The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 4 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The examples from Primary Mathematics Common Core Edition Grade 4 where connections are made between major and supporting work were not always noted in the Teacher’s Guide. Some examples of where the materials make connections between supporting and major work include:

• Unit 1, Lesson 1d connects generating and analyzing patterns (supporting standard, 4.OA.5) with place-value understanding (major work, 4.NBT.1). Student Workbook 4A, page 14, #3 says: “Create a regular number pattern that starts with 493,070 and increase each number by 10,000.” This connection is not noted in the Teacher’s Guide.
• Unit 5, Lesson 1a connects conversion of units (4.MD.A) to the major work of extending understanding of fraction equivalence and ordering (4.NF.A) and building fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (4.NF.B). Student Textbook 4A, page 150, #2 says: “How many months are there in 5/6 of a year?” This connection is not noted in the Teacher’s Guide.
• Unit 10, Lesson 2a connects generating and analyzing measurement data by making a line plot to display a data set including measurement sin fractions of a unit (4.MD.4) to the major work of adding fractions (4.NF.3). Student Textbook 4B, page 132, #3 says: “Carla measured the length of some earthworms to the nearest quarter of an inch. She also noted whether the worm had a swelling along its length or not.” [Students are given the data in a line plot and asked 7 questions related to the data.” These connections are not noted in the Teacher’s Guide.

Examples where units and/or lessons did not make connections between major and supporting work include:

• In Unit 8, Lessons 8.1a, 8.4a-b, 8.5a-b, 8.6a-b, and 8.8a-c address the supporting standards 4.G.1 and 4.G.2, involving measuring angles, without connections to major work.
• In Unit 9, there are missed opportunities to connect area and perimeter (supporting work, 4.MD.A) to the major work of fraction operations (4.NF.C). However, there are two questions including fractions of a whole number in the Review lesson.

The instructional materials for Primary Mathematics Common Core Edition Grade 4 partially meet expectations for the materials being consistent with the progressions in the standards. Overall, materials develop according to the grade-by-grade progressions of the standards; however, some of the content within Grade 4 reflects standards above grade level. Materials make connections to previous grades; however, content from future grades is not identified. For example:

• Students solve problems aligned to 5.NF.2, (Solve word problems involving addition and subtraction of fractions referring to the same whole…)
  • In Unit 3, students work with fractions beyond those expected in Grade 4. In Student Textbook 4A page 109: “Gwen bought 1 liter of tomato juice. She drank 2/7 of it in the morning. She drank 4/7 of it in the evening. How much tomato juice was left?” (5.NF.2)
  • In Unit 4, Student Workbook 4A page 124, students add/subtract with unlike denominators. For example, “Mrs. Lopez bought 3 3/4 kg of beans, 1 1/2 kg of lettuce, and 1 3/4 kg of carrots. How many kilograms of vegetables did she buy altogether?”
• Students solve problems aligned to 5.NBT.3 (Read, write, and compare decimals to thousandths.)
  • In Unit 6, Student Textbook 4B page 26, students read, write, and compare decimals to the thousandths (5.NBT.3). For example, “Arrange the numbers in increasing order…(b) 9.047, 9.076, 9.074, 9.067”
  • There are 12 games/activities offered as reinforcement in the back of Teacher’s Guide 4A. One of these activities compares decimals to the thousandths, which is above grade level.
• In Unit 7, Student Workbook 4B page 46, students perform decimal operations to the hundredths (5.NBT.7). For example, “Mitchell jogged 5.85 km on Saturday. He jogged 1.7 km less on Sunday than on Saturday. What was the total distance he jogged on the two days?”
• There are 10 games/activities offered as reinforcement in the back of Teacher’s Guide 4B. One of the games (1.5a) relates to order of operations (6.EE.2).

The Grade 4 Teacher’s Guides (4A and 4B) include a Developmental Continuum (4A-page vi-x and 4B page vi-x) that contains an overview of topics and skills for each grade level, K-5, but no specific standards are indicated. Standards specific to units and lessons are listed in the introduction to each unit. There are no connections to future grade-level content. In each Teacher’s Guide, there is a Notes section at the beginning of each lesson that includes work learned in previous grade levels as well as the connection to the current work in the lesson. For example:

• Unit 2 in Teacher’s Guide 4A, page 81 states, “In Primary Mathematics 3, students learned how to add and subtract 4-digit numbers using the standard algorithm, how to draw bar models for word problems, and how to use some mental-math techniques in addition and subtraction. Here they will review the addition and subtraction of numbers up to 4 digits and use the bar modes. Also, they will learn some new mental math strategies.”
• Unit 1 in Teacher’s Guide 4A, (page 5), states, “In Primary Mathematics 3A, students learned to interpret a 4-digit number in terms of thousands, hundreds, tens and ones. These are called place values. These concepts are reinforced and extended to numbers up to 1,000,000.”
• Unit 7 in Teacher’s Guide 4B, page 91 states, “In Primary Mathematics 3A, students learned the formal algorithm for multiplying a whole number by a one-digit whole number. The formal algorithm will be extended to decimals in this lesson. Students should know the basic multiplication facts well and have a good understanding of place value. Mental-math strategies will also be applied in this lesson.”

