7th Grade - Gateway 1

The instructional materials reviewed for Match Fishtank Grade 7 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 downloadable PDF documents. 

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

• Unit 1 Test, Question 6, “In the morning, a farm worker packed 3 pints of strawberries every 4 minutes. In the afternoon, she packed 2 pints of strawberries every 3 minutes. What was the difference between her morning and afternoon packing rates, in pints per hour? Show your work clearly.” (7.RP.1)
• Unit 2 Test, Question 3, “Which expression is equivalent to 4 - (-7)? Answer choices: a. 7 + 4, b. 4 - 7, c. -7 - 4, d. - 4 + 7.” (7.NS.1.c)
• Unit 3 Test, Question 7, “Find the value of the algebraic expression when $$a=-1$$ and $$b=2$$.”  (7.NS.3)
• Unit 5 Test, Question 5, “A museum opened at 8:00am. In the first hour, 350 people purchased admission tickets. In the second hour, 20% more people purchased admission tickets than in the first hour. Each admission ticket cost $17.50. What is the total amount of money paid for all the tickets purchased in the first two hours?” (7.EE.3).
• Unit 8 Test, Question 10, “Dana has 8 baseball cards, 10 football cards, 4 hockey cards, and 14 basketball cards. All the cards are the same size and shape. Dana will select one card at random. What is the probability that the card selected will be a hockey card? Show all of your work.”  (7.SP.1)

The instructional materials reviewed for Match Fishtank Grade 7 meet expectations for spending a majority of instructional time on major work of the grade, using the materials as designed. 

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 104 out of 117, which is approximately 89%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 115 out of 143, which is approximately 80%. 

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 89% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Match Fishtank Grade 7 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 6, Geometry, Lesson 4, 7.G.5 supports 7.RP.2 as students connect finding the unknown angle measurement using proportional relationships. Anchor Problem 2 is as follows:  “Two lines meet at a point that is also the endpoint of two rays. Questions: 1. Describe the angle relationships you see in the diagram.  2. Set up and solve an equation to find the value of x.  3. Find the measurements of ∠BAC and ∠BAH.” 
• Unit 7, Statistics, Lesson 4, Target Task, supporting standards 7.SP.B connect to major cluster standards 7.NS.A to meet the lesson objective: analyze data sets using measures of center and interquartile range.  The Target Task is as follows: “While waiting for their bus to arrive after school one day, 10 students wondered how many baskets from the free-throw line they could each make in 5 minutes. Each student took his or her turn. The results are: 14, 8, 12, 6, 20, 26, 9, 6, 11, 12. Questions: a. Find the mean and median number of baskets made by the students.  b. Which measure of center better represents the typical number of baskets made?  c. Ten players on the co-ed basketball team determined the number of baskets he or she could make from the free-throw line in 5 minutes. The interquartile range of their data set was 3. Which data set has the greater variability?” 
• Unit 7, Statistics, Lesson 7 connects 7.SP.A and 7.RP.A when representing sample spaces for compound events connects to analyzing proportional events in real-world problems. Anchor Problem 1: “Akilah is running for seventh grade class president. There are 100 students in the seventh grade at her school. To better understand her chances of winning, Akilah asks a random sample of 20 seventh graders if they plan to vote for her. In her sample, 12 of the 20 students said they planned to vote for her.  Akilah asks several friends to also ask a random sample of 20 students. Together, they combine their results to get a better understanding of her chances of winning. After winning the election, Akilah finds out that 55 out of the 100 seventh graders at her school voted for her. Using the situation above, define and describe the following terms: sample, population, sample population, population proportion, sample distribution.”
• Unit 8, Probability, Lesson 2 connects 7.SP.C and 7.RP.A as students define probability and sample space, and estimate probabilities from experimental data.  Anchor Problem 2 is as follows:  “A spinner with different colors on it was spun 20 times. The data recording the color of each spin is shown below. Questions: “a. What is the sample space of the spinner? b. Does it seem that each color is equally likely? Explain your reasoning. c. Estimate the probability of spinning each color on the spinner.”

Instructional materials for Match Fishtank Grade 7 meet expectations that the amount of content designated for one grade level is viable for one year. 

