The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 1 standards include:

• Module 2, Check-Up 1, Problem 1, “Solve each problem. Show your thinking. a. Jose scored 2 points in the first half of the game and 6 points in the second half. How many points did he score in total? b. 5 guests are at a party. 2 more guests arrive. How many guests are there in total?” (1.OA.1)

• Module 7, Performance Tasks, Problem 1, “Look at the gray blocks. a. Write the matching numeral. b. write the matching number name.” (1.NBT.1)

• Module 12, Quarterly Test A, Problem 14, “Choose the object that matches these clues. I can stack. I have exactly 5 surfaces.” (1.G.1)

There are some assessment items that align to standards above Grade 1; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include: 

• Module 11, Check-Up 2, Problems 1 and 2, assess above grade-level content. Problem 1, “Solve each problem. Write an equation to show your thinking.” Part c, “I have 5 cents. How much would I have with 2 extra nickels?” Problem 2, “Figure out the total amount of each collection of coins.” Part b provides pictures of a quarter and a nickel, and students write the total.

• Module 11, Performance Task, “Katherine spent (pictures for 3 quarters, 1 dime, and 1 nickel). Write or draw the toys you think she bought. Show more than one answer.”  These problems align to 2.MD.8.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 2, and Module 3 engage students in extensive work with 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.) In Module 1, Lesson 4, Number: Representing quantities (11 to 20), Student Journal, Step Up, page 15, Question 2, students match numbers to quantities within 20. Directions state, “Count the fruit. Write the matching numeral.” In Module 1, Lesson 5, Number: Writing teen number names, Student Journal, Step Up, page 19, Question 2, students practice writing teen number names. Directions instruct students to, “Write each number name.” In Module 2, Lesson 5, Addition: Reviewing the think big, count small strategy, Step 2, Starting the Lesson, Teachers notes, “Have the students count from 50 to 100. Say, We are going to play a listening game with the numbers we know. We need to clap when we say the numbers 50, 60, 70, 80, 90, and 100. Have the students count from 50 to 100 again, clapping for each multiple of ten. Repeat the activity clapping for the numbers that have a five (for example, fifty-five, sixty-five, and seventy-five). Select students to give number suggestions and repeat as time allows.” In Module 3, Lesson 3, Number: Writing tens and ones, and number names (without zeros), Student Journal, Step Up, page 88, Question 1, students represent larger quantities with written numerals and number names. Directions instruct students to, “Look at the number of counters on and off the frames. Write the matching number on the expander. Then complete the number frame.”

• Module 2, Module 5, Module 8, and Module 9 engage students in extensive work with 1.OA.3 (Apply properties of operations as strategies to add and subtract.) In Module 2, Lesson 6, Student Journal, Step Up, page 59, Question 2, students see pictures of dominoes with a numeral on one side, and dots on the other. Directions challenge students to, “Write the addition fact. Then write the turnaround fact.” In Module 5, Lesson 1, Addition: Introducing the double-plus-1 strategy, Student Journal, Step Up, page 159, Question 2, students see pictures of dominoes. Students are then asked to, “Write the doubles fact. Draw one more dot on one end. Then write the doubles-plus-one fact and it’s turnaround.” In Module 8, Lesson 2, Addition: Using the associative property, Student Journal, Step Up, page 284, Question 1, students see 3 pictures of 3 containers with different quantities of objects in them. Students are then instructed to, “Draw an arrow to show two groups that make 10. Write an equation to show how you add to find the total. ___+___+___=___” In Module 9, Lesson 4, Addition: Any two-digit number and 1, 2, 3 or 10, 20, 30 (hundred chart), Student Journal, Maintaining Concepts and Skills, page 331, Ongoing Practice, Question 1, students see pictures of dominoes. Next students are asked to, “Write an addition fact to match each picture. Then write the turnaround fact.”

