3rd Grade - Gateway 1

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 available online and/or in paper and pencil format. The series also includes a Topic Performance Task for each Topic. Additional assessments include a Grade 3 Readiness Test and four Cumulative/Benchmark Assessments that address Topics 1-4, 1-8, 1-12, and 1-16. Assessments can be found in the Assessment Resource Book in print or online. The materials also include an ExamView Test Generator.

Assessments contain grade-level content questions. Examples of questions include the following:

• Topic 3, Topic Assessment, Question 4 states, “Jamal broke up a large array into a 3x6 array and a 4x6 array. What was the large array?” (3.OA.2.5)
• In Topic 4, Topic Assessment, Question 7, students match each expression on the left with the equivalent expression. (3.OA.3.7) Expressions on the left include $$0\div8$$, $$36\div6$$, $$4\div4$$, $$35\div5$$. Expressions on the right include: $$8\div8$$, 6 x 0, 7 x 1, 1 x 6.
• Topics 1-8, Cumulative Assessment, Question 12 states, “Louise made the shape from tiles. What is the area of the shape. Explain.” The shape has 4 whole squares and 6 diagonal halves of squares around the outside. (3.MD.3.6)
• In the Topic 12, Performance Task students represent fractions on a number line (3.NF.2) and partition whole numbers into equal parts using a number line.
• In Topic 13, Topic Assessment, Problem 8, students compare equivalent fractions by filling them in on a double number line and has the number line missing $$\frac{1}{4}$$, $$\frac{2}{4}$$, and $$\frac{3}{4}$$, and its equivalent $$\frac{2}{8}$$, $$\frac{4}{8}$$, and $$\frac{6}{8}$$. (3.NF.1.3)

Questions that are above grade level could be omitted or modified. The following questions align to 4.NBT.2.6 as they include a remainder in the solution:

• In Topic 2, Performance Task, Question 6 states, “Carlos reads 10 pages every day. The book he is reading has 46 pages. How many days will it take him to finish his book? Complete the chart and explain your answer.”
• In Topic 4, Assessment, Question 10A states, “Jerome divided his baseball card collection into 2 equal groups. There was 1 baseball card left over. Describe the number of baseball cards Jerome has.”
• In Topics 1-4, Cumulative/Benchmark Assessment, Question 13, students answer a question that involves leftovers/remainders.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 86 out of 104, which is approximately 83 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 115 out of 144, which is approximately 80 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 83 percent of the instructional materials focus on major work of the grade.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 Lessons 7-1 through 7-4, students interpret data in scaled picture graphs and bar graphs (cluster 3.MD.2.3) and connect it to solving problems with equal groups, multiplication and division, and solving one- and two-step word problems involving multiplication and division. (clusters 3.OA.1.3 and 3.OA.4.8)
• In Lesson 10-2, students use place-value understanding and properties of operations (3.NBT.1.3) with the properties of multiplication. (3.OA.1.3)
• In Lesson 15-1, students describe quadrilaterals using the understanding of a fraction as the quantity formed when a whole is partitioned into equal parts. This connects the supporting work of (3.G.1.1) to the major work of (3.NF.1.1).
• In Lesson 15-4, students work with attributes of shapes (3.G.1.1) to answer problems about the area of shapes. (3.MD.3.7.b)

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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, 1 day each .
• There is a Topic Review and Assessment for each of the 16 Topics, 2 days per Topic.

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 3 meet the expectation for being consistent with the progressions in the standards. Content from prior grades is identified and 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 Edition Program Overview, all grade-level standards are present as noted in the section, "Correlation to Florida Grade 3 Standards."

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

For example, the Teacher Edition, Topic 5 Overview, Math Background: Coherence includes:

• Look Back: Grade 2: "In Topic 2, students began to work in equal groups of objects arranged in arrays. They learned to find the total number of objects by writing equations using rows or columns.” Earlier in Grade 3: "Understand Multiplication and Division Situations" and "Multiplication Facts" reference content from Topics 1 and 2 respectively.
• Topic 5 describes how the content is connected within the topic, including "Multiplication Tables," Use of  Strategies," and "Connecting Stories and Equations."
• Look Ahead: Later in Grade 3, "Fact Fluency" (Throughout the grade) and "Apply Multiplication and Division Facts" (Topic 6). In Grade 4, this topic is connected to "Whole Number Multiplication and Division" (Topics 3, 4, and 7) and "Extend Multiplication Concepts" (Topic 10).

The instructional materials give extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling task. 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. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to Independent Practice. During Independent Practice students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example, in the Student Edition, Lesson 16-3, “These plane figures each have equal sides that are whole numbers. One figure has a perimeter of 25 inches. Which could it be? Explain.” (3.MD.4.8)

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 3 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 1-4, the lesson objective states, “Use sharing to separate equal groups and to think about division,” which is shaped by 3.OA.1, “Represent and solve problems involving multiplication and division.”
• In Lesson 13-2, the lesson objective states, “Represent equivalent fractions on the number line,” which is shaped by 3.NF.1, “Develop understanding of fractions as numbers.”
• In Lesson 14-2, the lesson objective states, “Tell and write time to the nearest minute and measure time intervals in minutes,” which is shaped by 3.MD.1, “Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.”

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.

• In Lesson 2-1, 3.OA.1 connects to 3.OA.4 when students represent and solve problems involving multiplication and division while solving problems involving the four operations that include identifying and explaining patterns in arithmetic.
• In Lesson 14-5, 3.MD.1 connects to cluster 3.NF.1 when students connect solving problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects to developing an understanding of fractions as numbers.
• In Lesson 6-4, page 221A, 3.MD.3 connects to 3.OA.1 when students write an area equation for a rectangle with an unknown dimension.
• In Lesson 11-2, page 413A, 3.OA.4 connects to 3.OA.3 when students solve two-step word problems to develop fluency in multiplication and division facts.