The instructional materials can be completed in 143 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. Included in the 143 days are: 

• 117 lesson days 
• 18 review/flex days 
• 8 assessment days  

Each unit is comprised of 9 to 21 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. The breakdown is as follows:  

• 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 7 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. Each lesson provides the teacher with current standards and foundational standards which are addressed 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, Proportional Relationships, the Unit Plan Summary is as follows: “In sixth grade, students were introduced to the concept of ratios and rates. They learned several strategies to represent ratios and to solve problems, including using concrete drawings, double number lines, tables, tape diagrams, and graphs. They defined and found unit rates and applied this to measurement conversion problems. Seventh grade students will draw on these conceptual understandings to fully understand proportional relationships. In seventh grade, all of these skills and concepts come together as students now operate with all rational numbers, including negative numbers. By the time students enter eighth grade, students should have a strong grasp on operating with rational numbers, which will be an underlying skill in many algebraic concepts. In eighth grade, students are introduced to irrational numbers, rounding out their understanding of the real number system before learning about complex numbers in high school.” Foundational Standards identified: 6.RP.1-3, 6.NS.1, 6.EE.7 & 9, and 5.NF.6; while Future Standards listed are 8.EE.5 & 6, and 8.F.1-5.
• Unit 2, Operations With Rational Numbers, the Unit Plan Summary states the following:  “Starting in first grade, students learn about the commutative and associative properties of addition, and the relationship between addition and subtraction. In third grade, students extend their understanding of the properties of operations to include multiplication and the distributive property.” Additionally, the Unit Summary connects grade-level concepts to current and future standards. An example is located in Unit 2, Lesson 16,  the lesson objective is: compare and order rational numbers, and write and interpret inequalities to describe the order of rational numbers. (7.NS.1 and foundational standard 6.NS.7) In Unit 3: Numerical and Algebraic Expressions identifies Foundational Standards from: Expressions and Equations 6.EE.2, 6.EE.2.c, 6.EE.3, 6.EE.4, The Number System, 7.NS.1, 7.NS.2 Future Connections identified include: Geometry 7.G.4, 7.G.5, 7.G.6, Expressions and Equations 8.EE.7, 8.EE.8, 7.EE.4.
• Unit 5, Percents and Scaling, the Unit Plan Summary states the following: “These standards are foundational to this seventh-grade unit, and the first four lessons in this unit incorporate these concepts and skills. In eighth grade, students will refine their understanding of scale and scale drawings when they study dilations in their transformations unit. They will define similar figures and use dilations and other transformations to prove that two images are similar or scale drawings of one another.”
• Unit 5, Percents and Scaling, the Unit Plan Summary states the following: “In sixth grade, students learned several strategies to solve ratio and rate problems, including tables, tape diagrams, double number lines, and equations. They also defined percent as a rate per 100 and solved percent problems to find the whole, part, or percent.” 

The lessons also include connections between grade-level work, standards from earlier grades, and future knowledge. For example:

• Unit 1, Proportional Relationships, Lesson 1, “This lesson approaches standards 7.RP.1 and 7.RP.2 by reviewing concepts and skills from 6th grade standards in the Ratios and Proportions domain. These standards are foundational to this 7th grade unit, and will support students in later lessons.”  
• Unit 6, Geometry, Lesson 1, “Students studied angles in fourth grade, where they recognized angles as shapes formed when two rays share a common endpoint. They understood that angle measures are additive, and they solved addition and subtraction problems to find missing angles. In this lesson, students formally define complementary and supplementary angles, and they start to develop their understanding of angle relationships and how they can represent these relationships using equations.”
• For each unit in Grade 7, the Unit Summary connects the current grade-level skills to prior and future grade-level standards. The Unit 3 Numerical and Algebraic Expressions Unit Summary states that, “In sixth grade, students learned how the same rules that govern arithmetic also apply to algebraic expressions. They learned to expand and factor expressions using the distributive property, and they combined terms where variables are the same. With new knowledge of the number system, students go from working with expressions like 5(6x+3y) in sixth grade to those with rational numbers such as -(a+b) - 3/2(a - b) in the seventh grade.The next seventh-grade unit, Unit 4, Equations and Inequalities, will continue to engage students in working with expressions with rational numbers. In eighth grade, students will work with expressions and equations in one variable and two variables, solving single linear equations and systems of linear equations. Throughout all of their future work with expressions, students’ ability to look for and make use of the structure in expressions will be as important as their ability to work with them procedurally.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Anchor Problems 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. Target Tasks are aligned to the Objective and designed to cover key concepts and misconceptions. Target Tasks can be used as an indicator of student understanding or mastery of the Objective. For example:

• Unit 1, Proportional Relationships, Lesson 7, Anchor Problem 1 states, “In a video game, for every 3 coins you collect, you earn 4 points. a. Create a table of values to represent the relationship, b. Graph the relationship c. Determine the equation that represents the relationship.” (7.RP.2)
• Unit 5, Percent and Scaling, Lesson 3, the Target Task states, “At the Blackman High school, 86 seniors submitted college applications for early decision. This represented approximately 34% of the senior class. The Truman High School, across town from the Blackman High School, has 266 seniors. Which high school has the larger senior class?” (7.RP.3)
• Unit 3: Numerical and Algebraic Expressions, Lesson 6, the Target Task states, “Two expressions are given below. Expression A:   5q - r   Expression B: -2q + 3r - 4, a. Write a simplified expression that represents A + B. b. Write a simplified expression that represents A - B.” (7.EE.1) 
• Unit 5, Percent and Scaling, Lesson 10, Anchor Problem 3 states,  “Tyler bought two tickets to a basketball game on the website Game Finder. Each ticket cost $65, and the website charged a convenience fee that was a small percent of the ticket cost. If Tyler’s total bill came to $132.60, what percent was the convenience fee?” (7.RP.3)

