3rd Grade - Gateway 1

The instructional materials reviewed for Grade 3 do not meet expectations for assessment. For this indicator, the review team examined all components of the cumulative tests, which included the power-up tests, the cumulative tests, 10 extension tests, and the performance tasks. The team was unable to review the benchmark tests as they were not included in the materials. The instructional materials for Grade 3 assess several topics that are beyond the expectations for Grade 3 repeatedly in their assessments. Some of the assessments could have items modified or omitted so as to align to Grade 3 expectations, and in other cases, the inclusion of the above, grade-level expectations is mathematically reasonable. Overall, though, the amount of modifications or omissions needed significantly impacts the underlying structure of the instructional materials. Following is a list of the topics that align to expectations beyond Grade 3, the standards or clusters to which they actually align, and the assessments in which the topics appear.

• Comparing fractions with unlike numerators and unlike denominators aligns to 4.NF.A.2, “Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model,” and it appears in Cumulative Test 10 after lesson 55. The teaching of this topic is found in 5 lessons.
• Parallel and perpendicular lines along with types of angles are geometry topics that align to 4.G.A, “Draw and identify lines and angles, and classify shapes by the properties of their lines and angles,” and they appear in the following Cumulative Tests: 8A after lesson 45, 15A after lesson 80, 16A after lesson 85, 18A after lesson 95, and 21A after lesson 105. These topics are addressed in a total of 12 lessons.
• Multiplication of numbers whose product is bigger than 100 exceeds the expectations established by 3.OA.C, “Multiply and divide within 100,” and this topic appears in the following Cumulative Tests: 17A after lesson 90, 18A after lesson 95, 19A after lesson 100, and 21A after lesson 105. Multiplication of numbers where one factor is written in decimal notation to hundredths aligns to 5.NBT.B.7, “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used,” and this topic appears in Cumulative Tests 19A after lesson 100 and 21A after lesson 105. These two multiplication topics are addressed in a total of 11 lessons.
• Place value for numbers greater than 1,000 is an expectation that aligns to 4.NBT, “Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000,” and this topic appears in the following Cumulative Tests: 13A after lesson 70, 15A after lesson 80, 18A after lesson 95, and 21A after lesson 110. This topic is addressed in a total of 8 lessons.
• Conversion of measurements is a topic that aligns to standards in 4.MD.A, “Solve problems involving measurement and conversion of measurements”, and 5.MD.A, “Convert like measurement units within a given measurement system,” and this topic appears in the following Cumulative Tests: 13A after lesson 70, 18A after lesson 95, and 20A after lesson 105. This topic is addressed in a total of 12 lessons.
• Probability is a topic that aligns to 7.SP.C, “Investigate chance processes and develop, use, and evaluate probability models,” and this topic appears in the following Cumulative Tests: 9A after lesson 50, 10A after lesson 55, and 20A after lesson 105. This topic is addressed in a total of 3 lessons.
• Finding volume in cubic units is a topic that aligns to 5.MD.C, “Geometric measurement: understand concepts of volume”, and this topic appears in Cumulative Tests 16A after lesson 85 and 20A after lesson 105. This topic is addressed in a total of 3 lessons.

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 3 do not meet expectations for focus and a majority of time is not spent on major cluster of the grade. According to the manual, the author suggests a 60-minute class period consisting of a 30-minute block in which students complete written practice problems (distributed practice which does not particularly focus on or extend the new concept taught that day) and a 15-minute power up block. Because of this and the wide range of concepts addressed in the practice (which changes daily), it is difficult to trace the amount of time spent on each concept through this and the power up practice. This means the educator will focus only on the new concept lessons as the tool in which to base the review alignment to the major work of the grade level. The author allots a mere 15 minutes for the new concept lesson. The first 40 new concept lessons are largely reviewed from previous grades and the majority focus on the "additional cluster" 3.NBT and address addition and subtraction with procedural fluency (which goes beyond alignment). By contrast, there are only eight lessons devoted to fractions (3.NF.A) and only one lesson featuring two-step word problems (3.OA.D), which are both major work of the grade level. In fact, the very first non-review major work evidence found is in Lesson 29, fractions of a dollar. After extensive examination, only 40 of the 121 lessons (110 lessons plus 11 Investigations) actually address the major work of Grade 3, a mere 33%. Additional examples of misaligned lessons include:

• Lesson 81 says the lesson is aligned to major work but the objective exceeds the standards by asking for student to multiply two-digit numbers by one-digit numbers. The standard referenced is focused on multiplying two one-digit numbers.
• Lesson 82 is mostly focused on major work as students determine equal groups. Written practice is partially aligned to major work, problem-solving is not aligned to major work or grade level, power up is partially aligned to major work, new concept is aligned to major work (divide by 2 with multiplication table) and written practice is partially aligned.
• Lesson 84 multiplies two-digits by one-digit, which not aligned with major work. Written practice is partially aligned with major work.
• Lesson 85 is aligned to major work in the new concept and written practice is mostly aligned to major work.
• Lesson 86 is aligned to major work in the new concept (X fact families) and written practice is partially aligned.
• In lesson 88 even and odd is not major work of the grade and is part of Grade 2.
• In lesson 89, dividing by a one-digit number is major work of this grade but the limit is 100, not 144 like the table shows.
• In lesson 90, equal group stories reflect major work of grade level.
• In lessons 41-50, only Lessons 41 and 42 align within the new concept part of the lesson.
  • Lesson 43 has comparison of fractions with a denominator of 5. Grade 3 expectations are limited to denominators of 2, 3, 4, 6 and 8.
  • Lesson 44 asks for fraction identification with denominators of 5 and 7.
  • Lessons 45 and 50 focus on probability, not a Grade 3 standard.
  • Lessons 46-50 include fractions with 5 and 7 as denominators as well as mixed number concepts. Mixed numbers are not a Grade 3 standard. All of the written practice activities in the lessons have multiple questions that are not aligned as well.

The instructional materials reviewed for Grade 3 do not meet expectations for supporting content enhancing focus and coherence simultaneously. The lessons in the supporting clusters do not enhance focus and coherence, as evidenced by the following examples. Each of the supporting concepts are taught in isolation and it is doubtful that students will be able to make the necessary connections between the supporting and major work of the grade level.

• Investigation 1 in lessons 1-10 and investigation 3 in lessons 21-30 include work with scaled pictographs and bar graphs, but this work in the program only focus on creating graphs and organizing and identifying how many, which does not adequately cover the standard in 3.MD.
• Investigation 6 in lessons 51-60 presents scaled bar graph vertically and has simplistic questions identifying parts of the graph. There is no effort to connect the scaled pictograph and scaled bar graphs to 3.OA.A or 3.OA.D, where the graphs could serve as an interesting context for the one- and two-step word problems.
• Lessons 34, 35, 37 and 52 focus on learning how to measure and practice measuring in isolation.
• Section 8 in lesson 78 teaches the standard in isolation and therefore does not support the major work.

While there is an effort in some of the materials to relate some supporting work to major work, these examples do not justify partial or full expectation for the criterion.

• Lesson 106 supports 3.MD.C as it requires reasoning with shapes and their attributes to accurately estimate the area of a figure. For example, two triangles can fit together to form one square. Lesson 43 supports 3.MD.A as it requires the interpretation of a map as well as the length in inches from one point to another.

The instructional materials reviewed for Grade 3 do not meet expectations for viability for one school year in order to foster coherence between the grades. The curriculum consists of 110 lessons, 11 investigations and 21 cumulative assessment days for a total of 142 days needed to complete the curriculum. Although this is a manageable number of days for a school year, only 56 of the 121 lessons are aligned to the major work of the grade level, nine of the 121 lessons are aligned to the supporting work and 16 of the 121 lessons are aligned to additional work of the grade level. Of these purportedly aligned lessons, at least half are either from previous grade levels or go above Grade 3 content (e.g., multiplication and division fluency). The remaining 40 lessons (approximately 33% of the lessons) are either aligned to the MP-since they do not align to any Grade 3 content standards-or they contain above grade level content. For these reasons and the evidence cited in 1b, Grade 3 does not cover the major work with enough depth for students to be ready for the work of the next grade level.

