K-2nd Grade - Gateway 1

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

According to the Assessment Guide, summative assessments, including Course-Level, End-of-Module, End-of-Topic, and Performance Tasks are designed to measure mastery of concepts and proficiency in standards. These are present across Grades K-2 and consistently align with grade-level content, providing multiple opportunities to assess student understanding throughout the year.

The materials for Kindergarten contain five End-of-Module assessments, twelve End-of-Topic assessments, twelve Performance Tasks, and one End-of-Year assessment. An example of an End-of-Topic Assessment includes:

• Grade K, Topic 5, End-of-Topic Assessment, Question 7, “Ben has 9 cherries. Then, he eats 6 of the cherries. How many cherries does Ben have now?” Students are prompted to complete the sentence “Ben has ____ cherries now” and to draw a model representing the story. (K.OA.2)

The materials for Grade 1 contain five End-of-Module assessments, twelve End-of-Topic assessments, twelve Performance Tasks, and one End-of-Year assessment. An example of an End-of-Topic Assessment includes:

• Grade 1, Module 3, Topic 5, End-of-Topic Assessment, Question 10, “Write the unknown number to complete the equation. 9+6= _____” (1.OA.6)

The materials for Grade 2 contain five End-of-Module assessments, thirteen End-of-Topic assessments, thirteen Performance Tasks, and one End-of-Year assessment. An example of an End-of-Topic Assessment includes:

• Grade 2, Module 2, Topic 5, End-of-Topic Assessment Question 2, “Draw jumps on the number line to add. 88+4= _______” A number line is provided with points ranging from 86 to 94. (2.MD.6)

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meets expectations for including assessment information that indicates which standards are assessed. The materials identify mathematical practices for the assessment items within each grade level Assessment Guide, titled Habits of Minds.

Formal assessments, including End-of-Module, End-of-Topic, and End-of-Year Assessments, consistently align with grade-level content standards. Assessment Blueprints in the Assessment Guide include a chart with columns describing the item number, CCSS, item type, DOK, recommendations for EOY Activities, and connections to learning in a future grade level. For example:

• Grade K, Module 3, End-of-Module Assessment, Question 7, “Draw a picture in the box to model the sentence. 5 take away 2 is 3.” (K.OA.1)

• Grade 1, Module 4, End-of-Module Assessment, Question 5, “Write and solve an equation that represents the story problem. Aleki has some pet hamsters. They have 7 brown, 3 white, and 5 black hamsters. How many hamsters does Aleki have in all? (1.OA.2)

• Grade 2, End-of-Year Assessment, Question 22, “Art class starts at the time shown on the clock.  What time does art class start? a. 1:20 P.M., 1:40 P.M., 2:08 P.M., 2:40 P.M.”  There is a picture of an analog clock showing the time 1:40.  (2.MD.7)

The materials refer to the Standards for Mathematical Practice (SMPs) as “Habits of Mind”. The materials map each “Habit of Mind” to a corresponding SMP, and an alignment chart shows where students are expected to reflect on these habits. The SMPs appear primarily in the Re-Engagement Lessons within the Mindset Reflections. For example: 

• Grade K, Module 3, Topic 5, Lesson 11 identifies MP1, MP3, and MP4.

• Grade 1, Module 1, Topic 2, Lesson 4 identifies MP3, MP6, and MP7. 

• Grade 2, Module 4, Topic 9, Lesson 4 identifies MP2 and MP6.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative assessments occur at the lesson level through structures such as Ongoing Assessments, Purposeful Questions, Reflect and Summarize, My Just Right Problem, Mindset Reflections, Ready Check Assessments, and Snapshot Assessments. Summative assessments include End-of-Topic Assessments, End-of-Module Assessments, and Performance Tasks that capture student thinking through writing, illustrating, demonstrating, and modeling. These assessments provide opportunities for students to demonstrate understanding of grade-level content standards through a variety of item types, including choice tables, data displays, extended response, fill-in-the-blank, graphing, highlighting, hotspot, label images, matching, multiple choice, multiple select, number line, shading, and short answer.

