K-2nd Grade - Gateway 1

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

According to the Implementation Handbook, the assessment system provides a variety of opportunities for students to independently demonstrate their mastery of grade-level standards through formal summative assessments which include, Chapter Test, Big Idea Task, Multi-Chapter Test, Quarter DAP (Diagnostic Adaptive Progression - online only), End-of-Course Test, Post-Course DAP, and Alternative Chapter Assessment. These assessments vary in format, providing different ways to accurately describe student performance at a particular point-in-time. All assessments are aligned with grade-level content standards as represented in the “Assessment Correlation (by Standard)” and an “Assessment Correlation (by Course).” Both include a breakdown identifying content standards for each assessment item.

The materials in Grades K–2 are divided into 13 chapters, each containing Mid-Chapter Tests and Chapter Tests. The materials also include four Multi-Chapter Tests, a Prerequisite Skills Test, and an End-of-Course Test. Examples include:

• Grade K, Multi-Chapter Test 4, Exercise 12, students are shown a picture of two pencils: Pencil A is shorter and Pencil B is longer. Complete the sentence. Pencil A is _______ Pencil B.” Students drag and drop their answer into the drop zone to solve. The answer choices are “longer than, shorter than, and the same length as.” (K.MD.2)

• Grade 1, Chapter 5, Chapter Test, Exercise 1 states, “There are 15 balloons. 9 balloons pop. How many balloons are left?” (1.OA.1) 

• Grade 2, Chapter 8, Chapter Test, Exercise 7 states, “You drive 216 miles and stop for lunch. You drove 387 miles in all. Complete the equation to find how many miles you drove after lunch.” (2.NBT.7)

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

CCSS standards are identified on the digital assessments for each item on the following formal assessments: Chapter Performance Task, Big Idea Task, Chapter Test, Multi-Chapter Test, and End-of-Course Test. The print materials do not always identify the CCSS or Practices; however, the problems on the print assessments are identical to the problems in the digital assessments. Two correlation resources demonstrate assessment items alignment to the standards. The Assessment Correlation (by Course) is organized by assessment and identifies the standards addressed on each assessment. The Assessment Correlation (by Standard) lists every assessment item in which a specific standard is addressed. 

The Digital Teaching Experience and the Teacher Toolkit: Course Essentials identify the Standards for Mathematical Practice (SMPs) for Big Idea Tasks and Chapter Performance Tasks; however, the materials do not identify the SMPs consistently for each item on other formal assessments.

Examples include:

• Grade K, Chapter 4, Performance Task, Exercise 1 states, “Count the tools in each group. Write each number. Is the number of pairs of scissors equal to the number of combs? Circle the thumbs up for yes or the thumbs down for no.” Students are shown a picture of a hair styling station with seven pairs of scissors, seven combs, and three brushes. They are asked to write the number of scissors and combs they count in the picture. (K.CC.3, K.CC.5, K.CC.6, K.CC.7, K.MD.3, MP.1, MP.4)

• Grade 1, Multi-Chapter Test 3, Exercise 3 states, “You have 39 stars in a video game. Then you collect some more. Now you have 57 stars. How many stars did you collect?” Students choose from the multiple-choice answers provided: a. 18 stars, b. 22 stars, c. 28 stars, d. 96 stars. (1.NBT.4)

• Grade 2, Chapter 7, Mid-Chapter Test, Exercise 1states, “A school store sells 112 pencils on Monday. The store sells 10 more pencils on Tuesday. How many pencils did the store sell in all?” (2.NBT.7, 2.NBT.8)

The materials reviewed for Math & YOU Grades 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.

Students are exposed to a variety of question types, modalities, and complexity levels to develop and demonstrate their understanding of course content. The modalities and question types provide different contexts and settings, ensuring students have opportunities to demonstrate their understanding through tasks that require them to reason and communicate in a variety of ways. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, short answer, and extended response.

Formative assessments occur at the lesson level through structures such as the Prerequisite Skills Test, Chapter Performance Task, In-Class Practice, and Connecting Big Ideas. These assessments provide opportunities for students to demonstrate their understanding of grade-level content standards through a variety of item types, including Drag and Drop, Fill in the Blank, Matching, Multi-Select, Response Matrix, Short Response, and Single Select.

