6th Grade - Gateway 1

The instructional materials reviewed for Match Fishtank Grade 6 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. The materials do not assess topics before the grade level in which the topic should be introduced. Unit Assessments were examined for this indicator, and all materials are available digitally and through downloadable PDFs. 

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

• Unit 1 Test, Question 3, “Slater used 6 black Legos and 18 green Legos to build a tower. What was the ratio of the number of black Legos to the number of Legos in the tower? Answer choices: a. 1:3,  b.1:4, c. 1:6, d. 1:9.” (6.RP.1)
• Unit 1 Test, Question 7, “Wyatt hiked 6 miles in 2 hours. At this same rate, what is the total number of miles Wyatt could hike in 9 hours?” (6.RP.3.b)
• Unit 2 Test, Question 1, “Roya paid $48 for 12 cartons of orange juice. What is the unit rate per carton of orange juice that Roya paid? Answer choices: a. $3, b. $4, c. $6, d. $12.” (6.RP.2)
• Unit 5 Test, Question 4, “Which phrase is a description of 2m +7?  Answer choices:  a. more than 2 times m, b. 2 more than 7 times m, c. 2 times the sum of 7 and m, d. 7 times the sum of 2 and m.”  (6.EE.2.a)
• Unit 6 Test, Question 2, “A shelf has four books on it. The weight, in pounds, of each of the four books on the shelf is listed below.  ‘2.5, 3.2, 2.7, 2.3 Which inequality represents the weight, w, of any book chosen from the shelf? Answer choices: a. w > 2.3, b. w < 2.4 , c. w > 3.2 , d. w < 3.3.” (6.EE.b)

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

The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of chapters (units, modules, topics, etc.) devoted to major work of the grade (including assessments and supporting work connected to the major work) is six out of eight units, which is approximately 75%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 88 out of 118, which is approximately 75%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 112 out of 143, which is approximately 78%. 

A lesson-level analysis is most representative of the instructional materials because the units contain major work, supporting work, and assessments. As a result, approximately 75% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Match Fishtank Grade 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Supporting standards/clusters are connected to the major standards/clusters of the grade, for example:

• Unit 1, Understanding and Representing Ratios, Lesson 3, Anchor Problem 3, 6.NS.4 connects with 6.RP.1 by using common factors in order to find equivalent ratios. “Pam and her brother both open savings accounts. Each begins with a balance of 0 dollars. For every $2 that Pam saves in her account, her brother saves $5 in his account.  a) Determine a ratio to describe the money in Pam’s account to the money in her brother’s account. b) Create two equivalent ratios that describe the amount of money in Pam’s account and the amount of money in her brother’s account.” 
• Unit 3, Multi-digit and Fraction Computation, Lesson 5, Target Task, supporting standard 6.G.1 connects with 6.NS.1 through solving a real-world problem involving area. “There are other ways to think about division of fractions. Try these two questions. They both use division, but why? And how do you know what to divide by what?  1. The water level in the reservoir has gone down 2 1/2 feet in the last month and a half. How fast is the water level going down per month?  2.  Farmer Schmidt owns 3/4 of a square mile of land.  Her field is a rectangle. One side is 2/3 of a mile.  How long is the other side?”
• Unit 5, Numerical and Algebraic Expressions, Lesson 4, Target Task connects supporting standard 6.G.2 to 6.EE.2 as students use the formulas to find the volume and surface area of rectangular prisms. “A cube has 6 sides, each with an area of $$s^2$$ square units.  The surface area of a cube is the total of all 6 sides and is represented by the formula $$S = 6s^2$$. Find the surface area of a cube with the side lengths below. a.  s = 3 inches  b. s = 1.2 cm  c. s= 2/3 feet.”
• Unit 7, Geometry, Lesson 6, the Target Task fosters coherence between the clusters as students apply the standards from 6.G.A and 6.RP to determine the area of the trapezoid. “Find the deck area around the pool. The deck area is the white area in the diagram.”

