts (1.MD.4) with addition and subtraction and counting. Lesson 4-6 connects supporting work with bar graphs (1.MD.4) with addition and subtraction and counting.
- Unit six has two lessons and one practice which are supporting work, and they do not support the major work. In lesson 6-7. My Reference Book is introduced as a tool and sections are discussed, but the book is not used in a real problem-solving or classroom mathematics situation until this lesson. Connections to a tool that could be helpful for students should be made earlier in the year.
- Unit seven has four lessons which are supporting work, and they do not support major work.
- Unit eight has nine lessons and six practices which are supporting work, and no lessons or practices support major work.
- Unit nine has two lessons and five practices which are supporting work, and no lessons or practices support major work.
Indicator 1d
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 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The suggested pacing includes 109 days of lessons (100 lessons total) and another 24 days allowed for assessment, making 133 days of materials. According to the Teacher Guide on page xxxvi, each lesson is expected to last between 60-70 minutes. The online curriculum states to use Friday's as a Flex Day for games and intervention work. With Fridays being included as Flex Days, this curriculum allows for approximately 33 to 34 weeks of instruction.
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.
The instructional materials reviewed for Grade 1 do not meet the expectation for being consistent with the progressions in the standards. Content from prior grades is not clearly identified or connected to grade-level work, and students are not given extensive work with grade-level problems. Material related to future, grade-level content is not clearly identified or related to grade-level work. The Grade 1 materials have several instances where future grade-level content is present and not identified as such. For example, unit 3, lesson 5 is on skip counting by two's and five's, which is a Grade 2 standard, 2.NBT.A.2, and does not state it is future grade-level work or how it would relate to work of Grade 1. The same is true of unit 9 lesson 2, which is on solving money problems, a Grade 2 standard, 2.MD.C.8. This is true of all of the instances of off grade-level work.
The content does not always meet the full depth of standards. This mainly occurs because of a lack of lessons addressing the full depth. For example, there are three lessons which address 1.OA.2; however, only one of them, 4-10, is a full lesson. The other two are a very small part of the core lesson. Another example is 1.NBT.5; only four lessons have students mentally finding 10 more or 10 less than a number. A third example is 1.OA.1; only 2 lessons out of 17 have students solving addition and subtraction to 20. Three of the seventeen reach sums of 12, and the rest all only use within 10. Two lessons, 4-8 and 4-10, are the only lessons for properties of operations. Geometry is given slightly more attention than place value throughout the materials, and Geometry is given significantly more attention than measuring and iterating length units.
Everyday Mathematics Grade 1 materials do not provide extensive work with grade-level standards. For example, the instructional materials do not provide extensive work with the following standards:
- 1.OA.A.1: Much of the work in this series focuses on addition and subtraction within 10, not 20.
- 1.NBT.A.1: Most of the lessons in this series focus on numbers under 100, not 120. Lessons where students either work with or at least see numbers over 100 occur in 1-11, 3-8, 5-6 (only in the homework); 5-12 (using the number grid to subtract); and lesson 9-9 (homework to 107). The Number of the Day Routine does give the student work with numbers larger than 100.
- 1.OA.A.2: Word problems with 3 addends are fully attended to in two lessons, 4-10 and 6-6. Lessons 6-2 and 9-2 are identified with this standard and dedicate a small portion of the lesson to this standard. Other focus lessons labeled with this standard 9-5 and 9-6 are misidentified.
- 1.NBT.B.2: Only lessons 5-1, 5-2 and 5-3 address this standard with a few more questions in math journal and/or homework.
In lessons where prior knowledge is needed, the instructional materials do not state that prior knowledge is being used. When future grade-level concepts are introduced, there is no mention that the concept will be used in future grades. If the teacher uses the spiral trace at the beginning of the lesson or unit, the teacher will know where prior knowledge is used based on the spiral trace and when the student will use the skill/concept again in the future. For example, in lesson 3-9 on page 272, the spiral snapshot shows how the lessons progress through the materials. The spiral tracker is listed by lessons and not connecting standards. At the beginning of each unit, the spiral trace provides an explanation of what will occur by the end of the unit, but the spiral trace does not explain any further and does not connect to the next standard.
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.
The instructional materials reviewed for Grade 1 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings, but there are missed opportunities to provide problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.
The materials do include learning objectives which are visibly shaped by CCSSM cluster headings. In the teacher's lesson guide on page EM3, the materials show the Goals for Mathematical Content for Everyday Math and how they align to the CCSSM. From this alignment it is apparent the goals are shaped by the CCSSM cluster headings.
Instructional materials shaped by cluster headings include the following examples:
- Lesson 3-7: "More Counting to Add and Subtract," is shaped by 1.OA.C.
- Lesson 5-2: "Digits and Place Value," is shaped by 1.NBT.B.
- Lesson 7-7: "Exploring Attributes, Fractions, and Salute!" is shaped by 1.NBT.A.
- Lesson 8-8: "Time to the Half Hour," is shaped by 1.MD.B.
While the materials have many instances where two or more domains are connected, often the connections are only surface-level connections. For example, Lesson 2-3 shows a connection between 1.OA.6 and 1.NBT.1 The lesson has students adding within 10 but does not truly have them counting within 120. Lesson 5-4 shows a connection between 1.OA.6, 1.OA.7 and 1NBT.3. The lesson has students comparing numbers using the symbols for less than, greater than, and equal to, but it does not have students adding and subtracting. The connection between place value and adding or subtracting is very rare, and no explicitly stated connections could be found. Other times, lessons provide more than one standard or cluster that will be worked on, but these standards are mostly worked on separately in the different portions of the lesson, such as warm-ups, daily routines, focus lesson, and practice. Additionally, 60 of the lessons are only aligned to one domain.
A few lessons were found to have connections among domains. Lesson 1-8 includes students collecting, organizing, and interpreting data (1.MD.4) and using that data as a context for solving comparison word problems (1.OA.1). Lesson 5-10 includes students solving comparison word problems (1.OA.1) and understanding the relationship of addition and subtraction (1.OA.4) as they use either or both operations to solve (page 451).