4th Grade - Gateway 1

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that they assess grade-level content.

In i-Ready, Teach and Assess, Ready Classroom Mathematics, there are two versions of Unit Assessments: Form A and Form B for each unit. Form A assessments are editable. Form A assessments include a standards correlation chart, DOK levels, as well as a correlation to the lesson/s related to each assessment item. Form B assessments do not include this feature. In addition, in i-Ready, Teach and Assess, Assessments, Comprehension Checks are also available and can be used as an alternative to print mid- and end-unit assessments. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments. 

Examples of assessment items from the Classroom Resources aligned to grade-level standards include:

• In Unit 3, Assess, End of Unit Assessment, Form B, Item 2 states,  “A rectangle that is 9 inches long has an area of 72 square inches. What is the perimeter of the rectangle, in inches? Show your work.” (4.MD.A.3) 
• In Unit 4, Assess, End of Unit Assessment, Form A, Item 7 states, “Write 8/100 as a decimal.  Record your answer on the grid. Then fill in the bubbles.”(4.NF.C.6 )
• In Unit 5, End of Unit Assessment, Item 11 states, “Erin is drawing a diagram of a door opening. She wants the door opening in the diagram to have a 150° angle. Draw a 150° angle. Label the angle in degrees. Show your work.” (4.G.1)

Examples of assessment items from the Assess and Teach aligned to Grade 4 CCSS include:

• In Comprehension Checks, Comprehension Checks Details, Unit 1, Item 9 states, “Yelena takes 27,601 steps in one day. Round 27,601 to each given in the chart. Enter your answers in the boxes. (boxes state, ‘to the nearest ten thousand, to the nearest thousand, to the nearest hundred, to the nearest ten.’” (4.NBT.A.3)
• In Comprehension Check, Comprehension Checks Details, Mid-Unit 2 (Lessons 6-8), Item 8 states, “What do all of the numbers below have in common?  7, 14, 21, 28, 35 Choose all the correct answers.” The multiple choice answers are: They have 7 as a factor, They are multiples of 7, They are factors of 7, They have seven factors, They are multiples of 14. (4.OA.4)
• In Comprehension Check, Comprehension Checks Details, Mid-Unit 3, Item 8 states, “Kate packs and weighs her sports bag for football practice. The sports bag weighs 6 pounds. Then Kate removes her water bottle that weighs 14 ounces.What is the weight of Kate's sports bag, in ounces, now?” The multiple choice answers are 8 ounces, 82 ounces, 96 ounces, and 110 ounces. (4.MD.2)

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 4 out of 5, which is approximately 80%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 32 out of 39, which is approximately 82%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 125 out of 154, which is approximately 82%. 

An instructional day level analysis is most representative of the materials because the number of sessions within each topic and lesson can vary and each lesson includes specific objectives aligned to standards. When reviewing the number of instructional days for Ready Classroom Mathematics Grade 4 materials, approximately 82% of the days are focused on the major work of the grade.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 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 materials, 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 Classroom Resources:

• In Lesson 13, Session 3,  supporting standard 4.MD.1 connects to major work standard 4.NBT.5 as students solve, “Julie makes 4 liters of orange juice. How many milliliters of orange juice does Juile make?.” Students demonstrate an understanding of conversion related to the supporting standard, 4.MD.1 by applying multiplication strategies to find their answer. 
• In Lesson 22, Session 4, students make line plots and solve word problems about data (supporting standard 4.MD.4) using addition and subtraction of fractions with like denominators (4.NF.3c and 4.NF.3d). Students are given a line plot with dragonfly lengths displayed in inches as mixed numbers and answer questions. For example the materials state, “What is the difference between the lengths of the longest and the shortest dragonfly?”
• In Lesson 28, Session 2, standard 4.MD.2 supports major work standard 4.OA.3 as students solve word problems about money and time using fractions and whole numbers. The materials state, “Sadie spends $$1\frac {1}{2}$$ hours doing homework. She plays outside for 20 minutes and practices the piano for a quarter of an hour. How many more minutes does Sadie spend doing homework than practicing the piano and playing outside?