Instructional materials for Match Fishtank 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 143 days. Included in the 143 days are: 

• 118 lesson days 
• 17 review/flex days 
• 8 assessment days

Each unit is comprised of 12 to 18 lessons that contain a mixture of Anchor Problems, Problem Set Guidance, a Target Task, and a Mastery Response. These components align to the number of minutes needed to complete each part as provided in the Pacing Guide. Based on the pacing guide, the suggested lesson time frame is 60 minutes: 

• 5 - 10 mins Warm up 
• 25 - 30 mins Anchor Problems  
• 15 - 20 mins Problem Set 
• 5 - 10 minutes Target Task

The instructional materials for Match Fishtank Grade 6 meet expectations for the materials being consistent with the progressions in the standards. The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. 

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 relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior or future grades is clearly identified and related to grade-level work. Prior grade knowledge is explicitly related to grade-level concepts. The “future standards” align the work with future grade-level standards. Each lesson provides the teacher with current standards and foundational standards which are identified under the “Standards” tab. Through the Unit Overview, Tips for Teachers, and Unit Summary, teachers are provided explicit connections to prior and future knowledge for each standard.

The Unit Plan Summary section includes a list of foundational standards from earlier grades that are connected to the content standards addressed in that unit, as well as a list of future standards that relate. For example:

• Unit 1, Understanding and Representing Ratios, “In fourth and fifth grade, students learned the difference between multiplicative and additive comparisons and they interpreted multiplication as a way to scale. Students will access these prior concepts in this unit as they investigate patterns and structures in ratio tables and use multiplication to create equivalent ratios. The work students do in this unit connects directly to Unit 2: Rates & Percent and re-appears in Unit 6: Equations and Inequalities when students analyze and graph relationships between independent and dependent variables. Beyond sixth grade, students extend their understanding of ratios and rates to investigate proportional relationships in seventh grade. This sets the groundwork for the study of functions, linear equations, and systems of equations, which students will study in eighth grade and high school.” 
• Unit 2, Unit Rates and Percent addresses 6.RP.2, 6.RP.3, 6.RP.3.b, 6.RP.3.c, 6.RP.3.d, and 6.RP.4. Foundational standards are “Covered in previous units or grades that are important background for the unit: 4.MD.1, 4.MD.2, 5.MD.1, 5.NF.3, 5,NF.4.a, 5.NF.4.b, 5.NF.5, 5.NF.5.a, 5.NF.5.b, 5.NF.6, 4.NF.4.c, 4.NF.6,  and 5.NBT.6 from previous grades, and 6.RP.1 from a previous unit.”
• Unit 5, Numerical and Algebraic Expressions, “In elementary school, students used variables to represent unknown quantities, and they evaluated and described numerical expressions without exponents. They used the commutative property to enhance their understanding of multiplication and addition, and they used the distributive property when modeling partial areas. All of these concepts come together and support student understanding in this sixth-grade unit. Immediately following this unit, sixth graders will start a unit, Equations and Inequalities, where they will use algebra to model and solve real-world problems. They will also revisit percentages using new skills with expressions and equations to efficiently solve percent problems. In seventh and eighth grades, students continue to simplify and solve more complex expressions and equations using the same tools learned in this unit.” Foundational standards (5.OA 1&2, 4.OA.3, 4.NBT.5, & 5.MD.b) as well as future standards (7.EE.1, 7.EE.4). Additionally, 6.EE.5, 6.EE.7 and 6.EE.9 are considered future standards for this lesson as they are not identified until the next unit, Unit 6: Equations and Inequalities.

Lessons include connections between grade-level work, standards from earlier grades, and future knowledge. These can include problems from Open Up Resources Grade 6-8 Mathematics, Open Middle, Illustrative Mathematics, and EngageNY, Great Minds. For example:

• Unit 1, Understanding and Representing Ratios, Lesson 1 objective, “define ratio and use ratio language to describe associations between two or more quantities.” This lesson supports 6.RP.1 and links back to Foundational Standards from grade 4, 4.OA.2 and 4.MD.1, as evident in Anchor Problem 3, “Abigail mixed 2 cups of white paint with 6 tablespoons (T) of blue paint.” Students write at least four ratio statements to describe the situation.  
• Unit 2, Unit Rates and Percent, Lesson 2 includes Foundational Standards: 6.RP.1 and Future Connections: 7.RP.1, 7.RP.2, 7.RP.3. Lesson objective: define rate and unit rate and find rates from situations involving ratios. (6.RP.2, 6.RP.3b)
• Unit 5, Numerical and Algebraic Expressions, Lesson 6, teachers are directed to a Problem Set from Engage NY, which moves students from writing fractions to writing algebraic expressions as fractions. Students begin with writing 1 ÷ 2 without the division sign, then a ÷ 2, then proceed to the Problem Set: Problem 1. “Rewrite the expressions using the division symbol and as a fraction. Answer choices:  a. Three divided by 4,  b. The quotient of m and 11,  c. 4 divided by the sum of h and 7,  d. The quantity x minus 3 divided by y.  Problem 2. Draw a model to show that x ÷ 3 is the same as x/3.” (6.EE.2)

