4th Grade - Gateway 1

​The instructional materials reviewed for enVision Florida Mathematics Grade 4 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. In instances where there are above grade-level questions, the material could easily be omitted or modified by the teacher. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments.

The series is divided into topics, and each topic has a Topic Assessment that can be administered online and/or paper and pencil formats. In addition, there is a Topic Performance Task for each topic. Additional assessments include a readiness assessment found in Topic 1, four cumulative/benchmark assessments, and a cumulative end of year assessment. Assessments can be found in the Assessment Resource book in print or online. The materials also include an ExamView Test Generator that is able to be used.

Examples of assessments containing grade-level content questions include the following:

• In Topic 1, Performance Task, students compare numbers and write numbers in expanded form. (4.NBT.1.2)
• In Topic 2, Topic Assessment, Question 2, students find “3,000-2,450.” (4.NBT.2.4)
• Topic 6, Topic Assessment, Question 10, “Sabrina jogged 54 laps around the football field. Harry ran 9 laps. How many times as many laps did Sabrina run than Harry?” (4.OA.1.2)
• Topics 1-4, Cumulative/Benchmark Assessment, Question 14, “Which of the following shows how to find 4 x 567? Which property was used?” The solution makes use of parentheses so that students would add before multiplying. (4.NBT.2)

Questions that are above grade level could be omitted or modified. For example, there are two items in the Topic 12 Topic Assessment that align to 5.NBT.2.7, adding and subtracting decimals:

• Question 3 states, “Jackson spends $12.85 on a book, $5.89 for lunch, and $2.35 for a magazine. How much money did he spend in all?” (5.NBT.2.7)
• Question 5 states, “Maria takes the money shown to the art supply store. Part A) Does Maria have enough money for all three items? Explain.” (Adding and subtracting decimals aligns to 5.NBT.2.7.)

​The instructional materials reviewed for enVision Florida Mathematics Grade 4 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 16, which is approximately 75 percent.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 91 out of 104, which is approximately 88 percent
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 121 out of 144, which is approximately 84 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 88 percent of the instructional materials focus on major work of the grade.

​The instructional materials reviewed for enVision Florida Mathematics Grade 4 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards are used to support major work of the grade and often appear in lessons with connections to the major work of the grade.

Throughout the series, supporting standards/clusters are connected to the major standards/clusters of the grade. The following are examples of the connections between supporting work and major work in the materials:

• In Lesson 7-2, students identify factors (cluster 4.OA.2.4.a) using place-value understanding and properties of operations to perform multi-digit arithmetic. (cluster 4.NBT.2.5)
• In Lessons 11-1 and 11-3, students make line plots (4.MD.2.4) while adding and subtracting fractions. (4.NF.1.2 and 4.NF.2.3.d)
• In Lessons 13-4 and 13-5, students convert within metric measurements (4.MD.1.1) and solve multi-step word problems that involve operations with whole numbers. (4.MD.1.2, 4.OA.1.3, and 4.NF.3.7)
• In Lesson 15-2, students work with angles and unit angles (4.MD.3.5.a) to find the measure of an angle that turns through a fraction of a circle. (4.NF.1.1 and 4.NF.2.3.b)

​The instructional materials reviewed for enVision Florida Mathematics Grade 4 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades.

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 144 days.

• There are 104 content-focused lessons designed for 45 to 75 minutes including differentiation.
• There are eight 3-Act Math Lessons, which are one day each.
• There is a Topic Review and Assessment for each of the 16 Topics, two days per Topic (32 days).

There are also additional resources containing more lessons to be used after the last Topic, including Math Diagnosis and Intervention System, Florida Standards Practice, and 10 Step-Up Lessons.

​The instructional materials reviewed for enVision Florida Mathematics Grade 4 meet the expectation for being consistent with the progressions in the standards. Content from prior grades is identified or connected to grade-level work, and students are given extensive work with grade-level problems.

Overall, the materials develop according to the grade-by-grade progressions in the CCSSM. Typically, material related to prior and future grades is clearly identified or related to grade-level work. In the Teacher’s Edition Program Overview, all grade-level standards are present as noted in the section, "Correlation to Florida Grade 4 Standards."

The Teacher’s Edition contains a Topic Overview Coherence: Look Back, and a Lesson Overview Coherence: Look Back, which identify connections to content taught earlier in the grade and/or in previous grades, indicating the relevant topics and/or lessons. In the Topic Overview: Look Ahead, and the Lesson Overview: Look Ahead, include connections to content taught later in the grade and/or in future grades, topics, or lessons. Though explicit connections are made to prior and future work, standards are not listed in either the “Look Back” or “Look Ahead,” and the connections are written as general statements from the standards.

For example, the Teacher’s Edition, Topic 4 Overview, Math Background: Coherence includes:

• Look Back: “In Multiplication in Grade 3 Topics 1, 2, 3, and 5, students learned about multiplication and developed fluency with the basic multiplication facts. In Topic 10, students used place-value patterns to multiply and earlier in Grade 4, Topic 3, students used arrays, area models, the Distributive Property, and partial products to multiply.”
• Topic 4 includes: “ Estimation: In Lesson 4-3, students use rounding to estimate products. They use estimation to check the reasonableness of their answers in the remainder of the topic. Models and Distributive Property: Students use arrays, area models, and the Distributive Property throughout the topic as they use partial products to find the product of two 2-digit numbers."
• Look Ahead: “Later in Grade 4, students will use their understanding of multiplication and their skill in multiplying as they use patterns, models, and partial quotients to divide by 1-digit numbers. Estimation: In Lesson 4-3, students use rounding to estimate products. They use estimation to check the reasonableness of their answers in the remainder of the topic.

The instructional materials give extensive work with grade-level problems. All Topics begin with an optional, on grade-level project, and every other Topic incorporates on grade-level 3-Act Math tasks. During the Solve and Share, Visual Learning Bridge, and Convince Me, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. The Guided Practice allows students to solve problems and check for understanding before moving on to Independent Practice. The Independent Practice provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section provides additional practice problems for each of the lessons. For example, Student Edition, Lesson 13-6, “The area of a tabletop is 18 square feet. The perimeter of the same table is 18 feet. What are the dimensions of the tabletop?” (4.MD1.3)

There is support in the Quick Checks for each lesson to assign additional problems to students, including, Intervention Activity, Reteach to Build Understanding, Build Mathematical Literacy, Enrichment, Activity Centers, or Additional Practice (with leveled-assignment choices provided).

​The instructional materials for enVision Florida Mathematics Grade 4 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Examples of learning objectives that are visibly shaped by CCSSM cluster headings include:

• In Lesson 1-2, the lesson objective states, “Recognize the relationship between adjacent digits in a multi-digit number,” which is shaped by 4.NBT.1, “Generalize place-value understanding for multi-digit whole numbers.”
• In Lesson 4-6, the lesson objective states, “Use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems,” which is shaped by 4.NBT.2, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”
• In Lesson 8-3, the lesson objective states, “Use multiplication to find equivalent fractions," which is shaped by 4.NF.1, “Extend understanding of fraction equivalence and ordering.”

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

• Lesson 6-3, 4.OA.1 connects to 4.NBT.2 when students multiply whole numbers to solve multi-step word problems.
• Lesson 8-4, 4.NF.1 connects to 4.OA.1 when students use division to find equivalent fractions.
• Lesson 14-1, 4.OA.3 connects with 4.NBT.2 when students create and extend number sequences based on a rule.