The instructional materials reviewed for Grade 1 enVision Math 2.0 do not meet the expectations for giving attention to conceptual understanding. The materials rarely develop conceptual understanding of key mathematical concepts where called for in specific content standards or cluster headings. Most all of the lessons in the materials have students filling out pages from the student book in a very procedural manner.

Rarely do the materials feature high quality conceptual problems or conceptual discussion questions. Some of the lessons start with a problem which could develop conceptual understanding; however, the lessons quickly transition to simply filling out the page from the student book.

Cluster 1.NBT.B focuses on understanding place value.

• Topics 8 and 9 specifically address 1.NBT.B.
• Lesson 8-1 cites 1.NBT.2b. Part of the essential understanding for the lesson is that numbers 11-19 “can be written as a number word.” On page 450, the numbers and words for 11-19 are presented, and the lesson states that “(t)hese numbers are made up of one group and 10 and some left over. One group of 10 is called 1 ten. The leftovers are called ones.” Instead of beginning work with the numbers 11-19 by developing the concept of 10 as a bundle of ten ones, the materials introduce 10 as one group of 10 without specifying that 10 is a group of ten ones, and then the ones are simply leftovers. Although this lesson is students’ first exposure to understanding that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones, all of the questions on the pages from the student book require students to either read or write the number word names.
• Lesson 8-2 cites 1.NBT.2c. Although this standard is about understanding the numbers 10, 20, 30, 40, 50, 60, 70, 80 and 90 as referring to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones), this lesson really emphasizes counting by tens more than conceptual understanding of tens. Page 456 of the teacher’s guide states “Count by 10s” and tell students to notice that the “digit at the left increases by 1 every time you count 10 more” in order to write the number 40. The instructions for the guided practice and independent practice also state to “Count by 10s. Write the numbers.” Although the lesson begins with a hands-on activity using connecting cubes to make tens, the rest of the lesson focuses on pages from the student book and pictures of connecting cubes instead of hands-on activities.
• The essential question for Lesson 8-3, “Count with Groups of Tens and Leftovers,” on page 462 is “How do you know how many tens and how many leftovers are in a number?” Throughout the lesson, students count the number of tens and “leftovers” in pictures to complete pages from the student book. Although the instructions for items 7-8 on page 463 states to “(r)emind students that in a two-digit number, the digit at the left tells how many groups of 10, and the digit at the right tells how many leftover ones,” the lack of discussion of ones in the lesson does not help build conceptual understanding of the two digits of a two-digit number.
• Although Lesson 8-4 includes problems to develop student understanding of how many tens and ones are in a two-digit number, the pages from the student book primarily have students using pictures of number cubes throughout the lesson instead of hands-on activities.
• Lesson 8-5 cites 2.NBT.2 but focuses more on procedures than conceptual understanding. This lesson focuses on drawing models for two-digit numbers that use lines for the tens and dots for the ones.
• In Lessons 9-3 and 9-4 students compare two-digit numbers based on place value using symbols. Numbers on pages from the student book are represented with pictures of base ten blocks providing students with opportunities to understand the values and number composition. In Lesson 9-3, the teacher’s guide mentions on page 511 that students “may use real place-value blocks to help them make the physical connection between the numbers,” but students are not required to use the place-value blocks to make this connection.
• Lesson 9-5 focuses more on the procedure of using a number-line model to determine which numbers are greater than or less than a given number. For example, Lesson 9-5 begins with the number 24. Students are told to find a number greater than 24 and a number less than 24. Students are told numbers to the right of a number are greater than and numbers to the left are less than instead of being allowed to build the understanding needed.

Cluster 1.NBT.C focuses on using place value understanding and properties of operations to add and subtract.