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The Anchor Problem(s) help students make sense of the mathematics of the lesson as outlined in the Criteria for Success and Objective by providing them multiple opportunities to engage in the grade-level content in meaningful ways. The Problem Set Guidance provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills. The Target Task is aligned to the Objective and designed to cover key concepts from the lesson and identify any misconceptions students have. It serves also as an indicator of student understanding or mastery of the Objective. For example:

• Unit 1,Understanding and Representing Ratios, Lesson 16, Target Task, students solve a part:whole ratio problem using a tape diagram (6.RP.3). For example, the Target Task states, “When Carla looked out at the school parking lot, she noticed that for every 2 minivans, there were 5 other types of vehicles. If there are 161 vehicles, how many of them are minivans?” 
• Unit 3, Multi-Digit and Fraction Computation, Lesson 2, Anchor Problem states, “Leonard made 1/4 of a gallon of lemonade and poured all of it into 3 glasses, divided equally. How much lemonade is in each glass? Write a division problem and draw a visual model.” (5.NF.7)
• Unit 4, Rational Numbers, Lesson 6, the Target Task states, “Christina is trying to order the numbers -3 and -2 1/2 from least to greatest. She makes the claim below. Christina’s claim: “I know that  -2 1/2 is less than -3. So, -2 1/2 must be less than -3.” Is Christina correct in her thinking? Explain why or why not. Use a number line to support your reasoning.” (6.NS.6.c) 
• Unit 6, Equations and Inequalities, Lesson 7, Problem Set Guidance links to Illustrative Math, Fruit Salad, “A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?” (6.RP.a.3, 6.EE.b.7)

Standard 6.SP.5.b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement, is not addressed in any lesson, although it is listed in the Unit Overview for Unit 8: Statistics. 

Prior knowledge is explicitly identified and linked to grade-level work. For example:

• Unit 3, Multi-Digit and Fraction Computation, Lesson 1, Tips for Teachers, reviews multiplication and division concepts learned in elementary grades as it introduces the sixth grade standard. “This lesson is approaching 6.NS.1. It reaches back to concepts students learned in earlier grades around multiplication and division in order for students to be able to extend on these concepts in following lessons in the unit.”
• Unit 4, Rational Numbers, Lesson 1 objective states, “Extend the number line to include negative numbers. Define integers.” (6.NS.6, 6.NS.6c).  This is connected to prior knowledge of 3rd grade: Understand a fraction as a number on the number line and represent fraction on a number line diagram and use this knowledge to extend the number line to integers. (3.NF.2)
• Unit 6, Equations and Inequalities, Lesson Overview, teachers are reminded that this lesson brings together several concepts and skills students have worked on throughout the year. For example, some of those concepts are as follows: tables of equivalent values (6.RP.3), writing equations (6.EE.1), plotting points (6.NS.8), and determining values in ratio relationships (6.RP.3). Foundation skills (that link to several lessons) are also identified. For example, some of those skills are as follows: 5.OA.3, 6.RP.3, and 6.NS.6.c. This lesson contains several links to prior lessons such as Unit 3, Lesson 5, Target Task, “There are other ways to think about division of fractions. Try these two questions. They both use division, but why? And how do you know what to divide by what?” Question 1: “The water level in the reservoir has gone down 2 1/2 feet in the last month and a half. How fast is the water level going down per month?” Question 2: “Farmer Schmidt owns 34 of a square mile of land. Her field is a rectangle. One side is 2/3 of a mile. How long is the other side?” (6.NS.1)

The instructional materials for Match Fishtank Grade 6 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards. The materials include learning objectives that are visibly shaped by CCSSM cluster headings and problems and activities that connect two or more clusters in a domain or two or more domains, when these connections are natural and important.

