Kindergarten - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 85% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 6 / 8 |
The instructional materials reviewed for enVisionMATH California Common Core Kindergarten meet expectations for focus on major work and coherence in Gateway 1. For focus, the instructional materials do not assess topics before the grade level in which the topic should be introduced, and they devote the large majority of class time to the major work of the grade. For coherence, the instructional materials partially meet expectations for coherence by including an amount of content designated for one grade level that is viable for one school year and fostering coherence through connections at a single grade.
Criterion 1.1: Focus
The instructional materials reviewed for enVisionMATH California Common Core Kindergarten do not assess topics before the grade level in which the topic should be introduced. In the instances where the material is above grade level, the material could easily be omitted or modified by the teacher to address the grade-level standards.
Indicator 1a
The instructional materials reviewed for enVisionMATH California Common Core Kindergarten meet expectations for assessing grade-level content. Most of the assessments provide material that is appropriate for Kindergarten. In the instances where the material is above grade level, the material could easily be omitted or modified by the teacher to address the grade-level standards. Probability, statistical distributions, similarity, transformations, and congruence are not within these assessments.
The following are examples where the standards are representative of alignment to Kindergarten expectations:
- Topics 1, 2, 3 and 5 demonstrate a progression of standard K.CC.3.
- In Topic 1 lesson 1.3, Digital Quick Check, students write numbers 1 to 3 by counting objects and determining the number the objects represent.
- In Topic 2 lesson 2.7, students practice writing 0.
- In Topic 3 lesson 3.6, students practice counting objects and determining the number the objects represented for numbers 7-10.
- In Topic 5 lesson 5.4, students count and write numbers representing 18-20.
- In Topic 9 lesson 9.1, Digital Quick Check, item 1, students choose the answer that shows a way to make 5. (K.OA.3)
- In Topic 15 session 15.1, Digital Quick Check, students use directional words in conjunction with the names of shapes in terms such as inside, outside, etc. Item 1 pictures a circle inside a square. (K.G.1)
- In Topic 3 Performance Task, page 64, students count pictures of apples and bananas and write how many. (K.CC.1, K.CC.3) Students also draw between 6 and 9 oranges and write the number. (K.CC.4) A 3-point rubric is included.
- In Topic 7 Performance Task, page 144, students draw pictures to match the story of 5 gold coins in one treasure chest and 4 gold coins in the other. Students answer, “How many coins are there altogether?” (K.OA.1)
The assessment items that contain above grade-level content not specifically stated by the standards are noted in the following:
- In the Topic 6, session 1.1, Digital Quick Check, students count objects above 20 in the End-of-Topic Test: 1) 28 objects, 2) 25 objects, 3) 28 objects, 4) 27 objects, 5) 22 objects, 6) 84 objects, 7) 35 objects, 8) 40 objects, 9) 35 objects. This goes above the K.CC.5 into 1.NBT.1, where students count to 120, read, write numerals, and represent an number of objects with a written numeral.
- In the Topics 9-12 Benchmark Test, question 7 shows students three objects to sequence from shortest to longest. Question 8 shows four snowmen. Students determine which is tallest. K.MD.2 states, “Directly compare two objects with a measurable attribute in common, to see which object has “more of/less of” the attribute, and describe the difference.”
- The Online Topic 12 assessment, questions 9, 10, 14, 15 compare three objects; students place these in order according to length. K.MD.2 involves students comparing two objects to tell more or less of the attribute. In question 11, students compare each of the pencils to the first pencil; because they are not lined up, they would not be able to do a direct comparison. This would necessitate using a third object to indirectly compare the two objects, which is part of Grade 1. (MD.1 standard, compare the length of two objects indirectly by using a third object.)
- The Online Topic 16 Assessment, question 7 shows a trapezoid. (1.G.2) The students are prompted, “Which of these is part of the shape above?“ The choice students check is a trapezoid.
- The Topic 14 lesson 14-7, Quick Checks include analyzing flat surfaces of 3D figures beyond using informal language to describe similarities and differences based on their different sizes and orientations. (K.G.4) Students are shown a cone, then students are asked to decide, “Which shape matches the flat surface of the solid figure shown?” There are four choices presented, one of which is a circle and one a rectangle.
