2nd Grade - Gateway 1

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for assessing grade-level content. Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year. Above-grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

Examples of aligned assessment items include but are not limited to:

• Unit 2 Assessment, Item 6, “Take an even number of pennies. How many pennies did you take? How do you know that the number of pennies is even? Write a number model with your pennies as the sum. Use equal addends.” (2.OA.3)
• Unit 2 Cumulative Assessment, Item 6, “How much money?” 5 dimes and 2 pennies are displayed. (2.MD.8)
• Unit 7 Open Response Assessment, Items 1 and 2, “Maria represented the number 349 like this (3 hundreds, 4 tens, and 9 ones are shown). Bill represented the number 349 like this (2 hundreds, 13 tens, and 19 ones are shown). Write whether Maria, Bill, or both of them represented the number 349. Explain your answer. You may include drawings.” (2.NBT.1)
• End-of-Year Assessment, Item 3, “Shawn has 24 crayons. His teacher gave him 24 more. Then he lost 8 crayons. How many crayons does he have now?” A line is left blank to provide a number model. (2.OA.1)

There are some above-grade-level assessment items that can be omitted or modified. These include: 

• Unit 8 Assessment, Item 3, “Circle the shapes that have parallel sides.” (4.G.2)
• Mid-Year Assessment, Item 10, “Write the rule in the box. Then complete the table.” Students determine the rule and fill in the missing numbers in an in/out table. (4.OA.5)
• End-of-Year Assessment, Item 11, “Circle the largest number.” The numbers are 3,241; 3,421; 3,204; and 3,021. (4.NBT.2)

• End-of-Year Assessment, Item 12, “Complete the table.” Students are given the rule “Expanded Form” and fill in the missing numbers on an in/out table using standard and expanded form. (4.OA.5)

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for spending a majority of instructional time on major work of the grade. For example:

• There are 9 instructional units, of which 7 units address major work of the grade or supporting work connected to major work of the grade, approximately 78%.
• There are 108 lessons, of which 75.5 address major work of the grade or supporting work connected to the major work of the grade, approximately 70%.
• In total, there are 170 days of instruction (108 lessons, 39 flex days, and 23 days for assessment), of which 101 days address major work of the grade or supporting work connected to the major work of the grade, approximately 59%. 
• Within the 39 Flex days, the percentage of major work or supporting work connected to major work could not be calculated because the materials suggested list of differentiated activities do not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.

The number of lessons devoted to major work is most representative of the instructional materials. As a result, approximately 70% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of supporting standards/clusters connected to the major standards/clusters of the grade include but are not limited to:

• In Lesson 1-3, Focus: Counting Coins a Connection, students use skip counting to find the total value of coin combinations. This connects the supporting standard 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies,” to the major work of 2.NBT.2, “Count within 1000; skip count by 5s, 10s, and 100s.”
• In Lesson 4-2, Focus: Telling Time to the Nearest 5 Minutes, students tell time using an analog clock to skip count by fives and report the time as so many minutes past the hour. This connects the supporting standard 2.MD.7, “Tell and write time from analog and digital clocks to the nearest five minutes,” to the major work of 2.NBT.2, “Count within 1000; skip count by 5s, 10s, and 100s.”
• In Lesson 7-7, Focus: Making a Class Line Plot, students make a line plot using standing-jump data and answer questions to interpret the data. This connects the supporting standard 2.MD.9, “Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object,” to the major work of 2.NBT.5, “Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”
• In Lesson 7-8, Focus: Comparing Arm Span Measures, students measure their arm span in inches and use the data to create a frequency chart and then a line plot. This connects the supporting standard 2.MD.9, “Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object,” to the major work of 2.NBT.5, “Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”
• In Lesson 9-8, Focus: Making Equivalent Amounts with Coins and Bills, students find two ways of paying for grocery items. This connects the supporting work of 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies,” to the major work of 2.OA.1, “Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.”

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations that the amount of content designated for one grade level is viable for one year. 

Recommended pacing information is found on page xxii of the Teacher’s Lesson Guide and online in the Instructional Pacing Recommendations. As designed, the instructional materials can be completed in 170 days:

• There are 9 instructional units with 108 lessons. Open Response/Reengagement lessons require 2 days of instruction adding 9 additional lesson days.
• There are 39 Flex Days that can be used for lesson extension, journal fix-up, differentiation, or games; however, explicit teacher instructions are not provided.
• There are 23 days for assessment which include Progress Checks, Open Response Lessons, Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment.  

The materials note lessons are 60-75 minutes and consist of 3 components: Warm-Up: 10-15 minutes; Core Activity: Focus: 30-35 minutes; and Core Activity: Practice: 15-20 minutes.

