7th Grade - Gateway 1

The instructional materials reviewed for Achievement First Mathematics Grade 7 meet expectations that they assess grade-level content. Assessment questions are aligned to grade-level standards. No examples of above grade-level assessment items were noted. Each unit contains a Post-Assessment which is a summative assessment based on the standards designated in that unit. The assessments contain grammar and/or printing errors which could, at times, interfere with the ability to make sense of the materials. Examples of assessment items aligned to grade-level standards include: 

• In Unit 1 Assessment, Question 13 states, “Shonte’s bank statement shows that her balance is $25.40. She has an outstanding bill of $65.99 that she has to pay immediately in order to avoid paying a fine. What will her account balance show after she pays her bill?” (7.NS.3)
• In Unit 5 Assessment, Question 1 states, “Talik walked $$\frac{1}{2}$$ of a mile in $$\frac{1}{4}$$ of an hour. Cedric walked $$\frac{3}{4}$$ of a mile in $$\frac{3}{4}$$ of an hour. If these rates remain constant, which of the following statements is true? a) The two boys would walk the same distance in the same amount of time. b) Cedric would walk $$\frac{1}{2}$$ mile in less time tha(n) Talik. c) Talik would walk $$\frac{1}{2}$$ mile in less time than Cedric. d) Who walks faster depends on how far they walk.” (7.RP.1)
• In Unit 6 Assessment, Question 12 states, “There were 48 cookies and 40 brownies in a jar on Monday. The next day, the number of cookies in the jar increased by 25%, and the number of brownies in the jar decreased by 10%. Find the overall percent change in goodies in the jar to the nearest whole number.” (7.EE.3)
• In Unit 8 Assessment, Question 2 states, “Eight of the 32 students in your seventh-grade math class have a cold. The student population is 450. Your classmate estimates that 112 students in the school have a cold. a) Is this a reasonable conclusion to draw from the data? Explain why or why not. b) Describe a survey plan you could use to better estimate the number of students who have a cold. Include all necessary parts of the plan for creating a fair sample and collecting data.” (7.SP.1)
• In Unit 9 Assessment, Question 14 states, “A 3D figure was sliced perpendicular to its base and the plane section that resulted was a triangle. The figure was then sliced horizontally and the plane section that resulted was a square. What is the name of one 3D shape from which the plane section could have come from? Explain on the lines below.” (7.G.3)

The instructional materials reviewed for Achievement First Mathematics Grade 7 meet expectations for spending a majority of instructional time on major work of the grade. For example:

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6.5 out of 10, which is approximately 65%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 95 out of 140, which is approximately 68%.
• The number of minutes devoted to major work (including assessments and supporting work connected to the major work) is 7825 out of 12,600 (90 minutes per lesson for 140 days), which is approximately 62%. 

A minute level analysis is most representative of the instructional materials because of the way lessons are designed, where 55 minutes are designated for the lesson and 35 minutes are designated for cumulative review each day, so it was important to consider all aspects of the lesson. As a result, approximately 62% of the instructional materials focus on major work of the grade. However, because 62% is close to the benchmark and both other measures met or exceeded the benchmark, Grade 7 meets the requirements for spending the majority of class time on major clusters.

The instructional materials reviewed for Achievement First Mathematics Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.  Although connections are rarely explicitly stated, problems clearly connect supporting and major work throughout the curriculum. Examples where supporting work enhances major work include:

• In Unit 4, Lesson 9, supporting standard 7.G.4 enhances the major work of 7.EE.4. Students represent and solve multi-step geometric problems using a complex equation. Independent Practice Question 5 (Master level) states, “A hexagon has six congruent sides and each side length is $$\frac{1}{2}n+2$$. What is the measure of one of the side lengths if the perimeter is 25?”
• In Unit 5, Lesson 12, supporting standard 7.G.1 enhances the major work of 7.RP.2. Students understand a special kind of proportional relationship in scale drawings as either a reduction or the enlargement of a two-dimensional picture and determine the constant of proportionality that relates scale drawings as the scale factor. For example, Independent Practice Question 6 (PhD level) states, “On a blueprint for an apartment building, the height of the door is 4 inches tall. The actual door is 84 inches high. If the rest of the blueprint follows this exact same scale, what would be the actual dimensions of a room that is 10 inches long and 18 inches wide on the blueprint? Express your answer in terms of feet (12 inches = 1 foot).”
• In Unit 7, Lesson 6, supporting standard 7.SP.6 enhances the major work of 7.RP.2. Students develop uniform and non-uniform probability models and use proportional reasoning to predict the approximate relative frequency of outcomes (based on theoretical probability). For example, Independent Practice Question 6 (Master level) states, “Yasmine has a bag of snacks that contains 40% Cheetos, 25% Doritos, 10% Fritos, and 25% pretzels. a) If she reaches into the bag and grabs one snack, and does so 15 times, how many Cheetos do you expect her to get?  b) Yasmine likes all the types of snacks except for Doritos. If she grabs a total of 40 snacks, about how many times will she get a type of snack that she likes?”
• In Unit 10, Lesson 1, supporting standard 7.G.5 enhances the major work of 7.EE.4. Students define complementary and supplementary angles and determine the measurement of a missing angle by writing a simple equation. For example, in Partner Practice Question 5 (Master level), students are given a diagram of two intersecting lines and a ray coming out at $$90\degree$$ and asked, “In the diagram below, angle ABE is $$90\degree$$. Angle EBD measures $$3x$$ and angle DBC measures $$2x-10$$. What are the measures of angles EBD and DBC?”

Instructional materials for Achievement First Mathematics 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 140 days. For example:

• There are 10 units with 130 lessons total; each lesson is 1 day. 
• There are 10 days for summative Post-Assessments.
• There is an optional lesson in Unit 8 between Lessons 4 and 5. Since it is optional, it is not included in the total count.

According to The Guide to Implementing Achievement First Mathematics Grade 7, each lesson is completed in one day, which is designed for 90 minutes. 

• Each day includes a Math Lesson (55 minutes) and Cumulative Review (35 minutes). 
• The Implementation Guide states, “If a school has less than 90 minutes of math, then the fluency work and/or mixed practice can be used as homework or otherwise reduced or extended.”

The instructional materials for Achievement First Mathematics Grade 7 meet expectations for the materials being consistent with the progressions in the Standards. 

The materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. These connections are made throughout the materials including the Implementation Guide, the Unit Overviews, and the lessons. For example:

• The Unit Overview includes “Previous Grade Level Standards and Previously Taught and Related Standards” which describes in detail the progression of the standards within each unit. In Unit 1, “In 6th grade, students first developed a conceptual understanding of rational numbers “through the use of a number line, absolute value, and opposites, and extended their understanding to include ordering and comparing rational numbers (6NS5, 6NS6, 6NS7). They further extended their understanding of rational numbers within the context of the coordinate plane (6NS8). $$6^{th}$$ grade also marked the year when students were expected to fluently work with whole number, fraction and decimal operations (6NS1, 6NS2, 6NS3). Early in the unit, students leverage their knowledge of number properties and relationships between operations to understand addition and subtraction of rational numbers.” The end of the Overview previews, “Later, in $$8^{th}$$ grade, students continue to understand rational numbers as they learn about numbers that are not rational, called irrational numbers (8NSA). They also apply their understanding when working with integer exponents (8EEA), graphing and solving (pairs of) linear equations (8EEC), performing translations and dilations (8GA), and using functions to model and compare relationships between quantities (8FA, 8FB). For High School, fluency with rational numbers sets students up to focus on learning new algebraic material in High School that incorporates the use of these numbers and assumes knowledge of them. An understanding of rational number operations also facilitates the understanding of rational functions and how to work with them appropriately.”
• Throughout the narrative for the teacher in the Unit Overview, there are descriptions of how the lessons will be used as the grade level work progresses. Unit 4 states, “In lessons 4 and 5, students continue to solve two step linear equations using inverse operations and number properties but add on the increased complication of integers (lesson 4) and rational numbers (lesson 5). Students will rely heavily on their learning in the first two units to complete these lessons and future lessons.”
• The last paragraph of each narrative for the teacher in the Unit Overview describes the importance of the unit in the progressions. Unit 6 states, “While percents are not a focus of 8th grade, they may still be applied in a variety of contexts throughout the year, i.e. volume or statistics. In High School, students extend their understanding of percents when applying percents to exponential growth and decay modeling. They need a strong understanding of percentages and their decimal equivalence to be able to conceptually understand the key characteristics of the functions. There is also a connection to proportional reasoning in Geometry, but exponential functions in Algebra are where the connection is most clear.”
• For units that correlate with the progressions document, the materials attach the relevant text so that connections are made. In Unit 8, Appendix A, Teacher Background Knowledge (after the assessment), the “6-8 Statistics and Probability” progression document is included with the footnote, “From the Common Core Progression on Statistics and Probability.”
• Each lesson includes a “Connection to Learning and Conceptual Understanding” section that describes the progression of the standards within the unit. In Unit 4, Lesson 1 states, “In 6th grade, students solved one-step equations through logical reasoning. For example, $$6n = 42$$, students would reason that 6 times some number equals 42 so that number has to be 7. Students will draw from this experience to do the final step but will first have to manipulate the balance/equation in such a way that makes the equation into a one-step equation. Students will determine that they must first remove the additional units (constant) from both sides to keep the equation balanced.” 
• In the Scope and Sequence Detail from the Implementation Guide, there are additional progression connections made. The Cumulative Review column for each unit provides a list of lesson components and the standards addressed Prior (Remedial) standards are referenced with an “R” and grade level standards are referenced with an “O.” Unit 2 states,  “Unit 2, The Number System- Multiplying and Dividing Rational Numbers states, “Skill Fluency (4 days a week): 7.NS.1 (O), 7.NS.2 (O)” “Mixed Practice (3 days a week): 7.NS.1 (O), 7.NS.3 (O), 7.NS.2 (O), 6.NS.2 (R), 6.EE.2 (R), 7.EE.3.(R).”

The materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Each lesson provides State Test Alignment practice, Exit Tickets, Think About It, Test the Conjecture or Exercise Based problems, Error Analysis, Partner Practice, and Independent Practice, which all include grade-level practice for all students. The Partner and Independent Practice provide practice at different levels: Bachelor, Masters and PhD. Each unit also provides Mixed Practice, Problem of the Day, and Skill Fluency practice. By the end of the year, the materials address the full intent of the grade-level standards. Examples include:

• In Unit 1, Lesson 11, Exit Ticket, students solve real-world problems by adding and subtracting rational numbers. The materials state, “Death Valley sits at an elevation of $$212\frac{3}{4}$$ feet below sea level and the temperature at noon is 119.5 degrees.  Mt. Humphrey’s (the tallest point in Arizona) has an elevation of $$13,918\frac{9}{10}$$ feet and the temperature at the top is -19.07 degrees.  What is the change in elevation and temperature between the two locations?” (7.NS.1d)
• In Unit 3, Lesson 3, Independent Practice, Question 9 (PhD level), students understand how quantities are related by rewriting an expression in different forms,. The materials state, “Pretend that you are a test maker. Create four multiple choice answers (one has to be correct) for the problem below. Explain the error that each answer choice addresses. “Write an equivalent expression for $$-4n-3(-2n+3)$$.” (7.EE.2)
• In Unit 4, Lesson 20, Exit Ticket Question 1, students use the formula for the area of a circle to solve problems. The materials state, “The base of John’s coffee cup has a circumference of $$12\pi cm$$. Exactly how much space does the base of the coffee cup take up?” (7.G.4)
• In Unit 6, Lesson 13, Interaction with New Material, Question 1, students use proportional relationships to solve percent problems. The materials state, “Magdalena works at a clothing store and makes both an hourly wage of $8.00 and gets paid a commission rate of 5% on the total cost of all the sales she makes. During her 4-hour shift, only one customer purchased clothing. They bought 2 scarves that normally cost $15 each but were on sale for ‘Buy 1, get 1 50% off’.  How much money did she earn during her shift?” (7.RP.3)

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. This can be found in the progressions descriptions listed above, but also often focuses explicitly on connecting prior understanding. For example:

• Each Unit Overview provides a narrative for the teacher that introduces the student learning of the unit and the background students should have. Unit 3 states, “The content draws heavily from the work students did in the first two units with rational number operations as well as from the work they did with expressions in $$6^{th}$$ grade. $$6^{th}$$ grade marked the foundation for students beginning to apply algebraic princip to writing expressions that represent real world and mathematical problems. Specifically, students focused on evaluating expressions inclusive of all operations (6.EE.1) and variables and writing and reading expressions with variables (6.EE.2). They also wrote and identified equivalent expressions using their knowledge of properties of operations (6.EE.3, 6.EE.4). With these skills and knowledge, they applied expressions to represent and solve geometric problems (i.e. perimeter of a polygon) (6.G.A). Students must be fluent working with integer and rational number operations prior to this unit.”
• The narrative for the teacher in the Unit Overview makes connections to current work. The materials state, “Unit 7 is the first time students will formally learn about the concept of probability. While students have likely discussed the concept in other classes informally or in their lives outside of school, unit 7 is meant to formalize their understanding of probability and teach students how to utilize probability models and organizational methods to make sense of chance events in the real world. While students have not learned about probability in previous units or grade levels, they draw on previous knowledge learned in fraction, decimal percent and ratio reasoning units from earlier in $$7^{th}$$ grade as well as from previous grade levels.”
• Each lesson includes a “Connection to Learning and Conceptual Understanding” section that relates to prior knowledge. In Unit 5, Lesson 1 states, “In 6th grade, students work with ratios, rates, and unit rates. This intro lesson to unit 5 draws on the work that students have done in 6th grade to be able to write a rate (comparison of two different units) and convert it into a unit rate (a rate in which a unit is compared to 1 of another unit). In this lesson, students determine the units that are being compared and write two different unit rates and describe them in the context that they are given.”
• In the Scope and Sequence Detail from the Implementation Guide, the Notes + Resources column for some lessons includes a lesson explanation that makes connections to prior learning. Unit 6 states, “Students build off of what they learned about percents in 6th grade with setting up an equation (proportion) to solve problems. Now that they know how to solve equations algebraically, they can do so.”

The instructional materials for Achievement First Mathematics Grade 7 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives, identified as AIMs, that are visibly shaped by the CCSM cluster headings. The Guide to Implementation, as well as individual lessons display each learning objective along with the intended standard. The instructional materials utilize the acronym SWBAT to stand for “Students will be able to” when identifying the lesson objectives. Examples include:

• The AIM for Unit 3, Lesson 6: “SWBAT write an expression representing an unknown real-world value; SWBAT recognize that there are multiple equivalent expressions that can represent the same scenario,” is shaped by 7.EE.A: Use properties of operations to generate equivalent expressions.
• The AIM for Unit 5, Lesson 1: “SWBAT compute unit rates associated with quantities in different units,” is shaped by 7.RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.
• The AIMs for Unit 8, Lessons 3: “SWBAT make a prediction about an entire population based on data from a sample, Sub-AIM: SWBAT determine whether or not a prediction is possible based on the validity of the sample” and “SWBAT use multiple simulated samples of the same size to gauge the variation in estimates or predictions,” is shaped by 7.SP.A: Use random sampling to draw inferences about a population.

The materials include some 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. For example:

• In Unit 3 Curriculum Review, Problem of the Day 3.1, students solve real-world and mathematical problems involving the four operations with rational numbers (7.NS.A) when they analyze proportional relationships (7.RP.A). In the Problem of the Day 3.1, Day 1 states, “Mr. Milliken is baking a cake for his upcoming wedding! He is going to start with a layer of cake, then a layer of icing, and so on, until the cake is finished with a layer of icing.  When finished, each layer of cake is $$1\frac{1}{5}$$ inches tall and each layer of icing is $$\frac{2}{5}$$ of an inch tall. Mr. Milliken uses $$1\frac{1}{4}$$ cups of sugar for one layer of cake and one layer of icing together.  Ms. Nichols wants the cake to be 16 inches tall. How much sugar will Mr. Milliken use in creating this cake?” 
• Unit 3, Lesson 4 connects 7.NS.A and 7.EE.B as students use the full range of rational numbers when they solve algebraic expressions and equations. In the Independent Practice, Question 10 (PhD level) states, “Are the expressions $$-4.5n+3\frac{1}{2}r-2.25r-(-2\frac{3}{4}n)$$ and $$1\frac{1}{4}(1.4n+r)$$ equivalent? Prove it using two different methods.”
• Unit 6, Lessons 11-13 connect 7.RP.A and 7.EE.B as students solve simple interest problems by using equations such as the formula I = prt. In Lesson 12, Independent Practice (Masters level) #2 states, “What is the amount of interest that Mike earns on the following: deposit is $780, interest rate is 3.2% each year, for 18 months?”
• In Unit 9, Lesson 11, students construct geometric figures (7.G.A) which they use to solve mathematical problems involving surface area and volume (7.G.B). In the Independent Practice, Question 6 (PhD level) states, “A rectangular prism has dimensions 3 inches, 4 inches, and 5 inches. Find the dimensions of another rectangular prism with the same volume but less surface area. Prove your answer is correct showing all calculations.”