- The Topic 16 Digital Quick Check uses language that is not aligned with Kindergarten standards. Examples are: “1) Which does not slide? 2) Which stacks? or 3) Which rolls?”
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.
Students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. The instructional materials devote approximately 67 percent of class time to the major work of Kindergarten.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for enVisionMATH California Common Core Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.
- Topics 1 through 11 of 16 are devoted to major work of the grade, which is approximately 68 percent.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is approximately 110 out of 164 lessons, which is approximately 67 percent.
- The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 24 out of 35 weeks, which is approximately 68 percent.
A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each topic. As a result, approximately 67 percent of the instructional materials focus on major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for enVisionMATH California Common Core Kindergarten partially meet expectations for coherence. The instructional materials include an amount of content designated for one grade level that is viable for one school year and foster coherence through connections at a single grade. However, the instructional materials partially meet expectations for connecting major and supporting work and being consistent with the progressions in the Standards.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for enVisionMATH California Common Core Kindergarten partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. There are examples where supporting work engages students in the major work of the grade, but there are also multiple instances where supporting work is treated separately and does not engage students in the major work of the grade.
Examples of supporting content connecting to the major work of the grade include:
- In Lesson 13-6, students “count how many counters of each color there are, and color to show the number of each color counter in the graphs on the right. Then, circle the column that shows which group has fewer objects.” This connects K.MD.3 to the major standard of K.CC.5. (Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.)
- In the Problem-Based Interactive Learning in lesson 16-1, students determine how to take straws to make specific geometric objects. For example, “What shape was made? How do you know that it is a triangle?” This is a natural connection to K.CC.5. (Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.)
Examples of missed opportunities to connect supporting content to the major work on the grade include:
- Topic 12 Lessons 1, 3, and 5-8 focus on supporting work of comparing the measurement quantities. (K.MD.A) No connection to major work is established. This is a missed opportunity to make a connection to K.CC.6. For example, in lesson 5, page 230, students make cube trains for the numbers 3, 5, 7 and 10. There is a missed opportunity to have them compare two of these trains at a time to determine whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. This connection is missed again in lesson 6 page 233 and in the Additional Activity on page 234A.
- Topic 13 Lesson 3, Pose the Problem: "'There are 6 balls in the grass. You want to sort the balls in two ways. What do you need to know about the balls?' Model: In random order, place 2 big blue circles and 1 small blue circle from the attribute blocks on your left workmat. Then add 1 big yellow circle and 2 small yellow circles. Small group Instruction: Have partners listen to this problem: 'You are sitting on the floor with these 6 marbles. You want to sort the marbles in two ways. Place 1 big and 2 small yellow circles on the right work mat.' Provide prompts, such as: 'Think about different sizes and different colors.' Children sort and then color paper circles yellow and glue them to the right mat.” Students do not have the opportunity to count the number of circles on each side of the sorted mat, which would connect K.MD.3 to major work K.CC.4a.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
Instructional materials for enVisionMATH California Common Core Kindergarten meet expectations that the amount of content designated for one grade level is viable for one year.
As designed, the instructional materials can be completed in 164 days. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications.
The instructional materials consist of 110 lessons that are listed in the Table of Contents. Lessons are structured to contain a Math Background, Problem Based Interactive section, Develop the Concept: Visual section with two or three activities, Guided Practice problems, Independent Practice problems, Close/Assess and Differentiated problems, and Leveled Homework.
The instructional materials consist of 54 reteaching lessons and assessments that are listed in the Table of Contents. These include Reteaching, Topic Tests, Performance Assessments, Placement Tests at the beginning of the year as well as the end of the year, and Benchmark Tests every fourth Topic.
The publisher does provide information about the suggested time to spend on each lesson or the components within a lesson. The Implementation Guide has a chart that suggests time frames of 50-75 minutes per day. Morning Math is recommended but is not incorporated into the daily math block. The Morning Math time incorporates concepts and skills ranging from the Common Core Review to Quick Checks.
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 for enVisionMATH California Common Core Kindergarten partially meet expectations for the materials being consistent with the progressions in the standards.
