K-2nd Grade - Gateway 1

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

The formal assessments follow a consistent structure across grades, including Diagnostic Tasks, Topic Assessments, Online Topic Assessments (autoscorable), Parallel Topic Assessments, and Performance Tasks. Kindergarten includes thirteen Diagnostic Tasks, thirteen Topic Assessments, and thirteen Online Topic Assessments (autoscorable). Unique to Kindergarten, there are no Performance Tasks or Parallel Topic Assessments. Grade 1 includes fourteen Diagnostic Tasks, fourteen Topic Assessments, fourteen Online Topic Assessments (autoscorable), five Parallel Topic Assessments, and nine Performance Tasks. Grade 2 includes fourteen Diagnostic Tasks, fourteen Topic Assessments, fourteen Online Topic Assessments (autoscorable), seven Parallel Topic Assessments, and ten Performance Tasks. The Topic Assessments are designed in an interview-style and are available in print or online.

Examples include:

• Kindergarten, Topic 1: Counting, End of Topic Resources, Topic Assessment, Question 8, “Count Forward three more numbers. 6, 7, 8, … .” (K.CC.2)

• Grade 1, Topic 3: Comparing Numbers Within 100, Planning and Resources, Diagnostic Task, Question 1, “Which group has more? How do you know?” A group of six bowling pins and a group of four bowling pins are shown. (K.CC.6)

• Grade 2, Topic 9: Length, End of Topic Resources, Performance Task, Question 1, “Choose 2 or 3 of the measurement units you have learned about (inches, feet, yards, centimeters, and meters). Create a poster that shows what you know about measuring in those units. For example, you could show what you know about the answers to these questions: Why do you measure in units? When do you measure in each unit? How do you estimate lengths in units? How do you measure in each unit?" (2.MD.1, 2.MD.3)

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Assessment Item Correlations documents include item analysis charts for all formal assessments in the program (Diagnostic Tasks, Topic Assessments, and Performance Tasks). Each chart contains several key components: the item number for reference, a brief description of the mathematical content assessed (“Math Content” column), the aligned Common Core State Standard (“CCSS” column) with its cluster designation, the Depth of Knowledge (“DOK” column) level indicating the required cognitive complexity (Levels 1–3), and the Standards for Mathematical Practice (“SMPs” column) that students engage in while solving the problem. 

Examples include:

• Kindergarten, Topic 4: Comparing Quantities, End of Topic Resources, Topic Assessment, Question 3, “These questions are designed for you to share with your students orally. There is no page for students to view. Jeremy counted the apples: 1, 2, 3, 4, 5. Liam counted the bananas: 1, 2, 3, 4. Are there more apples or bananas?” The Assessment Item Correlations to CCSS states that the standards addressed are K.CC.6, MP5, MP6.

• Grade 1, Topic 7: Adding within 20, Planning and Resources, Diagnostic Task, Questions 1-3, “1. There are some cows and some sheep. There are 10 animals altogether. How many cows and how many sheep might there be? Think of a few answers. 2. How do you know that 8 + 3 = 11? 3. What addition do you see here?” The Assessment Item Correlations to CCSS states that the standards addressed are K.OA.3, K.CC.2, 1.OA.1, MP2, MP3, MP4, MP7. 

• Grade 2, Topic 4: Representing Numbers, End of Topic Resources, Performance Task, Questions 1 and 2, “1. Choose values for the blanks to create a three-digit number. \rule{0.5cm}{0.15mm}0\rule{0.5cm}{0.15mm}. 2. Represent your number in 3 ways. Each representation must show something different about your number. Describe what each representation shows." The Assessment Item Correlations to CCSS states that the standards addressed are 2.NBT.1, MP2, MP4, MP6, MP7.

In some cases, however, the identified standards do not accurately reflect the mathematical content of the assessment items. For example, in Grade 2, Topic 7: Time and Money, Topic Assessment (Interview), Questions 5-7 and 13-15 are correlated to 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) on the Assessment Item Correlations to CCSS document. In Questions 5-7, students skip-count coins by fives and skip-count with mixed coins, while in Questions 13-15, students represent an amount using a specific number of coins and add or subtract with money. These items assess money concepts rather than telling or writing time, and therefore, the standard identification is inaccurate.

