1st Grade - Gateway 2

​The instructional materials for enVision Florida Mathematics Grade 1 meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons include several opportunities that address conceptual understanding.

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where conceptual understanding for the topic is outlined.
• Lessons are introduced via video, Visual Learning Animation Plus, at PearsonRealize.com building on conceptual understanding.
• Each Lesson Overview includes Rigor highlighting how conceptual understanding is incorporated into the lesson.
• Each lesson includes Solve and Share where students are able to build and demonstrate conceptual understanding.

Materials include problems and questions developing conceptual understanding throughout the grade-level and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade.

• In Lesson 8-4, students use models to compose numbers to establish “a foundation for place-value concepts with three- and four-digit numbers as well as for addition with greater numbers.” In Visual Learning Animation Plus, students are given rods and cubes and to “Count the tens and ones. Then write the numbers.” (1.NBT.2.2 and 1.NBT.1.1)
• In Lesson 8-6, students build overall number sense by flexibly naming numbers. “This lesson lays the foundation for later work in Grade 2 on regrouping to add and subtract.” In Solve and Share, “students use objects to show two different ways to show a two-digit number.” This task gives students the opportunity to build conceptual understanding in regrouping to add and subtract. (1.NBT.2.2d and 1.NBT.2.2.a)
• In Lesson 10-6, students “learn that when they are adding a one-digit number to a two-digit number, they need to determine if they can make a ten by combining the ones in the addends. This builds a foundation for understanding the formal procedures involved in addition algorithms.” In Solve and Share, students “connect work with an addition fact to adding a two- and one-digit number.” This task builds conceptual understanding by helping students make sense of the addition algorithm. (1.NBT.3.4)
• In Lesson 10-8, students “use a variety of strategies based on place value and the properties of the operations in order to solve addition problems. As students solve problems in different ways, they develop flexibility in their problem solving skills.”  In Solve and Share, students “add two-digit numbers by using a strategy that they have previously learned.” (1 NBT.3.4 and 1.NBT.3.5)
• In Lesson 12-2, students “develop an understanding of transitivity for length, which is the principle that if A is longer than B and B is longer than C, then without measuring directly, A must be longer than C.” In Solve and Share, “students show how they can compare the lengths of two objects that are not aligned.” (1.MD.1.1)
• In Lesson 14-2, students “focus on understanding the attributes that do and do not define a two-dimensional shape. Students apply what they learned in Lesson 14-1, that shapes are defined by their number of straight sides and vertices and whether they are closed or not.” In Solve and Share, “students find similarities and differences among five shapes.” (1.G.1.1 and 1.MD.1.a)

​The instructional materials for enVision Florida Mathematics Grade 1 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade-level.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where procedural skill and fluency for the topic is outlined for teachers. The structure of the lessons include several opportunities to develop procedural skill and fluency, including:

• Activity Centers
• Reteach to Build Understanding
• Build Mathematical Literacy
• Enrichment

Later Topics include Additional Practice and Fluency worksheets, Math Diagnosis and Intervention Systems, and My Fluency Progress Forms. Additional practice is located online at PearsonRealize.com.

Materials include problems and questions intended to develop procedural skill and fluency throughout the grade-level and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade.

• Topic 2 includes 6 Fluency Practice/Assessment Worksheets which provide students opportunities to independently demonstrate procedural skills and fluency.
• In Lesson 2-1, “As students use the strategy of counting on to solve addition problems, they begin to develop fluency for addition facts within 10.” In Independent Practice, students solve addition problems within 10 using a number line. (1.OA.1.1, 1.OA.3.5, and 1.OA.3.6)
• Lesson 2-3 “emphasizes fluency with facts through 10 as students solve near doubles facts.” Visual Learning Animation Plus, Independent Practice, Build Mathematical Literacy, Enrichment and Additional Practice sections provide opportunities to add doubles facts within 10. (1.OA.1.1, 1.OA.3.5, and 1.OA.3.6)
• In Lesson 3-2, students demonstrate fluency with addition within 10 and use strategies to add within 20. Students “connect breaking apart numbers to the procedure of recording it in an open number line model.” In Solve and Share, Visual Learning Animation Plus, Independent Practice, Reteach to Build Understanding, and Enrichment, students construct their own solution and demonstrate this procedural skill. (1.OA.3.5 and 1.OA.1.1)

​The instructional materials reviewed for enVision Florida Mathematics Grade 1 meet expectations for teachers and students spending sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where applications for the topic are outlined for teachers. Each Topic also includes:

• Topic Opener, containing a contextual STEM problem designed to spark interest in the content of the topic,
• Topic Centers with application problems,
• 3-Act Math activities where students engage in application problems, and
• Performance Tasks, where students apply mathematics of the topic in multi-step, real-world situations.

The structure of the lessons includes several opportunities for students to engage in routine and non-routine application problems. Practice & Problem Solving sections provide students with a variety of problem types to apply what they have learned. The way in which application is incorporated into specific lessons is stated in the Rigor section of the Lesson Overview of those lessons.

