2nd Grade - Gateway 1

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for assessing 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 2 standards include:

• Module 3, Quarterly Test A, Problem 1 “Choose the equation you would use to solve the problem. Andrew had 11 pennies. His dad gave him 3 more. How many pennies does he have in total. A. 11 - 3 = 8, B. 11 + 3 = 14, C. 14 - 3 = 11.” (2.OA.1)

• Module 5, Check-Up 2, Problem 1, “Write the fact family to match the domino. 15 dots in total.” (2.NBT.5)

• Module 12, Performance Tasks, Problem 2, “Split these shapes into four equal parts. Use splits that are different from the splits on similar shapes in Question 1.” (2.G.3)

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Extensive work is provided as students engage with different types of problems in each lesson. There is a Student Journal with problems in three sections: Step In, Step Up, and Step Ahead. Maintaining Concepts and Skills 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 all grade-level standards are present within materials. Examples include:

• Module 1, Module 3, and Module 5 engage students in extensive work with 2.OA.2 (Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.) In Module 1, Lesson 10, Addition: Reviewing the count-on strategy, Student Journal, Maintaining Concepts and Skills, page 34, students are asked to “Draw a check mark beside each correct answer on Jennifer’s test paper. Count each check mark and write the total at the bottom of the page. Correct the facts that were wrong.” In Module 3, Lesson 12, Addition: Developing fact fluency, Student Journal, Step Up, page 116, Question 1 students are directed to, “Write the missing numbers to complete each equation.” Students are given 12 equations with missing parts to solve. In Module 5, Lesson 11, Subtraction: Reinforcing the think-addition strategy (make ten facts), Student Journal, Step Up, page 188, Question 1, students are given pictures of 6 dominoes. They are asked to, “Draw dots to help you complete the subtraction fact, then write the related addition fact.”

• Module 2 and Module 8 engage students in extensive work with 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) In Module 2, Lesson 7, Time: Reviewing on the hour, Student Journal, Step Up, page 62, Question 1, students see analog clocks with times shown to the hour. They must then “Write each time on the digital clock.” In Module 2, Lesson 8, Time: Reviewing half-past the hour, Student Journal, Step Up, page 65, Question 2, students see analog and digital clocks with times to the hour and half-hour. Next they must, “Write each time in words.” Students write the half-hour times as “Half-past twelve o’clock”. In Module 8, Lesson 10, Time: Working with five-minute intervals, Student Journal, Step Up, page 303, Question 1, students see analog clocks with time to the 5 minute, and matching digital clocks with time to the 5 minute. Students must then demonstrate their ability to, “Draw lines to connect the matching times. Cross out the digital clock that does not have a match.”

• Module 11, Lessons 10, 11, and More Math engage students in extensive work with 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?) In Lesson 10, Money: Identifying amounts of money, Student Journal, page 423, Step Ahead, “Peta has 4 coins in her pocket. The total is greater than 40 cents but less than 60 cents. Draw two different pictures to show the coins she might have in her pocket.” In Lesson 11, Money: Working with dollars and cents, Maintaining Concepts and Skills, Investigation 3, “Ramon has seven coins in his pocket. He has 35 cents in total. What coins could Ramon have in his pocket?” In More Math, Problem Solving Activity 4, Question d, “Mako has 2 quarters, three dimes, and 2 nickels in her wallet. She gave 25 cents to her sister. She then found 15 cents while walking home from school. How much money does Mako have now?”

The instructional materials provide opportunities for all students to engage with the full intent of 2nd 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 and Module 3 engage students with the full intent of 2.NBT.3 (Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.) In Module 1, Lesson 1, Number: Reading and writing two-digit numbers, Student Journal, Step Up, page 6, Question 1, students are given a number name and pictures of place value expanders. The paper unfolds to show the place value next to each digit. Students are instructed to, “Read the number name. Write the number with and without the expander.” In Module 1, Lesson 8, Number: Writing three-digit numbers, Student Journal, Step Up, page 26, Question 1, students see pictures of base-ten blocks and blank number expanders to answer questions for 3-digit numbers. They are then asked to, “Look at the picture of blocks. Write the matching number on the expanders.” In Module 3, Lesson 4, Number: Writing three-digit numbers in expanded form, Student Journal, Step Up, page 91, Question 2, students are given expanders filled in. They must then, “Write each number in expanded form.”