• Module 6, Lessons 8-11 engage students in extensive work with 1.G.3 (Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.) In Lesson 8, Common fractions: Identifying examples of one-half (length model), Student Journal, Step Up, Question 1, page 216, students are given pictures of paper strips with a line segmenting the strips into 2 parts. Directions instruct students to, “Color red one of the parts in each strip, then circle the strips that show one-half in red.” In Lesson 10, Common fractions: Identifying examples of one-fourth (length model), Student Journal, Step Up, Question 1, page 222, students are given pictures of strips. Students are then asked to, “Draw lines on each strip to show fourths.”

The instructional materials provide opportunities for all students to engage with the full intent of 1st 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 7, Lessons 10, 12, and More Math engage students with the full intent of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks.) In Lesson 10, Time: Introducing half-past the hour (analog), Student Journal, page 270, Question 1a, students see a picture of an analog clock with the hands showing 2:30. “Write the time showing on each clock. half-past ___ o’clock.” In More Math, Problem Solving Activity 3, students see pictures of analog and digital clocks showing half-hour increments between 1:00 and 7:00. “Cut out all the pieces. Then read the times and place the cards in order.” In Lesson 12, Time: Relating analog and digital, Student Journal, Step Up, page 276, Question 1c, students see a picture of an analog clock showing 4:30 and a picture of a blank digital clock. “Write each time on the digital clock.”

• Module 8, Lessons 7, 8, and 9 engage students with the full intent of 1.OA.7 (Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.) In Lesson 7, Equality: Reviewing concepts, Student Journal, Step Ahead, page 301, students see a picture of a pan balance with two blank cubes on one side of the balance, and a cube with the number 17 on it on the other side of the balance. “Write three different equations that would make this balance picture true.” In Lesson 8, Equality: Working with balance situations, Reflecting on the Work, students are shown the equation, 5 + 3 = 6 + 4. The teacher asks, “Is this equation true? How do you know? What would the pan balance look like if we used blocks to show the equation?” In Lesson 9, Equality: Balancing equations, Student Journal, Step Up, page 307, Question 2d, “Write true or false beside each equation. 7 = 9 - 2.”

• Module 9, Lessons 4, 9, and 11 engage students with the full intent of 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.) In Lesson 4, Addition: Any two-digit number and 1, 2, 3, or 10, 20, 30 (hundred chart), Student Journal, page 329, Question 2a, “Figure out and write the totals. 88 + 10 = ___.” In Lesson 9, Addition: One- and two-digit numbers (composing tens), Step 3 Teaching the Lesson, students are given a picture of the equation 63 + 8 = ___ and the corresponding base-ten blocks. “I would like you and your partner to try to find the total using the blocks.” In Lesson 11, Addition: Reinforcing place-value strategies (composing tens), Maintaining Concepts and Skills, Investigation 3, students see a picture of two large circular targets. Inside target 1 are base-ten representations for 34, 28, and 36. Inside target 2 are base-ten representations for 22, 17, and 12. “What possible totals could you get if you tossed one bean bag onto each target?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 6 out of 12, which is approximately 50%.

• The approximate number of lessons devoted to major work, or supporting, major work of the grade is 100 out of 144, which is 69%. 

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 112 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 1 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, Data: Reviewing yes/no graphs, Student Journal, Step In, page 36, connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.) to the major work of 1.OA.8 (Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = __ - 3, 6 + 6 = __.) “Complete this equation to show how many more students have been to a farm than those who have not been to a farm. __ - __ = __.”

• Module 7, Lesson 11, Time: Reading and writing half-past the hour (digital), Student Journal Step Up, page 275, connects the supporting work of 1.MD.3, (Tell and write time in hours and half-hours) to the major work of 1.NBT.1 (Read and write numbers to 120). Students tell and write time in hours and half-hours using analog and digital clocks. Question 2b, students are shown a digital clock showing 10:30 as the time. “Write each time in words.”