Examples of opportunities for students to engage in routine and non-routine application problems include:

• In Topic 1, Lesson 1-2, Solve & Share, students “solve a “put together” word problem situation. 4 red apples and 4 green apples. How many apples in all?  Show how you solve. Use cubes to help.” (1.OA.1.1)
• In Topic 5, enVision STEM Project, students draw a picture and work to solve addition and subtraction problems about animals that use sonar to communicate. (1.OA.1)
• In Lesson 10-9, Solve & Share, students solve, “Pam has 13 buttons. Julie gives her some more. Now Pam has 30 buttons. Use blocks or a number line to figure out how many buttons Julie gave Pam.” (1.NBT.3.4)

​The instructional materials for enVision Florida Mathematics Grade 1 meet expectations that the three aspects of Rigor are not always treated together and are not always treated separately.

Each Topic Overview contains Math Background: Rigor, where the components of Rigor are addressed. Every lesson within a Topic contains opportunities for students to build conceptual understanding, procedural skill and fluency, and/or application. During Solve and Share and Guided Practice, students explore alternative solution pathways to master procedural fluency and develop conceptual understanding. During Independent Practice, students apply the content in real-world applications, use procedural skills and/or conceptual understanding to solve problems with multiple solutions, and explain/compare their solutions.

In some instances, the three aspects of Rigor are present independently throughout the instructional materials. For example:

• Lesson 4-4 emphasizes Conceptual Understanding. A key goal of this topic “is understanding the relationship between addition and subtraction.” This lesson promotes conceptual understanding and “helps students begin to develop fluency with mathematical facts.” (1.OA.2.4)
• In Topic 8, Fluency Practice Activity, students “practice fluently adding to 10.” (1.OA.3.6)
• Lesson 12-4 emphasizes Application. “Rigorous mathematical instruction calls for the selection, management, and use of multiple problem-solving methods. Use the Thinking Habits shown in the Solve & Share task to help focus thinking in the lesson.” (1.MD.1.a)

Multiple aspects of Rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• In Lesson 5-5, Lesson Overview, Conceptual Understanding, Procedural Skill, and Application are the focus of the lesson. Conceptual Understanding: As students solve the problems (word problems with three addends), “students learn to apply the associative property of addition, which states that the sum of three or more addends does not change even if the addends are grouped and added in different ways. This exposure begins to build their conceptual understanding for the use of parentheses in equations at later grades. Procedural Skill: By using these properties, students develop procedural skills to record partial sums. Application: Students apply knowledge of adding three numbers to word problems.” Students demonstrate these aspects of rigor in the Solve and Share as they “apply different strategies to solve a word problem with three addends.” (1.OA.1.2 and 1.OA.2.3)
• In Lesson 7-5, Lesson Overview, Conceptual Understanding and Procedural Skill are emphasized. “Conceptual Understanding: As students use a number line to count by both 1s and 10s, they strengthen their abilities to count and to identify the numbers that come before and after a given number. Procedural Skill: Students also develop skills in how to model counting with a number line.” Students demonstrate these aspects of rigor in the Solve and Share as they “use an open number line to demonstrate counting on by 1s.”(1.NBT.1.1)

​The instructional materials reviewed for enVision Florida Mathematics Grade 1 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade-level.

The MPs are used to enrich the mathematical content and are not treated separately. MPs are highlighted and discussed throughout Topic Planners, Topic Overviews, 3-Act Math Tasks, and identified within each lesson of every topic. Additionally, the Math Practice and Problem Solving Handbook includes a list of the MPs and real-world scenarios modeled through questions and answers. The online tools offer a Math Practices Animation video that explains the MPs and offers problems that demonstrate each one.

Examples of the MPs identified within the materials include:

• In Topic 8, Topic Overview, the “math practices are highlighted in all lessons and are given special emphasis in lessons that focus on problems solving.” For example, MP.4.1: Model with mathematics, “Students model with mathematics and use drawings of tens and ones to represent numbers. (e.g., [Lesson 8-5], Convince Me!).”
• In Topic 11, 3-Act Math Task (So Many Colors), “As students carry out mathematical modeling, they engage in sense-making (MP.1.1), abstract and quantitative reasoning (MP.2.1), and mathematical communication and argumentation (MP.3.1). They use appropriate tools to develop their models (MP.5.1). In testing and validating their models, students attend to precision (MP.6.1) and look for patterns in the structure of their models (MP.7.1 and MP.8.1)."

Examples of where MPs are identified and used to enrich the content:

• In Lesson 3-2, MP.4.1, “Students use a specific tool, an open number line, to create a model of addition problems.” MP.4.1 is used to enrich the content as students solve a problem counting to add on using an open number line to solve how many miles a character ran.
• In Lesson 5-7, MP.6.1, “Students attend to precision as they use math symbols correctly and explain their reasoning about problems clearly.” MP.6.1 enriches the mathematical content in the Solve and Share, as students write a true equation with one number on one side and three on the other side, show their equation, and explain their reasoning.
• In Lesson 9-1, MP.8.1, “Students generalize that 1 more and 1 less always changes the ones digit and 10 more and 10 less always changes the tens digit.” MP.8.1 is used to enrich the content in the Solve and Share, as students solve problems finding 1 more and 10 more than a number using blocks or drawings.