The instructional materials reviewed for Kindergarten are partially consistent with the progressions in the standards. Although students are given extensive grade-level problems and connections to future work are made in the Skills Trace, future grade-level content is not always clearly identified within the lesson or topic for the teacher or student. 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. For example:
- In Topic 9, students create a graph. (2.MD.10) In the Practice, Center Activity, Digital Quick Check and Reteaching, students create graphs for their categorical data.
- In Topic 12, students compare three items, which is a Grade 1 standard. (1.MD.4) Lesson 12-3 introduces the vocabulary of longest/shortest. (1.MD.4) Lesson 12-4 begins with students comparing three pieces of string moving to visually comparing four pieces of string which is beyond Grade 1.
- Topic 13 Lesson 13-6 references a “real graph” in the visual learning lesson. (2.MD.10) Lesson 13-7 uses picture graphs. (2.MD.10)
- In Lesson 4-18, students count by 2s and 5s. (2.NBT.2)
- In Lesson 3-15, students make tens to add three addends. (1.OA.2)
The correlation between the CCSSM and the lessons is found in the Teacher e-text. In the e-text, a menu on the left side appears with Program Resources. Clicking on Program Resources leads to a drop-down menu with Printable Resources where a document called Common Core State Standards Skill Trace resides. Objectives, Essential Understandings, and a Math Background explain connections between prior knowledge and the lesson. Math Background provides a learning arc. For example, in Lesson 4-6, the Math Background states, “This lesson builds on the concepts introduced in Lesson 4-4. Review these concepts by asking children questions such as ‘How do you know if there is one fewer in a group of objects?’” Additionally, each Topic begins with a Progression Overview document. This document connects grade- level concepts to specific standards under the Looking Back Column, and connects grade-level concepts to future standards under the Looking Ahead Column. The Daily Common Core review in each lesson connects to prior knowledge. Materials provide students opportunities to work with grade-level problems. The majority of reteach and center activities provided are on grade level. Extension activities are embedded within lessons and allow students to engage more deeply with grade-level work. Additional extension activities are also provided online, as are reteach items.
The content does not always meet the full depth of the standards. Materials sometimes do not provide extensive work for all students. For example:
- For K.MD.1, Lesson, 12-1: Describing Objects by More than One Attribute is the one lesson to address “Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.”
- For K.G.4, there is one lesson involving three-dimensional shapes, Lesson 16-3: Comparing Solid Figures. The standard states, “Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/'corner’) and other attributes (e.g., having sides of equal length).” Students analyze three-dimensional shapes and compare the shapes based on “roll, stack, and slide.” The standard explicitly states that two- and three-dimensional shapes are to be analyzed and compared, but this lesson does not address the relationship between two-dimensional shapes and three-dimensional shapes.
- For K.G.6, Lesson 16-2: Making Shapes from Other Shapes addresses the standard: “Compose simple shapes to form larger shapes.” Students form larger shapes from simple shapes, but they do not compare what is happening when combining shapes.
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 enVisionMATH California Common Core Kindergarten meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. The connections are natural; using counting of objects to learn to count, read, write and compare numbers.
Each topic is structured by a specific domain and the learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:
- Topics 10 (Composing Numbers 11-19) and 11 (Decomposing Numbers 11-19) are shaped by K.NBT.A, “Work with numbers 11-29 to gain foundations for place value.” In these two topics, students explore composing and decomposing the teen values 11-19 using ten frames. Students fill one ten frame, and more objects are placed in another ten frame.
- In Topic 16 (Analyzing, Comparing, and Composing Shapes), page 303, K.G.B, students create 2D shapes. “Lin has 2 triangles. She thinks she can use them to make a shape she has learned - a circle, triangle, square, or rectangle. Try to make one of these shapes with your triangles. Tell what shape you made.”
Materials include problems and activities that sometimes serve to connect two or more clusters in a domain, or in two or more domains, where connections are natural and important.
- Lessons 1-3 and 1-6 connect two clusters, K.CC.A and K.CC.B. Lesson 1-3 is connected to Lessons 1-1 and 1-2 as students count objects. On page 7, students are shown a number card and practice writing the number 1. In lesson 1-6 page 14, students count objects up to 5 and write the numeral.
- Lesson 13-5 connects K.MD.B and K.G.A as students classify objects and count the number of objects in each category by identifying and describing shapes (squares, circles, triangles, rectangles, hexagons, cubes, cylinders, and spheres).