4th Grade - Gateway 1

The instructional materials reviewed for enVision Mathematics Common Core Grade 4 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, but are not limited to:

• Topic 6, Assessment, Question 1, states, “Jessica and her 2 sisters want to take a camping trip. They have $225 saved. Each of them will save $21 a week until they have at least $512 to pay for the trip. How much money will they save after 4 weeks? Will they have enough money to pay for the trip?” Students solve multi-step word problems with whole numbers and multiple operations (4.OA.3).
• Topic 16, Performance Task, states, “The Ottoman Empire lasted from 1299 until 1922. Much of the art from this period contained geometric shapes. The enlarged part of the figure shows 4 triangles that are all the same type. Classify these triangles by their sides and by their angles. Explain.” Students classify the triangles shown by properties of their lines and angles (4.G.2).
• Topics 1-4, Cumulative/Benchmark Assessment, Question 14, “Which of the following shows how to find 4 x 567? Which property was used?” Students use understanding of place value and properties of operations to perform multi-digit multiplication (4.NBT.5).
• Topic 12, Assessment, Question 3, states, “Lucy buys a puzzle for $3.89, a model airplane for $12.75, and a stuffed animal for $2.50. How much money did she spend in all? Draw or use bills and coins to solve.” Students perform operations with decimals to hundredths (4.MD.2).
• Topic 12, Assessment, Question 5, states, “Catalina takes the money shown to the bookstore. Does Catalina have enough for all three books? If not, how much more money does Catalina need? Explain. Draw or use bills and coins to solve. Catalina chooses to buy only 2 of the books. Choose two books for Catalina to buy, and then find how much money she will have left. Draw or use bills and coins to solve.” Students perform operations with decimals to hundredths (4.MD.2). 
• Topic 12, Performance Task, Question 2, states, “Analyze the amount of money that the students raised. How much more money did Yuna raise than Ali? Draw bills and coins to show your work.” Students perform operations with decimals to hundredths (4.MD.2).

The instructional materials reviewed for enVision Mathematics Common Core Grade 4 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 13 out of 16, which is approximately 81%.
• 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%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 120 out of 144, which is approximately 83%. 

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 88% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 4 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 7-2, students use multiplication knowledge (4.NBT.5) to find factors and factor pairs of whole numbers (4.OA.4). Question 25 states, “Any number that has 9 as a factor also has 3 as a factor. Why is this?”
• In Lesson 10-4, students solve word problems involving units of time (4.MD.2) using fractions and mixed numbers (4.NF.3d and 4.NF.4c). Question 11 states, “A boat ride at the lake lasts $$2\frac{2}{4}$$ hours. A canoe trip down the river lasts $$3\frac{1}{4}$$ hours. Show each time on the number line. How much longer is the canoe trip than the boat ride in hours? minutes?”
• In Lessons 11-1 and 11-3, students solve problems using data from line plots (4.MD.4) to compare, add, and subtract fractions (4.NF.2 and 4.NF.3d). Lesson 11-1, Question 12 provides a line plot with time in fraction form and states, “How much longer was the greatest amount of time spent completing the project than the least amount of time?”
• In Lessons 13-4 and 13-5, students convert metric units of length (4.MD.1) to solve problems involving operations with whole numbers (4.OA.3). Lesson 13-4, Question 14 states, “Signs are placed at the beginning and at the end of a 3-kilometer hiking trail. Signs are also placed every 500 meters along the trail. How many signs are along the trail? Explain.”
• In Lesson 14-3, students generate shape patterns following a rule (4.OA.5) and solve problems dividing whole numbers (4.NBT.6). Question 13 states, “Josie puts beads on a string in a repeating pattern. The rule is ‘Blue, Green, Yellow, Orange.’ There are 88 beads on her string. How many times did Josie repeat her pattern?”
• In Lesson 15-2, students find angle measures (4.MD.5) using fractional parts of a given whole (4.NF.3b). Question 11 states, “A mirror can be used to reflect a beam of light at an angle. What fraction of a circle would the angle shown turn through?”