 The Units are divided into Lessons focused on domains. Grade 6 standards are clearly identified in the Pacing Guide, Standard Map Document, and a CCSSM Lesson Map found in the Unit Summary of each Unit. Additionally, each lesson identifies the objectives that address specific clusters. Instructional materials shaped by cluster headings include the following examples:

• Unit 1, Understanding and Representing Ratios, Lesson 1, Objective, “Define ratio and use ratio language to describe associations between two or more quantities.” (6.RP.A)
• Unit 2, Unit Rates and Percent, Lesson 2, Objective, “Find unit rates and use them to solve problems.” (6.RP.A) 
• Unit 3, Multi-digit and Fraction Computation, Lesson 5, Objective, “Solve and write story problems involving division with fractions.” (6.NS.A)
• Unit 5, Numerical and Algebraic Expressions, Lesson 3, Objective, “Use variables to write algebraic expressions.” (6.EE.A)
• Unit 6, Equations and Inequalities, Lesson 8, Objective, “Define and identify solutions to inequalities.” (6.EE.B)
• Unit 6, Equations and Inequalities, Lesson 12, Objective, “Write equations for and graph ratio situations. Define independent and dependent variables,” (6.EE.C) 
• Unit 7, Geometry, Lesson 10, Objective, “Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.” (6.G.A)  

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. For example:

• Unit 2, Ratios and Proportional Relationships, Lesson 2, 6.RP.2 and 6.RP.3.b are connected when students demonstrate an understanding of a unit rate through drawing a tape diagram. Anchor Problem 2 states, “Adam’s Fruit Farm also has 100 acres, but he grows more than just apples. Oranges take up 60 acres of his farm. What percent of Adam’s farm is oranges? What percent is not oranges? Draw a 10 x 1 tape diagram to model the situation.”
• Unit 5, Numerical and Algebraic Expressions, Lesson 4, connects 6.EE.A and 6.NS.A as students evaluate expressions by multiplication and division of fractions and decimals. Anchor Problem 1 states, “A square prism is shown below. The formula $$V = s^2h$$ can be used to find the volume of the square prism. What is the volume of the prism when the side length of the base measures 1.5 inches and the height measures 8 inches?” 
• Unit 6, Equations and Inequalities, Lesson 12, connects 6.RP.A and 6.EE.C as students write equations in situations involving ratios. Anchor Problem 1 states, “A recipe for sugar cookies calls for 1 cup of sugar for every 2 cups of flour.” Questions posed:  a. “Use the ratio to complete the table.” b. “If you know the number of cups of sugar, s, in the recipe, how can you determine the number of cups of flour to use? What equation represents this relationship?”  c. “If you know the number of cups of flour, f, in the recipe, how can you determine the number of cups of sugar to use? What equation represents this relationship?” d. “In each equation, what is the independent variable and what is the dependent variable?”
• Unit 7, Geometry, Lesson 9, 6.G.1 supports 6.NS.3 as students use their understanding of integers to represent polygons on the coordinate plane. Anchor Problem 1 states, “A new park is being built in the city. In the park, there will be a cemented walkway that will wind through the park. The walkway will be completely enclosed by a short, gated fence that will line the path on all sides of the path. Each square unit in the coordinate grid represents 1 square yard.” Questions posed: “a. The city budget includes enough funds to include 50 square feet of cement and 60 yards of fencing. Will the budget cover the necessary expenses for cement and fencing? Defend your answer.  b. Two statues will be placed at point (-1,2) and (-1,-4). How far apart, in units, are the two statues?”
• Unit 8, Statistics, Lesson 9 connect 6.SP.A and 6.SP.B as students begin to understand spread and variability of data sets. Anchor Problem 2 states, “Jamie is planning to cover a wall with red wallpaper. The dimensions of the wall are shown below. Questions posed: a. “How many square feet of wallpaper are required to cover the wall?” b. “Wallpaper comes in long rectangular strips that are 24 inches wide. If Jamie lays the strips of wallpaper vertically, how  many strips will she use and how long will each strip be? Explain.” c. “If Jamie lays the strips of wallpaper horizontally, can she cover the wall without wasting any wallpaper? Explain.”