3rd Grade - Gateway 1

The instructional materials reviewed for Math Expressions Grade 3 meet expectations that they assess grade-level content.

The assessments are aligned to grade-level standards and do not assess content from future grades. The Grade 3 Assessment Guide includes a Beginning of Year Test, Middle of Year Test, End of Year Test, and tests for each Unit. Each Unit Test includes multiple choice, multiple-select, short answer, constructed response, and a separate performance task assessment.  The materials include a form A and form B assessment for each unit.

Digitally available assessments are PARCC and Smarter Balanced aligned practice tests. Each digital platform includes a variety of practice tests. Digital assessments assess grade-level content.

Examples of on-grade level assessment items include:

• Unit 1, Form B, Item 21, “Michelle’s bookcase has 4 shelves. It holds 9 books on each shelf. How many books will fit in the bookcase altogether?" (3.OA.3)
• Unit 3, Performance Assessment, Item 3, “Alberto has 62 pennies, 41 nickels, and 29 dimes. What strategy can you use to find the total number of coins? Describe it and show your work.” (3.NBT.1 and 3.NBT.2)
• Unit 6, Form A, Item 12, “Kevin has 368 marbles in his collection. His mom gives him 42 more marbles. He then gives some marbles to his friend. Kevin now has 352 marbles. How many marbles does he give to his friend? Answer: 58 marbles Is the answer reasonable? Tell why or why not. Then write an equation and solve the problem.” (3.OA.8)
• Grade 3, End of Year Test, Item 11, “Write an equation and solve the problem. Show your work. There are 3 dance classes with 10 students in each class. All of the classes are divided into 6 groups for the dance recital. How many students are in each group?” (3.OA.8)
• Grade 3, Middle of Year Test, Item 28, “Marisa measures 8/4 cups of sugar and 6/2 cups of flour. Does she measure more sugar or flour? Explain.” (3.NF.3c.)
• Grade 3, Smarter Balanced Test Prep Practice Test, Item 5, “Eleni bought 3 packs of crayons. She then found 3 crayons in her desk. Eleni now has 24 crayons. How many crayons were in each pack she bought? Explain how you solved the problem.” (3.OA.8)

The instructional materials reviewed for Math Expressions Grade 3 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 5 out of 7, which is approximately 71%.
• The number of Big Ideas, CCSSM clusters, devoted to major work of the grade (including assessments and supporting work connected to the major work) is 13 out of 18 , which is approximately 72%.
• The number of lessons devoted to major work (including assessments and supporting work connected to the major work) is approximately 77 out of 112, which is approximately 69%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each unit. As a result, approximately 69% of the instructional materials focus on major work of the grade.

The instructional materials for Math Expressions 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 150 days. The Pacing Guide can be found on page I18 in the Teacher Edition. 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.

• The program is designed with seven units and 98 lessons. Most lessons require one day.
• The Pacing Guide notes 19 lessons that may take two days, but this is not noted in the Day at a Glance for each lesson.
• All Units designate two days for Unit Assessments.
• The instructional materials consist of 18 days of Quick Quizzes and Strategy or Fluency Checks which are listed in the Pacing Guide.
• Unit 1 designates one day for the Prerequisite Skills Inventory Test.

Teachers start each lesson with a 5-minute Quick Practice and each lesson is comprised of several activities with estimated time ranging from a total of 55-65 minutes per lesson. Math Activity Centers are tailored for all levels of achievement across readiness and learning styles. They can be completed within the lesson or after, however, the time required for the activity is unstated.  

The instructional materials for Math Expressions Grade 3 meet expectations for the materials being consistent with the progressions in the Standards. Content from prior and future grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems.

The materials clearly identify content from prior and future grades and connect concepts to grade level work. Each unit includes a Unit Overview providing a Learning Progression. The Learning Progression states connections between the standards of the prior grade, current grade, and future grade. Additionally, each unit contains a Math Background Section. This section contains in depth information for the teacher articulating the learning progressions and the progression of the content between lessons. For example:

