6th Grade - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics Grade 6 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Within the i-Ready Classroom Mathematics materials, the Unit Assessments are found in the Teacher Toolbox and include two forms for Unit Assessment, Form A and Form B. Both Forms contain similar problems for each unit. The Unit Assessments can be found at the end of each unit in the materials. 

Examples of assessment items in i-Ready Classroom Mathematics include:

• Unit 1, Unit Assessment, Form A, Problem 5, assesses 6.G.1 as students find the area of a parallelogram by decomposing it into a rectangle. “The parallelogram shown on the grid represents Leta's current garden. The side of each grid square represents 1 ft. Leta wants to redesign her garden so that it is a rectangle with the same area as her current garden. Explain how Leta can redesign her garden.” A grid with a parallelogram (base of 4ft, height of 5ft) is provided.

• Unit 2, Unit Assessment, Form A, Problem 11, assesses 6.NS.1 as students compute quotients of fractions. “What does it mean to divide with fractions? Use models and words to describe how to divide with fractions. Use $$1\frac{1}{4}$$÷$$\frac{5}{8}$$ in your response. Show your work.”

• Unit 3, Unit Assessment, Form A, Problem 9, assesses 6.RP.3 as students use ratio and rate reasoning to solve a real-world problem. “Rashid reads a total of 35 pages every 5 days. Based on this information, how many days will it take Rashid to read a total of 84 pages? Record your answer in the grid. Then fill in the bubbles.”  

• Unit 4 Unit Assessment, Form B, Problem 6, assesses 6.RP.2 as students solve a real-world problem using unit rate. "At a fabric store, metallic ribbon costs $16 for 4 ft. White ribbon is priced at 3ft per dollar. Use rates to show which kind of ribbon is more expensive per foot. Show your work."

• Unit 6, Unit Assessment, Form A, Problem 2, assesses 6.EE.8 as students write and graph inequalities. “There are at least 6 tomato plants in Josephine’s garden. She plants 4 more tomato plants. Write and graph an inequality to show the number of tomato plants in her garden.”

One assessment item aligned to a standard beyond Grade 6. This problem can be omitted from the assessment and would not require major modifications to modify the assessment.

• Unit 5, Unit Assessment, Form A, Problem 8, “Stoyanka collects donations for an animal shelter. At the end of March, she had $545.40 in donations. In April, she collects donations of $20.20 each. At the end of April, she had $787.80 in donations. Use an equation with a variable to find the number of donations Stoyaka collects in April.” The materials align this problem to 6.EE.7, which indicates an equation in the form x + p = q.  This problem aligns to 7.EE.4, as it results in the equation in the form px + q = r. $545.40 + $20.20x = $787.80.

The materials reviewed for i-Ready Classroom Mathematics Grade 6 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. In the materials, there are ample opportunities for students to work with grade level problems. This includes:  

• Lessons contain multiple opportunities for students to work with grade-level problems in the “Try It”, “Discuss It”, “Connect It”, “Apply It”, and “Practice” sections of the lessons. 

• Differentiation of grade-level concepts for small groups are found in the “Reteach”, “Reinforce”, and “Extend” sections of each lesson. 

• Fluency and Skills Practice problems are included in the Math Toolkit in addition to the lessons.

• Interactive tutorials for the majority of the lessons include a 17 minute interactive skill tutorial as an option for the teacher to assign to students. 

Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• Unit 1, Lesson 2, Session 3, Apply It, Problem 8, students find areas of polygons by decomposing and composing the polygons in various ways (6.G.1). “The polygon represents the top of a desk. What is the area of the top of the desk? Show your work.” 

• Unit 2, Lesson 8, Session 2, Fluency and Skills Practice, using the standard algorithm for division provides students extensive work with grade-level problems to meet the full intent of 6.NS.2 (Fluently divide multi-digit numbers using the standard algorithm). The worksheet contains multiple problems for students to divide multi-digit numbers with up to 5 digit dividends. Problem 6, "$$75,232 ÷16$$."

• Unit 3, Lesson 13, Session 3, Apply It, Problem 9, students use ratio and rate reasoning to solve real-world problems by: completing a table of equivalent ratios and plotting the pairs of values on the coordinate plane (6.RP.3). “Every 4-oz serving of Yum’s Yogurt contains 8 g of protein. Complete the table of equivalent ratios. Then plot points on the graph to represent the ratios.” The table includes missing values in both columns of the table, and students are provided a labeled graph to plot the points.

• Unit 4, Lesson 18, Interactive Tutorials, Solve Problems with Percent, students use ratio and rate reasoning to solve real-world and mathematical problems (6.RP.3). Students are prompted throughout the tutorial to find equivalent ratios in tables, and use equations to solve the problems. The first three problems in the tutorial:

  • “At hockey practice, Coach Taylor always sets aside 20% of the total time for players to warm up. The rest of the practice is spent on game play. Today’s practice is 60 minutes. Coach Taylor needs to find out how much time players should spend warming up.”

