2nd Grade - Gateway 1

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. There are examples where supporting work engages students in the major work of the grade, but there are also multiple instances where supporting work is treated separately and does not engage students in the major work of the grade.

Lessons that connect supporting content to the major work on the grade include:

• Topic 12 addresses Geometry standards 2.G.1, 2.G.2 and 2.G.3. Lesson 12-5 connects to the major work of 2.OA.2. (Add and subtract within 20.) Students represent and solve problems, for example, in Practice Item 1 on page 402: “Use square tiles to cover the rectangle. Write number sentences to tell how you counted by rows and columns. Count by rows: ___ Count by columns: ___” Students are expected to write 6 + 6 = 12 and 2 + 2 + 2 + 2 + 2 + 2 = 12.
• In Topic 13, the Problem-Based Interactive Learning, Independent Practice, and Quick Check connect money (2.MD.8) to the major work of place value as students skip count by 5s and 10s to find the value of a set of coins. (2.NBT.2)
• Lesson 13-1 connects supporting work 2.MD.8 to major work 2.NBT.2. On page 421, there is a quarter, dime, nickel, and two pennies shown. Students add to find the value of the collection as 42 cents.
• In Lesson 16-1, students count by 5s on analog and digital clocks. (2.MD.7) This connects to major work 2.NBT.2.
• In Lesson 16-8, students solve one-step word problems using addition and subtraction. (2.OA.1) On page 538, students are given a picture graph about Meytal’s closet. Students are asked, “What type of clothing is there the least of in the closet?" And, “How many more pants than shirts are in the closet?” (2.MD.10)

Examples of missed opportunities to connect supporting content to the major work on the grade include:

• Teacher Edition Lesson 13-4, page 431, contains the problem, “Suppose the pig contains one dollar bill, one penny, one nickel and two dimes. What is the total value of the money in the pig? Where do you put the dollar sign and decimal point when writing money amounts?” Representations using decimal notation align to 4.NF.6.
• Lessons 14-1 and 14-2 address money. (2.MD.8) Students subtract within 100 in one-step word problems. (2.OA.1) There is a missed opportunity to have students do two-step word problems as stated in 2.OA.1. Students solve the word problems based on two-digit subtraction problems using the standard algorithm. (4.NBT.4)

The instructional materials for enVisionMATH California Common Core Grade 2 partially meet expectations for the materials being consistent with the progressions in the standards.

The instructional materials reviewed for Grade 2 are partially consistent with the progressions in the standards. Although students are given extensive grade-level problems and connections to future work are made in the Skills Trace, future grade-level content is not always clearly identified within the lesson or Topic for the teacher or student. The exception is the Topic titled, Step up to 3rd Grade, where the materials are clearly identified as Grade 3 materials. The Grade 2 materials have instances where future grade-level content is present and not identified as such. For example:

• In Lesson 13-3, a decimal point is taught as a vocabulary word. In Grade 4, the standard states, “Use decimal notation for fractions with denominators of 10 or 100. Use the four operations to solve word problems involving distances, …, and money.” (4.NF.6, 4.MD.2)
• In Lesson 13-4, page 432, decimal points are used to solve money problems. A dollar bill, a fifty-cent piece, a dime, and a penny are shown. Students are to count and write $1.62. (4.MD.2)

The correlation between the CCSSM and the lessons is found in the Teacher e-text. In the e-text, a menu on the left side appears with Program Resources. Clicking on Program Resources leads to a drop-down menu with Printable Resources where a document called Common Core State Standards Skill Trace resides. Objectives, Essential Understandings, and a Math Background explain connections between prior knowledge and the lesson. Math Background provides a learning arc. For example, Topic 6 of the Math Background states, “For success with mental addition, give children ample practice with basic addition facts. Children should be comfortable with the addition facts they have learned previously.” Additionally, each Topic begins with a Progression Overview document. This document connects grade-level concepts to specific standards under the Looking Back column and connects grade-level concepts to future standards under the Looking Ahead Column. The Daily Common Core review in each lesson connects to prior knowledge. Materials provide students opportunities to work with grade-level problems. The majority of reteach and center activities provided are on grade level. Extension activities are embedded within lessons and allow students to engage more deeply with grade-level work. Additional extension activities are also provided online, as are reteach items.

