4th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 71% |
|---|---|
Criterion 1.1: Focus | 0 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 6 / 8 |
The instructional materials reviewed for enVisionMATH California Common Core Grade 4 partially meet expectations for focus on major work and coherence in Gateway 1. The instructional materials do not meet expectations for focus as they assess topics before the grade level in which the topic should be introduced, but they do devote the large majority of class time to the major work of the grade. The instructional materials partially meet the 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 Grade 4 assess topics before the grade level in which the topic should be introduced. There are assessment items that assess above grade level statistics and probability standards.
Indicator 1a
The instructional materials reviewed for enVisionMATH California Common Core Grade 4 do not meet expectations for assessing grade-level content. Most of the assessments include material appropriate for Grade 4; however, there are two assessment items that assess above grade-level statistics and probability standards.
In the teacher edition, a Topic Test is available for each of the sixteen topics. In Topic 3, the instructional materials assess content that aligns to 7.SP.8. For example:
- In the Topic 3 Topic Test, question 9 states, “Betsy is making a flag. She can choose three colors from red, white, blue, and yellow. How many choices does Betsy have?”
- In the Topic 3 Topic Test, question 16 states, “Tammy wants to get change for 30 cents. The only coins she can get are quarters, nickels, and dimes. How many different ways can she get 30 cents using only these coins?”
Examples of the instructional materials assessing grade-level content include:
- In the Topic 4 Topic Test, question 1 states, “Joe got 34,867 points playing a video game, and Carlos got 29,978 points. How many more points did Joe get than Carlos?” Students subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4)
- In the Topic 8 Topic Test, question 7 states, “A school bought 28 new microscopes for its students to use. The price for each microscope was $87. How much did the microscopes cost in all?” Students multiply two-digit numbers by two-digit numbers. (4.NBT.5)
- In the Topic 14 Topic Test, question 12 states, “Andrea ran 400 meters in gym class. How many centimeters did she run?” Students convert measurements within a single system of measurement. (4.MD.1)
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 68 percent of class time to the major work of Grade 4.
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 Grade 4 meet expectations for spending a majority of instructional time on major work of the grade.
- The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 16, which is approximately 75 percent.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 114 out of 168, which is approximately 68 percent.
- The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 23 out of 34, 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 68 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 Grade 4 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. The instructional materials also miss some connections between major and supporting work and do not clearly identify content from prior and future grade levels.
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 Grade 4 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are not always used to support major work of the grade and often appear in lessons with few connections to the major work of the grade.
Throughout the series, supporting standards/clusters are typically taught in isolation and rarely connected to the major standards/clusters of the grade. Students can often complete problems aligned to supporting work without engaging in the major work of the grade. The following examples illustrate missed connections in the materials:
- In Topic 11 Lesson 11-1, students find factors of whole numbers. The supporting standard of 4.OA.4 has a natural connection with the major work standard 4.NF.1. Though these standards are not contained in the same lesson, the standards are within the same topic but do not simultaneously enhance coherence in the major work of the grade. In lesson 4, students do not use the understanding that a whole number is a multiple of its factors to help find equivalent fractions.
- In Topic 15 Lesson 15-2, students analyze and create line plots to solve problems. The supporting standard of 4.MD.4 is aligned to this lesson. 4.MD.4 has a natural connection to the major work standard 4.NF.B, adding and subtracting fractions. The lesson contains line plots that have whole units as well as decimal units, which is respectively below and above grade level. There are three questions in the lesson related to finding the difference between numbers; however, two of the three questions refer to line plots with whole or decimal units.
Examples that illustrate connections in the materials include:
- In Topic 14 Lesson 14-9, students express measurements in a larger unit in terms of a smaller unit. Independent Practice question 12 states, “8 km = __ m, 8 x 1,000 = __ m” The supporting standard of 4.MD.1 is used to enhance the focus on the major work standard 4.OA.1.
- In Topic 15 Lesson 15-3, students solve real-world area and perimeter problems. Problem Solving question 11 states, “Julie planted a rectangular garden that is 20 feet long. She placed 56 feet of fencing around her garden. Draw and label a sketch of her garden. What is the width of her garden? What is the area?” The supporting standard of 4.MD.3 is used to enhance the focus on the major work standard 4.NBT.5.
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 Grade 4 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 174 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 120 lessons that are listed in the Table of Contents. Lessons are structured to contain a Daily Review, Develop Concept-Interactive, Develop Concept-Visual, Close/Assess and Remediate, and Center Activities.
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 Test, Benchmark Tests, and End-of-Year Test.
The publisher does not 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 times for a multi-age classroom. The lessons within the multi-age classroom are structured differently than a single-age classroom. The multi-age lessons are structured to contain Problem Based Interactive Learning, Guided Practice, Center Activities, Independent Practice, Small Group Strategic Intervention, and Digital Assignments/Games. The suggested time for the multi-age lesson is 50-75 minutes per lesson.
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 Grade 4 partially meet expectations for the materials being consistent with the progressions in the standards.
The instructional materials do not clearly identify content from prior and future grade levels and do not use it to support the progressions of the grade-level standards.
Prior and future grade-level work is not clearly identified within each lesson. For example:
- In Topic 1 Lesson 1-1, the Teacher Edition lists the standard 4.OA.1 as the focus of the lesson. Students write addition sentences as well as multiplication sentences for a given set of pictures arranged in rows or groups. Independent Practice question 6 states, “Write an addition sentence and a multiplication sentence for each picture.” This is prior grade-level content aligned to 3.OA.1.
