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 for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.
Criterion 1.1: Focus
The instructional materials for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.
Indicator 1a
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations for assessing the grade-level content and if applicable, content from earlier grades.
Above grade-level assessment items could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Overall, summative assessments focus on Grade 6 standards with minimal occurrences of above grade-level work. Examples of assessment items which assess grade-level standards include:
- Chapter 3, Test A, Item 3, students will find missing values in a ratio table. (6.RP.3.a)
- Chapter 5, Performance Task, students are given four different real-life situations and use algebraic expressions to predict change over time. They answer the following questions for each data set:
- “What is the first recorded value in the data set?”
- “How much does the recorded value change each time period? Does the recorded value change by approximately the same amount each period?”
- “Write an expression for the form ax + b to model the data set, or explain why this type of expression is not appropriate.”
- “Use the expression to predict the next value, if possible.” (6.EE.6)
- Chapter 7, Alternative Assessment Item 1, students solve problems involving the shape of a park with a base of 200 feet and a height of 130 feet. Students form different shapes, then choose one to find the area and perimeter of the park. When given the dimensions, they draw possible shapes again and find the area. Next, they put shapes together to label and find the dimensions and finally determine the square footage of the entire park. Rubrics are provided to score student work. (6.G.A)
Examples of assessment items which are above grade-level content, but can easily be modified:
- Chapter 6, Quiz, Item 7, students write an equation that will be written in the form px + q =r. (7.EE.4a)
- Chapter 6, Test A and B, Item 11, students write a word sentence as an equation, that is in the form px + q =r. (7.EE.4.a)
- Chapter 6, Alternative Assessment, Item 1e, students write an equation that is in the form px + q =r. (7.EE.4a)
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.
The instructional materials for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations for spending a majority of class time on major work of the grade when using the materials as designed. Time spent on the major work was figured using chapters, lessons, and days. Approximately 75% of the time is spent on the major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 6 meet expectations for spending a majority of instructional time on major work of the grade. This includes all the clusters in 6.RP.A, 6.NS.A & C, 6.EE.A, B, and C.
To determine focus on major work, three perspectives were evaluated: the number of chapters devoted to major work, the number of lessons devoted to major work, and the number of instructional days devoted to major work.
- There are 10 chapters, of which 6.5 address major work of the grade, or approximately 65%
- There are 156 lessons, of which 117 address major work of the grade, or approximately 75%
- There are 156 instructional days, of which 117 address major work of the grade, or approximately 75%
A day-level analysis is most representative of the instructional materials because the number of days is not consistent within chapters and lessons. As a result, approximately 75% of the instructional materials focus on the 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 Big Ideas Math: Modeling Real Life Grade 6 meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, and the materials describe how the lessons connect with the grade-level standards. However, above grade-level content is present and not identified.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Supporting Domain 6.G enhances focus and coherence with the major standards/clusters of the grade, especially clusters 6.NS.A, 6.NS.C and 6.EE. There are natural connections including the use of fractions and decimals as the dimensions of the geometric figures. For example:
- In Chapter 4, Section 4.1, Area of Polygons, 6.G.1 is connected to the major work of 6.EE.2c as students evaluate the formula of polygons by substituting specific values into the expression.
- In Chapter 5, Section 5.5, Common Factors and Multiples, 6.NS.4 is connected to the major work of applying the properties of operations to generate equivalent expressions, 6.EE.3. Students use common factors to rewrite expressions using the distributive property.
- In Chapter 7, Section 7.1, Area, Surface Area, and Volume, Example 1, 6.G.1 is connected to 6.EE.3 as students use their equation solving skills to assist in solving problems using the formula for the area of a parallelogram.
- In Chapter 7, Sections 7.1-7.3, 7.5-7.7, and Chapter 8, Sections 8.6-8.8, domain 6.G is connected to domain 6.EE, as students connect their work with expressions and equations to problems with areas of triangles (6.G.1) and volumes of right rectangular prisms (6.G.2).
- Chapter 8, Section 8.6, Draw Polygons in the Coordinate Plane, 6.G.3 is connected to the major work of solving real-world math problems by graphing, 6.NS.8. Students graph the vertices of a secret chamber and determine the perimeter.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials for Big Ideas Math: Modeling Real Life 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 156 days.
The pacing shown in the Teacher Edition includes a total of 156 days. This is comprised of:
- 126 days of lessons,
- 20 days for assessment (one day for review, one day for assessment), and
- 10 days for “Connecting Concepts”, which is described as lessons to help prepare for high-stakes testing by learning problem-solving strategies.
