6th Grade - Gateway 1

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that they assess grade-level content and, if applicable, content from earlier grades. 

Each Grade Level Consists of 12 modules. Each module contains three types of summative assessments. Check-ups assess concepts taught in the module, and students select answers or provide a written response. Performance Tasks assess concepts taught in the module with deeper understanding. In Interviews, teachers ask questions in a one-on-one setting, and students demonstrate understanding of a module concept or fluency for the grade. In addition, Quarterly Tests are administered at the end of Modules 3, 6, 9, and 12.

Examples of assessment items aligned to Grade 6 standards include:

• Module 2, Check-Up 2, Problem 4, “Calculate the answer. a. 4.62\times 71, b. 9.3\times 5.12.” (6.NS.3)

• Module 6, Quarterly Test B, Problem 18, “Write an equation to the word problem. Hugo is given $25 to attend the school concert. He pays $7 for each entry ticket and $2.50 for each soda. Hugo pays for his ticket and drink and also for his little brother’s ticket and drink. How much change will Peter receive? Let c represent Hugo’s change.” (6.EE.2).

• Module 8 Performance Task, Problem 1, “This machine holds 150 gumballs with different flavors. Solve each word problem. Show your thinking. a. One-fifth of the gumballs are orange flavored. What percentage of the gumballs are orange? b. Forty percent of the gumballs are cherry flavored. How many gumballs are cherry? c. What is the difference between the number of orange and cherry gumballs?” (6.RP.3).

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials provide extensive work in 6th grade by including different types of student problems in each lesson. There is a Student Journal with problems in three sections: Step In, Step Up, and Step Ahead. Maintaining Concepts are in even numbered lessons and include additional practice opportunities, including Computation Practice, Ongoing Practice, Preparing for Module _, Think and Solve, and Words at Work. Each Module includes three Investigations and, within grade 6, students engage with all CCSS standards. Examples of extensive work from the grade include:

• Module 2, Lesson 3, Algebra: Order of operations involving exponents, engages students with extensive work with 6.EE.1 (Write and evaluate numerical expressions involving whole- number exponents). In the Student Journal, Step Up, page 51, Question 4, students evaluate numerical expressions that involve whole-number exponents. “Complete each equation. Show your thinking on page 80. a. 4(12 - 7)^2 b. (18 - 14) \cdot 2^2 \cdot10 c. 9 \cdot 8 - 7 \cdot 6 - 5^2.”

• Module 4, Lessons 4 and 6 engage students in extensive work with 6.NS.6 (Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.) as students reason about rational numbers. In Lesson 4, Algebra: Evaluating expressions given the value of the variable, Student Journal, Maintaining Concepts and Skills, page 131, Question 1a, “Write < or > to complete each statement. Use the number line to help your thinking. 0.3 ___ -0.4.” In Lesson 6, Algebra: Solving equations given a set of possible values, Student Journal, Maintaining Concepts and Skills, page 137, Question 1a, “Write <, >, or = to complete each statement. Use the number line to help. \left|-12\right|____$$\left|12\right|$$.” Student Journals in Lessons 2, 4, 6, 8, 10, and 12 of each module, include two pages called Maintaining Concepts and Skills that provide all students additional practice in order to engage in extensive work with grade-level problems.

• Module 10, Lesson 2, Statistics: Measuring variability using quartiles and interquartile range, engages students with extensive work with 6.SP.3 (Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number). In the Student Journal, Step In, page 360, students describe the spread of data in a dot plot using what they have learned about interquartile range. “Some students are asked about the number of hours that they spend on social media each week. The results are then recorded. Hours spent on social media: 7, 3, 5, 12, 10, 9, 2, 6, 0, 1, 5, 3. How could you display the data? What types of questions could this data answer? What does the distance between the first quartile and the third quartile indicate? What percentage of the values fall between the first and third quartiles?” An interquartile range is provided for students. 

The instructional materials provide opportunities for all students to engage with the full intent of 6th grade standards through a consistent lesson structure, including sections called Step In, Step Up and Step Ahead. Step In includes a connection to prior knowledge, multiple entry points to new learning, and guided instruction support. Step Up engages all students in practice that connects to the objective of each lesson. Step Ahead can be used as an enrichment activity. Examples of meeting the full intent include:

• Module 1, Lessons 6-8 engage students with the full intent of 6.NS.6 (Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.)  In Lesson 6, Number: Interpreting the negative symbol, Student Journal, Step Up, page 21, Question 2b, students reason about opposite numbers on a number line. “Interpret each expression. Then write the number that is opposite. Use the number line to help your thinking. -30  ___.”   In Lesson 7, Number: Comparing and ordering positive and negative numbers, Student Journal, Step Up, page 25, Question 4a, students order integers using a number line. “Shade five numbers. Then write the numbers that are shaded in order from least to greatest. You can draw a number line on page 42 to help your thinking. -6, 1, 3, -4, -7, 0, -1.”  In Lesson 8, Number: Introducing absolute value, Student Journal, Step Ahead, page 27, students use absolute value to reason about integers. “The temperatures of two different cities were measured at the same time. The absolute value of each city in degrees Fahrenheit is 8. Write the possible pairs of temperatures for the cities in the chart. Show your thinking.” 