Examples include:

• Grade K, Chapter 7, Big Idea Tasks, Exercise 1states, “a. There are 5 red apples on a tree. You pick some apples. Tell how many apples are left. Show how you know you are correct. b. There are 5 green apples on a tree. Your friend picks a different number of apples than you. Tell how many green apples are left. Show how you know you are correct.” Students are provided two blank number bonds to help them solve Part a and Part b. “c. Who picks more apples? How many more? Write a subtraction sentence to show how you know. _____ - _____ = ______ d. Are there more red apples or green apples on the tree? How many more? Write a subtraction sentence to show how you know. _____ - ______ = ______” The materials assess the full intent of MP.1 as students make sense of a multi-step problem, plan and carry out strategies using number bonds and subtraction sentences, justify their reasoning in each part, and demonstrate perseverance by comparing quantities, explaining how they know their answers are correct, and reflecting on their results to ensure their reasoning makes sense within the context of the problem.

• Grade 1, Chapter 10, Big Idea Tasks, Exercise 2 states, “a. Draw a line that is shorter than your pencil. Draw a line that is longer than your pencil. b. Circle the line that is longer. How can your pencil help you compare the lengths? Tell how you know you are correct. c. Can you use the string to compare the lengths of the lines you drew? Explain why or why not.” The materials assess the full intent of MP.5 as students strategically use tools such as a pencil and string to compare lengths, justify how those tools help them determine which line is longer, and explain the effectiveness and limitations of each tool for measuring and comparing objects.

• Grade 2, Chapter 10 Test, Exercise 3 states, “Part A. Your sunflower was 31 inches tall when you planted it in the garden. Now the sunflower is 55 inches tall. Complete the equation to find how many inches it grew. Use the ? for the missing number.” Exercise 5, “A garden snake is 24 inches long. One year later, the garden snake is 18 inches shorter than a corn snake. The corn snake is 48 inches long. How many inches does the garden snake grow?” The materials assess the full intent of 2.MD.5 as students use addition and subtraction within 100 to solve real-world word problems involving lengths in the same unit.

The materials reviewed for Math & YOU Grades 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 begins with an opening activity, Dig In or Motivate, followed by student-centered explorations in Investigate. Learning continues with Key Concept and concludes with opportunities to make real-world connections in Connect to Real Life. The Student Practice workbooks offer additional opportunities for students to reinforce the knowledge and skills developed through each lesson.

Three correlation resources demonstrate alignment to the standards and show that students engage with the full intent of the standards throughout the course. The Standards Correlation (by Course) is organized by course component and identifies the standards addressed in each lesson. The Standards Correlation (by Standard) lists every lesson in which a specific standard is addressed. The Standards-Based Practice Correlation connects each Standards-Based Practice activity in the Practice Workbook to a content standard and identifies lessons where that standard is reinforced. Across the program, students have multiple opportunities to independently demonstrate their understanding of the full intent of the standards.

Examples include:

• Grade K, Chapter 9, Lesson 3, engages students with the full intent of K.CC.5 (Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.) Students count objects arranged in scattered and structured configurations up to 20, model quantities with cubes, draw representations, and match or compare groups to given numbers to answer “how many” questions. Investigate states, “You have 14 crayons in your box. Your friend has 11 crayons in another box. Draw to show the number of crayons in each box.” Students use cubes to model the number of crayons and then draw a representation of their model. Key Concept, Exercise 2 states, “Circle the group that matches the given number.” The given number is 5. One group shows five scattered sharks, and another group shows eight scattered sharks. In Class Practice, Exercise 5, “Circle any group that matches the given number.” The given number is 15. Three groups of orange slices arranged in rectangular arrays are shown: group one has 15 oranges, group two has 10 oranges, and group three has 5 oranges. In Class Practice, Exercise 7 states, “You have 20 coins in your pocket. You drop them as you are waiting for the bus. You find the coins shown. Did you find all of your coins? Circle the thumbs up for yes or the thumbs down for no.” A rectangular array showing 18 coins is provided.

• Grade 1, Chapter 7, Lessons 2-4, engages students with the full intent of 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.) Students use place value understanding to compare two-digit numbers by identifying tens and ones, recording comparisons with words and symbols, and justifying which number is greater, less, or equal. Lesson 2, In-Class Practice, Exercise 2 states, two sets of tens and ones blocks are shown, three tens and four ones, and three tens and seven ones. Students count the tens and ones, write the corresponding numbers, and then circle whether 34 is “greater than” or “less than” 37 to solve. Lesson 3, In-Class Practice, Exercise 1 states, “Compare. Circle the digits that helped you decide. 61 is greater than or is less than 53.” Students identify and record the tens and ones in each number (“___ tens ___ ones”) to support comparison between the two numbers. Lesson 4, In-Class Practice, Exercise 4 states, “Compare using words and the symbols <, >, =.” Students use comparative words to complete “47 is ________ to 47” and the appropriate symbols to complete “47 ____ 47.”