The print resources do not contain a pacing guide for individual lessons. It should be noted that the work of solving inequalities in Section 8.8 of Chapter 8 is work from a future grade (7.EE.4b). The pacing guide allows three days for this section. Additional time may be spent utilizing additional resources not included in the pacing guide: Problem-Based Learning Investigations, Rich Math Tasks, and the Skills Review Handbook. In addition, there are two quizzes per chapter located in the Assessment Book which indicates where quizzes should be given. The Resources by Chapter materials also include reteaching, enrichment, and extensions. In the online lesson plans, it is designated that lessons take between 45-60 minutes. The day to day lesson breakdown is also noted in the teacher online resources.
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 Big Ideas Math: Modeling Real Life Grade 6 partially meet expectations for the materials being consistent with the progressions in the Standards.
The materials concentrate on the mathematics of the grade, and are consistent with the progressions in the Standards. The publisher recommends using four resources together for a full explanation of the progression of skill and knowledge acquisition from previous grades to current grade to future grades. These resources include: “Laurie’s Notes”, “Chapter Overview”, “Progressions”, and “Learning Targets and Success Criteria”. For example:
- Laurie’s Notes, “Preparing to Teach” describe connections between content from prior grades and lessons to the current learning. For example, in Chapter 3, Section 3.2, “Students have drawn tape diagrams (or bar models) in earlier grades. In this lesson, tape diagrams are used to solve ratio problems.”
- Chapter Overviews describe connections between content from prior and future grades to the current learning, and the progression of learning that will occur. For example, the Chapter 7 Overview states, “This chapter on geometric measurement is a strand in mathematics that connects numbers and the computational work students have learned to the study of geometry. In previous work, students explored two- and three-dimensional shapes. Now they will extend measurement concepts by deriving various area, surface area, and volume formulas.”
- Each chapter’s Progressions page contains two charts. “Through the Grades”, lists the relevant portions of standards from prior and future grades (grades 5 and 7) that connect to the grade 6 standards addressed in that chapter. For example, Chapter 7 “Through the Grades”, provides the relevant portions of a progression of standards from Grade 5 (finding the area of a rectangle with fractional side lengths), Grade 6 (finding the areas of triangles, special quadrilaterals, and polygons), Grade 7 (finding area of 3-dimensional figures). “Through the Chapter” identifies the sections in which the grade-level standards are addressed. This chart also identifies within grade-level progressions of learning with symbols that indicate where the materials are preparing students for grade-level learning (triangle) and where the learning will be completed (star). For example, “Through the Chapter” for Chapter 7, indicates with a triangle that content in Section 7.4 will prepare students for learning 6.G.4, that the learning will continue in Section 7.5 (indicated with a circle) and will be completed in Section 7.6 (indicated with a star).
- Each chapter’s Learning Targets and Success Criteria chart lays out the progression of learning for the chapter. In Chapter 7, the learning target for Section 7.1, is “Find areas and missing dimensions of parallelograms.” For Section 7.2, the learning target is “Find areas and missing dimensions of triangles, and find areas of composite figures”, and for Section 7.3, the learning target is “Find areas of trapezoids, kites, and composite figures.” (6.EE.2; 6.G.1)
Each lesson presents opportunities for students to work with grade-level problems. However, “Scaffolding Instruction” notes suggest assignments for students at different levels of proficiency (emergent, proficient, advanced). These levels are not defined, nor is there any tool used to determine which students fall into which level. In the Concepts, Skills and Problem Solving section problems are assigned based on these proficiencies, therefore, not all students have opportunities to engage with the full intent of grade-level standards. For example:
- In Chapter 3, Getting Ready for The Chapter, students begin to develop an understanding of the concept of a ratio as they write ratios, learn the term ratio, and begin to write ratios for various situations throughout the whole lesson and in the practice section. In Section 3.4, proficient and advanced students develop mastery with 6.RP.1 as they solve problems.
- In Chapter 3, Section 3.6, Concepts, Skills and Problem Solving, all students solve the You Be The Teacher, Problem 43, “Your friend converts 8 liters to quarts (work is shown in a diagram). Is your friend correct? Explain your reasoning.” (6.RP.3.d) However, students considered emergent or proficient in using ratio reasoning to convert measurement units (6.RP.3d) solve Problem 54, “You are riding on a zip line. Your speed is 15 miles per hour. What is your speed in feet per second?” and Problem 55, “Thunder is the sound caused by lightning. You hear thunder 5 seconds after a lightning strike. The speed of sound is about 1225 kilometers per hour. About how many miles away was the lightning?” Advanced students also solve Problem 56, “Boston, MA, and Buffalo, NY, are hit by a snowstorm that lasts 3 days. Boston accumulates snow at a rate of 1.5 feet every 36 hours. Buffalo accumulates snow at a rate of 0.01 inch every minute. Which city accumulates more snow in 3 days? How much more snow?”
