4th Grade - Gateway 1

The instructional materials reviewed for Math Expressions Grade 4 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 4 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 6, form A, item 4, “Dakota mixes flour and oats for a recipe. He uses 5/6 cup of flour. This is 4/6 cup more than the amount of oats he uses. How many cups of oats does Dakota use? Write an equation. Then solve.” ( 4.NF.3d)     
• Unit 7, Performance Assessment, Items 1 and 2, “Taxicabs downtown charge a flat fee of $2.50, plus a state tax of $0.50, plus $0.50 for each 1/5 mile they travel with a passenger. 1.) Explain how you could write 1/5 mile as a fraction with 10 in the denominator, a fraction with 100 in the denominator, and as a decimal. 2.) Travis took a taxicab from his office to a meeting on the other side of town. The cab ride cost $8.50, which includes a $2.00 tip. In decimal form, how far is it from his office to the meeting? Show your work.” (4.NF.5, 4.NF.6, 4.NF.3a)
• Grade 4, Smarter Balanced Test Prep Practice Test, Item 3, “Frank has two same-sized rectangles divided into the same number of equal parts. One rectangle has 3/4 of the parts shaded, and the other has 1/3 of the parts shaded. Part A: Into how many parts could each rectangle be divided? Show your work by drawing the parts of each rectangle and shading the correct amounts.” (4.NF.1)
• Grade 4, Middle of Year Test, Item 27, “Ron buys 2 1/4  pounds of chicken and 1 3/4 pounds of beef. How many more pounds of chicken does he buy than beef?” (4.NF.3c.)
• Grade 4, End of Year Test, Item 15, “There were 12,318 tickets sold at a stadium last weekend. There were 12,584 tickets sold this weekend. How many tickets were sold in all?” (4.NBT.4)

The instructional materials reviewed for Math Expressions 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 6 out of 8, which is approximately 75%.
• 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 18 out of 25, which is approximately 72%.
• The number of lessons devoted to major work (including assessments and supporting work connected to the major work) is approximately 89 out of 115, which is approximately 77%.

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 77% of the instructional materials focus on major work of the grade.

The instructional materials for Math Expressions 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 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 eight units and 99 lessons. Most lessons require one day.
• The Pacing Guide notes 9 lessons that could 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 25 days of Quick Quizzes and Strategy/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 4 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 1, the Learning Progression chart makes connections between Grade 3, Grade 4, and Grade 5 within the Numbers and Operations in Base Ten Domain as it relates to place value and multi digit addition and subtraction.
• Unit 5, Math Background quotes from the math Progressions Documents for Measurement/Data. For example, the Math Background for Lesson 3 connects information about elapsed time for the current grade to prior grade. “In the previous grade, students found elapsed time in hours and minutes and used these skills to solve real world problems.”
• Unit 6, Math Background quotes from the Progressions Documents for Number and Operations Adding Fractions. “This simple understanding of addition as putting together allows students to see in a new light the way fractions are built up from unit fractions. The same representation that students used in Grade 3 to see a fraction as a point on the number line now allows them to see a fraction as a sum of unit fractions: just as 5 = 1 + 1 + 1 + 1 +1, so 5/3 = 1/3+1/3+1/3+1/3+1/3 because 5/3 is the total length of 5 copies of 1/3. Armed with this insight, students decompose and compose fractions with the same denominator. They add fractions with the same denominator.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. 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 corresponds with the lesson and provides students the opportunity to work with grade level problems to extend concepts and skills. For example:

• Unit 3, Lesson 1, students discuss and complete activities illustrating the relationship between multiplication and division and are introduced to division with remainders. They use patterns in multiplication with zeros to divide numbers with zeros. In the Student Activity Book, problem 13, “What pattern do you notice when you multiply with zeros?”. Students practice solving division problems including those with patterns of zeros. Students relate the quotient to a multiplication problem to check the division work. (4.NBT.6)
• Unit 7, Lesson 1, students use prior knowledge of unit fractions to discuss comparing fractions with different denominators. “Encourage students to generalize what they have learned about comparing two fractions with different denominators and the same numerator. Just as with unit fractions, students should be able to reason that for fractions that have the same numerator, the fraction with the lesser denominator is greater.” Students discuss, compare, and order unit fractions using visual models and fraction reasoning. In Activity 2, students determine which fraction is greater, use inequality symbols to compare fractions, and construct a viable argument in the “What’s the Error?”portion of the lesson. (4.NF.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 6, Lesson 6, Homework, students write mixed numbers as fractions, add and subtract mixed numbers and fractions, and answer two real world problems involving addition and subtraction of mixed numbers.
• Unit 7, Lesson 6, Remembering, students write number sentences to convert metric measurements between units, complete addition equations with a missing fraction addend, simplify fractions, and compare three fractions in a real world context.

The instructional materials for Math Expressions Grade 4 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, Big Idea 1, “Place Value to One Million.” This Big Idea is shaped by 4.NBT.A, “Generalize place value understanding for multi-digit whole numbers.” Examples of lesson objectives in this section include, “Students will learn to identify the place value of numbers through thousands, students will learn how to read, write, and model numbers to a thousand, and students will learn to round and compare multi-digit whole numbers.”
• Unit 4, “Equations and Word Problems” is shaped by 4.OA.A, “Use the four operations with whole numbers to solve problems.” Students use the four operations with whole numbers to solve equations and multi-step problems.
• Unit 6, Lesson 8 learning objective states, “Students will solve problems involving multiplying a fraction by a whole number.” This is shaped by 4.NF.B, “Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.”

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 1, Lessons 6 and 13 connect two domains, 4.NBT.B and 4.MD.A, when students use denominations of money to build addition and subtraction fluency.
• Unit 3, Lesson 9 connects two domains, 4.OA.A and 4.NBT.B, when students interpret remainders of multi-digit division problems in a variety of ways. In the Student Activity Book, students solve, “Henry’s coin bank holds only nickels. Henry takes $4.42 to the bank to exchange for nickels only. How many nickels will he get from the bank?”
• Unit 7, Lesson 6 connects two clusters within a domain, 4.NF.A and 4.NF.C, when students compare fractions with unlike denominators using <, >, and = including some of the following: 4/5 __ 75/100, 3/4 ___ 8/10.