3rd Grade - Gateway 1

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 meet expectations that they assess grade-level content, and if applicable, content from earlier grades. In instances where above-level content is assessed, questions could easily be omitted or modified by the teacher. 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:

• Topic 9, Assessment, Question 1, states, “Find the sum of 458 and 342. Use place value and find the sums of the hundreds, tens, and ones.” Students use place value understanding to perform multi-digit arithmetic (3.NBT.2).
• Topic 12, Performance Task, Question 3, states, “Divide the number line into the number of equal parts of the cake. Then mark a dot on the number line to show the part of the cake that Bruno frosted. Write the fraction that he frosted.” Students represent a fraction on a number line (3.NF.2).
• 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 four whole squares and six diagonal halves of squares around the outside. Students use understanding of multiplication and addition related to area (3.MD.6).

Questions assessing content above grade level that can be omitted or modified include:

• 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.” This question requires students to calculate with remainders in the solution (4.NBT.6).
• Topics 1-4, Cumulative/Benchmark Assessment, Question 3, states, “A coach brought a cooler with 20 bottles of water for the baseball team. Each player gets the same number of bottles of water. There are 9 players on the team. Which statement is true?” This question requires students to calculate with remainders in the solution (4.NBT.6).

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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 14 out of 16, which is approximately 88%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87 out of 104, which is approximately 84%.
• 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%. 

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 84% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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 Lessons 7-1 through 7-4, students interpret data in scaled picture graphs and bar graphs (3.MD.3) to solve two-step problems using multiplication and division (3.OA.8). Lesson 7-1, Question 8 states, “How many more points were scored on October 10 and 24 combined than on October 3 and 17?”
• In Lesson 8-5, students round whole numbers (3.NBT.1) to determine the reasonableness of answers (3.OA.8). Question 17 states, “Zoe says 247 rounded to the nearest hundred is 300 because 247 rounds to 250 and 250 rounds to 300. Is Zoe correct? Explain.”
• In Lesson 15-3, students identify attributes of shapes (3.G.1) using area as an attribute (3.MD.7b). Question 11 states, “Explain which of the shapes at the right you can cover with whole unit squares and not have any gaps or overlays.”
• In Lesson 10-2, students use place-value to find multiples of whole numbers and 2-digit multiples of 10 (3.NBT.3) in multiplication problems (3.OA.3). Question 21 states, “Juanita buys 7 sheets of postage stamps at the post office. Each sheet has 20 stamps. How many stamps does she buy in all? Explain how you solved the problem. Tell why you chose that method”.
• In Lesson 12-6, students measure to the nearest half inch and use a line plot to share results (3.MD.4) representing fractional measurements on a number line (3.NF.2). Question 11 states, “Draw a number line from 0 to 2. Label the wholes. Divide each whole into thirds. Label each fraction.”
• In Lesson 15-1, students describe quadrilaterals (3.G.1) using fractional parts (3.NF.1). The Solve & Share Activity states, “The area of each small triangle on the paper represents a unit fraction of the whole square each of your quadrilaterals represents.”

Instructional materials for enVision Mathematics Common Core Grade 3 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 144 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 104 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 3 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 3 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 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, Topic 1, students developed conceptual understanding of multiplication and division. In Topic 2, students used arrays to understand multiplication facts. In Topic 4, students used the relationship between multiplication and division to learn division facts.”
• “Connections within Topic 5 include: In Lessons 5-1 and 5-2 students use multiplication tables to find patterns, products, and unknown factors. All Topic 5 lessons use the strategies of multiplication tables, breaking apart, and skip counting.”
• “Look Ahead: Students continue working towards being able to demonstrate fluency with multiplying and dividing within 100. In Topic 6, students develop an understanding of the relationship between multiplication and area. In Topic 7, students use multiplication to draw and interpret scaled picture and bar graphs. In Grade 4, Topics 3 and 4, students multiply and divide larger numbers using strategies and properties. In Topic 7, students work with factors and multiples.”

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 follow a consistent lesson structure that includes a topic project, and in every other topic there is a 3-Act Mathematical Modeling Task. Topic Lessons include Solve & Share, Visual Learning Bridge, and Convince Me! sections, where 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 with extensive work with grade-level problems for 3.OA.5 in Topic 3: Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8 (3.OA.5) as they engage in activities, including:

• In Topic 3, 3-Act Math, students watch a video of a teacher handing out water and juice boxes on a field trip. Students make predictions on “How many bottles of water did the students drink?” Students determine what information is needed to solve the problem, and are given additional information about juice boxes and water in order to model the solution.
• In Lesson 3-3, Convince Me!, students use the distributive property to find the product of unknown facts by breaking the unknown fact into the sum of two known facts. The question states, “Use a 5’s fact and a 1’s fact to find 6 x 9. Draw two arrays. Explain your drawings.”
• In Lesson 3-5, Problem Solving, Question 26 states, “Mr. Ling walks 5 miles each day. How many total miles does he walk in one week? Explain.”

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 1, Math Background Coherence: Understand Multiplication and Division of Whole Numbers the Look Back states, “In Grade 2, Topic 2, students explored even and odd numbers and used arrays to find totals. They also learned to write equations for arrays using rows or columns.”
• In Topic 6, Math Background Coherence: Connect Area to Multiplication and Addition the Look Back states, “In Grade 2, Topic 2, students began to work with equal groups of objects arranged in arrays. They also learned to find the total number of objects by writing equations using rows or columns.” 
• In Lesson 8-1, Look Back, “In Grade 2, students learned to add within 1,000, using models or strategies.” In this lesson, students solve addition problems using the commutative, associative, and identity properties of addition.
• In Lesson 14-1, Look Back, “In Grade 2, students learned to tell time to the nearest 5 minutes and they learned about patterns with 5 as a factor in Topic 2.” In this lesson students apply knowledge of counting by 5s and 1s to tell time to the nearest minute.

The instructional materials for enVision Mathematics Common Core Grade 3 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 3: “Focuses on using known facts and properties of multiplication to learn the multiplication facts with factors of 3, 4, 6, 7, and 8 (3.OA.B)”. For example, in Lesson 3-6, “students use the Associative (Grouping) Property of Multiplication to multiply with three factors.”
• In Lesson 5-1, the Mathematics Objective states, “Use the multiplication table and the distributive property to find patterns in factors and products.”  This is shaped by 3.OA.B: “Understand properties of multiplication and the relationship between multiplication and division”.
• In Lesson 14-3, the Mathematics Objective states, “Solve word problems involving addition and subtraction to measure quantities of time.” This is shaped by 3.MD.A: “Solve problems involving measurement and estimation.”  

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 2-2 connects 3.OA.A to 3.OA.D when students represent and solve problems involving multiplication while solving problems involving the four operations that include identifying and explaining patterns in arithmetic.   
• Lesson 6-2 connects 3.MD.C to 3.OA.A when students find areas of rectangles on grids using arrays.  
• Lesson 8-1 connects 3.NBT.A to 3.OA.D when students use place value understanding and properties of operations to perform multi-digit arithmetic to solve two step word problems.  
• Lesson 14-3 connects 3.MD.A to 3.NBT.A when students solve problems involving time using strategies based on place value and properties of operations to add and subtract.