- In Chapter 9, Section 9.3, Scaffolding Instruction, teacher guidance notes: “Finding median and mode is fairly easy for students, but their depth of understanding is apparent when students analyze the best measure of center, describe the effect of an outlier, and explain how changes to a data set affect the measures of center.”
- “Emerging: Students can find the median and mode, but they may need practice using these statistics in different situations and choosing a measure of center to represent a data set. Students may benefit from guided instruction with the examples." (6.SP.2-3)
- “Proficient: Students understand the meaning of median and mode, find them efficiently, and can apply them in different situations. Have students check their progress using the Try It exercises before completing the Self-Assessment exercises.” (6.SP.2-3)
Materials explicitly relate grade-level concepts to prior knowledge from earlier grades. At the beginning of each section in Laurie’s Notes, there is a heading marked “Preparing to Teach” which includes a brief explanation of how work in prior courses relates to the work involved in that lesson. For example:
- Chapter 1, Section 1.1, “In prior courses, students evaluated whole-number powers of 10. In this lesson, they will begin to evaluate other bases as well.” (6.EE.1). In Exploration 1, students write 10 x 10 using an exponent. This builds from their previous knowledge of using base 10 from previous grades (5.NBT.2).
- Chapter 2, Section 2.2, “In the previous course, students divided unit fractions by whole numbers and vice versa. The first exploration contains fractions other than unit fractions, which is the next step in the progression of fraction division (6.NS.1)."
- Chapter 7, Section 7.1, “In prior courses, students used rectangular area models to represent one- and two-digit multiplication. In this course, they used area models to represent the Distributive Property, which provides the basis for this chapter’s work with using the definition of the area of a rectangle to derive the formula for the area of a parallelogram.” In Example 1, students use the area model to find the area of a parallelogram.
- Chapter 8, Section 8.1, explicitly connects students’ prior work of locating fractions on a number line, 3.NF.2, and of making line plots, 4.MD.4, 5.MD.2, to represent points on a number line with negative numbers, 6.NS.6. For example, “Students will build upon their experiences with finding non-negative numbers on a horizontal or vertical number line to develop the number line to the left of 0 or below 0.”
- Chapter 10, Section 10.1, “Students know how to use dot plots to display and analyze data. Now they will add another data display to their toolkits, stem-and-leaf plot.”
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 Big Ideas Math: Modeling Real Life Grade 6 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.
Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Chapter headings indicate the learning targets for each section and are outlined at the beginning of each chapter in the Teacher Edition. Each chapter also begins with a table that identifies the standard that is taught in each section with an indication if the lesson is preparing students, or if it completes the learning, or if students are learning, or extending learning. For example:
- In the Teacher Edition, Chapter 3, Section 3.1, and in the student edition, the “Learning Target” is identified as “Understand the concepts of ratios and equivalent ratios”. This connects to Cluster heading 6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.
- In Chapter 2, Section 2.2, students multiply fractions. In Section 2.3, students divide fractions and apply and extend previous understandings of multiplication and division to divide fractions by fractions. This connects to Cluster heading 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- In Chapter 8, Section 8.3, students place integers on a number line. This connects to Cluster heading 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- In Chapter 5, Section 5.1, Learning Goals: “Evaluate algebraic expressions given values of their variables." This connects to cluster heading for 6.EE.A, Apply and extend previous understandings of numbers to the system of rational numbers.
- In Chapter 6, Sections 6.2 and 6.3, students explain the solution strategy of using inverse operations and properties of inequalities. This connects to for 6.EE.A, Apply and extend previous understandings of numbers to the system of rational numbers.
Materials consistently include problems and activities that 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. Multiple examples of tasks connecting standards within and across clusters and domains are present. These connections build deeper understanding of grade-level concepts and the natural connections which exist in mathematics. For example:
- Chapter 4, Section 4.3, Exploration 1 connects 6.RP.A to 6.NS.7 as students represent four numbers written as decimals, fractions, and percents by placing the numbers on a number line drawn on the floor, to order the numbers from least to greatest and to explain how to determine the placement of the numbers.
- Chapter 6, Section 6.4, Exploration 1 serves to connect the work of using ratio reasoning 6.RP.A to solve problems 6.EE.C. Given a ratio table and its graph for an airplane traveling 300 miles per hour, students determine which quantity is dependent, describe the relationship between the two quantities, and then use variables to write an equation that represents the relationship between time and distance.
- Chapter 9, Section 9.2, Practice Problem 20, students find the mean monthly rainfall, and compare the mean monthly rainfall for the first half of the year with the mean monthly rainfall for the second half of the year. This connects and extends their cluster work of computing fluently with multi-digit numbers, specifically decimals, 6.NS.B, to the cluster work of summarizing and describing distributions, 6.SP.B. In Section 9.4, students connect knowledge about fractions, decimals, and percents as they identify the quartiles and interquartile range as they solve problems.