Kindergarten - Gateway 1

The instructional materials reviewed for Kindergarten partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade.

The following detail supporting work in the instructional materials.

• Topic 5 consists of four lessons. Lesson 5-1 focuses on classifying objects into categories. There is a missed opportunity here to support major work through a connection of counting the number of objects within each group. Lesson 5-2 focuses on classifying objects and counting the objects in each group, connecting major and supporting work. Lesson 5-3 focuses on classifying objects, counting the objects in each group, and comparing the quantities, connecting major and supporting work. Lesson 5-4 focuses on classifying and counting objects which connects major and supporting work.
• Topic 12 is focused on identifying and describing shapes. While students are engaged in counting sides and vertices, this work is minimal. This topic is placed at the end of the materials, and the students are engaged in counting numbers beyond ten. If this Topic were moved to closer to the beginning where students are practicing counting with numbers to five then it would be more supportive of major work.
• Topic 13 is focused on analyzing, comparing, and creating shapes. Again, while students are engaged in counting sides and vertices, this work is minimal. Additionally, the placement of the topic at the end of the materials means the students are engaged in counting numbers beyond ten. If this Topic were moved to closer to the beginning where students are practicing counting with numbers to five, then it would be more supportive of major work.
• Topic 14 is focused on describing and comparing measurable attributes. This topic is treated separately and does not support the major work of the grade.

The instructional materials reviewed for Kindergarten partially meet the expectations for being consistent with the progressions in the standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade level.

Material related to future grade-level content is not clearly identified or related to grade-level work. The exception is the topic titled "Step up to 1st grade" where the materials are clearly identified as Grade 1 materials. The Kindergarten materials have several instances where future grade-level content is present and not identified as such. For example:

• Topic 11, lessons 2, 3, 4, 6 and 7 have students count groups past 20, 1.NBT.1.
• Lesson 9-7 asks students to count a set of objects greater than 10 in a scattered format. K.CC.5 states, "Count to answer how many questions about as many as 20 things arranged in a line, a rectangular array, or a circle, and as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects."

The content does not always meet the full depth of the standards. This occurs due to a lack of lessons addressing the full depth of the standards. For example:

• K.CC.2 has one lesson addressing counting on from any number besides 1, lesson 11-5.
• When looking at K.CC.1 counting to 20 is covered in-depth; however, the full depth of the standard, counting to 100, is not reached.
• K.G.5 has one lesson on analyzing and comparing shapes.
• K.G.6 has two lessons, one for two-dimensional shapes and one for three-dimensional shapes, having students compose shapes to make other shapes.
• Zero is a very difficult concept for students, and there are two lessons focused on zero for K.CC.3.
• There are some lessons which address K.OA.4; however, there are two lessons which have students finding a number that makes ten when added to a given number. This is a critical idea that is built upon in Grade 1.
• Lessons in Topic 11 are tagged with K.CC.2; however, it is unclear if the students are actually counting from any number or reading the numbers provided.
• For K.NBT.1, there are seven lessons which address teen numbers as ten ones and some additional ones, a major focus in Kindergarten. These lessons are consecutive within the text, providing limited opportunity to develop and maintain understanding.

The materials provide extensive work with grade-level problems, for example:

• Students engage in guided and independent practice, problem-solving contexts, and performance tasks. The opportunities for practice are balanced between each of the domains of the standards.
• Online resources include extra, on-level and advanced-practice materials.
• Interventions provided with lessons for students most often engage students more deeply in the work of the grade level than the lesson itself. Often, the lessons do not engage students because students are simply following directions instead of being engaged in problems. The following are some examples of lessons where the interventions would engage students more than the lesson: lessons 1-5, 1-6, 2-3, 2-6, 3-6, 3-7, 6-7, 6-9, 7-6, 7-7, 8-5 and 8-7.
• The numbers of topics addressing Kindergarten domains are as follows: 6 out of 14 topics address Counting and Cardinality; 2 out of 14 topics address Measurement and Data; 1 out of 14 topics addresses Number and Operations in Base Ten; 3 out of 14 Topics address Operations and Algebraic Thinking; and 2 out of 14 topics address Geometry.
• There are many opportunities for children to count objects within 10 and 20, and there are many opportunities for students to write numbers within 20 as stated in the standards. However, there are not many opportunities for daily counting above 20, which would enable students to more easily master counting to 100 by 1's and counting to 100 by 10's.
• There is concern that seven lessons address composing and decomposing numbers between 11 and 19 (K.NBT.A) as it pertains to gaining an appropriate understanding of place value for Kindergarten.