• Grade 2, Chapter 2, Lessons 3 and 4, and Chapter 3, Lesson 9 engages students with 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.) Students use addition and subtraction within 100 to solve one- and two-step word problems by applying models, drawings, and equations to represent taking apart, putting together, and comparison situations. Chapter 2, Lesson 3, Connect to Real Life, Exercise 18 states, “You and your friend counted 15 blue herons in all. You counted 8. How many did your friend count?” Students apply subtraction to solve a problem involving a taking apart situation. Lesson 4, Student Practice Workbook, Lesson Extra Practice, students apply a model to represent and solve a two-step problem. Exercise 17 states, “You, Newton, and Descartes have 14 crayons in all. Newton and Descartes each have 4. How many crayons do you have? Use a model to show your work.” In Chapter 3, Lesson 9, In Class Practice, Exercise 2, students use addition to solve a putting together problem. The materials state, “You are a veterinarian. You weigh one dog that weighs 22 pounds and another dog that weighs 59 pounds. What is the total weight of the two dogs?”

The materials reviewed for Math & YOU Grades 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 as included in the following grade-level breakdowns. 

Kindergarten:

• The approximate number of chapters devoted to major work of the grade (including assessments and related supporting work) is 10 out of 13, approximately 77%.

• The approximate number of lessons devoted to major work of the grade is 74 out of 95, approximately 78%.

• The approximate number of instructional days devoted to major work of the grade (including assessments and related supporting work) is 132 out of 169, approximately 78%.

Grade 1:

• The approximate number of chapters devoted to major work of the grade (including assessments and related supporting work) is 10 out of 13, approximately 77%. 

• The approximate number of lessons devoted to major work of the grade is 72 out of 90, approximately 80%. 

• The approximate number of instructional days devoted to major work of the grade (including assessments and related supporting work) is 129 out of 164, approximately 79%. 

Grade 2:

• The approximate number of chapters devoted to major work of the grade (including assessments and related supporting work) is 10 out of 13, approximately 77%.

• The approximate number of lessons devoted to major work of the grade is 72 out of 95, approximately 76%.

• The approximate number of instructional days devoted to major work of the grade (including assessments and related supporting work) is 131 out of 169, approximately 78%.

An instructional day analysis across Kindergarten through Grade 2 is most representative of the instructional materials as the days include major work, supporting work connected to major work, and the assessments embedded within each chapter. Approximately 78% of the materials in Kindergarten, 79% of the materials in Grade 1, and 78% of the materials in Grade 2 focus on major work of the grade.

The materials reviewed for Math & YOU Grades 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 within the Standards Correlation (by Course). 

An example of a connection in Kindergarten includes:

• Chapter 4, Lesson 5, Teacher Edition 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 classify objects into two categories, record the data in a chart, and compare the numbers in each category. Laurie's Notes Investigate states, “Discuss the different types of vehicles. ‘You want to show the number of objects in the water and the number of objects not in the water.’ Count the vehicles in the water first. Suggest covering each with a small counter or crossing it out as students count and make a mark for each object in the chart. When possible, place at most five tally marks on a line so that the tally marks are in groups of five. This will help prepare students for connecting counting tally marks to counting by 5s in a later grade.’” Student Edition, Directions state, “Show the number of objects in the water and the number of objects not in the water. Circle the category with the greater number of objects.”

An example of a connection in Grade 1 includes:

• Chapter 11, Lesson 2, Teacher Edition 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.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). Students work with the teacher to use data from a table to answer addition and subtraction word problems. Laurie’s Notes, Key Concept states, “‘Look at the ‘How You Get to School’ tally chart. You want to know how many more students ride a bus than walk. Tell your partner how you would find that from the tally chart. Have students discuss how they would determine the difference.’ Some students might say that they would subtract, especially since that is the equation provided. They might also say they could use a missing addend equation. This is also correct. Challenge students to rewrite the equation to a missing addend equation. ‘Tell your partner how you can find how many total students were asked.’ Review the completed equation and its relationship to the tally chart.” Students apply their knowledge in the In-Class Practice using a table that identifies the eye color of people. Student Edition, Directions state, “1. How many more students have brown eyes than blue eyes? 2. How many students were asked?”

