3rd Grade - Gateway 1

The instructional materials reviewed for Grade 3 do not meet expectations for assessment. The materials assess statistical distributions with questions that align to standards from 6.SP.A, “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions.”. There are also many other sessions in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. For this indicator, all of the identified assessments and end-of-unit assessments for the nine units were reviewed. Units and sessions accompanying above grade-level assessment items are noted in the following list.

• Assessment 2.3A in unit 2 assesses how to: describe the shape of ordered, numerical data; describe where data are spread out or contracted, where there are few data, highest and lowest values, and outliers; and describe data using the term range. These expectations align to standards within 6.SP. According to Table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6.
• Unit 4, session 2.6, assesses how to: design a shape for a given area; find area by counting or calculating whole and partial square units; find the perimeter of an irregular shape; and find the area of an irregular shape. These expectations partially align to 3.MD.C.7.Aa, “Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths,” and 3.MD.C.7.D.d, “Recognize area is additive. Find the areas of rectilinear figures by decomposing them into non-overlapping parts, applying this technique to solve real world problems.” There are four sessions that align to these expectations, and these four sessions would need to be modified or omitted in order for the expectations to align to the grade-level standards.
• In Unit 6, the end-of-unit assessment expects students to: read and interpret positive and negative temperatures on a thermometer and on a line graph; use tables to represent the relationship between two quantities in a situation with a constant rate of change; and compare situations by describing differences in the tables that represent them. These expectations align to 6.NS.C.5 , “Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g. temperatures above/below zero, elevations above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation,” and 6.RP.A.3., “Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.” There are twelve sessions that align to these expectations, and these twelve sessions would need to be omitted because modifications would eliminate the underlying structure and intent of the lessons.
• In Unit 7, the end-of-unit assessment expects students to: divide a single whole or quantity into equal parts; name those parts as fractions or mixed numbers; identify equivalent fractions; and find combinations of fractions that are equal to one and to other fractions. Adding and subtracting fractions with unlike denominators most closely aligns to 5.NF.A, “Use equivalent fractions as a strategy to add and subtract fractions.”. There are four sessions that align to this expectation, and these four sessions would need to be modified or omitted in order for the expectations to align to the grade-level standards.
• Problems 1 and 2 on the end-of-unit assessment for unit 8 involve computing with money. These problems align to 4.MD.A.2 , “Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements giving in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale,” and these problems could be modified or omitted from the assessment without significantly affecting the underlying structure of the materials.
• Unit 9, session 3.3, assesses how to: design patterns (nets) for boxes that will hold a given number of cubes; see that the cubes filling a rectangular prism can be decomposed into congruent layers; and determine the number of cubes that will fit in the box made by a given pattern (net). These expectations align to 5.MD.C, “Geometric measurement: understand concepts of volume”, and 6.G.B.4, “Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems”. There are seven sessions that align to these above, grade-level standards, and these seven sessions would need to be omitted because modifications would impact the underlying structure and intent of the lessons.

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 3 do not meet expectations for majority of class time spent on the major clusters of the grade. There are 166 sessions between assessments and lessons in the materials. Excluding assessments, there are 154 sessions that would be taught throughout the year. Within that 154, only 99 lessons are focused on the major concepts of grade three. This results in 64% of the year being dedicated to the major work. This percentage does not meet the recommended range of time spent on the major work (65%-85%). The following are examples where work is not accurately aligned to the standard as marked, thus diminishing the focus. Examples include:

• When in unit 9 students are asked to work with measuring volume, the problems include alignments with Grades 4, 5 and 6 standards and introduce transformational geometry which is a Grade 8 standard.
• The 6 sessions on division in unit 5 are insufficient material for 3.OA.B.6, and two of these are the same lessons for 3.OA.C.7 for fluency.
• Unit 7 investigation 3 on decimals is above the scope for the grade.
• 1.3 in unit 7 has students adding the unit fraction, which is more suitable for Grade 4.
• Unit 4, lesson 2.1 has transformations, which is a Grade 8 standard. Students are using slides, flips, and turns to prove congruence of shape.
• Unit 6 includes questions and activities on the shape of the data, which is more appropriately aligned with Grade 6.

In addition, much focus is given to straight addition computation (3.NBT.A), which is an additional cluster, and to addition and subtraction word problems (3.OA.D.8). The majority of these are not two-step problems as required in the standard. Addition and subtraction computation and word problems are the focus for 3 units, while multiplication and division is found in one 25-day unit, and fractions in a 15-day unit (of which many lessons are not sufficiently aligned to the standards).