There is no standard identification provided within the assessments themselves or in the Teacher Experience Guide for each topic.

The materials for Experience Math 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.

Each lesson follows a consistent three-part structure that engages students in extensive work with grade-level problems. The three parts include Minds On, Action Task (which provides open-ended problem-solving prompts that require collaboration and critical thinking), and Consolidate Questions. Each topic includes various games and activities that may feature Academic Vocabulary, Brain Benders, Data Tasks, Making Connections Tasks, Math Talks (including Number Talks and Data Talks), and Wonder Tasks, as well as Your Turn and Additional Practice. Across the materials, students have multiple opportunities to demonstrate understanding of the full intent of the grade-level standards. The materials provide extensive opportunities for students to engage with grade-level work aligned to the standards, with limited opportunities for extensive work with 2.MD.7 and 2.MD.9.

Examples include:

• Kindergarten, Topic 9: Simple 2-D Shapes, Lessons 2 and 3, Topic 13: Simple 3-D Shapes, Lessons 2 and 3 engage students with the full intent of K.G.4 (Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts, and other attributes). Topic 9, Lesson 2, Action Task, Directions states, “Say: 1 Look at these shapes. How are they the same? 2. How are the shapes different? 3. Now, look at these shapes. How are they the same? 4. How are the shapes different?” Students compare two-dimensional shapes. Lesson 3, Action Task, Directions states, “Say: 1. Lourdes sorted these shapes. Why do you think she put those shapes in the sorting circle and left the other ones out? 2. How else could the shapes be sorted?” Students sort, classify, and describe 2-D shapes based on geometric attributes. Topic 13, Lesson 2, Action Task, Directions states, “Say: 1. Look at these shapes. How are they the same? How are they different?” Students compare 3-D geometric shapes (spheres, cylinders, cubes, and cones). Lesson 3, Action Task, Directions states, “Say: 1. How do you think the shapes have been sorted? 2. What is another way you could sort the shapes?” Students sort 3-dimensional geometric shapes based on geometric attributes.

• Grade 1, Topic 14: Two-Digit Addition and Subtraction, Lesson 2 engages students with the full intent of 1.NBT.5 (Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used). Students mentally add or subtract 10 to or from a two-digit number. Action Task, Question 1 states, “Choose a number on the hundred chart. Add 10 to your number. Where do you land? Write an equation to say what happened.” Question 2 states, “Repeat Question 1 with three more numbers.” Question 3 states, “Now choose a different number. Subtract 10 from your number. Where do you land? Write an equation to say what happened.” Your Turn, What You Learned states, “I can add or subtract 10 from a number in my head. What is one thing you learned about adding or subtracting 10 in this lesson?” Supporting Activity, I Know About 10 More or 10 Less, Question 3 states, “You subtracted 10 from a number and got 82. What was your number?” Question 4, “You added 10 to a number and got 56. What was the number?” Supporting Activity: Where Did I Start? Question 2 states, “You end up at 52. a. Where did you start if you had added 10? b.Where did you start if you had subtracted 10?”

• Grade 2, Topic 4: Representing Numbers, Lesson 1, engages students with the full intent of 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a "hundred." The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds—and 0 tens and 0 ones). Action Task, Question 2 states, “How many sets of 10 items do you have? How do you know?” Question 5 states, “Each group started with 10 sets of 10 items. a. How many groups would you need to put together to have 9 hundreds? b. How do you know? c. How many sets of 10 is 9 hundreds?” Consolidate Questions, Question 1 states, “Why can any number of hundreds also be shown as a number of tens?” Question 2 states, ”A hundreds number is written as a number of tens. Are there more or fewer tens than hundreds? How do you know?” Additional Practice, Questions 3-5 directions state, “Write how many tens are equal to each group of hundreds.” 300, 500, and 800 are the numbers provided to students. Questions 6 and 7 directions state, “Write how many hundreds are equal to each group of tens.” 90 tens, 30 tens, 70 tens are the numbers provided to students. I Know About Representing Hundreds, Question 3 states, “How many tens are in 400?” Question 4 states, “How do you know that 30 tens is 300 and not 30?” 

