5th Grade - Gateway 1

The instructional materials reviewed for Math Expressions Grade 5 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 5 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 16, “It takes Juan's family 3 3/4 hours to drive to his grandparents’ house. That is 1 7/10 hours longer than it takes them to drive to his aunt’s house. How long does it take Juan’s family to drive to his aunt’s house?” (5.NF.1)
• Unit 4, Form B, Item 10, “Find the products: $$47\times10^1, 47\times10^2, 47\times10^3$$” (5.NBT.1, 5.NBT.2)
• Unit 7, Form A, Item 5, “Select the expression that represents dividing 6 by n and then subtracting 8. Mark all that apply.” (5.OA.2)
• Grade 5, Middle of Year Test, Item 18, “Latasha planted a fern tree in her yard that measured 1/3 meter tall. When she measured the tree a month later, it was 3/4 meter tall. How much did Latasha’s tree grow?” (5.NF.2)
• Grade 5, End of Year Test, Item 23, “A rectangular garden has a width of 2 2/3 yards. The length of the garden is 2 yards. What is its area?” (5.NF.4b.)
• Grade 5, PARCC Test Prep: Standard 5.NF.B.5a Practice Test, Item 5, “Stuart rode his bicycle 6 3/5 miles on Friday. On Saturday he rode 1 1/3 times as far as he rode on Friday. On Sunday he rode 5/6 times as far as he rode on Friday. Which statements are correct? Mark all that apply.” (5.NF.5a)

The instructional materials reviewed for Math Expressions Grade 5 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 15 out of 20 , which is approximately 75%.
• The number of lessons devoted to major work (including assessments and supporting work connected to the major work) is approximately 101 out of 111, which is approximately 91%.

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 91% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Math Expressions Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of connections between supporting work and major work include the following:

• In Unit 1, Lesson 10, students answer questions based on a given line plot (5.MD.B) supporting their work with operations on fractions (5.NF.A). The Student Activity Book includes an application problem, “Every week, Mr. Park asks for about 1 pound of potato salad at the deli. The line plot shows the actual weight of the salad the deli worker has given him for the past several weeks. What is the difference between the greatest and least width shown on this graph?”
• In Unit 3, Lesson 13, students answer questions from given line plots (5.MD.B) supporting their work with operations on fractions (5.NF.A). “Six students slept 8 1/2 hours. What total number of hours do these six values represent?” “Hala can ride her bike 7 1/2 miles in an hour. How far will she ride in 2/3 hours? How far will she ride in 1/3 of an hour?” “Mr. Dayton uses 8 cups of flour to make three identical loaves of bread. How much flour is in each loaf?”
• In Unit 8, Lesson 9, addresses supporting standard 5.MD.A, convert like measurements within a unit system, to support standard 5.NBT.A, understand the place value system. Students convert metric units using multiplication and division including decimals. Students complete real world problems requiring students to use metric conversions to determine the answer. Student Activity Book problem 14, “Erin’s water bottle holds 665 milliliters. Dylan is carrying two water bottles. Each one holds 0.35 liters. Who is carrying more water? How much more?”

The instructional materials for Math Expressions Grade 5 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 95 lessons. Most lessons require one day.
• The Pacing Guide notes 18 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 20 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 5 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 explains 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 Progress chart makes connections between Grade 4, Grade 5, and Grade 6 within Number and Operations-Fractions and Number System as they relate to addition and subtraction with fractions. “In Grade 4, students represented fractions as sums of unit fractions, composed and decomposed fractions and mixed numbers, and used bar models to represent equivalent fractions and find sums and differences. In Grade 5, students will use number lines to represent equivalent fractions, express fractions with unlike denominators in terms of the same unit fraction so they can be added or subtracted, use bar models to visualize a sum or difference, use equations and models to solve real world problems, and use estimation to determine whether answers are reasonable. In Grade 6, students will use number lines to represent rational numbers.”
• Unit 4, the Math Background quotes from the Learning Progressions for Numbers and Operations in Base Ten as it relates to place value. “Place Value and Shift Patterns - Students extend their understanding of the base-ten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths. New at Grade 5 is the use of whole number exponents to denote powers of 10. Students understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left.”

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 using models to extend concepts and skills. For example:

• Unit 2, Lesson 4 , students add and subtract decimals which leads to the standard algorithm. Students continue their work with decimals by relating decimals to metric lengths in Problem 14, “Tori had fabric that was 6.2 meters long. She used some and now has 1.45 meters. How much did she use?” (5.NBT.7)
• Unit 5, Lesson 1, students recall what they remember about division with whole numbers to activate prior knowledge. The Math Talk in this lesson includes students dividing with whole numbers and with decimals to hundredths. Students use estimation to check reasonableness of answers, and consider the contexts of real world division problems to determine the best way to handle remainders. In the Student Activity Book, Lesson 1, students compare three different methods for dividing. In the following lessons, students continue to work with division including remainders, division with two digit divisors, and dividing by numbers with decimals. (5.NBT.6)

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 3, Lesson 1, Homework, students practice multiplying by unit fractions and writing comparison statements.
• Unit 4, Lesson 2, Remembering, students use inequality symbols to compare fractions with unlike denominators, multiply fractions by whole numbers, and solve multiplication problems involving multiples of ten.

The instructional materials for Math Expressions Grade 5 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 2, Big Idea 1, “Read and Write Whole Numbers and Decimals” is shaped by 5.NBT.A, “Understand the place value system.” Lesson objectives in this section include, “Students learn about decimals as equal divisions of a whole. Students expand their understanding of decimals to thousandths. Students compare decimal numbers through thousandths.”
• Unit 7, Lesson 1, lesson objective states, “Students will learn to read and write numerical expressions.” This is shaped by cluster 5.OA.A, “Write and interpret numerical expressions.”

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, Lesson 10, cluster 5.MD.A connects to cluster 5.NF.A, when students solve problems involving addition and subtraction of mixed numbers with unlike denominators using data from a line plot.
• Unit 3, Lesson 7, cluster 5.OA.A, 5.NF.A, and 5.NF.B, are connected when students relate operations with fractions to operations with whole numbers as they engage in problems involving operations with fractions and evaluating expressions with parentheses. Teachers use the following example with students, 2/5 x (4/7 x 1/2) = (2/5 x 4/7) x 1/2.
• Unit 7, Lesson 4, 5.OA connects to 5.NF, when students generate and extend numerical patterns, identify relationships of corresponding terms, and use expressions to support their analysis of numerical patterns. In the Student Activity Book, Problem 1, “Write two expressions for the next term (the sixth term) in the pattern 3, 5, 7, 9, 11…”