5th Grade - Gateway 1

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that they assess grade-level content, and if applicable, content from earlier grades. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments.

Assessments are found in the Teacher Guide and the Assessment Sourcebook. Topic Assessment and Performance Tasks are provided at the end of every unit to assess student understanding of standards taught in the Topic. Cumulative/Benchmark Assessments are given after a group of topics have been taught. Customizable Digital Assessments allow teachers to edit, add questions, and build tests from scratch.

Questions assessing grade-level content include, but are not limited to:

• Topic 2 Assessment, Question 9, states, “Amber bought a hardcover book for $23.70 and a paperback for $6.91. How much did she spend in all? If she paid with 2 twenty-dollar bills, how much change did she get?” Students perform operations with decimals to hundredths (5.NBT.7).
• Topic 14, Performance Task, states, “Omar’s mother is a paleontologist. She digs up and studies dinosaur bones. Omar is helping at the dig site. The Dinosaur Bone Dig 1 grid shows the location of the tent and the triceratops skull Omar’s mother found.” Students name a point on the coordinate plane to solve real-world problems (5.G.2). 
• Topics 1-12, Cumulative Assessment, Question 11, states, “Bottles of water are packaged with 24 bottles per case. A store has 365 cases to sell. How many bottles of water does the store have to sell?” Students fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5).

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet  expectations for spending a majority of instructional time on major work of the grade. 

Evidence includes, but is not limited to:

• 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%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 92 out of 108, which is approximately 85%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 122 out of 148, which is approximately 82%. 

A lesson level analysis is most representative of the instructional materials since the lessons include major work, supporting work connected to major work, and assessments embedded within each topic. As a result, approximately 85% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are used to support major work of the grade and are connected to the major standards/clusters of the grade.

Examples of connections between supporting and major work of the grade include, but are not limited to:

• In Lesson 10-1, students read line plots (5.MD.2) and solve problems using operations with fractions (5.NF.2). Question 14 provides a line plot of weights of melons in fractional form and states, “Use the information shown in the line plot. What is the total weight of the 4 heaviest melons?”
• In Lesson 10-2, students make line plots (5.MD.2) using understanding of ordering fractions and decimals (5.NBT.3). Question 8 provides a data table of heights of tree saplings in fractional form and states, “Martin’s Tree Service purchased several spruce tree saplings. Draw a line plot of the data showing the heights of the saplings.”
• In Lesson 10-3, students solve problems with data in line plots (5.MD.2) using operations with fractions (5.NF.2 and 5.NF.6). Question 7 provides a line plot of rainfall in fractional inches and states, “Write and solve an equation for the total amount of rainfall, r, Susannah recorded.”
• In Lessons 12-1 and 12-8 students convert customary units of length (5.MD.1) to solve problems involving multiplication and division (5.NBT.5 and 5.NBT.6). Lesson 12-8, Question 9 states, “Marcia walked 900 meters on Friday. On Saturday, she walked 4 kilometers. On Sunday, she walked 3 kilometers, 600 meters. How many kilometers did Marcia walk over all three days?”
• In Lesson 12-5, students convert metric units of capacity (5.MD.1) using patterns of multiplying and dividing powers of 10 (5.NBT.2). Question 24 states, “Carla makes 6 liters of punch. She pours the punch into 800 mL bottles. How many bottles can she fill?”
• In Lesson 13-3, students interpret numerical expressions (5.OA.2) that involve operations with whole numbers and decimals (5.NBT.5). Question 12 states, “A four story parking garage has spaces for 240 + 285 + 250 + 267 + cars. While one floor is closed for repairs, the garage has spaces for 240 + 250 + 267 cars. How many spaces are there on the floor that is closed? Explain.”

Instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 148 days. 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. 

• There are 108 daily content-focused lessons. According to the Pacing Guide, “Each core lesson including differentiation, takes 45-75 minutes.” 
• There is a Topic/Vocabulary Review and Assessment for each of the 16 topics, which are suggested to take two days per topic.
• There are eight 3-Act Math activities where students solve problems using mathematical modeling, which are found in odd-numbered topics and are allotted one day each.

According to the Pacing Guide, additional time can be spent on the following resources (TE 23A):

• Lesson Resources: More days can be spent on some lessons for conceptual understanding, skill-development, and differentiation.
• Additional Resources: More days can be spent on the Math Diagnosis and Intervention System and the 10 Step-Up Lessons used after Topic 16.
• Assessments: More days can be spent on the Readiness Test, Review What You Know, Cumulative/Benchmark Assessments, and Progress Monitoring Assessments (Forms A, B, and C). 