The materials do not always meet the full intent of the standards and do not always provide extensive work to students for each standard. For example:

• 2.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.3 is addressed in one lesson, 5-6 (Even and Odd Numbers). The standard states, "There are two parts to the standard: determining odd/even by pairing objects and writing equations." In the Independent Practice, pages 145-146, teachers are guided to have students use cubes: “Children may have difficulty solving the exercises without visual support. Encourage them to use connecting cubes to solve the exercises.” On page 144, the teacher directions state, “In this lesson you will learn how to tell if a number is odd or even. If the number is even, you will write a number sentence to show the two equal parts and the total number of cubes.” In the lesson, students do not count by 2s to determine if a number is even.
• 2.MD.6: Represent whole numbers as lengths from 0 on a number line diagram with equally-spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. 2.MD.6 is addressed in Lessons 8-6 (adding using a number line) and 9-6 (subtracting using a number line). In the two lessons, students are given the number lines with the units included. Students do not create a number line with equally-spaced points, and rulers as number lines are not taught until Topic 15. This is a missed opportunity to use rulers when adding and subtracting within 100 in Topics 8 and 9.
• For 2.NBT.1b, there is one lesson, 10-1: Building 1000. The standard states, “The numbers 100, 200, 300, …, 900, refer to one, two, …, or nine hundreds (and 0 tens and 0 ones).” From this lesson, page 301, students understand the value of hundreds and can move to the next lesson putting numbers such as 245 into in the correct place of 2 hundreds and 4 tens and 5 ones in a place-value table.
• For 2.NBT.3, there is one lesson, 5-2: Reading and Writing Numbers. The standard states, “Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.” The lesson works on reading and writing two-digit numbers but not on expanded form or numbers greater than 90.
• For 2.NBT.9, there is one lesson, 11-9: Models for Subtracting with Three-Digit Numbers. The two previous lessons, 11-7 and 11-8, teach subtraction by estimation first, then base-ten blocks alongside the standard algorithm. Lesson 11-9 uses the standard algorithm. The materials do not provide extensive work to students addressing 2.NBT.9.
• For 2.MD.2, there is one lesson, 15-6: Measuring Length. The students start the lesson measuring with non-standard units. The lesson moves to students measuring using inches, feet, and yards. To have students understand that it takes more inches than feet is necessary, but it is not built upon in the lesson. Also, students do not have sufficient practice measuring inches and feet and are not responsible in the standards for yards.
• For 2.MD.4, there is one lesson, 15-8: Comparing Lengths. As both metric and customary measurements are being used in this cluster, centimeters were used to compare not inches, feet, and meters as stated in the standard.

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings.

• In Topic 2, students “Add and subtract within 20” (2.OA.B) by working on addition facts involving 0, 1, 2, using the doubling strategy, considering near doubles, and making 10 to add.
• In Topic 4, students “Work with equal groups of objects to gain foundations for multiplication” (2.OA.C) by repeated addition, building arrays, and drawing pictures.
• In Topic 5, students “Use place-value understanding and properties of operations to add and subtract” (2.NBT.B) by grouping objects into tens and ones, comparing two-digit numbers using symbols, and identifying and writing numbers that are 10 more and 10 less than a given number.

Materials do not include problems and activities that 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.

• There are missed opportunities to connect 2.OA.1 with 2.MD.10. Topics 1 and 16 are taught independently and do not make a connection between any other cluster within Grade 2.
• There are missed opportunities to connect 2.NBT.B to 2.NBT.A or 2.OA. Materials address parts of a standard at a time and do not connect those parts together or connect those to other standards.