5th Grade - Gateway 1

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. In instances where there are inconsistencies, 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 in paper and pencil formats. 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 or an online version is available. The materials also include an ExamView Test Generator that is able to be used.

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

• Topic 1 Assessment, Question 9 states, “Eddy’s plum weighs 3.042 ounces. Desta’s plum weighs 3.24 ounces. Whose plum weighs more? How can you tell?” (5.NBT.1.3.b)
• In the Assessment Sourcebook, Topic Assessment 2, Question 3, students find the sum of 5.92 + 3.48. Students are given a choice of four numbers, and each of the distractors represents a misconception students may have about decimals and place value. (5.NBT.2.7)
• Topics 1-4, Cumulative/Benchmark Assessment, Question 1 states, “When multiplying a number by $$10^5$$, how is the decimal point moved?” (5.NBT.1.2)
• Topic 4 Assessment, Question 16 states, “A forest preserve has an area of 1.6 square miles, and 0.3 of the forest preserve is open for hiking. Part A Shade the grid to model the multiplication. Part B How many square miles are open for hiking? Use an equation and the model to explain.” (5.NBT.2.7)
• In the Topic 7 Performance Task, students add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (5.NF.1.1)
• Topic 8 Assessment, Question 9 states, “Complete the equation. Explain how you got your answer. $$\frac{4}{5}$$ x $$\frac{3}{7}$$ =?” (5.NF.2.4.a)
• In Topic 9 Assessment, Question 14, students are given four equations, two whole numbers divided by a unit fraction, and two whole numbers multiplied. Students write numbers in the boxes to make the equations true and then make generalizations about the equations. (5.NF.2.7.b)

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 87.5 out of 108, which is approximately 81 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 123 out of 148, which is approximately 83 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 81 percent of the instructional materials focus on major work of the grade.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 10-2, students make line plots (cluster 5.MD.2.2) using the understanding of ordering fractions and decimals. (cluster 5.NF.1.2)
• In Lesson 10-3, students solve problems based on data from line plots (5.MD.2.2) using understanding of operations with fractions to solve problems. (5.NF.1.2)
• In Lesson 12-1, students convert customary units of length (5.MD.1.1) to solve problems involving multiplication and division. (5.NBT.2.5 and 5.NBT.2.6)
• In Lesson 12-5, students convert metric units of capacity (5.MD.1.1) to find patterns in multiplying and dividing a number by powers of 10. (5.NBT.1.2)
• In Lesson 12-8, students solve word problems using measurement conversions (5.MD.1.1) to solve problems involving multiplication and division of fractions. (5.NBT.2.5)

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 148 days.

• There are 108 content-focused lessons designed for 45 to 75 minutes including differentiation.
• There are eight 3-Act Mathematics Modeling 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 5 meet the expectation for being consistent with the progressions in the CCSSM. 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 standards. 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 5 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 Coherence: Look Ahead includes 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: Grade 4 Topic 3, “Students used strategies and properties to multiply 1-digit numbers by numbers with up to 4 digits. In Topic 4, they did the same to multiply 2-digit whole numbers. Some of the whole-number strategies, such as partial products, are applied to decimals in Grade 5, Topic 4. Early in Grade 5, Lesson 3-1, students explored patterns in multiplying whole numbers by powers of 10.”
• In Topic 4 includes: "Students are multiplying decimals by powers of 10 in Lesson 4-1 and estimate products of whole numbers and decimals.
• Look Ahead: “Later in Grade 5, students will use what they learn about multiplying with decimals when they divide with decimals in Topic 6.”

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 Mathematical Modeling 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, such as in the Student Edition, Lesson 12-3, "4 oz = ___lb.” (5.MD.1.1)

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 5 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 5-5, the lesson objective states, “Use place value and sharing to divide by 2-digit divisors,” which is shaped by cluster 5.NBT.2, “Perform operations with multi-digit whole numbers and with decimals to the hundreths.”
• In Lesson 7-3, the lesson objective states, “Add fractions with unlike denominators using equivalent fractions with a common denominator,” which is shaped by cluster 5.NF.1, “Use equivalent fractions as a strategy to add and subtract fractions.”
• In Lesson 11-1, the lesson objective states, “Find the volume of solid figures” which is shaped by 5.MD.3, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”

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.

• Topic 3, 3-Act Math, 5.NBT.1 connects to 5.NBT.2 when students use place-value understanding to perform operations with multi-digit numbers, including those with decimals.
• Lesson 4-5, 5.NBT.1 connects to 5.NBT.2 when students use place value understanding and models to multiply a decimal.
• Lesson 15-3, 5.G.1 connects to 5.OA.2 when students analyze and graph relationships using numerical patterns.