Examples include: 

• Kindergarten, Middle-of-Year Assessment, Question 19, and Module 5, Topic 11, End-of-Topic Assessment, Questions 1 and 6 develop the full intent of K.G.2 (Correctly name shapes regardless of their orientations or overall size). In this question, students answer Question 19, “What is the name of this shape? a. Circle, b. Square, c. Triangle,” with a picture of a square provided. Students continue working toward the full intent of this standard in Topic 11, End-of-Topic Assessment, Questions 1 and 6. In Question 1, students determine which shape is a triangle from three choices. In Question 6, students circle a shape that has six corners, with the shapes shown in different sizes.

• Grade 2, Module 4, Topic 9, End-of-Topic Assessment, Question 9, develops the full intent 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.) “A pet store sells 7 goldfish on Monday and some more goldfish on Tuesday. The pet store sells a total of 19 goldfish on Monday and Tuesday. How many goldfish does the pet store sell on Tuesday? Use words, pictures, or numbers to explain your thinking.”

While the assessments regularly address the full intent of grade-level content standards, they do not consistently provide opportunities for students to demonstrate the full intent of the course-level practices across the series. Materials do not include opportunities for students to demonstrate the full intent of MP3 or MP5 across the assessments. Examples include:

• Kindergarten, The Performance Tasks, Reflect activities, and End-of-Topic Assessments do not require students to construct mathematical arguments, critique the reasoning of others, perform error analysis of student work, justify strategies, evaluate peer arguments, or create conjectures. In Topic 10, Module 5, Lesson 6 Reflect students circle which equation is correct on a ten frame and discuss strategies for adding and subtracting within five, but they do not justify their reasoning, critique another student’s explanation, or determine whether another student’s argument makes sense. In Module 2, Topic 4, Lesson 2 Reflect students decide whether Ana, Leo, or both are correct when comparing the banana and the blueberry, but they do not analyze or respond to a student’s reasoning, explain why a comparison is correct or incorrect, or construct arguments using measurable attributes. In Module 5, Topic 11 Performance Task students draw and compare two towers made from three blocks, but they do not analyze another student’s work, identify or correct an error, justify their conclusions, or engage in discourse that requires constructing or critiquing mathematical arguments.

• Kindergarten, The Performance Tasks, Reflect activities, and End-of-Topic Assessments do not require students to choose appropriate tools or strategies, recognize the insight or limitations of different tools, use technological tools to deepen their mathematical understanding, or decide whether to use tools at all. In Module 3, Topic 5, Lesson 6, Reflect, students listen to a story and are told, “Draw a model to answer the question,” and teachers “Allow students to access manipulatives to model the problem before representing it with pictures” and “Remind students they can represent the ducks in the separating story with circles instead of drawing multiple ducks,” but students do not choose tools or compare the usefulness or limitations of different tools. In the Module 3, Topic 9 Performance Task students use Number and Symbol Cards and a printed number path to create and show equations, and the only materials available are “Number and Symbol Cards” which do not support tool choice or analysis. In the Module 1, Topic 6 Performance Task students draw grapes and write equations using only paper and pencil, and they do not select or compare tools. In the Module 5, Topic 12 End-of-Topic Assessment students match equations to ten-frames, show numbers on dominoes, and complete pictures of counters, but they do not choose tools or decide whether to use tools at all. In the Module 4, Topic 9 End-of-Topic Assessment students count objects, identify the next number, and draw jumps on a printed number path, but they do not select tools or engage in tool-based decision-making. 

• Grade 1, The Performance Tasks, Reflect activities, and End-of-Topic Assessments do not require students to construct mathematical arguments, critique the reasoning of others, perform error analysis of student work, justify strategies using models or drawings, evaluate peer reasoning, or create conjectures as outlined in the MP3 criteria. In Module 2, Topic 5, Lesson 1 Reflect students use colored rods to model an addition equation with a sum of five and share how they have used the rods in the past, but they do not analyze another student’s work, evaluate the correctness of an explanation, or justify their reasoning using evidence from their models. The Think-Pair-Share routine invites students to describe their experiences with the rods, but it does not require students to respond to a peer’s argument, determine whether another student’s reasoning makes sense, or ask questions to improve an argument. In Module 2, Topic 4, Performance Task students complete equations for Lila’s and Noah’s scores and represent their thinking to determine a possible target score for the second round, but the task does not provide student work to analyze or critique, require justification of strategies, or engage students in evaluating the reasoning of others. Students record their equations and find a target score, but they do not construct mathematical arguments, respond to a peer claim, or engage in discussion that would support the development of MP3. 