• Module 3, Lesson 3 and Module 5, Lesson 10 engage students with the full intent of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.) In Lesson 3, Ratio: Examining equivalence using tables, Student Journal, Step Up, page 89, Question 2a, students reason about ratios from a real world problem. “Read each story then answer the questions. Use a table to show your thinking. A math test has 7 multiplication questions for every 2 addition questions. Calculate the number of multiplication questions to addition questions for the following number of test questions:  27 Questions ____ : ____ ; 45 Questions ____ : ____.”  In Lesson 10, Ratio: Using a given ratio when the total is known, Student Journal, Step Up, page 814, Question 1a, students reason about ratios using a tape diagram. “Draw a tape diagram to represent each problem. You do not need to calculate the answer. A 15-bag pack of potato chips has a 1:4 ratio between plain chips and BBQ chips. How many packs of each flavor are there?”

• Module 7, Lessons 6, 8, and 10 engage students with the full intent of 6.EE.7 (Solve real- world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers). In Lesson 6, Algebra: Solving addition equations, Student Journal, Step Up, page 259, Question 2, students reason about and solve one step equations. “Calculate the value of each variable. Show your thinking and be sure to show each step. a. p + 3 = 21, b. 41 = m + 1, c. 65 = a + 5, d. w + 1.5 = 4.2, e. z + \frac{12}{20} = 2\frac{6}{10}, f. 48 + 3 = p + 30, g. z + 1.20 + 0.08 = 7.8, h. 58 + 34 = 26 + p + 30.” In Lesson 8, Algebra: Solving multiplication equations, Student Journal, Step Up, page 265, Question 1, students continue to reason and solve one step equations. “Calculate the value of each variable. Show your thinking. a. 2d = 16, b. 27 = 9y, c. 3h = 4.5, d. 32 + 24 = 7r, e. 55 = 4g + 7g, f. z + 8z = 4 + 32, g. 5\frac{2}{10} = 4g, h. 2z + z + 5z = 4.” In Lesson 10, Algebra: Solving word problems (addition and multiplication), Student Journal, Step Up, page 271, Question 2a, students write and solve an equation in the form of px = q for a real-world problem. “A machine assembles 60 bicycles in 4 hours. A person assembles 60 bicycles in 9 hours. How many bicycles does the machine assemble each hour? Let b represent the number of bicycles.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days are included.

• The approximate number of modules devoted to major work of the grade (including supporting work connected to the major work) is 11 out of 12, which is approximately 92%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work, but not More Math) is 114 out of 156, which is approximately 73%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 103 out of 144, which is approximately 72%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in.  As a result, approximately 72% of the instructional materials focus on major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. These connections are sometimes listed for teachers on a document titled, “Grade __ Module __ Lesson Contents and Learning Targets” for each module. Examples of connections include:

• Module 1, Lesson 11, Number: Calculating distance on a coordinate plane, Student Journal, Step Up, page 36 and 37, connects the supporting work of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices) to the major work of 6.NS.8 (Understand a rational number as a point on the number line. Students use a coordinate plane to graph polygons and find the perimeter.) Question 1, “Plot each set of coordinates on page 37. Then draw lines to connect the dots in alphabetical order. Shape 1 A(-4,10), B(8,10), C(8,6), D(-4,6). Shape 2 E(-8,3), F(-4,3), G(-4,-6), H(-8,-6). Shape 3 I(3,3), J(10,3), K(10,-4), L(3,-4). Question 2, “Calculate these side lengths. Shape 1 Side AB, Shape 2 Side EH, Shape 3 Side LK.” Question 3, “Dallas wrote this equation to help calculate the side length of one of the shapes \left|3\right| + \left|-4\right| = 7. a. Which shape and side length did she calculate? b. What steps could she now follow to calculate the perimeter?”

• Module 2, Lesson 8, Mass: Algebra: Using the distributive property, Step Up, page 65 connects the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples) to the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions). Students use greatest common factors to represent expressions. Question 3c, “Find the greatest common factor. Then use the distributive property to rewrite each expression. 75 + 99, = (___ x ___) + ( ___ x ___), = ___ ( ___ x ___).”

