4th Grade - Gateway 1

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 4 standards include:

• Module 2, Check-Up 2, Problem 3, “Complete each equation. Show your thinking. a. 9\times 35 =  b. 3\times94 = .” (4.NBT.5).

• Module 6, Quarterly Test B, Problem 2, “Choose the operation you would use to solve this problem. Victoria has 26 stamps in her collection. Her brother has 18 more stamps than Victoria. How many stamps are in her brother’s collection? A. Multiplication, B. Division, C. Addition, D. Subtraction.” (4.OA.2)

• Module 8, Performance Task, Problem 1, “a. Three people equally share the cost of this television. How much will each person pay? b. A fourth person joins the group to share the cost of the same television. How much less will each person have to pay?” An image shows the price of the television as $624. (4.MD.2 and 4.OA.3).

There are some assessment items that align to standards above Grade 4; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include: 

• Module 10, Check-Up 1, students add decimals: Problem 1a, 0.4 + 0.2, Problem 1b, 3.15 + 2.50, and Problem 1c, 0.6 + 0.25. (5.NBT.7).

• Module 10, Performance Task, students add decimals (5.NBT.7) in the six problems.

• Module 12, Quarterly Test A and Quarterly Test B, Problems 12 and 13, students add decimals (5.NBT.7).

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 4th 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 4, students engage with all CCSS standards. Examples of extensive work from the grade include:

• Module 3, Lessons 2 and 6 engage students in extensive work with 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm.) as students use the standard algorithm to solve addition problems. Lesson 2, Number: Comparing to order four-, five-, and six-digit numbers, Student Journal, Maintaining Concepts and Skills, page 87, Question 1a, “Estimate each total. Then use the standard addition algorithm to calculate the exact total. Estimate ______  1615 + 1472 =, Estimate ______ 2486 + 1373 =, Estimate ______ 2108 + 2095 =.” Lesson 6, Multiplication: Relating multiples and factors, Student Journal, Maintaining Concepts and Skills, page 99, Question 1a, “Estimate each total. Then use the standard algorithm to calculate the exact total. Estimate______ 4360 + 804 + 273 =, Estimate ______ 36020 + 2654 + 1168 = ,  Estimate ______ 52789 + 13540 + 3420 =.” 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 4, Division: Solving word problems with remainders, engages students with extensive work with grade-level problems with 4.OA.3 (Use the four operations with whole numbers to solve problems). In the Student Journal, Step Up, page 252, Question 1, students solve word problems with remainders. “Solve each problem. Show your thinking. a. Teresa is walking 60 miles for charity. She walks 7 miles a day. How many days will it take to complete the walk? b. 20 balls are packed into cans. There are 3 balls in each can. How many balls are left out?”

• Module 9, Lesson 3, Common fractions: Comparing and ordering, engages students with extensive work with 4.NF.2 (Extend understanding of fraction equivalence and ordering). In the Student Journal, Step Up, page 327, Question 3, students use number lines to compare and order common fractions. “Use the number lines in Questions 1 and 2 to help you write these fractions in order from least to greatest. a. \frac{8}{6}, \frac{13}{6}, \frac{6}{4}, \frac{8}{4} b. \frac{5}{4}, \frac{8}{3}, \frac{13}{4}, \frac{2}{3} c. \frac{11}{12}, \frac{18}{10}, \frac{7}{2}, \frac{12}{10} d. \frac{11}{5}, \frac{18}{8}, \frac{4}{5}, \frac{3}{1} e. \frac{11}{4}, \frac{7}{4}, \frac{7}{6}, \frac{12}{6} f. \frac{2}{1}, \frac{24}{8}, \frac{12}{8}, \frac{5}{5}.” 

The instructional materials provide opportunities for all students to engage with the full intent of 4th 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 3, Lessons 9 and 12 engage students in the full intent of 4.MD.3 (Apply the area and perimeter formulas for rectangles in real world and mathematical problems.)  In Lesson 9, Area: Developing a rule to calculate the area of rectangles, Student Journal, Step Up, page 107, students reason about area. Question 2a, “Calculate the area of each rectangle. Show your thinking. 4 yd 12 yd Area ____yd^2.” Question 3a, “Write possible dimensions for each rectangle. ____yd  ____yd   36 yd^2.”  In Lesson 12, Perimeter/area: Solving word problems, Student Journal, Step Up, page 114, students apply the formulas for area and perimeter. Question 1a, “Measure each side length in centimeters. Then calculate the perimeter and area. Perimeter ____cm   Area ____cm^2”  There is a rectangle for students to measure. Question 2a, “Solve each problem. Show your thinking. Remember to include the units in your answers. Zoe’s backyard is a rectangle. The short sides are 5 yards long. The long sides are twice as long. What is the area of her backyard?”  