• Grade 1, The Performance Tasks, Reflect activities, and End-of-Topic Assessments do not require students to choose appropriate tools or strategies, recognize the insight or limitations of different tools, use technological tools to deepen their mathematical understanding, or decide whether to use tools at all. In Module 3, Topic 7, Lesson 1, Reflect, students are given “Pattern blocks, 6 triangles, 3 rhombuses, and 3 trapezoids per student” and told to “Use triangle, rhombus, and trapezoid pattern blocks to fill the shape outlines in different ways,” but they do not choose tools or compare the usefulness or limitations of different tools. In the Module 2, Topic 5 End-of-Topic Assessment students model an addition equation using colored rods provided on the page, but they do not select a tool or decide whether to use tools at all. In the Module 3, Topic 7 Performance Task students fill outlines with pattern blocks and trace the blocks to show their work, but they do not choose among tools or engage in tool-based decision-making. In the Module 2, Topic 6 Performance Task students measure a drawing of a tree using “a set of 15 unit cubes,” limiting them to a single fixed tool with no opportunity to select or compare tools. In the Module 3, Topic 7 End-of-Topic Assessment students use pattern block shapes and printed grids that are already embedded in the tasks, but they do not choose tools or analyze tool effectiveness. 

• Grade 2, The Performance Tasks, Reflect activities, and End-of-Topic Assessments do not require students to choose appropriate tools or strategies, recognize the insight or limitations of different tools, use technological tools to deepen their mathematical understanding, or decide whether to use tools at all. In Module 2, Topic 4, Lesson 4, Reflect, students are told to “Use your centimeter ruler to answer each question” and complete tasks such as “Determine the length of the marker in centimeters,” “Beginning at the dot, draw a line that is 8 centimeters long,” and “What is the length of the key in centimeters?” Students do not choose tools, as teachers must “Ensure students have a ruler or a benchmark object” to complete the assignment. In the Module 4, Topic 11 End-of-Topic Assessment students label number lines, complete tiling on a printed rectangle, and work with pre-drawn models, but they do not select tools or engage in tool-based decision-making. In the Module 2, Topic 4 End-of-Topic Assessment students measure objects only with a ruler as tasks direct them to “Use a ruler to measure the length,” limiting them to a single predetermined tool with no opportunity to select or compare tools. In the Module 1, Topic 3 End-of-Topic Assessment students use base-ten blocks embedded on the page to add and subtract but do not choose tools or analyze the usefulness or limitations of different tools.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide students with consistent opportunities to engage in the full intent of all Grade K-2 standards. Each lesson includes an Activate, Explore, and Reflect. Modules also include Ready Checks, which are short assessments that address the prerequisite skills students need to access the module and topic content. The data can be used to determine when and how the teacher should re-engage students as they move through the modules and topics. Student Practice Books give students additional opportunities to reinforce the knowledge and skills developed throughout the topics with extra practice problems. The Review Center in Grades 1-5 includes Spaced Review activities, which provide students with opportunities to revisit previously learned content to reinforce or prepare for upcoming content.