• Unit 4, Math Background, contains quotes from the Learning Progressions for Fraction Concepts, “Grade 3 students start with unit fractions (fractions with numerator 1), which are formed by partitioning a whole into equal parts and taking one part…” This page also includes visual examples of fraction bars and a statement regarding prior work, “The work students have done with decomposing shapes gives them a foundation for this work with equal parts of a whole.”
• Unit 6, the Learning Progression chart shows connections between Grade 2, Grade 3, and Grade 4 within the Numbers and Operations in Base Ten and Operations and Algebraic Thinking domains. “In Grade 2, students used addition and subtraction within 100 to solve one- and two-step word problems and mastered using mental strategies to add and subtract within 20. In Grade 3, students will use drawings and equations with a symbol for the unknown number to represent the problem, write equations and solve types of word problems involving comparison and misleading language, and use properties of operations to explain patterns. In Grade 4, students will use drawings and equations with a symbol for the unknown number to represent the problem, represent verbal statements of multiplicative comparisons as multiplication equations, and write equations to represent problems with more than one step.”

The instructional materials provide extensive work with grade-level problems. Students work with grade-level problems in each lesson. Within each lesson, students practice grade level problems within Quick Practice, Student Activity Book pages, Homework, and Remembering activities. During modeled and guided instruction, students are given opportunities to engage in the grade level work by doing various examples with teacher and peer support. The independent practice in the Student Activity Book aligns with the lesson and provides students the opportunity to work with grade level problems to extend concepts and skills. For example:

• Unit 2, Lesson 4, Activity 1, students work in pairs to test one another on math facts using provided study sheets, then work independently for a few minutes to study the study sheets. In Activity 2, students identify which type of problem (array, equal groups, or area) is being solved and which operation will be used. Finally, students complete an error analysis of a multiplication equation, then write and solve multiplication and division equations for nine real world problems. (3.OA.A)
• Unit 3, Lesson 12, Activity 1, students practice ungrouping tens as the teacher “models” the skill. In the Student Activity Book students are ungrouping tens in subtraction problems and include “proof drawings” representing how they got their answer. This lesson also includes additional opportunities to practice making “proof drawings” to support subtraction. The formative assessment, “Check Understanding”, contains one more problem for students to ungroup tens in a subtraction problem, “Subtract. 300-156. Make a proof drawing to show that your answer is correct.” (3.NBT.2)

Each lesson contains Math Center Activities, as well as Homework and Remembering (spiral reviews) pages which provide additional practice with grade-level problems. For example:

• Unit 1, Lesson 8, Homework, students write and solve multiplication and division equations to match a real world problem.
• Unit 2, Lesson 9, Remembering, students write and solve multiplication and division equations and find unknown numbers for Fast Array Drawings. In Stretch Your Thinking, students answer the following question, “Cecelia says she can use addition to solve multiplication problems. Is Cecelia correct? Explain.”

The instructional materials for Math Expressions Grade 3 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Each unit is structured by specific domains and Big Ideas. Learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:

• Unit 1, Lesson 4, the lesson objective states, “Students will learn to relate division to multiplication with an unknown factor.” This is shaped by cluster 3.OA, “Represent and solve problems involving multiplication and division.”
• Unit 5, Lesson 8, the learning objective states, “Students will learn to use number lines to find two or more equivalent fractions.” This is shaped by 3.NF.A, “Develop understanding of fractions as numbers.”
• Unit 7, Big Idea 2, “Analyzing Triangles and Quadrilaterals” includes four lessons. This Big Idea is shaped by cluster 3.G.A, “Reason with shapes and their attributes.” Lesson objectives in this section include, “Students will learn to classify triangles according to their angle sizes and side lengths and to build and name polygons, students will learn about the relationships among different types of quadrilaterals, students will learn to draw quadrilaterals, students will learn to describe, sort, and draw quadrilaterals according to their attributes, and students will learn to use mathematical practices and content skills to solve problems about quadrilaterals.”

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. For example:

• Unit 3, Lesson 9, cluster 3.NBT.A connects to 3.OA.D, when students engage in addition and subtraction while they solve real world problems. Problem 20, “The florist ordered 398 roses and 562 tulips. How many flowers did the florist order in all?”
• Unit 4, Lesson 4, cluster 3.G.A connects to 3.NF.A, when students work with partitioning shapes relates to visual fraction models.
• Unit 6, Lesson 2, cluster 3.OA.A connects to 3.NBT.3, when students represent and solve word problems with unknown addends and unknown factors. Problem 8, “There are 56 cars in a parking lot. There are 8 rows and the same number of cars in each row. How many cars are in each row?”