6th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials reviewed for enVisionMATH California Common Core Grade 6 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 have supporting content that engages students in the major work of the grade, 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.
Criterion 1.1: Focus
The instructional materials reviewed for enVisionMATH California Common Core Grade 6 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 Grade 6 meet expectations for assessing grade-level content. Most of the assessments include material appropriate for Grade 6; however, above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.
In the Teacher Edition, a Topic Test is available for each of the fourteen topics. The instructional materials assess content that is above grade level or not aligned to a standard.
- In the Topic 3 Topic Test, questions 4 and 6, students find how many combinations are possible from given information. Question 4 states, “Jorge has 16 quarters to spend on arcade games. He only wants to play pinball and the racing game. If each game takes 2 quarters to play and he plays both games at least one time, how many different combinations of time can Jorge play the two games?” (7.SP.8)
- In the Topic 3 Topic Test, question 7 states, “The table shows the number of miles, m, hiked by the hiking club in h hours. Write an equation that fits the pattern.” Students write a two-step equation as the solution. (7.EE.4)
- In the Topic 3 Topic Test, questions 9, 11, and 12 assess two-step equations. Question 11 states, “The temperature was 6 degrees celsius and increased 2 degrees celsius each hour for 6 hours. The equation y = 6 + 2x shows the relationship between x, the number of hours, and y, the temperature. Make a table. What is the temperature after 5 hours?” Students create a table after analyzing a two-step equation. (7.EE.4)
- In the Topic 3 Performance Assessment, questions 2 and 3 assess two-step equations. Question 2 states, “Write an equation that fits the pattern you found in problem 1 above.” The solution that is provided is h = 3d + 2. (7.EE.4)
- In the Topic 8 Topic Test, question 8 states, “An amusement park charges $2 for admittance and $1.50 for each ride. If R equals the number of rides and C equals the total cost, copy and complete the T-table for the equation C = $2 + $1.50R to show the relationship between total cost and the number of rides taken.” Students analyze a two-step equation to complete a table. (7.EE.4)
Examples of the instructional materials assessing grade-level content include:
- In the Topic 2 Topic Test, question 6 states, “Which graph represents the solutions of the inequality $$p \geq 10$$?” Students identify which solution to an inequality is correct. (6.EE.5)
- In the Topic 6 Topic Test, question 13 states, “How many 3/4 foot long pieces of ribbon can be cut from a ribbon that is 7 3/8 feet long?” Students divide fractions by fractions to solve real-world problems. (6.NS.1)
- In the Topic 14 Topic Test, question 4 states, “The ages of the girls in the dance recital are listed below. What are the median and mode of the ages? 7, 6, 8, 6, 8, 7, 8, 7, 8, 6” Students calculate the median and mode of a set of data. (6.SP.3)
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 90 percent of class time to the major work of Grade 6.
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 6 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 9 out of 14, which is approximately 64 percent.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 134 out of 149, which is approximately 90 percent.
- The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 27 out of 30, which is approximately 90 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 90 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 6 meet expectations for coherence. The instructional materials have supporting content that engages students in the major work of the grade, 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.
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 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Supporting content is used to support the major work of the grade. For example:
- In Topic 4 Lesson 4-2, students evaluate addition and subtraction expressions. The supporting standard 6.NS.3 engages students with the major work standard 6.EE.2c when students evaluate expressions that include decimals. Independent Practice question 13 states, “t - 0.48; t = 5.187”
- In Topic 5 Lesson 5-6, students evaluate expressions with decimals. The supporting standard 6.NS.3 engages students with the major work standard 6.EE.2c when students evaluate algebraic expressions that include decimals. Independent Practice question 16 states, “Evaluate each expression for x = 1.8, x = 5, and x = 6.4. 3x + 1.2x”
- In Topic 6 Lesson 6-1, students use the greatest common factor and the distributive property to rewrite each sum. Independent Practice problem 16 states, “In 15 -18, use the GCF and the distributive property to rewrite each sum. 34 + 51” The supporting standard 6.NS.4 engages students with the major work standard 6.EE.3.
- In Topic 12 Lesson 12-1, students find the area of rectangles as well as the length of one side of a rectangle. The supporting standard 6.G.1 engages students with the major work standard 6.EE.2c when students use and manipulate the area formula to solve area problems involving variables. Guided Practice question 5 states, “In the example at the top, suppose Tessa used 24 ft squared of fabric to cover a bulletin board that is 3 ft. wide. How long is the bulletin board? Explain how you found the answer.” A sample answer is given using variables for length and width.
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 6 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 154 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 107 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 47 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 yearlong pacing guide lists Topic 6 to be covered for 15 days in November and 15 days in December for a total of 30 days. However, the pacing guide lists Topic 6 as a total of 15 days. There is a discrepancy with Topic 10 that lists 7 days in February and 6 days in March in the yearlong pacing guide as well as a total of 13 days listed in the pacing guide.