• Topics 10 and 11 specifically address 1.NBT.C.
• Lesson 9-2, “Make Numbers on a Hundred Chart,” also cites 1.NBT.5. In this lesson students are finding numbers that are 1 more, 1 less, 10 more, and 10 less than a given two-digit number. This lesson focuses more on the procedure of using the chart than conceptual understanding of 10 more and 10 less. Although page 504 states the “(y)ou can use place-value blocks to check how the numbers change,” the focus of the lesson is really on finding numbers to the left, top, right, and bottom of a given number on the hundred chart. When students begin the page from the student book, they are not asked to find 1 more, 1 less, 10 more, and 10 less than a number to complete items 1 and 2; they are asked to complete part of the hundred chart and are given a number in a square with blank squares to the left, top, right, and bottom.
• Topic 10 focuses on using models and strategies to add tens and ones. Only one lesson, Lesson 10-7, focuses solely on addition of two two-digit numbers.
• In Lesson 10-1, students add tens using models, mostly pictures of connecting cubes; however, the use of facts is stressed throughout the lesson. The first problem asks 3+5 before 30+50.
• In Lesson 10-2 students mentally find 10 more than a number. Although the concept is introduced using place value blocks to build conceptual understanding of 1.NBT.5, the lesson does not require students to explain their reasoning, as required in standard 1.NBT.5, for any of the 16 problems on the pages from the student book.
• In Lesson 10-3 students are adding tens and ones using a hundred chart. In Lesson 10-4 students are adding tens and ones using an open number line. Both of these lessons focus more on the procedure taught in the lessons than on the conceptual understanding of using place value to add. Using place value to add tens and ones is stressed in Lesson 10-5 as students are adding tens and ones using place-value models such as ten rods and ones cubes, but this lesson that stresses conceptual understanding based on place value occurs after the lessons focused more on following a procedure.
• Lesson 10-6 introduces students to a procedure for adding a one-digit number to a two-digit number. For example, students add 25 + 8 using place value blocks. The lesson tells the students to make ten to solve, and the teacher leads the students through how many tens in 25 and how many ones, then how many ones in the 8, finally asking them to make a ten with the ones and asking how many ones are leftover. The essential question on page 574 is “How does making a ten help you add?” The sample answer is “By making a ten with one addend, I change the problem into an easier problem.” This lesson is focused on the procedure of making ten and not building conceptual understanding.
• In Lesson 10-7, the sole lesson addressing addition of two two-digit numbers, the page from the student book begins with three problems written vertically that stress addition using place-value. However, the next four problems give two numbers that are labeled as “show” and “add,” and students fill in a horizontal equation losing the focus on place-value.
• Topic 11 focuses on using models and strategies to subtract tens.
• In Lesson 11-1 students subtract tens using models, mostly pictures of tens-rods.
• In Lesson 11-2 students are subtracting tens using a hundred chart. In Lesson 11-3 students are subtracting tens using an open number line. Both of these lessons focus more on the procedure taught in the lessons than on the conceptual understanding of using place value to subtract. Most of the items on the pages from the student book do not require students to explain their answers.
• In Lesson 11-4 students use addition to subtract tens. On the pages from the student book, 6 of the 10 problems set up both the addition and subtraction equations and students simply fill in a missing number in each.
• Lessons 11-5 and 11-6 allow students to practice subtracting 10. Although the pages from the student book for Lesson 11-5 suggests using 10-frames if needed, these two lessons are opportunities for students to practice strategies and procedures that they were taught in other lessons.

There are some interventions that encourage the development of conceptual understanding; however, these interventions are not meant for all students- only those not meeting the standard.

• For example, in Lesson 1-2 students in the intervention activity are actually connecting cubes to combine them instead of just counting cubes such as on the page from the student book from in the lesson.
• In the Lesson 1-3, students completing the intervention activity are seeing the actual manipulatives as they work on addition problems, and this is much more conceptual then the lesson pages.
• Lessons 9.1 page 501A and 9-4 page 519A have interventions developing conceptual understanding for 1.NBT.B
• Lessons 10-4, page 565A, and 10-7 page 651A have interventions developing conceptual understanding for 1.NBT.C.

The materials do not give enough opportunities for students to develop fluency and procedural skill throughout the text and especially where it is specifically called for in the standards.

There are many opportunities for children to count objects within ten and 20. However, there are not many opportunities for daily counting above 20 and not to 120 which is the first grade standard. Frequent practice with rote counting is needed in order to master counting to 120 by 1's and counting to 100 by 10's and build fluency.