The instructional materials for Match Fishtank Grade 7 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards. Overall, 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 7 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, Proportional Relationships, Lesson 4, the Objective states, “Write equations for proportional relationships presented in tables” connects with the major cluster of analyze proportional relationships and use them to solve real-world and mathematical problems (7.RP.A)
• Unit 2, Operations with Rational Numbers, Lesson 3, the Objective states, “Describe situations in which opposite quantities combine to make zero.” (7.NS.A) 
• Unit 3, Numerical and Algebraic Expressions, Lesson 10, the Objective states, “Solve multi-step, real-world problems with rational numbers.” (7.EE.B)
• Unit 4, Equations and Inequalities, Lesson 7, the Objective states, “Model with equations in the form px+q=r and p(x+q)=r” connects with the major cluster solve real-life and mathematical problems using numerical and algebraic expressions and equations.” (7.EE.B)
• Unit 8, Probability, Lesson 4,  the Objective states, “Use probability to predict long-run frequencies.” (7.SP.C)

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 1, Proportional Relationships, Lesson 11, Anchor Problem 1, 7.RP.1 connects with 7.NS.3 as students solve real-world problems involving the four operations with rational numbers. The Anchor Problem states, “A proportional relationship is shown in the graph. a. Describe a situation that could be represented by this graph. b. Write an equation for the relationship. Explain what each part of the equation represents.”  
• Unit 1, Proportional Relationships, Lesson 16, 7.RP.A and 7.EE.A are connected as students use their understanding of proportional relationships and equations in ratio and rate problems by setting up a proportion, including part-part-whole problems. For example, the Target Task states, “The table below shows the combination of dry prepackaged mix and water to make concrete. The mix says for every 1 gallon of water, stir 60 pounds of dry mix.  We know that 1 gallon of water is equal to 8 pounds of water. Using the information in the table, complete the remaining parts.”
• Unit 3, Numerical and Algebraic Expressions, Lesson 7 connects 7.NS.A and 7.EE.A when students simplify algebraic expressions that include rational numbers. Anchor Problem 2 states,  “Which expressions below are equivalent to 4 - 3(6x - 3)? Select all that apply.” Answer choices “ a. ( 4 - 18) x + 9     b. (4 + 9) - 18x     c. 4 - (18x - 9)     d. 4 - 18x - 3     e. 4 - 18x + 9     f. 6x - 3.” 
• Unit 3, Numerical and Algebraic Expressions, Lesson 2, connects 7.NS.3 and 7.EE.1 as students apply properties of operations while solving real world problems with rational numbers. Anchor Problem 2 states,  “Write an expression for each sequence of operations.  1: Add 3 to x, subtract the result from 1, then double what you have. Expression 2: Add 3 to x, double what you have, then subtract 1 from the result.”  
• Unit 3, Numerical and Algebraic Expressions, Lesson 10 connects 7.NS.C and 7.EE.C when students solve real world problems using positive and negative rational numbers. Anchor Problem 1 states, “Below is a table showing the number of hits and the number of times at bat for two Major League Baseball players during two different seasons. A player’s batting average is the fraction of times at bat when the player gets a hit. Who has the better batting average? Justify your answer.”
• Unit 5, Percent and Scaling, Lesson 3 connects 7.RP.A and 7.NS.A as students find the whole given a part and percent. Anchor Problem 1 states, “At the Kennedy Middle School, 280 students attended the end-of-year carnival, representing 80% of the students in the school.  a. Draw a visual representation of the problem. For example, you could draw a tape diagram or a double number line.  b. Determine how many students are at the Kennedy Middle School. Choose any strategy.  c. Find a peer who used a different strategy to solve than you did. Compare and discuss your strategies and solution.”
• Unit 5, Percent and Scaling, Lesson 5, Anchor Problem 2 connects 7.EE.2 and 7.RP.3 as students use proportional relationships to solve percentage problems and rewrite the expression in different forms. Anchor Problem 2 states, “On Sunday, 1,460 customers shopped at Pine Village Bookstore. On Monday, there were 60% fewer customers at the bookstore. Draw a diagram and use it to solve. Explain your reasoning.”
• Unit 6, Geometry, Lesson 12 connects 7.G.A and 7.G.B as students draw geometric shapes based on angles. Anchor Problem 4 states, “A triangle has an angle measure of 50º.  The two side lengths that form this triangle are 3 inches and 4 1\2inches long. Draw the triangle described above. Then determine the measure of the third side and the other two angles.”