• Module 8, Lessons 10-12 connect the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.) In Lesson 10, Data: Recording in a tally chart, Student Journal, Step Up, page 309, Question 3, students are given a tally chart with pictures of buttons that are a square, a triangle, and a circle. They count how many of each shape, complete the tally chart, and use it to answer questions. “b. How many buttons are shaped like a square or a triangle? c. How many buttons are shaped like a triangle or circle? d. How many more buttons are shaped like a circle than a square?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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:

• Module 2, Lesson 6, Adding: Using the commutative property, Teaching the lesson, Lesson notes, students write and solve equations within 20 (1.OA.C) while using the commutative property (1.OA.B).

• Module 5, Lesson 1, Addition: Introducing the double-plus-1 strategy, Teaching the lesson Lesson notes students write and solve equations within 20 (1.OA.C) while using the commutative property  (1.OA.B).

• Module 6, Lesson 4, Subtraction: Introducing the think-addition strategy (count-on facts), students subtract, Teaching the lesson, Lesson notes, (1.OA.D) and use the missing addend to find the difference (1.OA.B).  

• Module 7, Lesson 7, Subtraction: Introducing the think-addition strategy, Teaching the lesson, Lesson notes, students subtract to find the missing numeral (1.OA.D) then complete the addition facts (1.OA.B).

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

• Module 3, Lesson 11, Length: Counting non-standard units to measure, Teaching the lesson, Lesson notes, students use various objects to identify lengths (1.MD.A). There is a missed connection to 1.NBT.A where students count to 120.

• Module 7, Lesson 10, Time: Introducing half-past the hour (analog), Teaching the lesson, Lesson notes, students identify half past on an analog clock (1.MD.B), a missed connection to 1.G.A where students can view the hour hand as partitioning the circle into halves i.e. half past.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 1st 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 2, Lesson 1, Addition: reviewing concepts, Lesson Notes connect 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.), 1.OA.8 (Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.), and 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.) to Kindergarten standards (K.CC.1 and  K.CC.2,  K.OA.1 and K.OA.2) “In Lesson K.10.4, students use the technique of starting with the greater number and counting on the lesser number, regardless of the order presented in the addition fact. In this lesson, (2.1), students review the concepts of add to and put together addition.”

• Module 10, Lesson 10, 3D objects: Identifying and sorting objects, Lesson Notes connect 1.G.1 (Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes) to the work from kindergarten (K.G.3). “In Lesson K.9.6, students compare and sort 2D shapes and 3D objects. In this lesson (10.10), students examine some features of basic 3D objects.”

• Module 11, Mathematics, Focus, Coherence table “identifies the prerequisite standards and learning targets needed for Grade 1, Module 11.” Specific Lessons, Standards, and Learning Targets from previous grades are listed. For example, “Lesson 10.4, Standard K.OA.A.1, Learning Target: Represent addition situations”. 

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, 2D Shapes: composing shapes, Lesson Notes connect 1.G.2 (Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape) to the work of grade 2 (2.G.1). “In this lesson, students join 2D shapes together to make and name new shapes. In Lesson 2.7.9, students are introduced to the term polygon to describe a closed 2D shape that has only straight sides.”

• Module 7, Mathematics Overview, Coherence, “Lessons 7.1-7.6 focus on reading, writing and representing three-digit numbers to 120.” This “serves as a foundation for representing three-digit numbers to 999 (2.1.5-2.1.8).”

• Module 9, Lesson 12, Addition: Solving word problems, Lesson Notes connect 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten) to the work of grade 2 (2.NBT.7, 2.NBT.9). Lesson Notes, “In this lesson, students choose from a range of materials to solve problems that involve addition. In Lesson 2.9.1, students extend the count-on strategy to add two-digit multiples of ten to three-digit numbers.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices across the year and they are often explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, alongside the learning targets or embedded within lesson notes.

MP1 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Lesson 8, Number: Working with position, Student Journal, Step Up, page 27, students make sense and persevere in solving a word problem involving number position between 1 and 20. “Three friends collect baseball cards. Felipe has one more card than Samantha. Jamal has one fewer card than Felipe. How many cards could each person have?”