An example of a connection in Grade 2 includes:

• Chapter 11, Lesson 5, Teacher Edition 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 start by working with the teacher to create a bar graph from a tally chart identifying the number of certain trees in a park. Laurie’s Notes, Key Concept states, “‘Start with the pine tree. How many tally marks are there? Find 5 on the number line and go straight up to the line for pine. The bar ends at 5.’ Repeat for the other three trees. ‘The question asks us to find the most common tree. Explain to your partner how you can use the bar graph to answer the question, and the tally chart to check your answer.’ Listen for students to look for the longest bar and count the tally marks. ‘Which tree is the least common? Why? birch tree; it has the shortest bar and fewest tally marks.’” Students then complete their own bar graph with data from a tally chart and answer addition word problems. Students Edition, In-Class Practice, Directions state, “1. Use the tally chart to complete the bar graph.” A tally chart is provided with the number of different books on a shelf: History three, Fiction seven, Science five, and Poetry six. “2. How many books are there in all? 3. How many more fiction and history books are there than poetry books?”

The instructional materials for Math & YOU Grades 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 listed for teachers Standards Correlation (by Course) within the Digital Teaching Experience under Teacher Toolkit: Course Essentials and may appear in one or more phases of a typical lesson: Example, In-Class Practice, and Practice Exercises. 

An example of a connection in Kindergarten includes:

• Chapter 3, Lesson 4, Student Edition, 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 count a set of weather symbols, state the total aloud, and record the number in writing. In-Class Practice Exercise 7 states, “Count. Say the number. Write the number.” Students are given images of weather symbols; sunny, sunny with clouds, rainy, and cloudy, on a calendar that shows the days of the week.

An example of a connection in Grade 1 includes:

• Chapter 5, Lesson 7, Student Edition, connects the major work of 1.OA.C (Add and subtract within 20) to the major work of 1.OA.A. (Represent and solve problems involving addition and subtraction). Students use addition and subtraction to find the number of children at a bounce house. In-Class Practice Exercise 3 states, “A group of kids are at a bounce house. 8 of them leave and 4 more join. 12 kids are there now. How many kids were at the bounce house to start? Show your work.”

An example of a connection in Grade 2 includes:

• Chapter 10, Lesson 1, Student Edition, connects the major work of 2.MD.B (Relate addition and subtraction to length) to the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) Students add and subtract to solve real-life word problems involving length. In-Class Practice Exercise states, “1. You swim 15 meters and take a break. Then you swim 10 meters. How many meters do you swim in all? 2. You are climbing a ladder that is 20 feet long. You have climbed 13 feet. How many feet do you have left to climb?”

The instructional materials reviewed for Math & YOU Grades 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. Co-Author Notes, Insight Videos, and Coherence details in chapters and lessons explain how current learning builds from prior learning and extends to future learning. The Mathematics of the Chapter Overview in each chapter provides coherence perspectives through “What we’re doing,” “Why we’re doing it,” and “Essential background” insights. Standards for Content and Mathematical Practice provides COHERENCE Throughout the Grades presents chapter charts that show learning progressions, available in both the Teacher Edition and the Digital Teaching Experience, with Common Core standard codes for reference to prior, current, and future learning. Each lesson includes a Coherence section in the overview that summarizes the lesson focus within the broader learning progression.

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

• Chapter 2, Teacher Edition, Standards for Content and Mathematical Practice, COHERENCE Throughout the Grades, connects 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) and K.CC.7 (Compare two numbers between 1 and 10 presented as written numerals) to the development of operational thinking in Grades 1, where students compare two two-digit numbers using symbols (1.NBT.3). Mathematics of the Chapter states, ​”In this chapter, students learn to compare numbers 1 to 5. This learning begins with deciding whether two quantities are the same or not the same. Matching and comparing by counting are the first two strategies students use to compare two quantities. The third strategy presented is comparing written numerals.” These strategies lay the foundation for students to later “compare written numerals because of their understanding of quantity and their ability to visualize the numbers.”