The Mathematical Progressions and Connections Handbook provides extensive work with module-level Mathematical Progression maps showing how standards and concepts connect across the modules in the course. Arrows illustrate how mathematical ideas in one module relate to those in others. The topic-level Mathematical Progression maps highlight the standards addressed within each topic, and arrows show how concepts build from earlier work and extend into later topics. Examples of extensive work with grade-level problems to meet the full intent include:

• Kindergarten, Module 1, Topic 1, Lesson 2, students engage with the full intent of K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20, with 0 representing a count of no objects). In Explore 2, students practice writing the numeral 2 eighteen times. In Module 1, Topic 2, Lesson 4, Student Practice Book, “Write the number that matches the number of objects.” [Students count 5 fish in a box and write the numeral 5.] In Module 5, Topic 10, Lesson 2, Student Resource Book, Question 1, Explore, states, “Draw counters to match the numeral 14. Then, complete the sentence frame. 10 ones and ___ ones is ___.” In Lesson 2 of the Student Practice Book, six questions focus on Counting 10 and Some More. For example, Question 2 states, “Circle a group of 10 ones and count the extra ones to complete each sentence frame. 10 ones and ___ ones is ___.” [A picture of 14 blue circles accompanies the task.] In Module 5, Topic 10, Lesson 5, Re-Engagement Lesson, students complete one question and participate in two center activities and games focused on Counting 10 and Some More. Students can also be assigned digital games in MATHia Adventure to continue representing a number of objects with a written numeral.

• Grade 1, Module 5, Topic 11, Lesson 6, students engage with the full intent of 1.NBT.6 (Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90, 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). In the Student Resource Book, the lesson begins with Activate, “Think about each subtraction question. Share any patterns you notice.” [Each equation is a two-digit number minus 10.] Students participate in a Think-Pair-Share and discuss the strategies they used as a class. In Explore 1, “For each equation, use base-10 blocks to model subtracting tens. Then, write an equation and model jumps on the number line.” Students work in pairs and discuss the similarities and differences between subtracting using base-10 blocks and subtracting using an open number line. In Explore 2, “Draw the number of jumps on each number line. Then complete each equation.” [Students are provided number lines aligned to equations such as 62-20=42.] Students identify the size of the jump in each equation. During Reflection, “Read the story. Then, answer each question.” This is a My Just Right Problem, in which students complete all three and self-assess the “problem that feels just right for you.” In Lesson 8, students revisit these concepts in the Re-Engagement Lesson Subtracting Tens. During Activate, “Complete the table as you follow along with your teacher.” [In a table with two rows and eight columns, the teacher writes pairs of numbers such as 33, 13; 45, 25; 86, 66; 61, 41; 27, 7. Students complete the bottom row with related subtraction patterns such as 59, 39; 92, 72; 77, 57.] Students also engage with MATHia Adventure: Zorbit’s Math Adventure for adaptive online practice with subtracting tens.

• Grade 2, Module 2, Topic 4, Lesson 1, students engage with the full intent 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 Explore 1, “First, identify your benchmark object for 1 inch. Next, select objects to measure. Then, estimate each measurement using your benchmark. Lastly, determine each measurement using your inch ruler.” Sample objects include a paperclip, an eraser, and a thumb. This task develops a concrete visualization of an inch before using a ruler to measure. In Topic 4, Lesson 5, Explore 2, Questions 1–9 state, “Determine which unit you would use to measure each real object.” Examples include a fence, a stapler, a tree, and a coin. The options are centimeters or meters. This activity develops the standard by having students select the more efficient unit to measure the length of different objects. In Topic 4, Lesson 9, Explore 1, “Use the recording sheet to record each jump in your group to the nearest whole inch and centimeter.” In groups of up to six, students measure their long jumps with a tape measure marked in both inches and centimeters and record the results.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 75 percent of instructional time to the major clusters of the grade:

In Grade K:

• The approximate number of modules devoted to the major work of the grade (including assessments) is 5 out of 5, approximately 100%. 

• The number of topics devoted to the major work of the grade (including assessments) is 9 out of 12, approximately 75%. 

• The number of lessons devoted to major work of the grade (including assessments) is 124 out of 163, approximately 76%. 

• The number of instructional days devoted to major work of the grade, including assessments, is 124 out of 163, approximately 76%. 

In Grade 1:

• The approximate number of modules devoted to the major work of the grade (including assessments) is 4 out of 5, approximately 80%. 

• The number of topics devoted to the major work of the grade (including assessments) is 9 out of 12, approximately 75%. 

• The number of lessons devoted to the major work of the grade (including assessments) is 126 out of 166, approximately 76%. 