• Module 7, Lessons 5 and 8 engage students with the full intent of 4.NF.3a (Understand addition and subtraction of fractions as joining and separating parts referring to the same whole). In Lesson 5, Common fractions: Adding with same denominators, Student Journal, Step Up, page 256, Question 1, students use area models to represent the addition of fractions. “Each large rectangle is one whole. Shade parts using different colors to show each fraction. Then write the total fraction that is shaded. a. \frac{3}{8} + \frac{4}{8} = b. \frac{1}{6} + \frac{3}{6} = c. \frac{4}{10} + \frac{2}{10} =.” In Lesson 8, Common fractions: Subtracting with same denominators, Student Journal, Step Up, page 265, Question 2, students use a number line to subtract fractions. “Use this number line to help you write the differences. a. \frac{15}{6} - \frac{4}{6} = b. = \frac{20}{6} - \frac{8}{6} = c. \frac{17}{6} - \frac{2}{6} = d. = \frac{23}{6} - \frac{9}{6} = e. \frac{21}{6} - \frac{16}{6} = f. = \frac{18}{6} - 1 = \frac{18}{6}- 1.”

• Module 12, Lessons 2 and 3 engage students with the full intent of 4.OA.5 (Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself). In Lesson 2, Patterns: Investigating square numbers, Student Journal, Step Up, page 437, students analyze numerical and visual patterns. Question 3, “Norton is exploring square number patterns where there is a 2 in the one’s place of the original number. His results are shown in this table. Original number: 12, 22, 32, 42, 52. Square number: 144, 484, 1,024, 1,764, 2,704. a. Look at his pattern. Circle the numbers below that you think are square numbers. 6,241, 5,184, 2,401, 6,724, 9,409, 8,649. b. Explain your thinking.” In Lesson 3, Patterns: Analyzing number patterns, Student Journal, Step Up, page 441, students use a given rule to complete a pattern. Question 1, “a. Read the rule. Then complete the table. Number of circles = Picture number 2. Picture Number: 6, 4, 5, 20, 2, 15, __. Number of Circles: __, 8, __, 40, 4, __, 26. b. Do you think it is possible to record an odd number of circles? Explain your thinking.”

• One 4th grade standard, 4.MD.4, 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 measurements in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}) Solve problems involving addition and subtraction of fractions by using information presented in line plots.) For example, Module 6, Lesson 12, Angles: Estimating and calculating, Student Journal, page 231, 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}. Student Journal, Ongoing Practice, “These line plots show the distances run by an athlete during training.” Question 1a, “In which month did the athlete train for the greater number of days?” Question 1b, “ In which month did the athlete run the greater total distance?” Question 1c, “What is the difference between the total distances run in April and May?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 126 out of 156, which is approximately 81%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 114 out of 144, which is approximately 79%.

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 79% of the instructional materials focus on major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 3, Student Journal, Mathematical Modeling Task, page 118, connects the supporting work of 4.MD.A (Solve problems involving measurement and conversion of measurements) to the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic). Students solve word problems with area and price comparisons. “Hailey is buying carpet for three rooms in her house. The carpet for each room will be a different color. The main bedroom is 16 feet long and 12 feet wide. The office is 15 feet long and 9 feet wide, and the family room is 23 feet wide by 35 feet long. At Country Carpets, if you buy less than 250 square feet of the same color carpet, each square foot costs $8. If you buy 250 square feet or more of the same color carpet, the cost for each square foot is $6. How can Hailey use mathematics to figure out the total cost for carpeting the three rooms? Show your thinking.”

• Module 5, Lesson 12, Length/mass/capacity: Solving word problems involving metric units, Student Journal, Step Up, page 190, connects supporting work of 4.MD.A (Solve problems involving measurement and conversion of measurements) to the major work of 4.NF.B (Build fractions from unit fractions). Students convert between measurements and fractional parts of measurements to solve word problems. Question 1b, “Solve each problem. Show your thinking and be sure to use the correct units in your answer. Before an operation, a dog weighs 3\frac{4}{10} kg. Afterward, it is 3\frac{1}{10} kg. How many grams has the dog lost?” Question 2d “A pitcher holds 1\frac{1}{2} liters of water. Luis pours out some water and there is now 900 mL of water left. How much water was poured out?”