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

• Chapter 4, Teacher Edition, Mathematics of the Chapter, connects 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) to the previous work they completed in Chapter 2, where students compared two numbers between 0 and 5 (K.CC.7). Laurie's Note Overview states, ​“Students are familiar with comparing numbers to 5. They now will extend their comparison strategies to numbers within 10. These strategies include comparing by matching and comparing by counting. As the chapter progresses, students are asked to compare written numerals. A numeral is a symbol or name for a number. To keep the language easy for students to understand, we say ‘compare the numbers’ when the numerals are given. The last two lessons of the chapter focus on categorical data and comparing the quantities in two categories. Students must be able to tell whether an object belongs or does not belong to a category before comparing.”

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

• Chapter 7, Teacher Edition, Standards for Content and Mathematical Practice, COHERENCE Throughout the Grades, connects 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <) to the operational thinking in Grade 2, where students build upon this learning and compare two three-digit numbers using the symbols >, <, = (2.NBT.4). Mathematics of the Chapter, Laurie’s Notes states, ​“This chapter focuses on comparing numbers. Students already have a sense of the order of numbers from counting and from their work with the hundred chart in kindergarten and with the 120 chart this year. In Chapter 2, students developed strategies for addition and subtraction from situations that describe more than and less or fewer than. All of these experiences are building blocks for the work in this chapter and connections should be made. In this chapter, students will describe and analyze how place value determines numbers that are greater than or less than another. They will be introduced to and use the inequality symbols greater than (>), less than (<), and equal to (=). These experiences build toward the understanding that ‘the location of a digit in a number determines its value’ and that ‘this is our efficient way to write and compare numbers.’”

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

• Chapter 6, Teacher Edition, Standards for Content and Mathematical Practice, COHERENCE Throughout the Grades, connects 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 the previous work in Kindergarten, where students count by ones and by tens up to 100 (K.CC.1). Mathematics of the Chapter, Laurie’s Notes states, ​“In kindergarten, students counted by ones and by tens up to 100. As you talk with students throughout the day, you probably discuss different quantities of items or even count the number of days you have been in school. These connections can be recalled as you introduce this chapter. In this chapter, we build on students’ experience by counting and writing numbers to 120. Most importantly, this chapter moves from counting by ones and tens to understanding place value. This chapter develops one of the most pivotal concepts in mathematics-place value. Lessons are designed to progress from counting patterns, to decomposing numbers into tens and ones in various ways, and back to counting patterns and writing numbers up to 120. Place value is based on groups of ten. One ten is made up of ten ones and ten ones can be joined to make one ten. The groupings of ones and tens can be taken apart in different, but equivalent, ways. Patterns and grouping allow for more efficiently counting.”

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

• Chapter 6, Teacher Edition, Standards for Content and Mathematical Practice, COHERENCE Through the Grades, connects 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones) to the future work in Grade 4, where students use place value for numbers to 1,000,000 (4.NBT.1). Mathematics of the Chapter, Laurie’s Notes states, “In earlier grades, students learned to count and write numbers to 120 and compare numbers to 100. This work is now extended to the hundreds place value. Big ideas about place value that are introduced or extended in this chapter include the following: Numbers can be decomposed and composed in various ways. The location (place) of a digit in a number determines its value. Place value is based on groups of ten. The groupings of ones, tens, and hundreds can be taken apart in different, but equivalent, ways. Patterns and groupings allow us to count more efficiently. Students have used their understanding of tens and ones to develop addition and subtraction strategies with two-digit numbers. These skills are built upon an understanding of place value, one of the most pivotal concepts in mathematics. Students who have a robust understanding of place value move forward in mathematics with greater performance and achievement than students with an undeveloped understanding of place value (Van de Walle et al., 2016).”

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

• Chapter 1, Teacher Edition, Standards for Content and Mathematical Practice, COHERENCE Through the Grades, connects 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends) to the previous work of Grade 1, where students use properties of addition as strategies to add. (1.OA.3) Mathematics of the Chapter, Laurie’s Notes states, “The work students have done in Grade 1 has prepared them to continue working with the operation of addition. We want students to continue using manipulatives, actions, and drawings. A drawing provides a record for students to reflect on and share with peers their sense making of numbers and situation problems. In this chapter, we reinforce the doubles strategies and the vocabulary terms doubles, equation, row, and column. The new precise mathematical terms introduced are even, odd, equal groups, array, and repeated addition.” The addition skills are used as students transition to multiplication. “Arrays are also an important structure related to multiplication in Grade 3.”