6th Grade - Gateway 1

The instructional materials reviewed for Reveal Math Grade 6 meet expectations that they assess grade-level content. 

The materials provide three versions of each Module assessment which include a variety of Item types as well as a Performance Task for each Module. In addition, there are quarterly benchmark tests to show growth over the year. 

Examples of assessment items aligned to grade-level standards include:

• Benchmark 2 Assessment, Item 2: “Which expression is not equivalent to the other three? $$0.3^2 + 8; 2^3 + 0.09; 2^3 + 0.03^2; 3^2 ÷10^2 + 2^3$$” (6.EE.2c)
• End of Course Test, Item 2: “Students at a middle school were surveyed about their favorite cafeteria food. The table shows the results of the survey. Drag the tiles to order the favorite meals from least percent of students (at the bottom) to greatest percent of students (at the top).” Students order: 32 %, 1/5, 0.23, and 1/4. (6.RP.3c)
• Module 4 Test Form A, Item 3: “One winter night, the temperature outside was 3°F. Overnight, the temperature dropped to –17°F. How many degrees did the temperature drop overnight? Describe the steps you would follow to find the answer using a number line.” (6.NS.6)
• Module 1 Performance Task: “Mr. Jackson coaches the junior varsity track team. He has entered his athletes in a triathlon. He needs information to help him motivate and prepare his athletes for this challenging event. The triathlon consists of 1 mile of swimming, 25 miles of biking, and 6 miles of running. Mr. Jackson estimates that the average time spent on each phase of the race will be 30 minutes for swimming, 75 minutes for biking, and 60 minutes for running. He sets up a training schedule that includes two sports each day.” There are five parts to the Performance Task: students write ratios to represent the relationship between the two sports on a given day, set up a ratio table, graph the ordered pairs from the table on a coordinate plane, describe how the ratios of times compare for each pair of sports, represent average speed of each sport as a unit rate, and use the information in the tables to answer questions. (6.NS.4; 6.RP.A)
• Module 10 Test Form A, Item 1: “Which of the following are statistical questions? Select all that apply. A) How many 5 km marathons are in Kentucky in October? B) How many pairs of running shoes do you own? C) How many miles is a 5 km marathon? D) How many feet are in a mile? E) How fast can you run? F) How many marathons have you run?” (6.SP.1)

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. The materials are digital and download as a word document, making it easy to modify or omit Items. These items include:

• Benchmark Test 2, Item 14: “All entrees cost $10 at the Roadside Diner. Each side dish is an additional $2. The equation y = 2x + 10 describes the total cost, y, for the number of side dishes, x. Graph the equation of the line.” (8.F.3)
• End of Course Test, Item 3: “An electronics store reduces the price of a printer by 25%. The sale price is marked at $46.50. A) What percent of the original price is the sale price? B) What was the original price of the printer?” (7.RP.3)
• Module 2 Test Form A, Item 13: “The regular price of a baseball hat is $14.45. If Carlos buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20?” (7.RP.3)
• Module 2 Test Form A, Item 19: “A grocery store purchases bags of chips for $2 and marks the price up by 152%. The store is having a sale where everything is on sale for 10% off. Choose the most reasonable estimate for the final price of a bag of chips. A) $0.30 B) $2.70 C) $3.30 D) $4.54” (7.RP.3)
• Module 6 Performance Task, Part E: (Given - “Each scone sells for $1.50.”) “On cold days, the chorus also sells hot tea for $2 a cup. A science teacher bought a cup of hot tea and some scones. She spent $8. How many scones did she purchase? Write and solve an equation to find the number of scones. Compare this equation to the others you have been solving in Parts A, B, C, and D.” (7.EE.4a)

The instructional materials reviewed for Reveal Math Grade 6 meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 8 out of 10, which is approximately 80%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 44 out of 61, which is approximately 72%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 121 out of 168, which is approximately 72%. 