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 6 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 3 Lesson 3-4, the Teacher Edition lists the standard 6.EE.6 as the focus of the lesson. Students determine all the possible combinations within a group. This is future grade-level content and is aligned to 7.SP.8b.
- In Topic 10 Lesson 10-6, the Teacher Edition lists the standard 6.RP.3d as the focus of the lesson. Students use ratio and rate reasoning to solve real-world and mathematical problems to change between customary units of measurement. This is prior grade-level content and is aligned to 5.MD.1.
- In Topic 12 Lesson 12-1, the Teacher Edition lists the standard 6.G.1 as the focus of the lesson. Students find the area of rectangles and squares. This is prior grade-level content and is aligned to 4.MD.3.
- In Topic 13 Lesson 13-3, the Teacher Edition lists the standard 6.G.2 as the focus of the lesson. Students calculate volume with all whole numbers. This is prior grade-level content and is aligned to 5.MD.5b.
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 8 Lesson 8-3, the Link to Prior Knowledge states, “Which operation does separating the leather string into equal parts represent? Division. On the board, display the division expression to represent the problem. 4 divided by 2/3” 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 focuses on and provides students with extensive opportunities to practice grade-level problems. Within each lesson, students practice grade-level problems within a Daily Common Core Review, Practice, Reteaching, Enrichment, and Quick Check activities. For example:
- In Topic 10 Lesson 10-5, the Teacher Edition lists standard 6.RP.3b as the focus of the lesson. Students solve unit rate problems including those involving constant speed. Independent Practice question 7 states, “distance = 568 mi; time = 8 h; rate = ___”
- In Topic 6 Lesson 6-8, the Teacher Edition lists standard 6.NS.1 as the focus of the lesson. Students divide mixed-number equations and apply the concept to solve word problems. Problem Solving question 36 states, “The biggest diamond ever found weighed 1 ½ pounds uncut. If this diamond were cut into 3 equal pieces. How much would each piece weigh?”
- In Topic 9 Lesson 9-1, the Teacher Edition lists standard 6.RP.1 as the focus of the lesson. Students write ratios three different ways to express the ratios in a part-to-part and part-to-whole relationship. Independent Practice question 6 states, “A person’s blood type is denoted with the letters A, B, and O, and the symbols + and -. The blood type A+ is read as A positive. The blood type B- is read as B negative. Use the data file to write a ratio for each comparison in three different ways. O+ donors to A+ donors.”
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 specific topic numbers from previous and future grades and their related grade-level standards.
- In Topic 3, the Skills Trace lists the standards 6.EE.6 and 6.EE.9 as the focus of the topic. These standards are linked to a “Looking Back” list where it lists the standard 5.OA.3 as the focus in Topic 15 within the Grade 5 instructional materials. The standards 6.EE.6 and 6.EE.9 are also linked to a “Looking Ahead” list where it lists the standards 6.EE.2c, 6.EE.6, and 6.EE.7 as the focus in Topics 4, 5 and 6 within the current Grade 6 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 6 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 6 Lesson 6-1, the lesson objective states, “Students will find common factors and the greatest common factors of numbers.” This is shaped by the cluster 6.NS.B, Compute fluently with multi-digit numbers and find common factors and multiples.
- In Topic 10 Lesson 10-1, the lesson objective states, “Students will find the unit rate for a given rate.” This is shaped by the cluster 6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.
- In Topic 12 Lesson 12-2, the lesson objective states, “Students will develop and use formulas for the areas of parallelograms and rhombuses.” This is shaped by the cluster 6.GA, Solve real-world problems and mathematical problems involving area, surface area, and volume.
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 1 Lesson 1-6, cluster 6.EE.A connects to cluster 6.EE.B when students write expressions using variables. Independent Practice question 10 states, “Write an algebraic expression for each situation. 12 less than 7 times a number x.”
- In Topic 6 Lesson 6-9, cluster 6.EE.A connects to cluster 6.NS.A when students evaluate expressions at specific values of their variables including word problems involving division of fractions by fractions. Problem Solving question 19 states, “The expression 9 1/3 $$\div$$ d can be used to find how many days of feed the bin holds, where d is the amount of feed a horse eats each day. Explain how to use the expression to find the days of feed for a horse that eats 1/6 cubic feet of feed each day.”
- In Topic 14 Lesson 14-1, cluster 6.SP.A connects to cluster 6.SP.B when students identify statistical questions and interpret data. Independent Practice question 11 states, “Kim asked her class, 'How many other states have you visited?' She got the following responses: 0, 1, 2, 1, 2, 0, 3, 1, 0, 5, 5, 1, 3, 1, 0, 2, 4, 1, 3, 0. Make a dot plot to display the data.”