Materials do not present all students with extensive work of 2.MD.7 and 2.MD.9. Examples include:

• Students have limited opportunities to engage in extensive work of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.). This is the only lesson that addresses 2.MD.7. In this lesson, students relate times to events that could occur at those times and tell time to the nearest 5 minutes. Topic 7: Time and Money, Lesson 1, Minds On Activity, Question 1 states, “Which time do you think doesn’t belong?” Four clocks are displayed, three showing times to the half hour and one showing time to the quarter hour. The teacher reviews telling time to the half hour. Teacher Guidance, After the Minds On Activity states, “Ask if anyone knows why it is called ‘something-30.’ Some students might suggest that it is half of 60, and there are 60 minutes in an hour. Others might know that you count the number of ticks after the 12 and there are 30 ticks. Still others might know how to count by 5s following the numbers around the clock.” The teacher reviews skip counting by fives to fifty and demonstrates how skip counting by fives is used to tell time. Teacher Guidance states, “Review skip counting by 5s to 50 and then show how skip counting is used to tell the times 1:00, 1:05, 1:10, 1:15, and so on, up to 2:00. Write each of the times for students to see.” Action Task, Teacher Guidance, In This Task … states, “Students change a number of analog clock times to digital times and digital times to analog times. They also consider events that might occur at those times.” Questions 1-7 state, “For each time below, tell something you might be doing at that time. Then write the way the time would look on a digital clock.” Students work with digital clocks displaying time to the nearest five minutes; however, they are not required to tell or write time to the nearest five minutes or include A.M. and P.M. in their responses. This is the first and only lesson in the materials focused on telling and writing time. Consolidate Questions, Teacher Guidance, In This Discussion states, “Students reflect on what they have learned about the use of digital and analog clocks and how using clocks is really about measuring.” Question 1 states, “Why might one person say he was sleeping at a certain time that was shown on a clock, but someone else might say that she was in school?” Students are provided with a picture of an analog clock showing 10:00, a digital clock displaying 8:00, and a digital and analog timer. These representations are not connected to telling time to the nearest five minutes or to identifying A.M. and P.M. Question 3 states, “When you read a time on an analog clock, how do you decide what the hour is? How do you decide what the minutes after the hour are?” Your Turn: What You Learned, Journal states, “What is one thing you learned about telling time in this lesson?” Based on this single lesson, students are not provided the opportunity to engage in extensive work with telling and writing time to the nearest 5 minutes or using A.M and P.M.

• Students have limited opportunities to engage in extensive 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). This is the only lesson that addresses 2.MD.9. In this lesson, students create line plots based on measurement data. Topic 10: Representing Data with Graphs, Lesson 5, Minds On Activity, students are provided with measurement data showing the heights of students in a Grade 2 class. Question 1 states, “Organize the heights into these groups.” Provided groups include, “42-44 inches, 45-47 inches, 48-50 inches, and 51-53 inches.” Question 2 states, “Make a graph.” Teacher Guidance, And the Point Is … states, “This Minds On Activity is set up to introduce the line plot, although students may come up with different ways to organize the data first and display it, whether using a bar graph, picture graph, or tally chart. sets up the opportunity to see number ranges as categories, which leads to using individual numbers as categories, which is the basis for the use of line plots.” Action Task, Teacher Guidance, In This Task … states, “Students create a line plot based on given data. Students then collect their own measurement data.” Question 1 states, “Some students looked at different linking-cube trains to decide how long they were. When they measured with a ruler, they got these numbers: 3, 6, 9, 12, 9, 9, 6, 8, 9, and 15 inches. Make a line plot to show these data.” This question provides students with the opportunity to create a line graph based on the provided measurement data. Question 2 states, “Measure the lengths of the 10 ribbons you received. Make a line plot to show the data.” Students do not have the opportunity to experience extensive work with collecting their own measurement data and then creating their own line plot based on the data. Consolidate Questions: students reflect on the creation and usefulness of line plots. Question 1 states, “How do you make a line plot?” Question 2 states, “How is a line plot like a picture graph?” Question 3 states, “When is a line plot useful? Why is a line plot useful?” Exit Ticket states, “Create a line plot to show this information about the number of pets each child in a group of children has: 0 3 0 1 1 0 4 2 1 1 0.” The exit ticket does not connect to 2.MD.9 as students are asked to create a line plot with data that is not measurement data.” Your Turn, What you Learned, Learning Goal states, “I can create a line plot to show measurements and tell how it is useful. Journal: What is one thing you learned about creating line plots in this lesson?” A picture of a line plot with the title, “Lengths of Linking-Cube Trains in Inches” is provided. Based on this single lesson, students are not provided the opportunity to engage in extensive work with collecting measurement data and then creating a line plot.