​The instructional materials reviewed for enVision Florida Mathematics Grade 1 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Several structures exist within the Grade 1 materials prompting students to construct viable arguments such as:

• In Convince Me!, students answer open-ended questions to demonstrate how they know the answer.
• In the 3-Act Math activities, Critique Reasoning, students share solutions and analyze the work of others that allows students to construct viable arguments.
• In most lessons, Construct Arguments, students answer open-ended questions to construct viable arguments.
• In Solve and Share, there is an opportunity for students to critique the reasoning of others and construct viable arguments.
• In Visual Learning Bridge, there is an opportunity for students to construct viable arguments.
  
  

Student materials consistently prompt students to both construct viable arguments and analyze the arguments of others.

• In Lesson 1-9, students “construct arguments as they explain their solution strategies for addition and subtraction word problems. They also analyze and critique strategies of others.”
• In Lesson 4-9, Problem Solving, Item 7, Construct Arguments, “Ask students to identify the whole and the parts in each equation. What is the whole in 6 - 4 = 2?, 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?”
• In Lesson 6-4, Guided Practice, Convince Me!, students discuss, “How did Abby know to count up from 5 to 12 in the problem above?”
• In Lesson 7-3, Convince Me!, Construct Arguments, “Explain and point out on a number chart that the number that is 1 more is to the right of a number.”

​The instructional materials reviewed for enVision Florida Mathematics Grade 1 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking.

• At the beginning of each lesson the Solve and Share contains After: Discuss Solution strategies and Key Ideas.
• Each lesson has Convince Me! in the Visual Learning Bridge where teachers are provided with prompts to assist students in constructing viable arguments.
• The 3-Act Math Activity has Construct Arguments with prompts for the teacher to use during the activity.
• The Math Practices and Problem Solving Handbook for each grade level identifies the lessons for each grade level focusing on constructing viable arguments and critiquing the reasoning of others (Lessons 1-10 and 5-4).

Teacher materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others frequently throughout the program:

• In Lesson 3-9, Convince Me!, Critique Reasoning, “Sharon wrote the equation 8 - 5 = 3 to solve the problem and said that 3 more dogs came to play. Do you agree or not agree with her thinking?”
• In Lesson 9-1, Solve and Share, “How does Pearl’s work show that Chris has 1 more marble than Sarah? How does Pearls’ work show that Lucia has 10 more marbles than Sarah?”
• In  Lesson 10-8, Visual Learning Bridge, Convince Me!, Construct Arguments, “You may wish to have students solve the same problem two different ways to show that they can use any strategy that correctly shows and solves the problem.”

​The instructional materials reviewed for enVision Florida Mathematics Grade 1 meet expectations for explicitly attending to the specialized language of mathematics.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them.

• The Teacher Edition Topic Overview: Build Mathematical Literacy outlines multiple ways the materials address mathematics vocabulary. These components can be found in every topic under Build Mathematical Literacy:
• Build math vocabulary: “using the vocabulary cards, vocabulary activities, vocabulary review, and glossary plus the online glossary and vocabulary game.”
• My Word Cards: “Vocabulary cards for a topic are provided online at PearsonRealize.com. Students use the example on the front of the card to complete the definition on the back.”
• Vocabulary Activities: “The Teacher’s Edition provides vocabulary activities at the start of topics. These include activities for vocabulary in My Word Cards or activities for vocabulary in Review What You Know.”
• Vocabulary Review: “A page of vocabulary review is provided at the end of each topic. It reviews vocabulary used in the topic.”
• Glossary: “A glossary is provided at the back of Volume 1 of the Students’ Edition.”
• Animated Glossary: “An online, bilingual, animated glossary uses motion and sound to build understanding of math vocabulary.”
• Online Vocabulary Game: “An online vocabulary game is available in the Game Center.”
• Lesson-specific vocabulary can be found in each Topic Planner. For example, in the Teacher Edition, Topic 2, Lesson 2-1: number line; Lesson 2-2: doubles fact; Lesson 2-3: near doubles fact; and so on. The same vocabulary words are listed in the Lesson Overview under Lesson Resources.
• A Glossary is provided in the back of the Student Edition.
• Both the topic and the lesson narratives contain specific guidance for the teacher to support students to communicate mathematically. Within the lesson narratives, new terms are highlighted in yellow and explained as related to the context of the material.
• Topic 8, Vocabulary Review, “students review vocabulary words used in the topic.” Oral Language: “Before students do the page, you might reinforce oral language through a class discussion involving one or more of the following activities: Have students define the terms in their own words. Have students say math sentences or math questions that use the words. Play a “What’s My Word?” guessing game in which you or a student thinks about one of the words and says a clue that others listen to before they guess the word.”
• Topic 10, Vocabulary review, the words, “add, ones, open number line, tens.” Students demonstrate understanding by, “1. Use the models to add the tens. 2. Use the models to add the tens…. 4. Solve 20+6 using an open number line. Explain how you solved it using terms from the word list.”

No examples of incorrect use of vocabulary, symbols, or numbers were found within the materials.