7th Grade - Gateway 1

The instructional materials reviewed for Into Math Florida Grade 7 meet expectations for assessing grade-level content. An Assessment Guide, included in the materials, contains two parallel versions of each Module assessment, and the assessments include a variety of question types. In addition, a Performance Task has been created for each Unit, and Beginning, Middle, and End-of-Year Interim Growth assessments.

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

• Module 6, Form A, question 10 states, “Logan is on a ski slope at an elevation of 3,154.68 meters. He skis down the mountain to the ski lodge. His change in elevation is -487.21 meters. What is the elevation, in meters, where the ski lodge is located?” (7.NS.1.1c)
• Module 1, Form B, question 7 states, “Brody’s town is building a pool based on a scale drawing that is 20 cm by 10 cm and uses the scale 1cm:250 cm. What is the area of the pool, in square meters?”
• Module 11, Form B, question 8 states, “A cube has a surface area of 96 mm2.  Part A) What is the volume, in mm3, of the cube?  Part B) The length of each side of the cube is doubled. What is the new volume?  A) 512 mm3   B) 384 mm3   C) 128 mm3   D) 64 mm3 “ (7.G.2.6)
• Module 2, Form B, question 6 states, “Darius is a broker who earns a $68,000 annual salary, a 3.15% commission on his clients’ investments, and a fee of $4.25 for each online transaction. If Darius’s clients had a total of $3.6 million in investments and made 1,375 online transactions this year, what are Darius’s earnings? Round your answer to the nearest dollar.” (7.RP.1.3)
• Module 6, Form A, question 11 states, “The drama club sold 209 evening show tickets for $18.50 each and some matinee show tickets. They want to make $5,700 for the two shows. If matinee tickets cost $11.75 each, how many matinee tickets do they need to sell to reach their target amount?”  (7.EE.2.3)

The instructional materials reviewed for Into Math Florida Grade 7 meet expectations for spending a majority of instructional time on major work of the grade.

• The number of Modules devoted to major work of the grade is 11 out of 15, which is approximately 73%.
• The number of Lessons devoted to major work of the grade (including supporting work connected to the major work) is 39 out of 59, which is approximately 66%.
• The number of Days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 94 out of 136 days, which is approximately 69%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and isn’t dependent on pacing suggestions. As a result, approximately 66% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Into Math Florida Grade 7 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 1.6, students find the scale using complex fractions based on a given diagram (7.G.1.1, 7.RP.1.1), write the appropriate y = mx equation (7.RP.1.2c), and solve related problems using the equation.
• In Lesson 7.5, students write and solve equations (7.EE.2.4) based on different angle relationships (7.G.2.5). For example, “Angle A and Angle B are adjacent. The sum of their measures is 92 degrees... Angle A measures 2x+50 degrees. Angle B is three times the size of angle A. Write an equation to determine the value of x. Then solve your equation and find the measures of both angles.”
• In Lessons 10.1-10.4, students use formulas to find the circumference of a circle (7.G.2.4) and areas of various figures (7.G.2.6) in multiple real-world situations (7.EE.2.3).
• Lesson 10.1 connects 7.G.2.4 to 7.RP.1.2 with, “Describe what you notice about the ratio C/d in your table. Does the relationship between the circumference and diameter of a circle appear to be proportional? Explain.”
• In Lessons 11.2-11.4, students use formulas and solve equations to find surface areas and volumes of various figures (7.G.2.6) in multiple real-world situations (7.EE.2.3).
• In Lesson 12.2, students use a random sample and proportional reasoning (7.RP.1.2) to make inferences about a population (7.SP.1). For example, Step It Out question 3, “A worker randomly selects one of every 7 sets from the 3,500 sets of headphones produced. The results are shown. Write the ratio of defective headphones to the total headphones in the sample. Then write the ratio as a decimal and solve an equation to find the number of headphones in the population that can be predicted to be defective.”
• In Lessons 14.1-14.4, students use probabilities 7.SP.3, ratios, and proportional relationships to solve problems in real-world situations (7.RP.1.3). For example, in Lesson 14.4, Step It Out question 2, students use proportional reasoning to predict the number of students in the whole school that prefer math.
• In Lesson 15.4, students calculate simple and compound probabilities (7.SP.3.8) using rational numbers in various forms (7.NS.1.3).

The instructional materials for Into Math Florida Grade 7 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 160 days: 106 days for lessons and 54 days for assessments.

• The Planning and Pacing Guide and the planning pages at the beginning of each module in the Teacher Edition provide the same pacing information.
• Grade 7 has six Units with 15 Modules containing 59 lessons.
• The pacing guide designates 41 lessons as two-day lessons and 18 as one-day lessons, leading to a total of 100 lesson days; there is no information provided about the length of a “day”.
• Each Unit includes a Unit Opener which would take less than one day. There are six Openers for Grade 7 (six days).

Assessments included:

• The Planning and Pacing Guide indicates a Beginning, Middle, and End of Year Interim Growth test that would require one day each (three days).
• Each Module starts with a review assessment titled, “Are You Ready?”. There are 15 Modules (15 days).
• Each Unit includes a Performance Task indicating an expected time frame ranging from 25-45 minutes. There are six Performance Tasks for Grade 7 (six days).
• Each Module has both a review and an assessment. There are 15 Modules (30 days).
• Based on this, 54 assessment days can be added.