The materials for Experience Math Kindergarten through Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

The pacing guide indicates that Kindergarten lessons typically take one day, with each lasting about 45 to 65 minutes, including differentiation. In Grades 1 and 2, lessons generally span two days, taking approximately 90 to 130 minutes each. All grades include additional days for review, assessment, and connecting or extension tasks. Overall, at least seventy-five percent of instructional time is devoted to the major work of the grade.

In Kindergarten:

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

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 59 out of 77, approximately 77%.

• The number of days devoted to major work of the grade (including assessments and related supporting work, but excluding a review day) is 118 out of 142, approximately 83%.

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 127 out of 142, approximately 89%.

In Grade 1:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 10 out of 14, approximately 71%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 44 out of 55, approximately 80%

• The number of days devoted to major work of the grade (including assessments and related supporting work, but excluding a review day) is 108 out of 152, approximately 71%.

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 118 out of 152, approximately 78%.

In Grade 2:

• The number of topics devoted to the major work of the grade (including supporting work connected to the major work) is 10 out of 14, approximately 71%.

• The number of lessons devoted to major work (including supporting work connected to the major work) is 40 out of 52, approximately 77%.

• The number of days devoted to major work of the grade (including assessments and related supporting work, but excluding a review day) is 100 out of 146, approximately 68%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 110 out of 146, approximately 75%.

An instructional day analysis of Kindergarten through Grade 2 is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, tasks, and the assessments embedded within each topic. Approximately 89% of the materials in Kindergarten, 78% 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 Experience Math 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 found within Topics and Lessons. 

An example of a connection in Kindergarten includes:

• Topic 5: Sorting, Student Experience Book, Lesson 4, 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). Students interpret organized data and then use that organization to make direct comparisons. The Minds On Activity and Action Task involve students interpreting sorted collections (e.g., dinosaur figures) that are already categorized. Probing questions prompt students to compare the sizes of these categories. Teacher Experience Guide states, “Can you tell if Luke has more T-Rex figures or more Stegosaurus figures?” Students engage with the organizational aspect by observing or actively sorting objects into categories. They then compare the quantities within these categories to determine which group has “more” or “most,” using visual matching or counting. Student Experience Book, Action Task states, “1. Does Luke have more stegosaurus figures or T-Rex figures? 2. Does he have more stegosaurus figures or brontosaurus figures? 3. What kind of dinosaur figure does Luke have the most of? 4. What else do you know about Luke’s dinosaur figures?”

An example of a connection in Grade 1 includes:

• Topic 5: Representing and Interpreting Data, Student Experience Book, Lesson 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 fewer 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). Students interpret organized data and use it to create and solve addition problems with three addends. In the supporting activity, students view a pictograph that represents red, blue, and yellow counters. Based on the data, students answer questions using addition and subtraction. Teacher Experience Guide, Supporting Activity: I Know About Reading and Interpreting Data Displays (Assessment for Learning), Teacher Guidance states, “Students read and interpret real-object graphs and tally charts. This activity can be used as an assessment tool for learning in Lesson 4. You can introduce it when you think you need more information about what particular students are able to do. You could ask individual students or pairs the questions.” Student Experience Book, Supporting Activity, I Know About Reading and Interpreting Data Displays states, “1. Answer these questions about his graph: How many red counters are there? How many blue counters are there? How many more yellow counters are there than blue counters? How many counters are there altogether?” A graph is provided for students to use with three red, one blue, and five yellow counters.