The materials relate grade-level concepts to prior knowledge within the introduction of each topic, for example:

• "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Kindergarten, explaining connections to the content within the topic, and explaining what will come later in Kindergarten and in Grade 1. An example can be found on pages 1c-1d for Topic 1.
• Individual lessons also include coherence headings. An example is in lesson 3-5 on page 163 that includes the heading, "Coherence: Engage learners by connecting prior knowledge to new ideas. Students use counters to represent and count a set of 10. This prepares them for the next part of the lesson where they practice representing and counting sets of 10."

The instructional materials reviewed for Kindergarten partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two or more domains in the grade.

The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.

• The focus of topic 1 is K.CC.A, Knowing number names and the count sequence, and K.CC.B, Count to tell the number of objects. Lesson objectives in Topic 1 include: L1 - Count 1, 2, and 3 objects, L2 - Count groups of 1, 2, and 3 objects in different ways, L3 - Read and write the numbers 1, 2, and 3, and L11 - Use math to explain what you know about counting.
• A similar example for Topic 2 can be found on pages 85I - 85J.

The materials for Kindergarten enVision Math 2.0 do not foster coherence through grade-level connections. Most lessons in the kindergarten program focus within a single domain and cluster. Of 106 lessons, 83 lessons focus within a single cluster and domain.

• In Topic 1, only one lesson, lesson 1-9, is identified as addressing standards within two domains K.CC.4 and K.OA.3.
• All lessons within Topic 2 are within a single cluster and domain.
• Five of eight lessons in topic 3 (3-2, 3-4, 3-6, 3-7, 3-8) address standards in two clusters, with two of those within different domains.
• Topic 4 includes two of six lessons that address two clusters, both within the same domain.
• In Topic 5, addressing supporting work, three of the four lessons address two clusters and domains, Measurement and Data and Counting and Cardinality.
• Of the 10 lessons in Topic 6, one lesson addresses standards within two clusters and domains, K.CC.2 and K.OA.1.
• All lessons within Topic 7 are within a single cluster and domain.
• All lessons within Topic 8 are within a single cluster and domain.
• Although six of the seven lessons in Topic 9 address two clusters, both clusters are within the same domain.
• All lessons within Topic 10 are within a single cluster and domain.
• All lessons within Topic 11 are within a single cluster and domain.
• Although four of the eight lessons in Topic 12 address two clusters, both clusters are within the same domain.
• Although one lesson focuses on supporting work, of the seven lessons in Topic 13 that address two clusters, both clusters are within the same domain.
• All lessons within Topic 14 are within a single cluster and domain.

Further analysis of Topics 5 and 13, both of which address supporting work, and Topic 10, which addresses major work of number and operations in base ten, provided the following examples:

• In Topic 5, as students classify objects, they also count how many objects are in different categories (5-2), use counting to compare how many objects are in categories (5-3), and tell whether the way objects have been sorted, counted, and compared makes sense (5-4). There is a missed opportunity in lesson 1 to count the number of objects in each sorted group.
• In Topic 10, as students work with teen numbers, they write two-digit numbers (K.CC.3), although this standard is not tagged within the unit. There are missed opportunities within this unit for students to further develop counting skills, such as counting teen numbers and forward and backward from any number. Counting is mentioned as an extension for early finishers but is not part of the main lesson (10-2).
• In Topic 13, as students work with shapes, there are many opportunities for students to count and compare numbers; however, counting is limited within the topic to finding a shape with a given number of sides or vertices. There are missed opportunities for students to count the number of shapes within given sets. For example, in lesson 13-3 after identifying solid figures with flat surfaces, students could count the number of shapes they identified or the number of shapes that did not fit that criteria. This same context would also allow for students to compare the number of items within each group.