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations for the materials 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. All grade-level standards are present in the Teacher Edition Program Overview “Grade 5 Common Core Standards.”

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. The Teacher Edition contains a Topic Overview Coherence: Look Back, which identifies 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 later in the grade and in future grades, topics, or lessons. For example, the Teacher Edition, Topic 4 Overview, Math Background: Coherence, includes:

• “Look Back, Grade 4: In 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 two 2-digit whole numbers. Some of the whole-number strategies, such as partial products, are applied to decimals in Grade 5, Topic 4. Earlier in Grade 5, Lesson 3-1, students discovered to find the product of powers of 10, they should look at the number of zeros and then place the number of zeros on the end of the factor, and that the decimal moves to the right when multiplying decimals by a power of 10.”
• “Connections within Topic 4 include: Students multiply decimals by powers of 10 and estimate products of whole numbers and decimals. Students use number sense to place the decimal point in the product after multiplying as if the decimals were whole numbers.”
• “Look Ahead: In Topic 6, students use what they learn about multiplying with decimals when they divide with decimals. In Topic 12, students use what they learn about multiplying decimals by powers of 10 to convert from one metric unit of measurement to another. In Grade 6, students fluently multiply decimals using the standard algorithm.”

The instructional materials attend to the full intent of the grade-level standards by giving all students 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 & Share, Visual Learning Bridge, and Convince Me! sections, 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 the 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, students engage in extensive work with Cluster 5.NF.A grade-level problems in Topic 7: Use Equivalent Fractions to Add and Subtract Fractions, including:

• In Topic 7, 3-Act Math, students watch a video of a girl baking banana bread with the measurements for the recipe given. Students make predictions: “Is the red bowl big enough?” Students discuss what information would be needed to solve the problem, and the teacher provides the necessary information so the students can model the solution.
• In Lesson 3, Convince Me!, students use number sense to analyze the information given in the problem to explain why equivalent fractions that use different numbers in the numerator and denominator can have the same value. The question states, “In the example above, would you get the same sum if you used 12 as the common denominator? Explain.”
• In Lesson 7, Problem Solving, Question 18 states, “Paul said, ‘I walked $$2\frac{1}{2}$$ miles on Saturday and $$2\frac{3}{4}$$ miles on Sunday.’ How many miles is that in all?”

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. In the Math Background: Coherence section for each Topic, the Teacher Edition provides explicit connections to prior learning, but standards are not provided. Additionally, some lesson Look Back sections detail connections to previous grades.

Connections to prior grade-level learning include, but are not limited to:

• In Topic 3, Math Background Coherence: Fluently Multiply Multi-Digit Whole Numbers, the Look Back states, “In Grade 4, Topic 1, students learned to round whole numbers. Then throughout Grade 4, they used rounding and compatible numbers to estimate computations with all four operations. They used estimates to check reasonableness of computations.”
• In Topic 7, Math Background Coherence: Use Equivalent Fractions to Add and Subtract Fractions, the Look Back states, “In Grade 4, Topic 7, students learned how to find all the factors of a number and to identify and list multiples”.
• In Lesson 9-1, the Look Back states, “In Grade 4, students extended their understanding of division to recognize $$\frac{a}{b}$$ as a multiple of $$\frac{1}{b}$$, that is $$\frac{a}{b}=a$$x$$\frac{1}{b}$$.”
• In Lesson 11-1, the Look Back states, “In previous grades, students have learned about measuring length, weight or mass, capacity, and area by using manipulatives and standard units of measurement.” In this lesson students find the volume of solid figures.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Examples include, but are not limited to:

• The Topic Planner states Topic 2: “Focuses on developing understanding of addition and subtraction of decimals using models, strategies and understanding of decimal place value (5.NBT.A and 5.NBT.B).” For example, in Lesson 2-2, “students estimate decimal sums and differences using rounding and compatible numbers.”
• Lesson 8-1, the Mathematics Objective states, “Multiply a fraction by a whole number.” This is shaped by 5.NF.B: “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.” 
• Lesson 11-2, the Mathematics Objective states, “Find the volume of rectangular prisms using a formula.”  This is shaped by 5.MD.C: “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. Examples include, but are not limited to:   

• Lesson 4-1 connects 5.NBT.A to 5.NBT.B when students use what they learned about place value patterns to multiply decimals by powers of 10.  
• Lesson 11-4 connects 5.MD.5c to 5.NBT.5 when students solve problems involving volumes of rectangular prisms to developing fluency in multiplication. 
• Lesson 15-2 connects 5.OA.3 to 5.NBT.5 when students identify relationships between patterns using their understanding of multiplication of whole numbers.