• Module 3, Lesson 8, Number: Solving Puzzles, Lesson Notes, Step 3 Teaching the Lesson, students make sense of a number puzzle and persevere in solving it. The teacher is instructed to project a slide with the following word problem: “I am a two-digit number. My tens digit is greater than my ones digit. My number ends with a 7. What number could I be?” “Project slide 1, as shown. Read the clues and repeat each clue slowly. Then ask the problem-solving prompts below: What information do we know? How can it help us to solve the problem? What do we need to find out? What could you use to help solve the problem?

• Module 7, Lesson 9, Subtraction: Reinforcing all strategies, Step 3 Teaching the lesson, students make sense of problems involving subtraction and persevere in solving them. In small groups, students are given word problem cards. The teacher asks “students to discuss a solution plan, then follow it to find the solution. Help them make sense of their problem by discussing the points below: How would you describe what is happening in your own words? What strategy do you think would be helpful?”

• Module 9, Lesson 1, Addition: Extending the count-on strategy, Student Journal, page 321, students “make sense of count on addition problems and persevere in solving them”. Students use a number track from 84 to 94 to solve, “Valentina has 87 cents. Noah has 2 cents more than Valentina. Mary has 3 cents more than Noah. Ryan has 2 cents more than Mary. How much money does Ryan have? ___ cents” “If some students have difficulty, have them restate the problem in their own words to ensure understanding.”

MP2 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 2, Lesson 1, Addition: Reviewing concepts, Step 3 Teaching the Lesson, students reason quantitatively and abstractly as they decontextualize addition problems using connecting cubes. “Read the problem to the students. Ask, How could you use your cubes to show the addition in this problem? Read the problem again, and allow time for the students to model the problem using their connecting cubes. Then say, Turn to the student on your left and talk about how you used the cubes to show the problem. After, ask a few students to give the total and explain their thinking. Highlight examples where an addition equation is provided as part of the explanation. Repeat for the remaining two problems (slides 5 and 6). (MP2)”

• Module 5, Lesson 3, Addition: Introducing the doubles-plus-two strategy, Step 3 Teaching the lesson, students reason abstractly and quantitatively as they write equations to match domino addition facts. “Project slide 1 and ask, What do you see on this card? (Dot arrangements, numbers.) How can you figure out the total? (Use a strategy, or count the dots.) What double will help you? (Double 4.) Invite individuals to describe their thinking. Project slide 2 to support the thinking that begins with double 4. As a student describes their thinking, project slide 3 to reinforce the thinking “4 plus 6 is double 4 add 2 more.” Ask, What addition fact helps us figure out the total? What addition fact can we write? What turnaround fact can we write? Have individuals write the facts 4 + 4 = 8, 4 + 6 = 10, and 6 + 4 = 10 on the board and relate each to the thinking above (MP2). Repeat the activity with 6 + 8 (slides 4 to 6).”

• Module 8, Lesson 2, Addition: Using the associative property, Step 3 Teaching the lesson, students reason abstractly and quantitatively when they reason about the quantities in addition problems and how they are related, then represent them symbolically. Students make three different colored trains out of connecting cubes. The teacher asks, “How many cubes are in each train? How many cubes are there if the three trains are joined together? How do you know? What equation can we write to show the three numbers?”

• Module 10, Lesson 1, Subtraction: Writing related facts, Step 4 Reflecting on the lesson, students contextualize and decontextualize as they write word problems and equations to match subtraction situations. Students view the big book, How Many Legs?, and “create various pictures using the animals. Encourage students to create stories to match the pictures and write the related subtraction facts (MP2).”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to meet the full intent of MP3 over the course of the year as it is explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, and alongside the learning targets or embedded within lesson notes.

Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments. In some lessons, teachers are provided questions and sentence stems to help students critique  the reasoning of others and justify their thinking. Convince a friend, found in the Student Journal at the end of each module and Thinking Tasks in modules 3, 6, 9, and 12, provide additional opportunities for students to engage in MP3. 