• The number of instructional days devoted to major work of the grade (including assessments) is 126 out of 166, approximately 76%.

In Grade 2:

• The approximate number of modules devoted to the major work of the grade (including assessments) is 4 out of 5, approximately 80%. 

• The number of topics devoted to the major work of the grade (including assessments) is 9 out of 13, approximately 69%. 

• The number of lessons devoted to major work of the grade (including assessments) is 124 out of 166, approximately 75%. 

• The number of instructional days devoted to major work of the grade (including assessments) is 124 out of 166, approximately 75%.

An instructional day analysis across Kindergarten through Grade 2 is most representative of the instructional materials, as the lessons include major work, supporting work connected to major work, and embedded assessments. As a result, approximately 76% of the materials in Kindergarten, 76% of the materials in Grade 1, and 75% of the materials in Grade 2 focus on the major work of the grade.

The materials reviewed for ClearMath Elementary Kindergarten through 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 that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers in their Mathematical Progressions and Connections handbook, on the Course-Level Coherence Map. Examples of a connection include:

• Grade K, Module 2, Topic 4, Lesson 5, Explore 2, How Do the Groups Compare, connects the supporting work of K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count) to the major work of K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies). Directions state, “Write the number of objects in each group. Then, circle the group that has more.” There is a 2-column chart with large shapes (3) and small shapes (4).

• Grade 1, Module 1, Topic 1, Lesson 4, Student Practice, Question 4, 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 are in each category, and how many more or less are in one category than in another) to the major work of 1.OA.2 (Solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). Directions state, “Answer each question about the animals Nia saw on a nature hike. Nia saw ______ animals in all.” A chart is provided with deer, raccoons, and birds on a bar graph.

• Grade 2, Module 2, Topic 4, Lesson 8, Explore 2, Question 1, connects the supporting work of 2.MD.5 (Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem) 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). Directions state, “Read each question. Then, solve by using a bar model. John David runs 67 yards. Emma runs 83 yards. How many more yards does Emma run than John David?” Two bar models are provided, one with a complete bar and one with a partial bar. Students label the bars, then write and solve the matching equation.

The instructional materials for ClearMath Elementary Kindergarten through 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. 

Connections among the major work of the grade are present throughout the materials where appropriate. These connections are listed for teachers in the Mathematical Progressions and Connections section of the Course-Level Coherence Map, and they may also appear in one or more parts of a typical lesson (Activate, Explore, Additional Centers, or Reflect). Examples of a connection include:

• Kindergarten, Module 2, Topic 3, Lesson 3, Student Practice, connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.CC.B (Count to tell the number of objects). Students apply their understanding of number names and the count sequence to make sense of counting to tell the number of objects. For example, Question 1 asks students to draw objects to represent the number 5. In Question 4, students are asked to “Fill in each domino with the numeral that matches the quantity.” The domino in Question 4 has four dots.

• Grade 1, Module 1, Topic 2, Lesson 9, Reflect: Birds in the Yard, connects the major work of 1.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 1.OA.B (Understand and apply properties of operations and the relationship between addition and subtraction). Students read the story, “Abby counted birds in her yard this morning. She counted 5 robins and 2 sparrows.” Students then answer three questions: “1) How many birds did Abby count in all? 2) What equation can you write to show how many birds Abby counted? Explain your thinking. 3) Abby also counts 4 doves. How many birds has Abby seen now?”

• Grade 2, Module 5, Topic 13, Lesson 10, Reflect and Summarize, connects the major work of 2.OA.B (Add and subtract within 20) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). Students determine which car traveled more miles. Directions state, “Determine which car traveled more miles. Show your strategy. Car A: Trip 1: 44 miles, Trip 2: 14 miles, Trip 3: 72 miles, Trip 4: 9 miles; Car B: Trip 1: 82 miles, Trip 2: 7 miles, Trip 3: 36 miles, Trip 4: 22 miles.” The strategy provided in the Student Resource Book, Volume 2, Answer Key is decomposing the four numbers, adding tens and ones, then adding the totals of tens and ones.

The instructional materials reviewed for ClearMath Elementary Kindergarten through 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.