• Module 6, Lesson 12, Angles: Estimating and calculating, Student Journal, Ongoing Practice, page 231, connects the supporting work of 4.MD.B (Represent and interpret data) to the major work of 4.NF.B (Build fractions from unit fractions). Students analyze two line plots with fractional values to answer questions. “These line plots show the distances run by an athlete during training.” Question 1a, “In which month did the athlete train for the greater number of days?” Question 1b, “In which month did the athlete run the greater total distance?” Question 1c, “What is the difference between the total distances run in April and May?”

• Module 7, Lesson 11, Common fractions: Solving word problems, Student Journal, Step Up, page 275, connects the supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expression measurements given in a larger unit in terms of a smaller unit) to the major work of 4.NF.3 (Understand a fraction \frac{a}{b}with a > 1 as a sum of fractions \frac{1}{b}.) Students solve addition and subtraction word problems involving mixed numbers and common fractions. Question 2, “Solve each problem. Show your thinking. a. Oscar cuts 5 oranges into sixths for a picnic. Afterward, there is only \frac{4}{6} of an orange left. How much orange has been eaten? b. Two statues are being packed into a box. One weighs 7\frac{3}{8} lb and the other weighs 9\frac{4}{8} lb. What is their total mass? c. Two full 2-liter bottles of water are placed in a fridge. After four days, one bottle is half full. The other has 1\frac{3}{10} liters left in it. How much water is there in total? d. A chain is 8\frac{5}{12} feet long. It is joined to another chain so the total length is 10\frac{9}{12} feet. How long is the extra piece of chain?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 3, Addition: Reviewing the standard algorithm (composing hundreds), students use the four operations with whole numbers to solve problems, 4.OA.A, and use place value understanding and properties of operations to perform multi-digit arithmetic, 4.NBT.B by explaining and discussing the effects of order of operations on an equation.

• In Module 4, Lesson 11, Common fractions: Introducing mixed numbers, Teaching the lesson, Lesson notes, students extend understanding of fraction equivalence and ordering, 4.NF.A, and build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers, 4.NF.B, by using equivalence to add fractions.

• In Module 7, Lesson 11, Common fractions: Solving word problems, Teaching the lesson, Lesson notes, students extend understanding of fraction equivalence and ordering, 4.NF.A, and, build fractions from unit fractions 4.NF.B, and represent and interpret data by solving real world problems with fractions and mixed numbers, 4.MD.B.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 4th 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 1.8–1.12 focus on reviewing mental multiplication and extending the focus of multiplying by tens, hundreds, or thousands. This work builds on the prior work with multiplication strategies (3.3.3, 3.3.6, 3.5.1–3.5.2, 3.10.7).”

• Module 5, Lesson 6, Length: Exploring the relationship between meters and centimeters, Lesson Notes connect 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit) to work from grade 2 (2.MD.1, 2.MD.3, 2.MD.10). “In Lesson 2.9.11, students measure and compare the lengths of longer objects by repeatedly using a 1 meter length. In this lesson (5.6), students consider what the numbers and markings represent on tools that measure unit of length. They express measured lengths in both meters and centimeters, and use abbreviations.”

• Module 7, Lesson 1, Division: Halving two-digit numbers, Lesson Notes connect 4.NBT.6 (Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division) to the work from grade 3 (3.OA.3 and 3.OA.7). “In Lesson 3.12.5, students reinforce the think-multiplication strategy to solve division problems beyond the number fact range. In this lesson (7.1), students review strategies to divide by 2. They use base-10 blocks to model sharing situations, and multiplication equations and diagrams to relate the operations of multiplication and division.” 

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 6, Lesson 8, Length: Exploring the relationship between miles, yards, and feet, Lesson Notes connect 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit) to grade 5 (5.MD.1). “In this lesson, students focus on the relationships between miles, yards, and feet and the count of the units when converting miles to yards, then to feet. In Lesson 5.4.7, students convert between feet and inches. The lesson builds upon earlier grade level work as students begin to convert lengths that involve fractions. They convert inches to feet.”

• Module 10, Lesson 12, Decimal fractions: Solving word problems, Lesson Notes connect 4.MD.2 (Solve problems involving addition and subtraction of fractions by using information presented in line plots) to the work of grade 5 (5.NBT.7). “In this lesson, students solve word problems involving decimal fractions as related to units of measurement. In Lesson 5.5.1, students review strategies to add tenths to tenths, hundredths to hundredths, and tenths to hundredths. The examples do not require regrouping.”

• Module 11, Mathematics Overview, Coherence, “Lessons 11.9–11.12 focus on the geometry work of points, lines, line segments, and rays and transformations that involve reflective symmetry. This work builds on experiences with estimating, calculating, and measuring angles (4.6.9–4.6.12) and serves as a foundation for work with parallelograms and triangles (5.5.10–5.5.12).”