Students engage with MP3 in connection to grade level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Module 5, Student Journal, page 195, Convince a friend, students construct a viable argument as they compare place value for two digit numbers. “Nadia says 29 is greater than 32 because 9 is greater than both 3 and 2. Is she correct? Show your thinking.”

• Module 7, Lesson 4, Number: Writing numbers and number names to 120, Step 4 Reflecting on the work, students construct viable arguments when they use base-ten blocks or pictures to justify their thinking about the value and representation of three-digit numbers. Given the numbers 117 and 107, the teacher asks, “How are these numbers the same? How are they different? Which number is greater? How do you know?” The teacher encourages “students to use base-ten blocks or draw pictures of base-ten blocks on the board to justify their thinking (MP3). Ask other students to respond using sentence stems such as: I agree/ disagree because ... , I don’t understand …, I figured it out by …”

• Module 9, Lesson 11, Addition: Reinforcing place-value strategies (composing tens), Student Journal, page 351, Step Ahead, students construct viable arguments and critique the reasoning of others as they analyze an error in a two-digit addition problem. Students are given 27 + 14 = 311 with a picture of 3 base-ten ten rods and 11 unit cubes. “Jacinta added these two groups. Write the correct total. Then talk about the mistake that was made with the student beside you.”

• Module 10, Student Journal, page 395, Convince a friend, students construct viable arguments and critique the reasoning of others as they reason about addition and subtraction. A picture includes a ten frame with 7 counters on the frame and 3 counters off the frame. “Chloe says she sees 7 + 3 = 10. Marvin says he sees 10 - 3 = 7. Who do you agree with? Show your thinking.”

• Module 11, Lesson 1, Subtraction: Introducing the think-addition strategy (make-ten facts), Step 3 Teaching the lesson, students construct viable arguments and critique the reasoning of others as they reason about and solve subtraction equations. “Project the equation 15 - 9 = __ and the number track (slide 7). Instruct students to solve the problem using think-addition and make-ten strategies. . . Encourage students to listen attentively to others' answers and strategies. Prompt critique (MP3) with questions such as: Do you agree with the strategy that (Maka) used? Why or why not? Does anyone need (Maka) to explain something they heard in (his) answer? How is your strategy the same as (Maka’s) strategy? How is it different?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within lesson notes.

MP4 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 2, Lesson 4, Addition: Reinforcing the count-on strategy, Student Journal, page 52, Step In, students model with mathematics as they reason about addition facts. “There are 6 pennies in the purse and some outside the purse. How could you figure out the total number of pennies? What addition fact could you write?”

• Module 4, Lesson 3, Subtraction: Writing equations, Step 3 Teaching the lesson, students model with mathematics as they create and model subtraction stories. “Organize students into small groups and distribute the resources. Explain that each group is going to create and solve their own Cupcake Capers story, using one of the following: the Cupcake Capers online tool, concrete materials like connecting cubes, paper to draw pictures, or by acting out the story (MP4). Afterward, invite each group to present their subtraction story to the class, highlighting the tool or strategy they used to solve the problem, and how it was modeled (MP4).”

• Module 7, Lesson 3, Number: Writing numbers and number names to 120 (without teens), Step 3 Teaching the lesson, students model mathematics as they “compare the different models they have used and recognize that they all represent the value in each place of a three-digit number.” “Distribute the expanders and markers to each group. Have them choose a number between 101 and 110, then represent their number with base-10 blocks, on the expander, and in words.” The teacher says, “You represented your number in three different ways. How are they the same? How are they different? Students should notice that each model represents the number of hundreds, tens, and ones in their number. (MP4)”

• Module 8, More math, Problem solving activity 4, Word problems, students model with math as they represent addition and subtraction word problems.“ Directions state, “Project slide 1 and read the word problem with the students. Ask, what do we need to solve the problem? Is there information we do not need? How could you show your thinking? (For example, act it out, draw a diagram, or write an equation.”  Question d, “Amber has 3 green beads, 4 blue beads, 4 red beads, and 5 white beads. She wants to put the beads into two groups so they each have an equal number of beads. How many of each color could Amber put into each group?”