  • At hockey practice, Coach Taylor always sets aside 20% of the total time for players to warm up. The rest of the practice is spent on game play. Coach Taylor wants to know the total practice time if he has the players warm up for 15 minutes.

  • At hockey practice, Coach Taylor always sets aside 80% of the total time for game play. The rest of the practice is spent on the warm up. At practice yesterday, players spent 72 minutes on game play. The players want to know the total practice time.”

• Unit 5, Lesson 19, Session 1, Connect it, Problem 2a, students demonstrate how two expressions are equivalent (6.EE.4). “The expressions 36+20 and 4(9+5) both represent the area, in square feet, of the outer rectangle. They are equivalent expressions because they have the same value. Show that these expressions are equivalent by finding the value of each expression.” Problem 2b, “You can also use the distributive property to show that the sum 36+20 is equivalent to the product 4(9+5). To rewrite 36 + 20 as a product, you can use the greatest common factor (GCF) of 36 and 20 as one of the factors. The GCF of 36 and 20 is __ . Rewrite each term using the GCF as a factor. __×9+__×5. Use the distributive property. __× ( __+ __).” (6.NS.4) 

• Unit 7, Lesson 31, Session 2, Practice, Problem 2, students demonstrate their understanding of median and variability (6.SP.5). “Abran sees his favorite granola bar from the example in a vending machine at an airport. The cost is $2.75. What are the new values of the median, lower quartile, and upper quartile? Show your work.”

The materials reviewed for i-Ready Classroom Mathematics Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. Materials were analyzed from three different perspectives; units, lessons, and days. Each analysis includes assessments and supporting work connected to major work of the grade.  

• The approximate number of units devoted to major work of the grade is 5.5 out of 7 units, which is approximately 79%. 

• The number of lessons, including end of unit assessments, devoted to major work of the grade is 36 out of 47 lessons, which is approximately 77%. 

• The number of days, including end of unit assessments, devoted to major work of the grade is 113 out of 152, which is approximately 74%. 

A day-level analysis is the most representative of the materials because the number of sessions within each topic and lesson can vary. When reviewing the number of instructional days for i-Ready Classroom Mathematics Grade 6, approximately 74% of the days focus on major work of the grade.

The instructional materials reviewed for i-Ready Classroom Mathematics Grade 6 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Throughout the materials, supporting standards/clusters are connected to the major standards/ clusters of the grade. The following are examples of the connections between supporting work and major work in the materials: 

• Unit 1, Lesson 3, Session 3, Connect It, Problem 3 connects the supporting work of 6.G.4 with the major work of 6.EE.2a when students analyze an expression for finding the surface area of a net. There are no variables in the expression, but at this point in the course it is mathematically reasonable because that standard has not yet been introduced. “Aisha wrote the expression $$2(\frac{1}{2})(4⋅3)+6(3+4+5)$$ for the area of the net. Explain why the expression represents the area of the net.”

• Unit 2, Lesson 7, Session 3, Apply It, Problem 8 connects the supporting work of 6.NS.3 with the major work of 6.EE.2c when students “Evaluate expressions at specific values of their variables. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order. What is the value of the expression $$x^2y$$ when $$x=0.8$$ and $$y=3.15$$? A $$0.2016$$, B $$0.504$$, C $$2.016$$, D $$5.04$$.”

• In Unit 2, Lesson 11, Session 2, Connect It, Problem 2 connects supporting work of 6.G.2 to major work in 6.NS.1 using fractions to solve volume problems. For example, “Why could you fill the prism with cubes that have edges that are $$\frac{1}{8}$$ft long? How many cubes would fit along each edge of the prism?

• Unit 4, Lesson 16, Session 3, Try It, connects supporting work of  6.NS.2 and 6.NS.3 to major work in 6.RP.A as students find unit rates involving decimal numbers. “Antonio uses dish soap in his recipe for giant bubbles. He compares the prices of two brands of dish soap. Which is the better buy?” A diagram shows Brand A costs $2.56 for 32 oz and Brand B costs $4.80 for 48 oz.

• Unit 6, Lesson 28, Session 3, Practice, Problem 2, connects supporting work of 6.G.3 to major work in 6.NS.8 as students graph points in all four quadrants of the coordinate plane to draw polygons and find the length of the sides. “A rhombus is a four-sided figure with all sides the same length. Points F(-2,-2), G(-2,3), H(2,6) are three vertices of the rhombus FGHJ. Vertex J is directly below vertex H. a. Graph rhombus FGHJ. Label J with its coordinates. b. What is the perimeter of the rhombus? Show your work.”

