7th 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 7 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 7 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 7 meet the expectations for assessing the grade-level content and if applicable, content from earlier grades.
There are no above grade level assessment items for Grade 7. Examples of assessment items which assess grade-level standards include:
- Chapter 1, Quiz 2, Item 9, students use a vertical number line that shows elevations of a submarine after certain events to determine the distance the submarine rises after diving and the original elevation of the submarine. (7.NS.1.c)
- Chapter 3, Test A, Item 13, students factor a linear expression in order to determine the length of a square patio that has a perimeter of 16x + 12 feet. (7.EE.1)
- Chapter 3, Performance Task, Item 1, students write and simplify expressions from information provided in a diagram and a table. They describe and explain what they notice about the two expressions. (7.EE.1-2)
- Chapter 5, Test A, Item 6, students find the density of a substance in grams per millimeter by examining a graph. (7.RP.2.d)
- Course Benchmark 2, Item 30, students find the actual perimeter and area of a square using information about the scale drawing of a square. (7.G.1)
- Chapter 8, Alternative Assessment, Item 1, students are given the scenario about finding out how the residents in their town feel about opening a new gas station. Students describe how to conduct a survey so that the sample is biased, and unbiased survey of 200 people. They project how many residents out of 6200 will support the gas station if 80 out of 200 supported it. (7.SP.1-2)
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 7 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 78% 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 7 meet expectations for spending a majority of instructional time on major work of the grade. This includes all the clusters in 7.RP.A, 7.NS.A, and 7.EE.A, B.
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 7.4 address major work of the grade, or approximately 74%
- There are 152 lessons, of which 119 focus on the major work of the grade, or approximately 78%
- There are 152 instructional days, of which 119 focus on the major work of the grade, or approximately 78%
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 78% 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 7 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 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The supporting domain Statistics and Probability enhances focus and coherence to major standard/clusters of the grade, especially domains 7.NS and 7.RP. For example:
- In Chapter 5, Section 5.2, Solve Problems Involving Scale Drawings of Geometric figures (7.G.1) is connected to the major work of analyzing proportional relationships (7.RP.A). Students write and solve a proportion using the scale and ratios of the lengths of a drawing.
- In Chapter 7, Section 7.1, 7.SP.5 is connected to 7.RP.A as students work with probability as the ratio of desired outcomes to possible outcomes, and examine the probability between 0 and 1 including 0 and 1 of an event. Relative frequency is also defined as a ratio. For example, in Problem 4, students describe the likelihood of each event when making three-point shots or missing the shots.
- In Chapter 7, Section 7.3, Compound Events, connects 7.G.8a with 7.RP.3 when students determine probability by computation of rational numbers, and representing answers as fractions and percents. For example, Problem 4 expresses the probability as 1/6 or 16 2/3%.
- In Chapter 7, Section 7.3, Probability of Compound Events, 7.SP.8 is connected to the major work of solving real-world problems with rational numbers involving the four operations, 7.NS.3. Students solve simple and compound probabilities using rational numbers in various forms.
- Chapter 8, Section 8.1, Example 3 utilizes proportions to solve a problem to make projections for modeling real world problems. After randomly surveying 75 students, students use the results to estimate the number of students from the total population of 1200. Cluster 7.SP.A supports 7.RP.3.
- In Chapter 8, Section 8.2, Self-Assessment, Problem 4, students apply and extend previous understandings of operations with fractions (7.NS.A) to draw inferences about a population (7.SP.A). Students find the means of three samples of the number of hours music students practice each week, and use the means to make one estimate for the mean number of practice hours. The calculations result in a rational number that, when converted to a decimal, results in a repeating decimal, which they make sense of in order to answer the question about the number of hours music students practice each week (7.NS.2).
- Chapter 9, Section 9.5, Problem Solving with Angles, 7.G.5 is connected to the major work of solving word problems leading to equations, 7.EE.4.a as students write and solve equations to find the missing angle using properties of supplementary, complementary, adjacent, and vertical angles.
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 7 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 152 days.
The pacing shown in the Teacher Edition includes a total of 152 days. This is comprised of:
- 122 days of lessons (62 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. 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 7 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 4, Section 4, “Students should know how to graph numbers on a number line and how to solve one-variable inequalities using whole numbers. In the exploration, students will be translating inequalities from verbal statements to graphical representations and symbolic sentences.”
- 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, Chapter 5, “Laurie’s Notes: Chapter Overview”, “The study of ratios and proportions in this chapter builds upon and connects to prior work with rates and ratios in the previous course.” This supports Standard 6.RP. In Sections 5.1 and 5.2, students decide whether two quantities are in a proportional relationship using ratio tables. This supports Standard 7.RP.2.a and uses unit rates involving rational numbers. During Sections 5.3, 5.4, and 5.5, students write, solve, and graph proportions. This supports Standard 7.RP.2.a-7.RP.3, “Graphing proportional relationships enables students to see the connection between the constant of proportionality and equivalent ratios”, but the term “Slope”, Standards 8.EE.5-6, is not included. In Section 5.6, students work with scale drawings, which supports Standard 7.G.1.
- Each chapter’s Progressions page contains two charts. “Through the Grades”, lists the relevant portions of standards from prior and future grades (grades 6 and 8) that connect to the grade 7 standards addressed in that chapter. For example, Chapter 4, Sections 4.1-4.2, students use algebra tiles to review the process of solving one-step equations. This is identified as revisiting work from a prior grade-level in the “Chapter Exploration and supports grade-level work in section 4.3 of solving equations of the form px + q =r and p(x + q) =r. This supports Standard 7.EE.4a.