The instructional materials for Into Math Florida Grade 7 meet expectations for being consistent with the progressions in the Standards. In general, the materials identify content from prior and future grade-levels and relate grade-level concepts explicitly to prior knowledge from earlier grades. 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.

• In the Teacher Edition, the introduction for each Module includes Mathematical Progressions Across the Grades, which lists standards under the areas of Prior Learning, Current Development, and Future Connections and clarifies student learning statements in these categories. For example, in Module 5, Multiply and Divide Rational Numbers, “Prior Learning: Students applied the properties of operations to generate equivalent expressions.” (6.NS.2.3); “Current Development: Students develop and use the rules for multiplying signed numbers.” (7.NS.1.2); “Future Connections: Students will solve pairs of linear equations.” (8.EE.3.8)
• The beginning of each Module has Teaching for Success, which sometimes includes Make Connections. Make Connections references prior learning, for example in Module 8, “In this module, students will build on their prior knowledge of inequalities to solve both one and two-step inequalities. Students will also solve real-world mathematical problems using numerical and algebraic expressions and equations.“
• In Activate Prior Knowledge at the beginning of each lesson, content is explicitly related to prior knowledge to help students scaffold new concepts.
• Some lessons provide direct scaffolding for students reminding them of prior learning. For example, in Lesson 1.1, Build Understanding Question 1d, students complete a table comparing Small Jars of Salsa and Ounces of Salsa. “You previously learned that a unit rate is a rate in which the second quantity in the comparison is one unit…” (6.RP.1.2), and in Lesson 4.1, Build Understanding Question 1b, “Recall that the absolute value of a number is the number’s distance from 0 on a number line.”
• Each Module includes a diagnostic assessment, Are You Ready?, explicitly identifying prior knowledge needed for the current module. For example, in Module 2, Are You Ready? states, “Complete these problems to review prior concepts and skills you will need for this module.” Students multiply decimals by whole numbers (5.NBT.2.7) and find a percent of a whole (6.RP.1.3c). In this module, students use these skills to find percent change, find markups, discounts, taxes, gratuities, commissions, fees, and simple interest (7.RP.1.3).”

Examples where standards from prior grades are not identified include:

• The Module Opener activities utilize standards from prior grade-levels, though these are not always explicitly identified in the materials. For example, in Module 2 students, “write a sentence for each diagram that describes the percent of the whole that is shown.” This Module Opener aligns to 6.RP.1.3, and in Module 3 students, “plot each rational number on the number line next to it,” which aligns 6.NS.3.6c.

Examples of the materials providing all students extensive work with grade-level problems include:

• In the Planning and Pacing Guide, the Correlations chart outlines the mathematics in the materials. According to the chart, all grade-level standards are represented across the 15 modules.
• Within each lesson, Check Understanding, On My Own, and More Practice/Homework sections include grade-level practice for all students. Margin notes in the Teacher Edition also relate each On My Own practice problem to grade-level content. Examples include:
• In Lesson 2.1, More Practice Question 9, ”Cary makes 80% of his free throws in basketball, but that measure varies by 5%. If he makes 200 free throw attempts in a season, what is the range of successful free throws he can expect to make? Show your calculation.” (7.RP.1.3, 7.EE.2.3)
• In Lesson 7.4, On My Own Question 5, “Dirk sold 7 more than 2 times as many gym memberships this month than last month. This month he sold 43 memberships. Write and solve an equation to find the number of memberships Dirk sold last month.” (7.EE.2.4a)
• When work is differentiated, the materials continue to develop grade-level concepts. An example of this is Lesson 2.2, which explores markups and discounts. The corresponding Reteach page provides guided notes for students to follow in order to access the concept; the Challenge page lists the cost of pants, socks, and a shirt before they are marked up by a store. Students calculate the percent increase given, new sales prices, the new price after a coupon is used, and finally investigate if the store will break even if they offer a percent discount equal to the percent markup of an item.

The instructional materials reviewed for Into Math Florida Grade 7 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives visibly shaped by CCSSM cluster headings, and examples of this include:

• In Lesson 9.4, the learning objective is, “Draw, construct, and analyze two-dimensional figures, including circles,” and this is shaped by 7.G.1.
• In Lesson 10.2, the learning objective is, “Use a random sample to make inferences about a population,” and this is shaped by 7.SP.1.
• In Lesson 2.2, two objectives are, “Students will calculate markups, markdowns, retail prices, and discount prices, and represent them using equations of the form y = kx” and “Use the terms markup, markdown, and retail price to explain the solutions to real-world problems,” and these are shaped by 7.RP.1.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

• In Lesson 2.1, students perform operations with rational numbers (7.NS.1) to solve multi-step problems involving percent of change (7.RP.1).
• In Lesson 2.3, students write and solve an equation (7.EE.2) to calculate the cost of dinner including a tip (7.RP.1).
• In Lesson 4.4, students solve multi-step real-world problems by writing equations (7.EE.2) and performing appropriate calculations while applying the properties of operations (7.NS.1).
• In Lesson 7.2, students write an expression showing the perimeter of a yard with side lengths containing variables and rational number coefficients and create an equivalent expression by combining like terms (7.EE.1), which requires them to add rational numbers (7.NS.1).