An example of a connection in Grade 2 includes:

• Topic 10: Representing Data with Graphs, Student Experience Book, Lesson 2, connects the supporting work of 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 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). Students interpret data from graphs and use addition and subtraction within 100 to answer questions about how many more or how many less of a particular object. In the Action Task, students interpret data from a bar graph and use addition and subtraction to identify information the graph provides. Student Experience Book, Action Task states, “A restaurant owner watched how many people drank juice, coffee, or tea at a restaurant in 1 hour. 1. Tell 8 things the graph shows. Make sure you tell whether you used addition or subtraction for some of your answers. Use the space below and on the next page to show your work.” Students see a bar graph showing what people drank: juice 6, coffee 12, and tea 10.

The materials reviewed for Experience Math Kindergarten through Grade 2 meet expectations for including problems and activities that 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 within Topics and Lessons.

An example of a connection in Kindergarten includes:

• Topic 2: Representing Numbers to 10, Lesson 4, Student Experience Book, 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 notice and discuss the numeral 5, wonder about its use, and use counters or loose items to represent the quantity it names. Teacher Experience Guide, Consolidate states, “Help students notice and name the numeral 5. You might even introduce the term ‘numeral.”’ For example, you could ask, Why do you think it might be useful to have a quick way to write ‘five’? How is a 5 like a letter? Help students see that a numeral does not communicate a sense of quantity. For example, you could ask, Do you think the size of the numeral 5 changes how much 5 is? You might ask additional questions to ensure students understand the critical concepts. Student Experience Book, Action Task states, “1. What do you notice? 2. What do you wonder about? 3. Use Tools [Provide students with counters or loose items.] How could you show that many?”

An example of a connection in Grade 1 includes:

• Topic 7: Adding within 20, Lesson 5, Student Experience Book, 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 solve addition problems while using the properties of operations, including the associative property of addition. Student Experience Book, Action Task states, “1. Why can you write 3+5 to tell how many yellow balls there are?” Students are given an image that shows three yellow balls on a top shelf and five on a bottom shelf. “Suppose you move 1 yellow ball from the bottom shelf to the top shelf. What addition expression could you write for the yellow balls now? Why is that expression equal to 3+5? 2. Why can you write 4+8 to tell how many red balls there are? How could you move some red balls to make a double?” Students see 4 red balls on the top shelf and 8 on the bottom shelf. Teacher Experience Book, Teacher Guidance, and the Point Is… states, “This Action Task helps students understand that the total of two numbers remains the same when an amount is taken from one addend and added to the other. Rearranging numbers in this way can make an equivalent addition that is easier to solve.”

An example of a connection in Grade 2 includes:

• Topic 9: Length, Lesson 6, Student Experience Book, connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction)to the major work of 2.MD.B (Relate addition and subtraction to length). Students measure the length of objects and use addition and subtraction strategies to compare the lengths. Student Experience Book, Action Task states, “1. Choose 3 classroom items to measure in inches. One should be shorter than your ruler. One should be longer than your ruler. The third can be any item. Measure the length of each item. For Questions 2-5, write an equation and solve it. 2. Choose 2 of the items you measured. Put together their lengths. Tell what their total length would be. 3. Choose 2 of the items you measured to compare. Tell how much longer one item is than the other item.”

The materials reviewed for Experience Math 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 materials provide multiple features to support coherence across grade levels. Connecting to Concepts Beyond the Grade notes at each grade and topic guide teachers to see how current instruction fits within the broader K-8 progression of learning. These notes identify how current instruction prepares students for future standards and clarify the significance of these connections by sharing the progression of mathematical understanding. For example: 