- In Topic 3 Lesson 3-6, the Teacher Edition lists the standard 4.NBT.1 as the focus of the lesson. Students find and record all possible outcomes for a situation. This is future grade-level content aligned to 7.SP.8.
- In Topic 13 Lesson 13-5, the Teacher Edition lists the standards 4.NF.5 and 4.NF.6 as the focus of the lesson. Students name the point on a number line from a given fraction. The Guided Practice question 1 states, “Use the number line below to name the fraction. 1/8” This is prior grade-level content aligned to 3.NF.2.
- In Topic 13 Lesson 13-5, the Teacher Edition lists the standards 4.NF.5 and 4.NF.6 as the focus of the lesson. Students name the point on a number line from a given decimal. The decimal is not a multiple of 10. The Guided Practice question 3 states, “Name the point on the number line for each decimal. 1.33” This is future grade-level content aligned to 5.NBT.3.
Some of the lessons include a section in the Teacher Edition called, Link to Prior Knowledge. The Link to Prior Knowledge poses a question or strategy that has previously been learned for students to connect to the current lesson. The Link to Prior Knowledge does not explicitly identify standards from prior grades. For example:
- In Topic 11 Lesson 11-5, the Link to Prior Knowledge states, “Have students fold one of the paper strips into halves, another into fourths, and the third into eighths. They should mark the ends with 0 and 1, and mark each fold with the appropriate fractions: e.g., 1/4, 2/4, 3/4. Have each student lay their fraction strips next to a number line strip and transfer their fractions on to the number line. Do any of the marks from the fraction strips line up? Sample answers: Yes, some of the folds from the paper strips name the same point on the number line.” The publisher does not connect this prior knowledge to a specific prior grade level.
The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.
The majority of lessons within the 16 topics focus on and provide students with extensive opportunities to practice grade-level problems. Within each lesson, students practice grade-level problems within Daily Common Core Review, Practice, Reteaching, Enrichment, and Quick Check activities. For example:
- In Topic 5 Lessons 1-4, the Teacher Edition lists the standard 4.NBT.5, Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models, as the focus of the lesson. Students multiply whole numbers using strategies based on place value and properties of operations. In lesson 5-1, Independent Practice question 9 states, “Draw and array and find each product. 9 x 10”
- In Topic 9 Lesson 9-3, the Teacher Edition lists the standard 4.NBT.6, find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation using equations, rectangular arrays, and/or area models, as the focus of the lesson. Students find whole-number quotients using strategies based on place value. Guided Practice question 1 states, “Use multiplication facts to help estimate each quotient. 3,340/8”
- In Topic 13 Lesson 13-1, the Teacher Edition lists the standard 4.NF.4a, apply and extend previous understandings of multiplication to multiply a fraction by a whole number, as the focus of the lesson. Students use models when multiplying fractions by a whole number. Independent Practice question 7 states, “Write the fraction as a multiple of a unit fraction. Use fraction strips to help. 3/4 = ___ x 1/4”
The instructional materials contain a Common Core State Standards Skills Trace for each topic that can be found in the Printable Resources section of the Program Resources Document. This document contains the grade-level standards for each topic and the standards from previous and future grade levels that are related to the standards focused on in the specified topic. The document states the specific topic numbers from previous and future grades to which the grade-level standards are related.
- In Topic 15, the Skills Trace lists the standard 4.MD.2 as the focus of the topic. This standard is linked to a “Looking Back” list where it lists the standard 3.MD.2 as the focus in Topic 15 within the Grade 3 instructional materials. The standard 4.MD.2 is also linked to a “Looking Ahead” list where it lists the standard 5.MD.1 as the focus in Topic 13 within the Grade 5 instructional materials.
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 for enVisionMATH California Common Core Grade 4 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.
Each topic is structured by a specific domain and the learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:
- In Topic 1 Lesson 1-7, the lesson objective states, “Students will multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.” This is shaped by the cluster 4.OA.A, Use the four operations with whole numbers to solve problems.
- In Topic 5 Lesson 5-2, the lesson objective states, “Students will use basic multiplication facts and numbers patterns to multiply by multiples of 10 and 100.” This is shaped by the cluster 4.NBT.B, Use place-value understanding and properties of operations to perform multi-digit arithmetic.
- In Topic 12 Lesson 12-2, the lesson objective states, “Students use computational procedures to add fractions with like denominators and solve problems.” This is shaped by the cluster 4.NF.B, Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Instructional 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 the connections are natural and important.
- In Topic 4 Lesson 4-6, cluster 4.NBT.B connects to cluster 4.OA.A when students use models/diagrams and equations involving multi-digit numbers to solve word problems. Guided Practice question 1 states, “Solve. Draw a picture to help you. Sandy earned $36 from babysitting and $15 for doing her chores. Write an equation and find the total amount, t, that Sandy earned.”
- In Topic 7 Lesson 7-4, cluster 4.NBT.A connects to cluster 4.NBT.B when students use estimation and rounding to solve multiplication problems involving two two-digit numbers.
- In Topic 10 Lesson 10-7, cluster 4.OA.A connects to cluster 4.NBT.B when students solve multi-step word problems posed with multi-digit whole numbers and having whole-number solutions. Independent Practice question 10 states, “Use the data at the right for 8 through 11. How much more would it cost to buy 24 T-shirts at Just Jerseys than at Shirt Shack?”