The instructional materials reviewed for Ready Classroom Mathematics 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 165 days consisting of: 

• There are 130 lesson days.  
• There are 9 days for unit assessments, 6 days for i-Ready diagnostic assessments, and 5 days review, for a total of 20 days. 
• There are 10 days for Math in Action activities.
• There are 5 days dedicated to lesson 0 at the beginning of the school year to set up instructional routines with students that will be used throughout the year. 

According to Ready Classroom Mathematics Implementation, sessions are designed to be 45-60 minutes in length. Pacing information from the publisher regarding viability for one school year can be found in the document titled “Yearly Pacing” found in the “Program Implementation” tab on the home page for each grade level. The “Yearly Pacing” includes a list of units, lessons within each unit, and the number of days each lesson encompasses, a note that lessons are 45-60 minutes in length and number of days for assessments. Pacing information is also verified in the “Classroom Resources” tab in each unit for each lesson in the “Lesson Overview and Family Connection” that includes a “Lesson Pacing Guide” with more detailed information that lists sessions and minutes for each lesson.

The instructional materials reviewed for Ready Classroom Mathematics 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. ​

Overall, the materials develop according to the grade-by-grade progressions in the standards and prior year content is identified as prerequisite skills at the lesson level. In the Unit Overview, the materials include a Learning Progression which clearly identifies the lessons in prior years that contain skill students would connect to the current unit of instruction. For example, in Unit 3, Lesson 16, Find Perimeter and Area (4.MD.3), builds from Grade 3, Lesson 14, 15, and 32, and leads to Grade 5, Lessons 1 and 2 (Volume). In addition to the lesson description and standard correlation, teachers can find a Unit Flow and Learning Progression video which highlight how concepts in this unit progress through grade levels.

The materials give all students extensive work with grade-level problems. Units consist of lessons, which are designed to last between three and five days. Within each lesson, days are broken into Explore, Develop, and Refine sessions. Develop and Refine sessions have ample practice problems for students to understand and apply concepts, and Develop sessions also include Fluency and Skills Practice pages. Each unit also includes a Math in Action lesson, which provides further work with grade-level problems over 2 days. In addition, each lesson includes math center activities and enrichment activities, which both provide more work with grade level concepts. For example: 

• Lesson 8 is focused on 4.OA.B.4. In Session 1, Explore, students look back at previous learning with multiplication facts. In Sessions 2, 3, and 4, Develop, students use pictures, number lines, and other models to develop their understanding of factors and multiples. Fluency and Skills Practice pages accompany each of these Develop Sessions. In Session 5, Refine, students are presented with problems for practice and application of this skill. Math in Action, a two day problem solving lesson, provides further practice with these concepts.
• Lesson 16, Math in Action, focuses on 4.MD.A (Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit). Over the two sessions, students solve increasingly complex problems applying their knowledge of measurement. In Session 1, students study the following example problem and solution, “The zoo is planning to build a new area for birds. The zoo is going to use recycled materials. There will be three different-size rectangular cages as shown below. Beau needs to find a possible length and width for the rectangular floor for each size cage. What is the possible length, width, and perimeter for each cage’s floor?” Students evaluate the sample solution and try another approach, discussing different models and strategies to solve the problem. In Session 2, students persevere by building on the first problem. The materials state, “Beau’s report about recycling was very popular, He decides to write a similar report about recycling rainwater. He will post both reports on the bulletin board at the Community Center. Here is some information Beau found about this topic. What should Beau include in his report.”
• In Lesson 20, students learn to add and subtract fractions 4.NF.3 (Understand a fraction a/b with a>1 as a sum of the fractions 1/b). In Session 1, Explore, students solve problems such as, “Maria, Jon, and Kara share a set of 10 animal stickers. Maria gets 2 stickers, Jon gets 4 stickers, and Kara gets the rest of the stickers. What fraction of the stickers does Kara get?”  In Session 2, Develop, students develop an understanding adding fractions. Session 3, Develop focuses on subtracting fractions. In Session 4, students decompose fractions, and in Session 5, students refine their understanding of adding and subtracting fractions.