Instructional materials reviewed for Grade 3 do not meet expectations for coherence because the content in the materials does not support focus and coherence. Overall the review team concluded that there were very few lessons that had supporting/additional clusters that supported the major work. Examples include:

• Unit 4, investigation 3 teaches standard 3.G.1 in isolation.
• Unit 6 is Data Analysis: Investigation 1 focused on reading a graph about temperatures on the hour, and all lessons did not simultaneously engage students.
• All lessons in investigation 2 focus on patterning which is not a standard for Grade 3.
• Supporting content 3.MD.B.3 involves scaled pictographs and bar graphs which could be used as an appealing context for one- and two-step word problems involving multiplication (OA.A.3). However this opportunity was missed as the scaled graphs are taught in unit 2, prior to the multiplication work taught in unit 5. There are no scaled bar or picture graphs utilized in unit 5 in order to make this connection.
• In unit 9, the use of nets as representations for 3D shapes is included, which is work of Grade 6.

The instructional materials reviewed for Grade 3 do not meet expectations for viability of content for the scope of one year. The curriculum consists of 166 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, the review team found that the major work is not adequately covered in the materials and therefore, would not be viable for the year in order to support students as they prepare for Grade 4. The domain of number and operations-fractions, which is major work, is greatly under-represented in this series. Only unit 7 teaches fractions and of its 16 lessons, only 2 (sessions 1.1 and 1.2) are aligned correctly to Grade 3 standards.

The instructional materials reviewed for Grade 3 do not meet expectations for consistency with the progressions. The materials do not develop according to the progressions, and they do not give students extensive work with grade-level problems. In addition, while there are teacher notes in the "Looking Back" section of each unit, there is not explicit connection to specific standards addressed in prior grades. Examples of evidence include:

• In unit 2, line plots focus on numerical data and the focus is on the "shape of data" and includes references to mode and outlier, which is future work.
• Unit 6 focuses on patterns and line graphs, and neither concept is a Grade 3 expectation.
• Angles are introduced in unit 4 as an attribute which helps define and categorize squares and rectangles. A Math Note on page 126 explains that teachers can use the angle vocabulary in this grade, but the concept is formally introduced and becomes an expectation in future grades.
• In unit 7, students are introduced to a few decimal fractions in the context of money. In the Mathematics in this Unit section on page 11, it is explicitly stated that there is no benchmark for this work with decimals and that the extensive work will be in Grades 4 and 5. With the limited focus on fractions in the Grade 3 materials, this is not consistent with the progressions in the standards.
• A good deal of "extensive work" is missing - there are no real two-step problem-solving opportunities. Most of these opportunities have been simplified by guiding students through the steps by using parts a, b, c in the problems.
• The "Looking Back" note in unit 1 (page 10) specifically refers to how students work with place value and the properties of addition and subtraction, as well as their work with addition and subtraction fluency with 1-digit combinations. While this is the foundation for their work within addition and subtraction problems in Grade 3, this is not made explicit with connections to CCSSM from prior grades.
• Units 6 and 9 are not aligned with grade level content.

The instructional materials reviewed for Grade 3 do not meet expectations for fostering coherence through connections at a single grade. The materials do not include learning objectives that are shaped by cluster headings and do not include some problems that connect clusters and domains. Examples include:

• In unit 7, 11 lessons and 2 assessments are labeled with an alignment between 3.G.A.2 and 3.NF.A, however, upon further review only four of the lessons actually support this coherence. The lessons, investigation 2.2, 2.4, 1.4, 1.5 and 3.1-3.3 may have partitioning but it is with a denominator outside of the scope of the grade. The work also includes dividing parts of a set and involves dividing decimals in money context to hundredths which is all outside of the scope for Grade 3.
• All focus points are in units 6 and 9, as these units are not aligned with grade level content.
• Unit 2 aligns with Grade 6, such as when describing the shape of ordered, numerical data, or where data are spread out or concentrated, where there are few data, highest and lowest values and outliers.
• Unit 4 aligns with Grade 8, such as when determining the geometric moves needed (slides, flips and turns) to prove or disprove congruence between two shapes.
• Unit 7 aligns with Grade 4, such as when using mixed numbers to represent quantities greater than 1.
• In unit 2, scaled graphs are taught in isolation and before the multiplication work in unit 5, so a natural connection between the two is missed.