3rd Grade - Gateway 1

The instructional materials reviewed for Grade 3 do not meet expectations for assessment. The materials assess symmetry of shapes with questions that align to 4.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; 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;” and they assess similarity, congruence and geometric transformations with questions that align to 8.G.A, “Understand congruence and similarity using physical models, transparencies, or geometry software.”. There are also many other lessons in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. Units and lessons accompanying above grade-level assessment items are noted in the following list.

• In unit 1, lessons 1, 3, and 5 have assessment items that align to standards from 6.SP.A “Develop understanding of statistical variability,” and 7.SP.A, “Use random sampling to draw inferences about a population. The Key Assessment Opportunities Chart shows the expectation that students be able to represent the variables and procedures of an investigation in a drawing and make predictions and generalizations about a population from a sample using data tables and graphs. 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. These lessons account for seven to eight class sessions of the first unit, which encompasses nine to ten class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
• In unit 5, lessons 3, 4, and 5 have assessment items that align to standards from 6.SP.B, “Summarize and describe distributions”.. The Key Assessment Opportunities Chart shows the expectation that students be able to find the median of a data set and make predictions and generalizations about a data set using data tables, graphs, and diagrams. 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. These lessons account for six to seven class sessions of Unit 5, which encompasses 11 to 14 class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
• In unit 11, lessons 4, 7, and 8 have assessment items that align to 4.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 standards from 8.G.A, “Understand congruence and similarity using physical models, transparencies, or geometry software.”. The Key Assessment Opportunities Chart shows the expectation that students be able to identify congruent shapes and lines of symmetry. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of symmetry of shapes should not occur before Grade 4 and assessment of similarity, congruence, or geometric transformations should not occur before Grade 8. These lessons account for six class sessions of unit 11, which encompasses 17 to 20 class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
• In unit 12, lesson 1, 2, and 3 have assessment items that align to standards from 5.G.A, “Graph points on the coordinate plane to solve real-world and mathematical problems.”. The Key Assessment Opportunities Chart shows the expectation that students be able to plot points and find locations or objects on a map using coordinates and make a point graph using ordered pairs and draw a best-fit line. These lessons account for four to five class sessions of unit 12, which encompasses 11 to 14 class sessions total, so the omission of these lessons would have a minor impact on the structure of this unit.

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 3 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 3 or on standards that are above Grade 3.

• A large amount of time is devoted to addition and subtraction, which is prior to Grade 3, and there is little time spent solving problems involving the four operations.
• Unit 3 covers exploring multiplication; unit 9 addresses parts and wholes; and unit 10 explores multiplication and division. There are also multiple units on non grade-level topics including two units on addition and subtraction (units 6 and 7).
• Units 2, 4, 6, 7 and 11 are on non-major clusters of Grade 3, and 3 of the 6 lessons in unit 12 are on non-major clusters of the grade. This means that 5.5 out of 13 units (42%) address non-major clusters of Grade 3, so at most 58% of the instructional materials address the major clusters of Grade 3.

The instructional materials reviewed for Grade 3 do not meet the expectations for having the supporting content enhance 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 3.

• Lesson 5, unit 1; lesson 2, unit 9; and lesson 6, unit 10 are the only three lessons in which supporting content enhances the major work of the grade.
• In unit 4, lesson 3, students are representing numbers to 100, but they are not using place value to help them add, subtract, or multiply. This does not enhance the major work, which would have students representing and solving multiplication and division.
• In unit 11, lesson 2, students are asked to find the area of the shape using triangles and tangrams. However, there is not a connection to 3.MD.C where students would be asked to understand concepts of area and relate area to multiplication and addition. It is also not supporting 3.MD.A where students solve problems involving measurement and estimation of intervals of time, liquid, volumes and masses of objects.
• The supporting cluster, reason with shapes and their attributes, is present in unit 11, lessons 2 and 4-9, but these do not engage students in major work of the grade.
• The supporting cluster, represent and interpret data, is present in unit 1, lessons 3-5, but these do not engage students in major work of the grade.

The instructional materials reviewed for Grade 3 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 future grade-level content is not connected to grade-level work as evidenced by lesson 4, unit 5; lessons 4 and 8, unit 11; and lesson 1, unit 12.
• The future grade-level content is not identified and not connected to grade-level work as evidenced by lesson 8, unit 13.
• Because of the amount of time spent on off-grade level work, students do not have extensive work with grade-level problems.
• There are no explanations provided for the teacher or student linking prior knowledge from prior grades.
• Only five of 13 units include major work, and of those only one focuses on fractions.
• No explanations or connections are provided connecting work from prior grade levels. Unit 2 provides the strongest evidence for this, but there is not a direct link to the prior knowledge used in Kindergarten, Grade 1 and Grade 2.
• There is no evidence of differentiation for below- or above-level students. All students and all learning levels are not accounted for.

The instructional materials reviewed for Grade 3 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.
• The materials do not provide connections between two or more domains.
• Units are compartmentalized, lacking connections among different units.
• The student guides and "at home practice" are not labeled with objectives.
• In unit 10, lesson 4, students are asked to represent problems with a number line, but it is a one-step problem having them write the number sentence and give a brief explanation why.
• The materials do not clearly link or connect domains, but there are a few areas where the materials attempt to link domains in different clusters.