• In Grade 1, Teachers Experience Guide, Connecting to Concepts Beyond the Grade links the work in Grade 1 to related concepts in later grades, including Grades 2, 3, 4, and 5. Measuring Length and Time (Topic 8) states, ​“Topic 8 develops students’ understanding of measurement concepts through a structured progression focused on length and time. Students move from direct comparison of lengths to indirect comparison (using a third object), then to measuring with nonstandard unit, and them moving to standard units. This developmental sequence—from direct comparison to indirect comparison to nonstandard units and eventually to standard units—establishes a pattern that will be repeated with other attributes in future grades. In Grade 2, students extend their measurement work to standard units of length. By Grade 3, they apply a similar progression to area measurement: first comparing areas directly by superimposing shapes, then using nonstandard units like square tiles, and finally applying standard units such as square inches or square feet. In Grade 4, this progression extends to angle measurement, and by Grade 5, to volume measurement. The work with time benchmarks in Topic 8, where students relate clock times to familiar daily events (such as associating 3:00 pm with the end of the school day), extends to benchmark references for other measurements in later grades. In Grade 2, students establish length benchmarks (an inch is about the width of a thumb). By Grade 3, they develop weight benchmarks, and in Grade 5, they establish volume benchmarks. The measurement concepts introduced in Topic 8 establish a coherent framework that students will apply across various measurement contexts throughout their mathematical education. By experiencing this consistent progression from direct comparison to standard units with length measurement, students develop a generalizable approach to understanding any measurable attribute. This foundation helps students recognize the underlying principles common to all measurement, regardless of the attribute being measured, and supports their ability to select appropriate tools, establish reasonable benchmarks, and develop measurement sense across contexts.”

Going Back notes emphasize prior knowledge and skills that form the foundation for grade-level learning, while Going Forward notes describe how current concepts will be extended and applied in later grades. Together, these supports strengthen coherence across grade levels by helping teachers make explicit links between prior, current, and future learning.

An example of a connection to future grades in Kindergarten includes:

• Topic 3: Representing Fractions, Teachers' Experience Guide, Planning and Resources, Topic 3: Planning connects the recognizing quantities of work in Kindergarten to the future work in Grade 1, where students count to 120. Teachers' Experience Guide, Going Forward states, “In Grade 1, students move beyond 100 to rote count up to 120. They also start thinking about place value, that is, when we write numbers as tens and ones and using that idea, count greater quantities than in Kindergarten.”

An example of a connection to prior knowledge in Kindergarten includes:

• Topic 8: Adding and Subtracting, Teachers' Experience Guide, Planning and Resources, Topic 8: Planning connects adding and subtracting, composing and decomposing numbers, and representing addition and subtraction in Kindergarten to prior work where students developed knowledge of representing addition and subtraction.

An example of a connection to future grades in Grade 1 includes:

• Topic 2: Representing Numbers, Teachers' Experience Guide, Planning and Resources, Topic 2: Planning connects the number representation work of Grade 1 to the future work of Grade 2 as students extend to larger numbers. Teachers' Experience Guide, Going Forward states, “In Grade 2, students become more comfortable with three-digit numbers.”

An example of a connection to prior knowledge in Grade 1 includes:

• Topic 8: Length and Time, Teachers' Experience Guide, Planning and Resources, Topic 8: Planning connects measuring with nonstandard units in Grade 1 to prior work in Kindergarten, where students were introduced to the concept of length. Teachers' Experience Guide, Going Back states, “In Grade K, students learn what length is and measure length directly, moving to more indirect measures in Grade 1.” 

An example of a connection to future grades in Grade 2 includes:

• Topic 2: Adding and Subtracting within 20, Teachers Experience Guide, Planning and Resources, Topic 2: Planning connects adding and subtracting within 20 in Grade 2 to the future work in Grade 3, where students add and subtract three-digit numbers. Teachers' Experience Guide, Going Forward states, “In Grade 3, students move to more fluency and more symbolic approaches to addition and subtraction. The standard algorithms, however, are not required until Grade 4. The problems solved in Grade 3 tend to involve more three-digit numbers and may be somewhat more complex.”

An example of a connection to prior knowledge in Grade 2 includes:

• Topic 5: Comparing Numbers within 1,000, Teachers Experience Guide, Planning and Resources, Topic 5: Planning connects comparing numbers to 1,000 to prior work in Grade 1, where students compared numbers to 100. Teachers' Experience Guide, Going Back states, “While students in Grade 1 concentrate on numbers to 100, students in Grade 2 move to 1,000 and also think about creating number lines in varied ways.”