5th Grade - Gateway 1

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 meet expectations that they assess grade-level content and, if applicable, content from earlier grades. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

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 5 standards include:

• Module 3, Check-Up 2, Question 2, “Color the circle below the greatest number in each group. a. 0.62, 0.6, 0.607. b. 0.317, 0.36, 0.321.” (5.NBT.3).

• Module 6 Quarterly Test A, Problem 17, “Package A weighs \frac{3}{12} kilogram, Package B weights 1frac{5}{6} kilograms, and Package C weighs \frac{3}{4} kilograms. What is the total mass of Package A and C? Show your thinking.” (5.NF.2).

• Module 9 Performance Task, Problem 2, “A student thinks that \frac{1}{5} divided by 6 is equivalent to \frac{1}{5} ≅ \frac{1}{6}. Are they correct? Draw a picture or write sentences to explain your answer.” (5.NF.3 and 5.NF.7).

There are some assessment items that align to standards above Grade 5; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include: 

• Module 12, Performance Task, directions for the assessment state, “Use the standard algorithm to calculate the quotient” (6.NS.3).

• Module 12, Quarterly Tests A and Test B, Problems 10, 11, and 12, the directions state, “Use the standard algorithm to divide” (6.NS.3).

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 5th 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 5, students engage with all CCSS standards. Examples of extensive work from the grade include:

• Module 5, Lessons 2 and 4 engage students in extensive work with 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.) as students perform calculations with decimals. In Lesson 2, Decimal fractions: Adding (with composing), Student Journal, Maintaining Concepts and Skills, page 163, Question 2a, “Calculate each total. Draw jumps on the number line to show your thinking. 7.4 + 2.55 =.” In Lesson 4, Decimal fractions: Using the standard algorithm to add more than two addends, Student Journal, Maintaining Concepts and Skills, page 169, Question 2b, “Calculate the total. Show your thinking. $2.50, $3.70.” 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 7, Lesson 3, Common fractions: Subtracting (unrelated denominators), engages students with extensive work with 5.NF.2 (Use equivalent fractions as a strategy to add and subtract fractions). In Student Journal, Step up, page 251, Question 3, students subtract common fractions with unrelated denominators. “a. Three-fifths of a field is planted with potatoes. Another second of the field is planted with garlic. Eleven-twelfths of the field is planted in total. What fraction of the field is planted with garlic? b. In a park, \frac{5}{8} of the animals are pigeons and \frac{2}{10} of the animals are squirrels. What fraction of all the animals in the park are not pigeons or squirrels?” 

• Module 9, Lesson 11, Length/mass/capacity: Solving word problems (metric units), engages students with extensive work with 5.MD.1 (Convert like measurement units within a given measurement system). In the Student Journal, Step Up, page 359, Question 1, students convert measurement units and solve real-world problems. “a. Sheree pours 2 L of water equally into 10 cups. Each cup can hold 400 mL. There is no water left in the bottle. How much water is in each cup? b. A customer orders 8 bags of rice that each weigh \frac{1}{2} kg, and 12 packets of popcorn that each weigh 150 g. What is the total mass of the order?” 

The instructional materials provide opportunities for all students to engage with the full intent of 5th 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 2, Lessons 8-12 engage students with the full intent of 5.MD.5 (Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.) Lesson 9, Volume: Developing a formula, Student Journal, Step Up, page 68, Question 2, “Here are the dimensions of another prism. Length 8 cm Width 3 cm Height 5 cm Write how you can calculate the volume without counting cubes.” Lesson 10, Volume: Finding the dimensions of prisms with a given volume, Student Journal, Step Ahead, page 71, “Prism A is made with inch cubes. It is 4 cubes long, 5 cubes wide, and 2 cubes high. Prism B is made with centimeter cubes. It is 10 cubes long, 2 cubes wide, and 2 cubes high. Which prism has the greater volume? Explain your thinking.” Lesson 12, Volume: Solving real-world problems, Student Journal, Step Up, page 76, Question 1a, “Use the box sizes above. Calculate the total volume that each group of boxes would occupy. Show your thinking. a, 2 large boxes and 3 medium boxes. b. 3 large boxes, 2 medium boxes, 6 small boxes.” 