The Teacher's Implementation Guide contains a Module Overview that identifies overall learning in the module, including fluency work and content expectations. A Topic Overview identifies specific learning within the topic, links to standards, and notes connections to both prior and future learning. In both the Module Overview and Topic Overview, a table titled “Connection to Prior Learning” and “Connection to Future Learning” is explained with narrative and example problems. For Grade K, the Topic Overviews include a chart with Content Expectations for each topic but do not include Readiness Expectations. In Grades 1 and 2, the Topic Overviews also include a chart with Content Expectations, and they additionally identify learning from prior grades as Grade K or Grade 1 Readiness Expectations. The Mathematical Progressions and Connections document supports teachers in developing their understanding of the Common Core State Standards by highlighting connections within and across grade levels. “About the Math” sections within the Module Overview, Topic Overview, and Lesson Overview extend teachers’ understanding beyond individual standards to make sense of these connections. 

An example of a connection to future grades includes:

• Kindergarten, Module 5, Topic 11, Topic Overview, highlights the connections to future grades. In this topic, students build on their knowledge of shapes by exploring three-dimensional figures (K.G.3). They use spatial reasoning to describe, compare, and analyze both two-dimensional and three-dimensional figures (K.G.4). Connection to Future Learning, “In Grade 1, Topic 1, Bar Graphs and Picture Graphs, students apply their understanding of attributes to create graphs of sorted objects.”

• Grade 1, Module 5, Topic 12, Topic Overview, highlights the connections to future grades. In this topic, students synthesize their understanding of measuring lengths with iterated units to determine the length of objects (1.MD.2) to build marble runs. They apply their understanding of adding and comparing lengths of different marble runs (1.MD.1). Connection to Future Learning, “In Grade 2, Topic 4, Measuring Length, students learn about measuring length in standard units. My estimate: ____ inches. Using my ruler: ____ inches.” A picture of a pencil with a measurement mark under it is provided.

• Grade 2, Module 2, Topic 6, Topic Overview, highlights the connections to future grades. In this topic, students apply their understanding of data collection to display graphs (2.MD.10) and use rulers to measure lengths for generating data displayed in line plots (2.MD.9). Connection to Future Learning: “In Grade 3, students will use what they learn about multiplication to create scaled picture graphs and scaled bar graphs. They will then use what they learn about fractions to create line plots with fractional measurements.” A line plot titled “Grade 2 Hand Spans” with a number line beginning with 4 and ending with 7, including the fractions \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, each whole number, is shown below this explanation.

An example of a connection to prior grades includes:

• Kindergarten, Module 1, Topic 1, Topic Overview, highlights the connections to prior grades. In this topic, students connect quantities to written numerals and begin to formalize their understanding of numbers (K.CC.4). They learn number names, practice writing numerals within five (K.CC.3), and use them to describe and order quantities. Connection to Prior Learning, “Before Kindergarten, students may have learned to rote count to time an event, such as washing their hands, playing a game, or running from one location to another.” 

• Grade 1, Module 1, Topic 2, Topic Overview, highlights the connections to prior grades. In this topic, students use addition and subtraction within 20 to solve problems (1.OA.6). They progress from representing numbers as data to representing them more abstractly (1.MD.4). They refine their addition and subtraction strategies to solve unknown-addend problems (1.OA.4). Connection to Prior Learning, “In Kindergarten, students learned to think flexibly about quantities when they composed and decomposed them in different ways.” A picture of three sets of hands with various fingers showing is included.

• Grade 2, Module 1, Topic 2, Topic Overview, highlights the connections to prior grades. In this topic, students deepen their understanding of place value to units of 100 (2.NBT.1). They compose and decompose numbers in multiple ways using hundreds, tens, and ones to represent and compare quantities (2.NBT.4). Connection to Prior Learning, “In Grade 1, students used base-10 blocks and drawings to represent 2-digit numbers with different models. They traded 10 ones for 1 ten and 1 ten for 10 ones to regroup numbers.” A picture of base-10 blocks with 10 ones and 1 ten is included. Arrows show the back and forth of regrouping tens and ones.