Instructional materials for enVision Mathematics Common Core Grade 4 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 4 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 4 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 3: In 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 1-digit numbers by multiples of 10. Earlier in Grade 4, Topic 3 students used arrays, area models, the distributive property, and partial products to multiply multi-digit numbers by 1-digit numbers.”
• “Connections within Topic 4 include: Students use rounding to estimate products and estimation to check reasonableness of answers. 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. Students apply strategies for whole-number multiplication to solve real-world problems.”
• “Look Ahead: In Topic 5, students use their understanding of multiplication and their skill in multiplying with patterns, models, and partial quotients to divide by 1-digit numbers. In Topic 6, students use multiplication to compare. In Grade 5, Topic 3 students use the standard algorithm to multiply multi-digit whole numbers. In Topic 4, students use models and strategies to multiply decimals to hundredths.”

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 Standard 4.NBT.5 grade-level problems in Topic 3: Use Strategies and Properties to Multiply by 1-Digit Numbers, including:

• In Topic 3, 3-Act Math, students watch a video of a boy covering the sides of a box with square stickers. Students make predictions to determine “How many stickers do you need to cover the box?” Students discuss what information is needed to solve the problem and are given additional information in order to model the solution.
• In Lesson 3, Convince Me!, students use the distributive property to break apart 13 as 10 + 3 and multiply each addend by 5. The question states, “How are the partial products represented with the place-value blocks?”
• In Lesson 7, Problem Solving, Question 23 states, “Elaine rents a car for 5 days. It costs $44 each day to rent the car and $7 each day for insurance. At the end of the trip she spends $35 to fill the car with gas. What is the total cost for Elaine to use the car?”

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 2, Math Background Coherence: Fluently Add and Subtract Multi-Digit Whole Numbers the Look Back states, “In Grade 3, Topics 8 and 9, students developed fluency in adding and subtracting whole numbers within 1,000. They estimated sums and differences, added and subtracted mentally, and used strategies such as partial sums and partial differences.”
• In Topic 6, Math Background Coherence: Use Operations with Whole Numbers to Solve Problems the Look Back states, “In Grade 3, Topics 1-5, students solved word problems involving basic facts and the foundational understandings of multiplication and division. In Topics 8 and 9, students solved word problems as they developed fluency with addition and subtraction through 1,000. In Topic 10, students solved word problems involving multiplying by multiples of 10.” 
• In Lesson 9-1, the Look Back states, “In earlier grades, students developed an understanding of the meaning of addition of whole numbers as joining, and they developed an understanding of the meaning of a fraction $$\frac{a}{b}$$ as a number of unit fractions $$\frac{1}{b}$$.” In this lesson, students use fraction strips and number lines to add fractions.
• In Lesson 12-2, the Look Back states, “In Grade 3, students represented fractions on a number line. In Grade 4, Lesson 8-2, they represented equivalent fractions on a number line.” In this lesson students locate and describe fractions and decimals on number lines.

The instructional materials for enVision Mathematics Common Core Grade 4 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 fluency with standard algorithms for addition and subtraction (4.NBT.B)”. For example, in Lesson 2-2, “Students use rounding to estimate sums and differences.”
• In Lesson 6-1, the Mathematics Objective states, “Interpret comparisons as multiplication or addition equations.” This is shaped by 4.OA.A: “Use the four operations with whole numbers to solve problems.”  
• In Lesson 12-2, the Mathematics Objective states, “Locate and describe fractions and decimals on number lines.” This is shaped by 4.NF.C: “Understand decimal notation for fractions, and compare decimal fractions.” 

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 4.NBT.B to 4.OA.A when students use strategies for estimating sums and differences presented in the context of solving a multi-step word problem.  
• Lesson 5-3 connects 4.OA.A to 4.NBT.B when students solve multi-step word problems involving the four operations.
• Lesson 8-3 connects 4.NF.A to 4.NBT.B when students find equivalent fractions using multiplication.
• Lesson 14-2 connects 4.OA.5 to 4.NBT.2 when students use rules to develop shape patterns and solve problems involving multiplication and division. In Independent Practice, Problem 5: Rule Divide by 5, students complete a chart with the number of fingers listed as 5, 10, 15, 20; and the number of hands as 1, 2, _, _.