• Module 3, Lessons 1-9 engage students in the full intent of 5.NBT.3 (Read, write, and compare decimals to thousandths.) Lesson 6, Decimal fractions: Recording in expanded form, Student Journal, Step Up, page 96, Question 1a, “Write the missing numbers. 9.164  (___ x 1) + (___ x 0.1) + ( ___x 0.01) + (___ x 0.001)” Question 2, “Write each decimal fraction in expanded form using one of the methods from page 96. a. 6.256 b. 1.907, c. 5.005, d. 1.840.” Lesson 8, Decimal fractions: Comparing and ordering thousandths, Student Journal, Step Up, page 103, Question 2a, “Write each group of fractions in order from least to greatest. Use the number line to help you. 0.505, 0.890, 0.550, 0.915.” 

• Module 11, Lesson 3, Algebra: Introducing the coordinate plane, engages students with the full intent of 5.G.1 (Graph points on the coordinate plane to solve real-world and mathematical problems). In the Student Journal, Step In, page 402, students describe points on the coordinate plane. “Imagine you took two number lines and turned one of them 90 degrees so that they intersect at 0. You can identify a point on the horizontal number line, or a point on the vertical number line. You can also identify a point between the two number lines by making a grid. On this grid, the horizontal number line is called the x-axis. The vertical number line is called the y-axis. The origin is where the two number lines intersect. The position of the red point in the grid on the right can be described using coordinates, or an ordered pair. The first number in an ordered pair is the x-coordinate. It tells the distance to move from the origin along the x-axis. The second number is the y-coordinate. It tells the distance to move from the origin along the y-axis. The coordinates of the blue point in the grid are (2, 5). What are the coordinates of the red point?” In Step Ahead, page 403, students solve real-world problems using ordered pairs. “Two teams are trying to find each other’s base in a game. Each team has a map with a coordinate plane on it. Team A has heard that Team B’s base is at a certain position on the map. When added together the coordinates for the base have a total of 7. Write all the possible ordered pairs for Team B’s base.”

• One 5th grade standard, 5.MD.2, does not include opportunities for students to engage with problems that meet the full intent of the standard. (Make a line plot to display a data set of measurement in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}). Use operations on fractions for this grade to solve problems involving information presented in line plots) For example, Module 9, Lesson 12, Mass/data: Interpreting a line plot to solve problems, students engage with making a line plot to display a set of measurements in fractions of a unit with \frac{1}{2}, but none with \frac{1}{4} or \frac{1}{8}.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 9 out of 12, which is approximately 75%.

• 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 128 out of 156, which is approximately 82%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 116 out of 144, which is approximately 81%.

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 81% of the instructional materials focus on major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 4, Lesson 10, Mass: Converting customary units, Student Journal, Step Up, page 147 connects the supporting work of 5.MD.A (Convert like measurement units within a given measurement system) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths). Students multiply and divide to convert measurements. Question 2a-2c, “Convert pounds to ounces to complete these. Show your thinking. a. 3.5 lb = ___ oz b. 2.75 lb ___ oz c. 4.25 lb ___ oz.”

• Module 5, Lesson 9, Decimal fractions: Subtracting (decomposing multiple places), Student Journal, Step Up, page 183, connects the supporting work of 5.OA.A (Write and interpret numerical expressions) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths). Students use operations to solve expressions using parentheses. Question 3a “Solve each problem. Show your thinking. 8\times15.6 + 2.40.”

• Module 8, Lesson 5, Common fractions: Finding a fraction of a whole number symbolically (non-unit fractions), Student Journal, Step Up, page 295, connects the supporting work of 5.OA.1 (Use parenthesis, brackets, or braces in numerical expressions, and evaluate expressions with these symbols) to the major work of 5.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.) Students multiply a whole number and a fraction as they solve problems with grouping symbols. Question 4b, “Solve each problem. Show your thinking. \frac{8}{10}\times(17-2)= __.”

• Module 9, Lesson 7, Common fractions: Solving word problems involving unit fractions, Student Journal, Step Up, page 339, connects the supporting work of 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them) to the major work of 5.NF.7c (Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.) Students solve division word problems involving unit fractions. Question 2, “Write an equation to represent each problem. Use a letter to show the unknown amount. Then calculate the answers. Show your thinking. a. A granola recipe requires \frac{1}{3} of a cup of raisins.  How many batches can be made with 3 cups of raisins? b. Thomas’s shirt costs $8, which is $$\frac{1}{6}$$ of the price of Ruby’s shirt. How much does Ruby’s shirt cost? c. Juan scores 8 goals in \frac{1}{4} hour. Kayla scores 24 in the same time. How many times greater is Kayla’s score than Juan’s score? d. An assembly line produces a new car every 6 minutes. What fraction of an hour is 6 minutes? How many cars are produced in 8 hours?”