The instructional materials explicitly connect prior learning to grade-level content. In the Lesson Overview, the Learning Progression identifies the mathematics taught in earlier grades or earlier in the grade, and connects it with the mathematics in the lesson. In Small Group Differentiation, Prepare, there is a link to Prerequisite Lessons. The Family Letter can also contain information on the learning progressions for students. For example:

• In Lesson 7, the Lesson Overview identifies Grade 3, Lessons 12, 17, and 18 as prerequisites for learning. Grade 3, Lesson 12 focuses on multiplication facts, while Lessons 17 and 18 center around one-step word problems. In Grade 4, Lesson 7, students build upon this learning from Grade 3, as they work on more complex multiplication and division problems.  
• In Lesson 18, Lesson Overview, the Family Connection states, “In Grade 3 students used models to compare two fractions with the same numerator or the same denominator by reasoning about their size.” Information is given about the Grade 4 lesson, and then reads, “In grade 5 students will apply their understanding of fraction comparison when they learn to compare decimals.”
• In Lesson 21, Lesson Overview, Prerequisite Skills include, “Understand addition as joining parts. Understand subtraction as separating parts. Write whole numbers as fractions. Add and subtract fractions that have the same denominator. Decompose a fraction as a sum of fractions with the same denominator.” In Small Group Differentiation, Prepare, Ready Prerequisite Lesson is identified as Grade 3, Lesson 21.

The instructional materials reviewed for Ready Classroom Mathematics Grade 4 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include lesson objectives that are visibly shaped by CCSSM cluster headings. 

The instructional materials identify a Learning Objectives in each Lesson Overview, and in the Student Workbook, Learning Targets are provided for students. Examples of lesson objectives that are visibly shaped by CCSSM cluster headings in Classroom Resources include:

• In Student Workbook, Lesson 2, the Learning Target states, “Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on the meaning of the digits in each place, using >, =, and < symbols to record the results of comparisons.” This learning target aligns with 4.NBT.A (Generalize place value understanding and properties of operations to perform multi-digit arithmetic).
• In Lesson 4, Lesson Overview, one of the Learning Objectives states, “Use place-value strategies to add two or more multi-digit whole numbers.” This lesson objective is shaped by standard cluster 4.NBT.B which states, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”
• In Student Workbook, Lesson 26, the Learning Target states, “Use decimal notation for fractions with denominators 10 or 100.” The Lesson 27 Learning Target is to “compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole.” These learning targets align with 4.NF.C, understand decimal notation for fractions and compare decimals.

There are many instances of problems and activities within the materials that serve to connect two or more clusters in a domain or two or more domains in a grade in Classroom Resources. For example: 

• In Unit 4, Math in Action: Use Fractions and Decimals, Session 1 connects clusters 4.NF.A (Extend understanding of fraction equivalence and ordering) to 4.NF.C (Understand decimal notation for fractions, and compare decimal fractions), as students solve problems using both fractions and decimals.  The materials state, “Luna made these notes after she made a sand art design in a 2- cup jar. ‘I used a glass jar that holds 2 cups. I used less than 1 cup of yellow sand. I filled less than 0.4 of the jar with pink sand. I filled more than 0.2 of the jar with purple sand.’ Luna wants to write specific instructions for making the same kind of design that would work for a jar of any size. Find fractions or decimals to tell exactly what part of each jar to fill with pink, purple, and yellow sand. Write instructions using those numbers.”
• In Lesson 11, Session 1 connects 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic) and 4.NBT.A (Generalize place value understanding for multi-digit whole numbers), as  students solve, “You can use arrays, area models, and partial products to break apart numbers to help you multiply. The array at the right uses base ten blocks to show 3 x 157. Part A: Write 157 in expanded form. Part B: Fill in the blanks below to show how to find 3 x 157. 3 x 157 = (3x ____) + (3 x ____) + (3 x ____).”  
• In Lesson 9, Session 2 connects 4.OA.C (Generate and analyze patterns) and 4.OA.B (Gain familiarity with factors and multiples), as students given multiples of 3 and asked to “describe the pattern of 3, 6, 9, 12, 15, 18.”