• Modules 6, 7, and 8 engage students with the full intent of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) In Module 6, Lesson 12, Data: Introducing vertical bar graphs, Student Journal, Step Up, page 198, Question 1b, “Write the missing totals. If 4 + 4 = ___ then 40 + 40 = ___” In Module 7, Lesson 3, Subtraction: One-digit numbers from two-digit numbers bridging tens (number line), Maintaining Concepts and Skills, Problem Solving 1 activity, students are given the numbers 2, 5, 0, 9, a blank equation _ _ - _ _ = _ _, an empty number line, and a hundred chart. “Kevin chose these four number cards. He wants to write a subtraction equation that will give him the greatest possible difference. What equation should Kevin write? Use the number line or hundred chart to help your thinking.” In Module 8, Lesson 4, Subtraction: Reinforcing two-digit numbers (decomposing tens), Student Journal, Maintaining Skills and Concepts, Preparing for Module 9, page 293, Question a, students are given a number line. “Draw jumps to show how you could count on to figure out each of these. Then write the total. 52 + 17 = ___.”

• Module 8, Lessons 9-12 engage students with the full intent of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) In Lesson 9, Time: Identifying five-minute intervals, Student Journal, Step In, page 307, Question 2a, students see a picture of an analog clock showing 7:20. “Write numbers to show each time. ___ minutes past ___.” In Lesson 12, Time: Identifying and recording time using a.m and p.m, Student Journal, Maintaining Concepts, Ongoing Practice, page 317, Question 2a, students are given a picture of an analog clock showing 6:15 and a blank digital clock under the heading wake up. “Write the digital time for each event. Then write a.m. or p.m. to match the event.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of modules devoted to, or supporting, major work of the grade is 5 out of 12, which is approximately 42%.

• The approximate number of lessons devoted to major work, or supporting major work of the grade, is 102 out of 144, which is approximately 71%. 

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 111 out of 156, which is approximately 71%. 

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 71% of the instructional materials focus on major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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 2, Lesson 10, Addition: Reviewing the doubles strategy, Step 4 Reflecting on the Work, connects the supporting work of 2.OA.3 (Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.) to the major work of 2.OA.2 (Fluently add and subtract within 20 using mental strategies.) “Direct their attention to Question 3. Ask, Is it possible to double a number from 1 to 9 and record a total that is odd? How do you know? How can you prove your thinking? Facilitate debate among the class (SMP3). If necessary, draw one long row of circles to show a number. This number is then doubled by drawing a matching row of circles directly below, as shown. Point out that each circle has a partner, so the number is even.”

• Module 9, Lesson 12, Length/data: Using line plots to record length, connects the supporting work of 2.MD.9 (Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole- number units) to the major work of 2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.) In the Student Journal, page 353, Question 2a, “Your teacher will give you a piece of drinking straw. Use a centimeter ruler to measure its length. Write its length here __cm” Question 2b, “With your teacher’s help, record the length of each student’s straw.” Question 2c, “Use the measurements above to complete the line plot below. Show your measurement first.”

• Module 11, Lesson 5, Multiplication: Adding equal rows, connects the supporting work of 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.) to the major work of 2.OA.2 (Fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know from memory all sums of two one-digit numbers.) Student Journal, Step Up, page 408, Question 1c, students see a picture of 6 ladybugs arranged in 3 rows of 2. “Circle each row of bugs. Write the missing numbers. ___ rows, ___ ladybugs in each row, ___+____+___=___.” There are four of these problems in Question 1. Student Journal, Step Ahead, page 409, students use an array as an addition tool. “Draw an array of worms that has 5 rows. Then write a story and an equation to match.”