MP5 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to identify and use a variety of tools or strategies, working with the support of the teacher and independently, throughout the modules to support their understanding of grade level math. Examples include:

• Module 1, Lesson 1, Number: Representing quantities (up to ten), Step 2 Starting the lesson, students use appropriate tools in order to represent five. “Organize students into pairs to explore the different ways they can represent five. Allow them to choose from a variety of hands-on resources to support their thinking (MP5). Invite pairs of students to share and model their answers. Record the different representations around the numeral 5 on the board. Connect each representation to the numeral to form a number web.”

• Module 7, Lesson 7, Subtraction: Introducing the think-addition strategy (near-doubles facts), Student Journal, page 262, “students choose between the think-addition strategies of doubles-plus-1 and doubles-plus-2 to solve subtraction problems, and choose math tools to support their thinking”. Question 1b, students are given a picture of a domino with 5 dots on one side with the number 5 above it and no dots on the other side with a fill-in-the-blank space above it. The total 12 is written below the domino as is ___ + 5 = 12. Step 3 Teaching the lesson, “Inform students that they can use math tools such as connecting cubes, counters, ten-frames, and number tracks to support their thinking (MP5).”

• Module 10, Lesson 3, Subtraction: Writing related equations (multiples of ten), Step 3 Teaching the lesson, students select tools to solve a real world problem involving subtraction. On slide 6, students see pictures of snacks with price tags attached: apples 20¢, pear 10¢, banana 30¢, orange 40¢, and nuts 50¢, “I have 50 cents. If I buy the ____. How much money will I have left? Encourage students to select a tool they could use to solve the problem. If necessary suggest things such as a hundred chart, base-10 blocks, dimes, or their fingers. (MP5) Students may apply counting or place-value strategies and figure out the answer in their head.”

• Module 11, More math, Problem solving activity 4, Word problems, students choose different strategies as tools to solve real world problems involving addition and subtraction. Slide 1, “Natalie has 15 balloons. Some of the balloons are yellow and some of the balloons are red. How many of each color might Natalie have?” The teacher asks, “How could you show your thinking? (For example, act it out, draw a diagram, or write equations.)”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. MP6 is explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes. 

Students have many opportunities to attend to precision in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 4, Lesson 12, 2D Shapes: Composing shapes, Student Journal, page 153, Step Up, Question 2, students attend to the precision of mathematics by accurately tracing shapes to create new shapes. “2) Choose 3 different pattern blocks. a) Join them. Then trace around them. b) How many sides does your new shape have?”

• Module 5, Lesson 10, Number: Introducing comparison symbols, Step 3 Teaching the lesson, students attend to the precision of mathematics by accurately using mathematical symbols when comparing two-digit numbers. “Write the numbers of cubes on the board with the great number first, then with the smaller number first. Allow space to write is less than or is greater than between each pair of numbers. Ask, What words can we write between the numbers to describe how they compare? Encourage students to suggest writing is greater than and is less than. Write the appropriate phrase between each pair of numbers. Say, We can write symbols instead of writing all those words. Does anybody know the symbols that we can write? Write the matching symbolic sentence below each word sentence, for example, 8 > 5 and 5 < 8. Ask, What is different about the two symbols? Bring out that the symbols point in opposite directions. (MP6)”

• Module 8, Lesson 10, Data: Recording in a tally chart, Step 3 Teaching the lesson, students attend to precision when they “accurately record data and interpret a tally chart.” Pairs of students collect five to ten crayons. The teacher says, “I want you to count the total number of crayons you have and represent them using tally marks. If students are struggling, discuss the points below (MP6): How many crayons do you have? How many tally marks would you draw to show one crayon? Two crayons? What does a tally mark look like? How many tally marks are shown in each group? (5.)”