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 at the end of each lesson 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 the Teacher Edition, Chapter 6, Section 6.5, the assignments for proficient and advanced students includes a reasoning task in which students determine the price of a drone that is discounted 40%, and then discounted an additional 60% a month later. This reasoning task is omitted from the assignments for emerging students.
- In the Teacher Edition, Chapter 9, Section 9.2, the assignments for advanced students include a critical thinking task in which students determine how increasing the radius of a circle impacts the area of the circle. This critical thinking task is omitted from the assignments for emerging and proficient students.
- Each section within a chapter includes problems where the publisher states, “students encounter varying “Depth of Knowledge” levels, reaching higher cognitive demand and promoting student discourse”. In Chapter 8, Section 8.1, students examine a sample of a population for validity. This supports Standard 7.SP.1 and use a random sample to draw inferences about a population which supports Standard 7.SP.2.
- In “Exploration 1” students “make conclusions about the favorite extracurricular activities of students at their school” by first identifying the population and samples of the population, (DOK Level 1) and then by evaluating the differences between two samples and evaluating their conclusions for validity and explain their thinking, (DOK Level 3).
- Problem 2 students compare two samples to determine which sample is unbiased, (DOK Level 2).
- In Chapter 4, Section 4.6, students roll two different colored dice with negative and positive numbers on each cube. When the students roll a pair of dice, they write an inequality to represent them. Then they roll one die and multiply each side of the inequality to represent them. They are then asked if the original inequality is still true. Finally, they are asked to make conjectures about how to solve an inequality of the form ax
- In Chapter 6, students use a percent model to justify their answers, instead of assessing the reasonableness of answers using mental computation and estimation strategies. Mental computation and estimation are strategies specifically called for in standard 7.EE.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. In some cases it outlines what happened in prior courses, but is not specific to which grade or course this happens. For example:
- In Chapter 1, Section 1.1, it states that in prior courses students were introduced to integers, absolute value, and number lines. For example, “It is important that students review these foundational skills because they are necessary for adding and subtracting rational numbers.” In Chapter 1, Section 1.1, students review the concept of absolute value (6.NS.7). This leads into Section 1.2 where students begin adding integers (7.NS.1.b).
- In Chapter 3, Section 3.3 states that students have used the distributive property in previous courses. It adds, “They will extend their understanding to include algebraic expressions involving rational numbers. This property is very important to algebraic work in future courses”. In Chapter 3, Section 3.3, Exploration 1, students build upon their experience with the distributive property to include rational numbers. In Example 1, students apply the distributive property to simplify expressions.
- In Chapter 5, Section 5.2, the Preparing to Teach notes, explain the connection between students’ prior work with ratios (describing ratio relationships, completing tables), (6.RP.A), and the content in Section 5.2, stating, “In this lesson, they will extend their work with ratios to include fractions, making connections to their recent work with fractions.” In Section 5.1, students complete ratio tables, and write and interpret ratios, but now with fractions, forming a bridge to upcoming work of finding and using unit rates involving rational numbers (7.RP.1).
- In Chapter 6, Section 6.1, Preparing to Teach, notes state students “should know how to solve simple percent problems, and how to use ratio tables, Standard 6.RP.3.” The remainder of Chapter 6, “will build upon this understanding to write and solve percent proportions.” (7.RP.3)
- In the Resources by Chapter book, each chapter has a few questions that are named as “Prerequisite Skills Practice”. The intent is for practice from prior knowledge. There is no mention of previous grade knowledge or previous lesson knowledge.
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 7 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, if it completes the learning or if students are learning or extending learning. For example:
- In Chapter 5, Algebraic Expressions and Properties, 6.EE, Apply and extend previous understandings of arithmetic to algebraic expressions is directly related to the Chapter 5 learning goals of, “Evaluate algebraic expressions given values of their variables (Section 5.1), Write algebraic expressions and solve problems involving algebraic expressions (Section 5.2), Identify equivalent expressions and apply properties to generate equivalent expressions (Section 5.3), Identify equivalent expressions and apply properties to generate equivalent expressions (Section 5.4), and Factor numerical and algebraic expressions (Section 5.5).
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:
- In Chapter 3, students engage simultaneously in Standards 7.NS.A and 7.EE.A, as they simplify, add, subtract, factor and expand linear expressions involving positive and negative number coefficients. For example, in Section 3.1, Try It, Problem 9, students simplify 2s - 9s + 8t - t. In Section 3.3, Try It, Problem 5, students use the distributive property to simplify the expression -3/2 (a - 4 - 2a).
- In Chapter 4, students use operations with integers, Cluster 7.NS.A to solve problems using numerical and algebraic expressions and equations, Cluster 7.EE.B.
- In Chapter 5, Domain 7.RP connects ratio with computations with rational numbers 7.NS, as students explore rates and unit rates. For example, in Section 5.6, students analyze proportional relationships and use them to solve real-world problems.
- Chapter 6, the problems and activities provide connections between the skills and understandings of Cluster 7.EE.B to those of Cluster 7.RP.A as students write proportions and equations to represent and solve percent problems, and to write equations to solve problems involving discounts and markups. In Section 6.3, Practice, Problem 23, students write and solve an equation to determine the percent of sales tax on a model rocket costing $24 with a sales tax of $1.92.
- Chapter 8, Section 8.4, students use random sampling to draw inferences about a population, connecting 7.SP.A with drawing informal comparative inferences about two populations, 7.SP.B.