A lesson level analysis is most representative of the instructional materials because lessons directly reflect the grade-level concepts identified for each lesson. In addition, teachers have flexibility in the length of time they may spend on different aspects of the lesson. As a result, approximately 72% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Reveal Math Grade 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Examples of how the materials connect supporting standards to the major work of the grade include: 

• In Lesson 5-6, 6.NS.4 supports 6.EE.3 as students use greatest common factor (GCF) to factor numerical expressions and use the distributive property to write the product of two terms. The lesson starts with an Interactive Presentation (slide format) where students are guided through steps for finding a GCF with prime factorization and rewriting an expression as a product of factors, then as a product of two terms. For example: “8 + 56 = 8(1) + 8(7) = 8(1 + 7).” Teachers can stop at every point for explanation, discussion, and practice. Students also have access to watch the presentation again as needed. After the video, there is “Talk About It!” to prompt discussion: “How can you determine what remains in the parentheses after the GCF has been factored out of the expression?” 
• In Lesson 8-1, 6.G.1 supports 6.EE.2 as students develop area formulas for various parallelograms and substitute numerical values into the formulas to evaluate the expressions. In Explore and Develop, Apply - Landscaping: “Andy, a city horticulturist, is developing a new park over an old city lot. The center of the park features a koi pond that will cover 1,245 square feet. The remaining space will need to be covered with grass seed. If a 50-pound bag of grass seed covers up to 7,500 square feet, how many bags of grass seed will Andy need to buy to seed the rest of the park?” Practice Question 6 states, “What is the area of the parallelogram with sides 11 in. and 9 in.?”
• In Lesson 10-7, 6.SP.5 supports 6.RP.3c as students interpret a data set to reason about percent. Practice Question 6 states, “The histogram shows the number of candy bars each player on a football team sold. One player claimed that more than 50% of the players sold 90 or more candy bars. Is the player correct?”

The instructional materials for Reveal Math Grade 6 meet expectations that the amount of content designated for one grade-level is viable for one year. 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. As designed, the instructional materials can be completed in 168 days.

• The pacing guide is based on daily classes of 45 minutes. 
• Grade 6 includes 61 lessons which account for 126 instructional days.
• Each Module includes one review day and one assessment day for 20 days. The assessment could be a performance task or the module test. 
• Put It All Together are mid-module checkpoints which could be used as an assessment, a review, or homework which are each allocated a half-day of instruction. There are 16 Put It All Togethers for Grade 6, which leads to eight days of instruction. 
• There is one day allocated for each Module introduction and pre-assessment, which is 10 days. 
• Each grade includes four benchmark assessments during the year. 
• Differentiation activities are not specified in the pacing guide.

The instructional materials for Reveal Math Grade 6 meet expectations for the materials being consistent with the progressions in the Standards. Off grade-level material is identified and is relevant to grade-level work; it does not interfere with the work of the grade. In addition, the instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The instructional materials identify prior knowledge at both the Module and Lesson level in the vertical alignment.

In the Teacher Edition and the Vertical Alignment tab online, the introduction for each module includes a progression of concepts and standards across the grades. The beginning of each module states: “The mathematical content in this module connects with what students have previously learned and what they will learn in upcoming modules.” Vertical alignment is provided at both the module and lesson level using the format of previous-now-next. Many of the connections provided are within the current grade. For example:

• Module 1: “Previous - Students understood a fraction as part of a whole, and fraction equivalence. (3.NF.1, 4.NF.1); Now - Students use ratio and rate reasoning to solve real-world and mathematical problems. (6.RP.1-3); Next - Students will use ratio reasoning to find the percent of a number. (6.RP.3, 6.RP.3c)”
• Lesson 4-7: “Previous - Students graphed reflections of points within the coordinate plane. (6.NS.6, 6.NS.8); Now - Students use absolute value to find the distance between points on the coordinate plane. (6.NS.8); Next - Students will solve problems involving adding integers and rational numbers. (7.NS.1)”

The materials provide all students the opportunity to engage with extensive, grade-level work. For example: 

• The Correlation to Mathematical Standards document delineates the content, indicating that all grade-level standards are represented throughout the course.
• Each lesson includes grade level practice for all students in the Interactive Presentation, Explore, Apply, and optional Practice pages. Online, each lesson also includes Reflect and Practice which contains an Exit Ticket and Practice pages for student use. 
• In the Teacher Edition, each Module includes leveled discussion questions and differentiated practice questions to support all students with grade-level concepts.
• When work is differentiated, the materials continue to develop grade-level concepts. For example, in Lesson 4-4, the corresponding interactive review lesson guides students through ordering sets of rational numbers while the extension lesson provides the opportunity to classify real numbers.
• There is opportunity for additional digital practice with every lesson. For each example or application in Explore and Develop, students are prompted to “Go Online” to complete an “Extra Example”. 