Students have frequent opportunities to attend to the specialized language of math in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Lesson 5, Number: Writing teen number names, Step 4 Reflecting on the work, students attend to the specialized language of mathematics by defining a teen number. Discuss the students’ answers to Student Journal 1.5. Ask the students to share and justify the number names they colored for Step Ahead. Ask, Why did you not color the word twenty? Why did you not color the word eight? How did you decide what numbers to color? How would you tell someone what a teen number is? Organize students into pairs to discuss the questions. Then invite students to share their definitions with the class. (MP6) Compare the varying definitions. In context, many students will consider a teenager as somebody whose age ends in teen, while those who adopt a more mathematical standpoint may consider a teen number as a number that is represented with one ten and some more ones. Welcome each of the perspectives as they are each socially or mathematically correct.” 

• Module 2, Lesson 8, Addition: Introducing the doubles strategy, Step 3 Teaching the lesson, students engage in the specialized language of mathematics by accurately reading a doubles fact. “Open the Addtron online tool. Invite a student to drag pictures onto the work area to show a double. Have the class say the double using correct language and without counting. (MP6) For example, “Double five is ten,” or “Five add five is ten.” Then ask another student to use the writing tool to write the doubles fact in the white panel. Repeat for different doubles.”

• Module 3, Module overview, Vocabulary development, students can attend to the specialized language of math as teachers are provided a list of vocabulary terms. “The bolded vocabulary below will be introduced and developed in this module. These words are also defined in the student glossary at the end of each Student Journal. A support page accompanies each module where students create their own definition for each of the newly introduced vocabulary terms. The unbolded vocabulary terms below were introduced and defined in previous lessons and grades. Addition, balance, cents, clock, coins, corners, count on, dime, double, equals, equation, fact, fewer, hour, length, less, longer than, longer, longest, measure, minute hand, more, number name, number, ones, order, penny, shape, shorter, shortest, sides, smallest, subtract, tens, total.” Students are provided with a Building Vocabulary support page. The page includes: Vocabulary term (the bolded terms), Write it in your own words, and Show what it means.

While there are examples of the intentional development of MP6, Attend to precision, throughout materials, there is also evidence of imprecise language or content connections that are not grade-specific. Example include:

• Module 9, Lesson 3, Addition: Exploring patterns (hundred chart), Step 4 Reflecting on the work, the term “turnaround” is used for the commutative property and “add” is used in place of the word, “plus”. “Write 2 + 46 = ___ on the board and ask, How could you figure out the total? As students explain their strategy, encourage thinking that uses the turnaround. Ask, What is the turnaround for 2 add 46? What is the total?”

• Module 11, Lesson 9, Money: Relating all coins, Step 3 Teaching the lesson, connects to grade 2 content. “MP6 - when students accurately describe the trade between coins”. The teacher asks, “How many nickels could you trade for one quarter? (5) Have each group count out 25 pennies to represent the value of one quarter. The 25 pennies are then split into groups or stacks of five to determine the equivalent number of nickels. The same reasoning is then applied to figure out the number of nickels that can be traded for one dime. (MP4 and MP6)” This connects to 2.MD.8, solving word problems involving money.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices throughout the year and they are often explicitly identified for teachers in several places:  Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes.

MP7 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:

• Module 1, Lesson 6, Number: Representing teen numbers, Step 3 Teaching the lesson, students look for and make use of structure while representing teen numbers on ten-frames. “Distribute a ten-frame and 20 counters to each pair. Ask, How many counters do you need to fill the frame? How can you show a number that is greater than ten? Establish that 10 counters fill the frame and that loose counters can be placed beside the frame to show a number that is greater than ten. Say, Use the frame to show 14. What does it look like? How many counters are on the frame? How many counters are beside the frame? Reinforce the language of 10 and 4 more. Repeat for 17 and 12. (MP7)”

• Module 2, Lesson 9, Addition: Reinforcing the doubles strategy, Student Journal, page 68, Step Up, Problem 1a, students look for and make use of structure when completing problems using the doubles strategy. “Use the same strategy to figure out these.” Students are given a picture of 2 identical bead strings with the bead segmented into 5 and 2 beads. “Double 5 is ___. Double 2 is ___. So Double 7 is ___.”