Students in Grade 4 do not have extensive work with grade-level problems due to the amount of above grade-level work in the lessons which detracts from the grade-level work. There are limited opportunities for enrichment and reinforcement of grade-level work.

• In Primary Mathematics Teacher’s Guide 4A, Lesson 1.4 - Factors, page 47 under the “Notes” section, states, “In Primary Mathematics 3, students learned the term product. Here, they will learn the term factor, how to find factors of whole numbers, and how to find common factors.” (first paragraph) Further down the page it states, “Finding the greatest common factor will only be covered in Grade 5, though you may point out the greatest common factor when appropriate.” This should be noted as a Grade 6 standard (6.NS.4).

The instructional materials for Primary Mathematics Common Core Edition Grade 4 partially meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

The materials for Primary Mathematics Common Core Edition for Grade 4 include learning objectives that are visibly shaped by the CCSSM cluster headings. For example:

• In Unit 1, Lesson 1.1 (Teacher’s Guide 4A, page 5), students find the standard, expanded, and written forms of numbers to the hundred-thousands place value (4.NBT.2), which is shaped by 4.NBT.A: “Generalize place value understanding for multi-digit whole numbers.” For example, Student Workbook 4A, page 7: “Mr. Royce sold his car for this amount of money [diagram included of 10,000s, 1,000s, and 100s]. (a) Write the amount of money in figures. (b) Write the amount of money in words.”
• In Unit 3, Lesson 3.2a (Teacher’s Guide 4A, page 172), students add fractions with like denominators using models and digits (4.NF.3a and 4.NF.3b), which is shaped by 4.NF.B: “Build fractions from unit fractions.” For example, in Student Textbook 4A, page 91, “Lila drank 1/5 liters of milk. Her brother drank 2/5 liters of milk. How much did they drink together?” [Students are given pictures of measuring cups indicating the level of milk in each.]
• In Unit 8, Lesson 8.1a (Teacher’s Guide 4B, page 139), students distinguish between and identify points, lines, line segments, rays, and angles, both in isolation and within figures (4.G.1), which is shaped by the 4.G.A: “Draw and identify lines and angles, and classify shapes by properties of their lines and angles.”

The materials for Primary Mathematics Common Core Edition Grade 4 include problems and activities that serve to 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. For example:

• Unit 2, Lesson 2.2c (Teacher’s Guide 4A, page 111) connects the major cluster, “Use the four operations with whole numbers to solve problems” (4.OA.A) with major cluster, “Use place-value understanding and properties of operations to perform multi-digit arithmetic” (4.NBT.B). Students solve multi-step problems, most involving money to the one thousands place and involving addition, subtraction, and multiplication. For example, in Student Textbook 4A, page 56: “Mr. Cohen earns $2,935 a month. If he spends $1,780 each month and saves the rest, how much will he save in 6 months?”
• Unit 11, Lesson 11.1d (Teacher’s Guide 4B, page 245) connects the supporting cluster, “Solve problems involving measurement and conversion of measurements” (4.MD.A) with the supporting cluster, “Represent and interpret data” (4.MD.B). Students build different shapes with the same number of cubes and find the volume of multiple solids.

The materials in Primary Mathematics Common Core Edition Grade 4 include problems and materials that do not make connections with two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

• Unit 3 - Fractions (Teacher’s Guide 4A, pages 157-203) and Unit 4 - Operations on Fractions (Teacher’s Guide 4A, pages 204-266) focus on Domain “Numbers and Operations - Fractions” and the major clusters within the domain without any connections to other domains or clusters. Connecting this work to the major cluster “Uses place-value understanding and properties of operations to perform multi-digit arithmetic," (4.NBT.B) represents a missed opportunity.
• Unit 5 - Measures (Teacher’s Guide 4A, pp.267-302) addresses the cluster, “Solve problems involving measurement and conversion of measurements” without connections to other clusters or domains. Connecting this mathematics to the cluster within the same domain, “Represent and interpret data,” would be natural and important.