Standard 1.OA.6 is adding and subtracting within 20, demonstrating fluency for addition and subtraction within 10.

• There are 21 lessons addressing the standard; however, all of the lessons are within Topics 2-4. The lessons fall within the first 36 lessons of the year.
• Only 9 lessons deal with subtraction, Lessons 2-6, 2-7, 2-8, 4-2, 4-3, 4-4, 4-5, 4-6 and 4-7.
• When looking at fluency within 10, there only ten lessons addressing this portion of the standard. They are all within Topic 2, and only three of those lessons focus on subtraction. Lessons 2-6, 2-7, and 2-8 are the three lessons addressing subtraction within 10. Of the three subtraction lessons, two of them use addition to subtract, so the problems in the lesson all include addition and subtraction equations. For example, in Lesson 2-7, “Think Addition to Subtract,” one problem is “6+__=8. So, 8-6=___.” The materials provide few opportunities for students to add and subtract within 10 in these lessons.
• Fluency Practice Activities aligned to 1.OA.6 are found at the end of Topics 2-14. These activities are all either "Point & Tally," “Show the Word,” or "Find a Match" activities. These thirteen pages are found at the end of each Topic, not within a Lesson, so teachers would have to intentionally incorporate these activities into the lessons. Also, in some of these activities more problems are devoted to addition within 10 than subtraction within 10. For example, on page 139, there are six addition problems and two subtraction problems. On page 733, students only add to complete the activity. On page 841, there are six addition problems and two subtraction problems.
• Six Fluency Practice/Assessment pages from the student book aligned to K.OA.5 are included in the instructional materials. These pages from the student book can be seen on page 75P of the teacher's edition. These pages from the student book each have 19 problems. Of the 19 problems on each sheet, 15 are addition problems. Only three problems have students use a provided addition equation to fill in the answer to a subtraction problem. One problem includes both addition and subtraction.

As stated on page 75, the Game Center at PearsonRealize.com provides online mathematics games to help build fluency, but when you go to the games only one is beneficial for a student in Grade 1 to play when practicing fluency. The "Fancy Flea" game is a game that would be better used at a higher level. It requires more conceptual knowledge, and it would be difficult for most students in Grade 1 to maneuver and understand what is expected. The "Flying Cow Incident" game is good for building fluency and the concept of using a number line to add and subtract, but since it focuses on numbers within 20 it is better suited for Grade 2. The "Jungle Quest" game is actually more about focusing on patterns than it is on addition and subtraction, which is a Grade 4 standard. The game is very confusing and you have to make sure to click the learn button to understand what is expected. The "Launch the Sheep" game is confusing and above the Grade 1 level. It is actually more of a function table type problem. "Gobbling Globs" uses numbers larger than 120. It is a good game for students in Grade 2 learning to count by 100's and 10's but too advanced for Grade 1. "The Fluency Game" is a good game for building fluency at a first grade level. Although these games are listed in the Math Background pages, they are not actually mentioned in the lesson to suggest to teachers when they may be beneficial.

The instructional materials do not meet the expectations for balance. The majority of the lessons are very procedural. However, the fluency of facts is underdeveloped, and subtraction fluency is only given three lessons in the materials. There is a lack of conceptual understanding in the materials; most of the materials labeled as conceptual understanding miss opportunities to develop understanding and instead teach a procedure. Many lessons only focus on one aspect of rigor at a time. Often when more than one aspect of rigor is the focus of a lesson, the aspects are conceptual understanding and procedural skills. For example, in Topic 4, of the nine lessons, three target conceptual understanding and procedural skills, four target conceptual understanding, and two target application. In Topic 5, of the five lessons, four target procedural skill and conceptual understanding and one targets application. There are many missed opportunities to connect the different aspects of rigor.

The instructional materials reviewed for Grade 1 do not meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials do not treat each MP in a complete, accurate, and meaningful way.

The lessons give teachers some guidance on how to implement the standards. However, many of the MPs are misidentified in the materials. Also, the materials often do not attend to the full meaning of some of the MPs.