Examples of grade-level work:

• Lesson 1-3 Practice: 1) “There are 10 coins in Suri’s coin purse. Six of them are dimes. Write a ratio that compares the number of dimes to the total number of coins as a fraction in simplest form. Then explain the meaning of the ratio.” (6.RP.3)
• Lesson 5-5 Practice: “Use the Distributive Property to expand each algebraic expression. 1) 3(x+8); 2) 5(6+x); 3) 9(3+x)” (6.EE.3)
• Lesson 5-4 Practice: “The expression ½a(b + c) can be used to find the area of a trapezoid. What is the area of a trapezoid if a = 5.5, b = 5, and c = 7.2?” (6.EE.1)
• Lesson 10-3 Practice: “The table shows the number of minutes Kenny spent practicing piano. What is the difference between the mean and median of Kenny’s practice times?” (6.SP.3) 

The materials reference prior knowledge at both the Module and Lesson level. Standards are explicitly referenced in Vertical Alignment for several lessons. For example:

• Each Module contains “Are You Ready?” and a Module Pretest which identify prior knowledge and diagnose student readiness. The materials do not explicitly identify the standards that are below grade level, though it is clear that this is previous learning. For example, in Module 2, the Pretest addresses simplifying fractions, comparing fractions, and writing decimals in word form.
• Each Module includes “Be Sure to Cover” for teachers that states, “Students need to have a thorough understanding of the prerequisite skills required for this module.” Then identifies 2-3 skills and provides the prompt, “Use the Module pretest to diagnose students’ readiness for this module. You may wish to spend more time on the Warm Up for each lesson to fully review these concepts.”
• In the Teacher’s Edition, the Warm Up exercises at the beginning of each Lesson list “prerequisite” topics related to current material. The skills are from previous grade-level lessons as well as previous grades. The materials do not explicitly identify when the skills are below grade level. For example, Lesson 1-2 Warm Up Question 1: “Evaluate each expression. 12 x 5.” Question 5: “Marcel has 45 party favors that he wants to distribute evenly to 15 different gift bags. How many favors will be in each bag?” These questions are not aligned to previous standards (4.OA.3), but they are identified as prerequisite knowledge. 
• Lesson 3-1, Vertical Alignment, Previous: Students divided four-digit dividends by two-digit divisors (5.NBT.6); Now: Students find quotients of multi-digit whole numbers. (6.NS.2)

The instructional materials for Reveal Math 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 and essential questions that are visibly shaped by CCSSM cluster headings. Examples include:

• In Module 1, the Goal, "Solve problems involving ratios and rates" is shaped by 6.RP.A. 
• In Module 3, the Essential Question, “How are operations with fractions and decimals related to operations with whole numbers?” is shaped by 6.NS.A.
• In Module 8, the Essential Question, “How can you describe the size of a three-dimensional figure?” is shaped by 6.G.A.

Materials 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. 

• In Lesson 7-4, 6.EE.C and 6.RP.A are connected as students use ratio tables to show relationships between dependent and independent variables. Practice Question 1 states, “A school sells tickets to their school play through an online ticket company. Each ticket costs $8 and the company charges a $2.50 processing fee per order. Represent the relationship between the number tickets bought and the total cost c with an equation, a table and a graph.”
• In Lesson 5-3, 6.EE.A and 6.EE.B connect to each other as students write and evaluate expressions using variables. In Explore and Develop, Example 2 states, “Write ten dollars more than Anthony earned as an algebraic expression.” Example 3 states, “Write four and one-half times the number of gallons as an algebraic expression.”
• In Module 7, 6.RP.A, 6.NS.C, and 6.EE.C are connected as students find ordered pairs on a graph, complete tables showing independent and dependent variables, determine rates, and write equations. In Lesson 7-1, Explore and Develop, Learn - Find Dependent Variable Values in a Table, Talk It Out states, “The unit cost is $0.25 per game. How is this rate shown on the table? Explain.” Given a 3-column table: Column One: Input (Independent Variable)/Number of Games Played (shown on the next row); Column Two: Rule (Relationship between the input and output)/0.25g; Column Three: Output (dependent variable)/Total Cost. In Lesson 7-3, Practice Question 1 states, "The equation p = 144b represents the number of pencils p in b boxes. Graph the relationship on the coordinate plane."