• Module 9, Lesson 7, Addition: Introducing place-value methods, Student Journal, page 338, Step Up, Question 1a, students look for and make use of structure as they “use known facts and place value thinking to solve addition problems.” Students see a picture of the numeral 50 and 5 base-ten rods and the numeral 20 and 2 base-ten rods. “Add the two groups. Then write the matching equation. Use blocks to help you.” Reflecting on the work, “Discuss the students’ answers to Student Journal 9.7. Encourage students to explain their thinking. Ask, Is it easy to add tens? Why? Prompt several responses such as “Adding 50 and 20 is just like adding 5 and 2, because 50 is 5 tens and 20 is 2 tens.” (MP7)”

• Module 10, Lesson 4, Subtraction: Writing related addition and subtraction facts, Step 2 Starting the lesson, students look for and make use of structure when they “use the structure of the same parts and total to write related addition and subtraction facts.” Students are given a picture of a domino with 6 dots on one side and one dot on the other side, the teacher asks, “What two addition facts can we write to show the total of these two numbers? (6 + 1 = 7 and 1 + 6 = 7.) What two subtraction facts can we write to match? (Yes. Either 7 - 1 = 6 and 7 - 6 = 1.) What do you notice about all four facts? (The same numbers are used in different positions.) (MP7)”

MP8 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade level math concepts. Examples include:

• Module 4, Lesson 2, Subtraction: Reviewing concepts (take from), Step 2 Starting the lesson, students look for and express regularity in repeated reasoning by counting orally forward and backward. “Distribute one numeral card to each student. Say, Today we are going to play a game called I have, who has? I will start and when you hear a question that your card answers, you stand up and continue the game. Ready? I have (19), who has 18? Prompt the student with the card for 18 to stand up and repeat the question for their number. Afterward, have students exchange cards, and start the game with a different number, such as 9 and counting forward. Repeat as time allows (MP8)”

• Module 6, Lesson 5, Subtraction: Reinforcing the think-addition strategy (count-on facts), Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning by using the known count-on strategy to find the missing part in a subtraction situation. “Write the two equations that match the card on the board, discussing the think-addition strategy as 4 add what makes 5. Point out that the unknown number can be one of the parts and does not have to be the total. Invite the students to talk about which strategy they would use to solve the problem. Encourage students to share their thinking with the class. Repeat the discussion for slides 3 to 5. (MP8)”

• Module 7, Lesson 10, Time: Introducing half-past the hour (analog), Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning when they “make connections between half-past the hour shown on an analog clock and one-half represented with an area model (circle).” Students view the Flare Clocks online tool showing 4:00. The teacher asks, “Where would the minute hand point if it went halfway around the clock? What do you think that would tell us about the time? Prompt students to discuss and describe the position of the minute hand when it points at the 6, as halfway between one on-the-hour time and the next on-the-hour time.” The teacher asks, “When have you heard the words half and one-half before? Encourage and highlight responses that refer to one-half as one of two equal parts that make one whole. Students who make connections between concepts like this are demonstrating flexible thinking. (MP8)”

• Module 12, Lesson 5, Subtraction: Exploring patterns, Student Journal, page 447, Step Up, Questions 2a-b, students look for and express regularity in repeated reasoning when they “extend subtraction patterns to find unknowns in equations.” Directions state, “Think about the numbers between 1 and 50. a. Write all the numbers that have 6 in the ones place. b. Write the numbers that are 2 less than the numbers you wrote.” Step 4 Reflecting on the work, the teacher asks, “What is the answer when you subtract 2 from 11? What do you think will be the answer when you subtract 2 from 21? What will be the answer if you subtract 2 from 61? What happens in the ones place? What happens in the tens place? (MP8)”