The materials reviewed for i-Ready Classroom Mathematics Grade 6 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Examples of problems and activities that serve to connect two or more major clusters or domains in a grade: 

• Unit 5, Lesson 22, Session 2, Apply It, Problem 9, connects the major work of 6.EE.C to the major work of 6.RP.A as students represent a given ratio relationship as an equation in terms of the independent and dependent variable. “A company makes several sizes of phones. For each size, the ratio of the height of the screen to its width is 18:9. Write an equation that shows how to find the height in inches of any of the company’s phone screens based on the screen’s width in inches.”

• Unit 6, Lesson 26, Session 2, Apply It, Problem 10, connects the major work of 6.EE.B to the major work of 6.NS.C when students must apply their understanding of rational numbers to write and represent an inequality of a given situation. “A state park has several campsites. All of the campsites are at an elevation of less than 6m. An elevation of 0m represents sea level. Use an inequality and a graph to represent the possible elevations of a campsite in the park.”

Examples of problems and activities that serve to connect two or more supporting clusters or domains in a grade are: 

• Unit 2, Lesson 8, Session 5, Apply It, Problem 2, connects the supporting work of 6.NS.B to the supporting work of 6.G.A when students divide decimals to find the height of a parallelogram when given the area and base. “The area of the parallelogram is 29.4 cm^2. What is the parallelogram’s height?” The image shows a parallelogram with the base, b=5.25cm. 

• Unit 7, Lesson 32, Session 4, Apply It, Problem 1, connects supporting work of the grade 6.SP.B and 6.NS.B as students find the mean of a data set containing decimal numbers. “Roberto sells lemonade to raise money for a charity. He collects data on the cost of lemonade at other lemonade stands. He uses the mean of his data as the price of lemonade at his stand. How much does lemonade cost at Roberto’s stand? Show your work.” A table with 15 data points for the cost of lemonade include 2.00, 1.00, 1.25, 1.50, 0.50, 1.25, 1.00, 0.50, 3.00, 1.00, 1.25, 1.50, 1.25, 1.25, 1.25.

The materials reviewed for i-Ready Classroom Mathematics Grade 6 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each Unit contains the Teacher’s Guide which includes a Unit Flow and Progression video, a Lesson Progression, a Math Background, and a Lesson Overview that contains prior and future grade-level connections to the lessons in the unit. Examples include:

• Unit 2, Lesson 7, Lesson Progression, Add, Subtract, and Multiply Multi-Digit Decimals, builds on Grade 5, Lesson 10, Add Decimals, 5.NBT.7, Grade 5, Lesson 11, Subtract Decimals, 5.NBT.7, and Grade 5, Lesson 16, Multiply Decimals, 5.NBT.7. This lesson prepares students for Grade 7, Lesson 10, Add and Subtract Positive and Negative Numbers, 7.NS.1 and Grade 7, Lesson 11, Understand Multiplication with Negative Numbers 7.NS.2. 

• Unit 4, Beginning of Unit, Math Background, Ratio Reasoning, Prior Learning, “Students should; be able to multiply and divide whole numbers, fractions, and decimals,” and “be able to convert measurement units by multiplying and dividing.” (5.NBT.B and 5.MD.A) Future Learning states, “Students will move on to extend their understanding of rates and percentages. Students will: identify, analyze, and represent proportional relationships,” and “solve multistep percent problems, such as problems about markups and markdowns.” (7.RP.A)

• Unit 5, Beginning of Unit, Lesson Progression, describes how students connect work in Lesson 20, Understand Solutions of Equations 6.EE.5 to the prior learning in Grade 5, Lesson 30 Evaluate, Write, and Interpret Expressions 5.OA.A.

• Unit 6, Lesson 24, Overview, Learning Progression, “In earlier grades, students located and labeled positive whole numbers, fractions, and decimals on the number line and compared them using inequality symbols and words. They ordered positive rational numbers.” “In this lesson, students compare and order positive and negative rational numbers. They interpret inequalities as statements about the relative position of numbers on the number line. They also write inequalities to represent and interpret inequalities in real-world contexts.” “In Grade 7, students will write inequalities with a variable to represent real-world situations with unknowns. They will solve inequalities that include a variable and graph solutions to inequalities on the number line.”

• Unit 7, Lesson 30, Overview, Learning Progression, describes learning for earlier grades connected to using dot plots and histograms. “In earlier grades, students made picture graphs and bar graphs. They used line plots to display and interpret a data set of measurements in fractions of a unit.” (5.MD.B) Then, “In Grade 7, students will understand that random sampling can be used to gain information about a population and that generalizations are only valid if the sample is representative of the population.” (7.SP.A)