• Module 11, Lesson 12, Money: Solving word problems, connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.) In Step 3, Teaching the Lesson, Slide 3, students solve word problems using money. “Oliver has a 1 bill, 3 nickels, 1 dime, and 2 pennies. How much money does he have?” Student Journal, Step Up, page 429, Question, “2b. Daniela has 74 cents and Felipe has 2 dimes, a quarter, and a nickel. If they combine their money, how much will they have in total? 2d. William has five quarters fewer than Nicole. William has 6 quarters. How much money does Nicole have?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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 10, Length: Working with feet and inches,Teaching the lesson, Lesson notes, students solve a word problem (2.OA.A) using units of length to add (2.MD.B). 

• In Module 6, Lesson 9, Addition: Two-digit numbers (composing tens and hundreds), Teaching the lesson, Lesson notes, students solve two-digit addition word problems (2.OA.A) with sums greater than 100 (2.NBT.B). For example, “78 cars are parked on the top floor of a parking garage. There are 65 fewer cars parked on the top floor of the parking garage than the bottom floor. How many cars are parked on the bottom floor?” 

 However, there are a few missed opportunities to foster coherence through connections at a single grade. Examples include:

• In Module 5 Lesson 2, Addition: Skip counting by five or ten (number line), and Lesson 10, Subtraction: Reviewing the think-addition strategy (make-ten facts), students use a variety of strategies to add and subtract two digit numbers, including using a number line and ‘make ten’ (2.NBT.A). However, place value is not referenced, so there is a missed connection to 2.NBT.B.

• In Module 12 Lesson 3, students create halves and fourths from shapes (2.G.A). A connection to reinforce money (dollars as the whole, \frac{1}{4} as 1 quarter, etc. (2.MD.C)) is omitted.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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 2nd 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 5, Number: Working with hundreds, Lesson Notes connect 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.), 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s.), 2.NBT.3 (Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.), and 2.NBT.8 (Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.), to work from grade 1 (1.NBT.2). “In Lesson 1.12.1, students use the hundred chart and their knowledge of place value to investigate two-digit numbers. In this lesson (1.5), students make groups of 10 and then groups of 100 to represent numbers greater than 100. Emphasis is also placed on composing and decomposing quantities of blocks to show that the same number can be represented in more than one way.”

• Module 6, Lesson 10, Data: Introducing picture graphs, Lesson Notes connect 2.MD.10 (Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems using information presented in a bar graph) to the work from grade 1 (1.NBT.1, 1.MD.4). “In Lesson 1.1.12, students collect and display data in simple picture graphs. In this lesson (6.10), students survey the class and collect the data using tallies. They then show their survey results in a one-to-one picture graph.” 

• Module 9, Mathematics, Focus, Coherence table “identifies the prerequisite standards and learning targets needed for Grade 2, Module 9.” Specific Lessons, Standards, and Learning Targets from previous grades are listed. “Stepping Stones Grade 1 Lesson 3.10, Standard 1.MD.A.1, Learning Target: Use indirect comparison to compare and order length.”

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 4, Lesson 12, Length: Working with customary units, Lesson Notes connect 2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.), 2.MD.2 (Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.), 2.MD.3 (Estimate lengths using units of inches, feet, centimeters, and meters.), to work in grade 4 (4.MD.1, 4.MD.4). “In this lesson, students estimate the length of pieces of string. They then measure each length, justifying the measurement unit and tool that they decided to use. In Lesson 4.6.6, students review different units of length, focusing on the relationship between the size of feet and inches. A line plot is used to display the lengths of alligators.”

• Module 7, Lesson 12, 2D shapes: Drawing polygons, Lesson Notes connect 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes) to the work of grade 3 (3.G.1). Lesson Notes, “In this lesson, students draw 2D shapes to match given criteria. In Lesson 3.2.10, students examine the properties that define rectangles. The concept that squares are also rectangles is reinforced.”

• Module 10, Mathematics Overview, Coherence, “Lessons 10.1-10.12 focus on using all strategies for subtraction of up to three-digit numbers from three-digit numbers.” This “prepares students for using count-back and count-on strategies for subtraction of up to three-digit numbers from three digit numbers with regrouping (3.5.8-3.5.12).”