The instructional materials reviewed for Grade 3 do not meet expectations for consistency with the progressions in the standards. This is evident through examples below which were based on 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. Examples of work that are not consistent with the progressions are:

• Lessons 13, 14, 16, 19, 23, 24 and 28, revolve around the supporting work of addition and subtraction computation (3.NBT.A) which becomes the focus rather than the application within two-step problems (3.OA.A), so it serves to displace grade-level content.
• Lesson 81 is about multiplying two-digit numbers using the procedure aligned to 3.OA.C, but is above grade-level content and inaccurately aligned to a Grade 3 standard.
• Lesson 45 is about probability (MP.3) and belongs in Grade 7 materials.
• Lesson 65 is about angles (MP.6) which is work in future grades.
• In lessons 36, 39, and 40, most of the problems identified as 3.OA.D.8 never truly address the major work as they are limited to one-step word problems
• In lessons 16, 18 and 20 students subtract two-digit numbers which is part of Grade 2. They also work with story problem types that should be mastered by the end of Grade 2.
• In lessons 22 and 25, students name dollars and cents and exchange dollars, dimes and pennies and count dollars and cents. This is aligned with Grade 2.
• Lesson 26 has students add and subtract dollars and cents, but decimal work does not begin until Grade 4. Column addition in lesson 24 introduces a procedure that should not be introduced until Grade 4.
• Lesson 100 multiplies dollars with a decimal sign, which is a Grade 6 standard. This displaces grade level content.
• Lesson 109 has coordinate graphing.
• In lesson 73, the new concept is volume-future standard. The written practice in this lesson has 20 questions and 11 are on grade level. The 11 are all aligned to different standards.
• Lessons 55 and 56 only show how to use a multiplication table and are aligned to 3.OA.B, but nowhere are properties of multiplication or division discussed.
• Lessons 81 and 84 focus on procedural fluency with 2-digit multiplication and are aligned to 3.OA.C, yet the lessons have nothing to do with fluently multiplying and dividing within 100 using strategies or properties of operations.
• A limited number of lessons in lessons 29, 41-43, part of 46 and 47-49 in the 3.NF.A cluster present fractions in an extremely rote way, which does not help students to actually understand fractions and therefore will not offer extensive work in this standard. There is not enough work included in the curriculum for a major standard in Grade 3.
• The new concept in lesson 64 is multiplying by nines. It is introduced by giving a multiplication table and no other examples. No prior knowledge is incorporated into lesson.

In no instances did the review team find evidence that the materials explicitly made these connections to prior knowledge. Additionally, due to the structure of the curriculum, the amount of time spent on new concept lessons is only a small fraction of the entire lesson time, thus preventing work from being extensive.

The materials reviewed for Grade 3 do not meet expectations for coherence through connections at the grade level. Materials do not include learning objectives shaped by CCSSM. Each individual lesson contains power up questions, new concept explanation and a written practice that is a spiraling review. All lessons and daily components do not state the CCSSM, MP and learning objectives. For example:

• Lesson 92 lists parenthesis, using compatible numbers and using order of operations as the focus. These are topics but not learning objectives.
• In looking at lessons aligned to 3.OA.B, the learning objectives stated are not visibly shaped by the CCSSM heading and in some cases, do not even relate to the cluster heading. None address the relationship between multiplication and division. Some examples include:
  • The lesson 55 multiplication table deals only with how to read a multiplication table.
  • The lesson 56 multiplication facts are about zero, one and 10.
  • The lesson 59 multiplication facts are about two and five.
  • In looking at lessons aligned to 3.NF.A, the learning objectives stated in most of the lessons are not visibly shaped by the CCSM heading. The objectives in lessons 41-44, 46, 47 and 49 do not promote an understanding of fractions as numbers, but rather as part of a whole region or set. The only lesson that remotely promotes fractions as numbers is Lesson 48.

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.

• In the lesson 62 area and extension activity, rectangles with the same area or same perimeter could be connected as they both address Grade 3 clusters but are treated separately and the extension may be completed with some students but not all.
• Lesson 84 focused on multiplying two-digit numbers with the extension activity focused on finding the area of combined rectangles. The first exceeds the expectations of Grade 3 and the extension reflects work with the distributive property, something all Grade 3 students need to master.
• Student work partitioning shapes into parts with equal areas (3.G.2) does not relate to visual fraction models (3.NF.A) as there are no real lessons aligned to 3.G.2 in the book. Lessons 42, 47, 62 and 63 are listed in the correlation guide as addressing 3.G.2, but upon close inspection, they do not.
• Student work with scaled pictographs and scaled bar graphs (3.MD.3) does not provide a visually appealing context for solving multiplication problems. There was no explicit multiplication connection made in investigation 1, investigation 3, or investigation 6 and no multiplication or division questions were featured.