• Module 9, Lesson 12, Mass/data: Interpreting a line plot to solve problems, Student Journal, Step Up, page 353, connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}), Use operations on fractions for this grade to solve problems involving information presented in line plots.) to the major work of 5.NF.A (Use equivalent fractions as a strategy to add and subtract fractions.) Students make a line plot and then analyze the data to solve problems using operations with fractions. Question 1, “Draw a dot to represent each mass shown at the bottom of page 352.” A line plot titled “Pumpkins” is labeled with Mass (kg) from 4 to 10 and halves included on the axis and 20 pumpkin measurements provided. Question 3a, “The pumpkins that weigh more than 5\frac{1}{2} kg are put together in a box to sell. What is the total mass of these pumpkins?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 4, Lesson 7, Length: Converting between inches and feet, students use equivalent fractions as a strategy to add and subtract fractions (5.NF.A) and convert like measurement units within a given measurement system (5.MD.A) by measuring different times and comparing them.

• In Module 6, Lesson 10 students perform operations with multi-digit whole numbers and with decimals to hundredths (5.NBT.B) and apply and extend previous understandings of multiplication and division (5.NF.B) to multiply and divide fractions by working with decimal remainders. 

• In Module 11, Lesson 12, Volume: Solving word problems, Student Journal, p. 429 Problem 2c, students understand concepts of volume and relate volume to multiplication and to addition (5.MD.C) and convert like measurement units within a given measurement system, (5.MD.A) by using volume in like measurements to solve real life problems. “Suitcase A is 2.5 feet long, 2 feet wide, and 2 feet high. Suitcase B is 36 inches long, 24 inches wide, and 18 inches high. What is the difference in volume?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 5th 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, Mathematics Overview, Coherence, “Lessons 5.1.1–5.1.7 focus on reading, writing, comparing, and ordering numbers from six to nine digits, including on a number line and including millions expressed as fractions. This work builds on experiences with six-digit numbers (4.3.1–4.3.4).”

• Module 3, Lesson 1, Decimal fractions: Reviewing tenths and hundredths (area model) connects 5.NBT.3 (Read, write, and compare decimals to thousandths) to work from grade 4 (4.NF.7). “In Lesson 4.10.8, students use various strategies and models to compare and order decimal fractions with one or two decimal places (comparison symbols). In this lesson, students use the area model to identify common fractions that can be expressed as tenths and/or hundredths.”

• Module 5, Lesson 10, 2D shapes: Identifying parallelograms, Lesson Notes connect 5.G.3 (Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category) and 5.G.4 (Classify two-dimensional figures in a hierarchy based on properties) with work from grade 3 (3.G.1). “In Lesson 3.2.12, students examine shapes whose properties allow them to belong to more than one shape family. Venn diagrams are used to sort shapes. In this lesson, students examine a defining feature of parallelograms.”

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 3, Lesson 11, Decimal fractions: Rounding with unequal decimal places, Lesson Notes connect 5.NBT.4 (Use place value understanding to round decimals to any place) to work in grade 6 (6.NS.5). “In this lesson, students round decimal fractions with up to three decimal places to the nearest whole number and nearest tenth. In Lesson 6.1.2, students explore decimal fractions beyond thousandths.”

• Module 7, Lesson 12, Number: Representing whole numbers using exponents, Lesson Notes connect 5.NBT.2 (Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10) to the work of grade 6 (6.NS.5, 6.EE.1). “In this lesson, students use expanded form together with exponents to represent whole numbers. In Lesson 6.1.1, students explore the different ways to represent numbers to one trillion. These representations include number names, numerals, expanded form, and exponents.”

• Module 11, Mathematics Overview, Coherence, “Lessons 5.11.1–5.11.6 focus on number patterns and coordinate planes. This work connects to future work of interpreting tables, investigating number patterns and rules, exploring different representations of patterns, identifying independent and dependent variables, and backtracking to solve equations (6.4.8–6.4.12).”