• MP1: Lesson 1-6 cites MP1. Students are asked to cross out the objects in the larger group to solve comparison problems; however, there is not a rich problem attached, only a page from the student book where the objects are already printed for the student. This does not provide the opportunity to make sense of a problem or persevere in solving it. Lesson 2-2 cites MP1. Again, a rich problem is not attached. Lesson 3-8 cites MP1; the problems provided are for fluency practice and do not provide students with rich problems to solve.
• MP4: Lesson 1-1 cites MP4; however, giving the students the materials to model with and then telling them how to model them is not meeting the intention of the MP. Lesson 1-3 asks students to draw spiders both inside and outside the cave to represent the whole; telling the students what to draw does not meet the intent of MP4. Lesson 2-4 cites MP4; again, students are told how to model the problem. Lesson 2-5 cites MP4, and again, students are told how to model the problem. In Lesson 8-3 on page 462, an image shows groups of ten cubes being circled with the question posed, "Why is it helpful to circle groups of 10?" The guided practice section of this lesson directs students to circle groups of 10 and write the numbers. Students are not modeling with mathematics within this task.
• MP5: Lesson 1-4 cites MP5; giving students cubes to use does not meet the intent of using appropriate tools strategically. To meet the intention students should be choosing and using their own mathematical tools. Lesson 2-1 cites MP5 but gives students a number line to use. Lesson 2-7 cites MP5, yet the lesson tells the students which tools to use. Although Lesson 4-1 gives students a number line as the tool, it cites MP5.
• MP7: Lesson 2-4 cites MP7, but telling the students what to write and the numbers to look for does not have them looking for structure. Lesson 3-7 cites MP7; however, the problem does not have students looking for or making use of structure. Lesson 4-3, cites MP7. Again, the students are told how to use the ten frames, so the opportunity to look for and use structure is taken away from them.
• MP8: Lesson 3-6 cites MP8, but telling students how to put the counters into the ten-frames does not have students looking for repeated reasoning. Lesson 4-5 cites MP8; telling students they can use addition to help solve subtraction word problems does not have students looking for repeated reasoning.

The materials do not meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Usually questions have one correct answer, and there is not much guidance for teachers on how to lead discussions beyond the provided questions and answer. There are many missed opportunities to guide students in analyzing the arguments of others.

• In Lesson 1-3, on page 21 students are asked, "Show how you could place the 5 pencils in these two cups. Complete the equation to show your work. Then talk to a classmate. Are your equations the same?" Students are not provided with additional guidance to help students compare equations.
• In Lesson 3-10, students are given the problem statement, "A pet store has 9 frogs. 5 of the frogs are green and the rest are brown. Lidia adds 5+9 and says the store has 14 brown frogs. Circle if you agree or do not agree with Lidia's thinking. Use pictures, words, or equations to explain." Teachers are provided with one question to pose that gets at the idea of what you can do to decide if you agree or disagree with someone's thinking about the way he or she solved a problem (page 210). This question is the only one in the lesson that will elicit deeper thinking about MP3, and there is limited support for teachers on engaging students in a discussion around this idea. There are several opportunities for students to agree/disagree with a given idea, but there is limited support to develop the skills to do this.
• In Lesson 4-9 on page 282, teachers are given a direction, "Ask students to identify the whole and parts in each equation. What is the whole in 6-2=4. What are the parts in your equation? What is the whole in your equation in Item 6? Are the parts and the whole the same in each equation? Are the two equations in the same fact family?" Teachers are provided with single correct responses and no support or guidance for developing a discussion or constructing arguments.
• In Lesson 8-2, students explain how they know that two tens is the same as twenty and use cubes to show their answer. Teachers are not provided any guidance about how to help students construct their explanations.
• In Lesson 9-2 on page 504 of the Teacher's Edition, teachers are told to "(h)ave students explain how numbers change when they show 10 more." Teachers are not provided sample explanations or guidance.
• In Lesson 13-3 students are asked the following questions: "How many minutes are there in an hour?" and "Why do you think a half hour is 30 minutes?" Teachers are provided with single correct responses and no support or guidance is provided.