• Module 9, Lesson 6, Statistics: Identifying the mode, Student Journal, Step Up, page 334, connects the supporting work of 6.SP.2 (Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape) and 6.SP.3 (Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number) to the major work of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, eg., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.) Students use ratio reasoning to answer questions about statistical data represented on a dot plot. Question 1, “Look at the dot plot on the right above and answer the following questions. a. What is the mode? b. What fraction of the words are above the mode? c. What fraction of the words are below the mode? d. Based on your answers for the previous two questions, do you think the mode is a good measure for that data set? Explain your answer.”

• Module 10, Lesson 9, Volume: Rectangular-based prisms with one fractional side length, Student Journal, Step Up, page 382, connects the supporting work of 6.G.2 (Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems) to the major work of 6.EE.6 (Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.) Students use a formula to calculate the volume of rectangular prisms. Question 1, “Calculate the volume of each object. Show your thinking. a. 6in, 5in, and \frac{1}{4} in. b. 7m, 25m, and \frac{1}{5}m.”

The materials reviewed for ORIGO Stepping Stones 2.0 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.

Materials are coherent and consistent with the Standards. Examples of connections include:

• In Module 2, Lesson 8, Algebra: Using the distributive property, Teaching the lesson Lesson notes, students apply and extend previous understandings of arithmetic to algebraic expressions, 6.EE.A, tand compute fluently with multi-digit numbers and find common factors and multiples, 6.NS.B to by solving word problems involving common factors and algebraic expressions.

• In Module 4, Lesson 2, Algebra: Writing equations to match word problems, Teaching the lesson, Lesson notes, students apply and extend previous understandings of arithmetic to algebraic expressions, 6.EE.A, and reason about and solve one-variable equations and inequalities, 6.EE.B by solving real-life problems using their knowledge of expression to solve one-variable equations.

The materials reviewed for ORIGO Stepping Stones 2.0 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. 

Materials relate grade-level concepts from 6th Grade explicitly to prior knowledge from earlier grades. These references are consistently included within the Topic Progression portion of Lesson Notes and within each Module Mathematics Focus. At times, they are also noted within the Coherence section of the Mathematics Overview in each Module. Examples include:

• Module 1, Lesson 2, Number: Reviewing fractions, Lesson Notes connect 6.NS.5 (Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation) to previous work in grade 5 (5.NBT.4). “In Lesson 5.3.11, students round decimal fractions with up to three decimal places to the nearest whole number and nearest tenth. In this lesson, students work to explore decimal fractions beyond thousandths.”

• Module 8, Lesson 3, Ratio: Introducing percentage (area model), Lesson Notes connect 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations) to the work from grade 5 (5.NF.2). “In Lesson 5.4.6, students are encouraged to use a range of strategies to solve multistep word problems involving the comparison of two or more common fractions. In this lesson (8.3), students are introduced to the concept of percentage using a hundredths square. They learn that a percentage is a representation of a number of parts out of 100 parts.” 

• Module 9, Mathematics Overview, Coherence, “Lessons 9.5–9.8 focus on introducing statistics and interpreting a set of data with mean, median, and mode. This work builds on interpreting data using line plots (5.3.12, 5.4.12, 5.9.12).”

Content from future grades is identified within materials and related to grade-level work. These references are consistently included within the Topic Progression portion of Lesson Notes and within the Coherence section of the Mathematics Overview in each Module. Examples include:

• Module 2, Lesson 8, Algebra: Using the distributive property, Lesson Notes connect 6.NS.4 (Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor) and 6.EE.2 (Write, read, and evaluate expressions in which letters stand for numbers) to work in grade 7 (7.EE.1). “In this lesson, students use the distributive property to model equivalent expressions. They also build on the content from the previous lesson by using the greatest common factor to represent an equivalent expression using the distributive property. In Grade 7, students apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.” 

• Module 3, Overview, “Lessons 3.1–3.7 focus on ratios as part-part and part-whole relationships. This work builds on previous work with relationships in numerical patterns (5.11.1–5.11.6) and serves as a foundation for comparing, measuring, and solving problems with ratios (6.5.8–6.5.12).”

• Module 10, Lesson 12, Volume: Solving word problems, Lesson Notes connect 6.G.2 (Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems) to the work of grade 7 (7.G.6). “In this lesson, students review how to calculate the volume of rectangular-based prisms with fractional side lengths. They then solve multistep word problems involving volume. In Grade 7, geometry, students solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.”