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for being consistent with the progressions in the Standards. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades and present extensive work with grade-level problems. The instructional materials relate grade-level concepts with work in future grades, but there are a few lessons that contain content from future grades that is not clearly identified as such.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past”. This section describes “how standards addressed in the Focus parts of the lessons link to the mathematics that children have done in the past.” Examples include:

• Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Past” for 2.NBT.2, “In Grade 1, children counted within 120, starting at any number less than 120.”
• Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Past” for 2.OA.3, “In Unit 1, children explored even and odd numbers using concrete and visual models. In Grade 1, children wrote number models to represent pictures of real-world items with paired features.”
• Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Past” for 2.MD.6, “In Unit 2, children used number lines to add 2-digit numbers to 10. In Grade 1, children used number lines to count and add.”
• Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Past” for 2.OA.1, “In earlier units, children solved number stories using addition and subtraction facts. In Grade 1, children modeled and solved number stories within 20 of all different types, with the position of unknown varying.”
• Teacher’s Lesson Guide, Section 8 Organizer, Coherence, “Links to the Past” for 2.G.2, “Children begin their informal exploration of area in Grade 2. In Unit 1, children determined that squares are the best shape for covering a rectangle. In Unit 3, they used 1- and 2-inch squares to explore how measurement relates to the size of the unit.”

The instructional materials relate grade-level concepts with work in future grades. Each Section Organizer contains a Coherence section with “Links to the Future”. This section identifies what students “will do in the future.” Examples include:

• Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Future” for 2.OA.2, “In Unit 2, addition fact strategies from Grade 1 will be reviewed and extended. In Grade 3, children will apply their knowledge of basic addition and subtraction facts to solve addition and subtraction problems within 1,000.”
• Teacher’s Lesson Guide, Section 3 Organizer, Coherence, “Links to the Future” for 2.NBT.5, “Throughout Grade 2, children will represent and solve problems involving addition and subtraction within 100. In Unit 6, children will be introduced to partial-sums addition. In Unit 9, they will be introduced to expand-and-trade subtraction. In Grade 3, children will add and subtract within 1,000 using strategies and algorithms.”
• Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Future” for 2.NBT.1, “Throughout Grade 2, children will apply their understanding of place value in a variety of contexts, including addition and subtraction. In Grade 3, children will use place-value understanding to round whole numbers to the nearest 10 and 100.”
• Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Future” for 2.MD.5, “Throughout Grade 2, children will solve number stories involving lengths. In Grade 3, children will solve number stories involving real-world situations including time intervals and masses or volumes.”
• Teacher’s Lesson Guide, Section 8 Organizer, Coherence, “Links to the Future” for 2.G.2, “In Grade 2, children will informally explore area by partitioning rectangles into rows and columns and counting to find the total. In Grade 3, children will apply their understanding of square units to find the area of plane figures in a variety of contexts.”

In some lessons, the instructional materials contain content from future grades that is not clearly identified as such. Examples include:

• Lesson 1-10, Focus: Skip Counting with a Calculator, “Children use calculators to skip count.” “Children practice programming their calculators by setting them to count up by 1’s. Next try group counts by numbers other than 2, 5, and 10, such as by 3, 4, and 9. Children press the appropriate keys on their calculators as they count in unison. Suggestions: Count from 22 by 3s. Count from 22 by 4s. Count from 80 by 6s. Count from 180 by 9s.” This lesson is labeled 2.NBT.2, “Count within 1000; skip-count by 5s, 10s, and 100s.” Identifying arithmetic patterns, including patterns in the addition table or multiplication table, is aligned to a Grade 3 standard [3.OA.9, “Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations”]. 
• Lesson 7-7, Warm Up: Mental Math and Fluency, “Dictate pairs of numbers for children to write on their slates and compare, recording the results with >, <, and =. Ask children to explain their answers in terms of place value. 1,054 and 1,154, 1,243 and 1,233, and 1,522 and 1,622.” This lesson is labeled 2.NBT.4, “Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.” Comparing two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons is aligned to a Grade 4 standard (4.NBT.2, “Read and write multi-digit whole numbers using base-10 numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons”).
• Lesson 9-4, Focus: Introducing Half-Inches, “Explain that measuring in half-inches, rather than inches or feet, produces more-precise measurements.” Students then practice measuring to the ½ inch throughout the lesson and on page 227 of their Math Journal. This lesson is labeled 2.MD.1, “Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes” and 2.MD.4, “Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.” Measuring to the ½ inch is a Grade 3 standard (3.MD.4, “Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch”).

The instructional materials give students extensive work with grade-level problems except for 2.NBT.6, “Add up to four two-digit numbers using strategies based on place value and properties of operations”. This standard is the focus of three lessons and practiced nine times throughout the materials. Also, when students do add four two-digit numbers, none of the sums are greater than 100.

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations that materials foster 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. Focus and Supporting Clusters addressed in each section are found in the Table of Contents, the Focus portion of each Section Organizer, and in the Focus portion of each lesson. Examples include:

• Lesson 1-6, Focus: Counting on a Calculator is shaped by 2.NBT.A, “Understand place value.” Students skip count up and back using a calculator. 
• In Lesson 3-1, Focus: Making 10 on a Double Ten Frame is shaped by 2.OA.B, “Add and subtract within 20.” Students share how they determined the number of dots on their double ten frames.
• Lesson 4-2, Focus: Telling Time to the Nearest 5 Minutes is shaped by 2.MD.C, “Work with time and money.” Students use analog clocks to tell time to the nearest 5 minutes. 
• Lesson 8-3, Focus: Comparing Triangles is shaped by 2.G.A, “Reason with shapes and their attributes.” Students compare triangles and discuss polygons.
• Lesson 9-4, Focus: Measuring to the Nearest Half-Inch is shaped by 2.MD.A, “Measure and estimate lengths in standard units.” Students use rulers to measure objects to the nearest half-inch.

The 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. Examples include:

• In Lesson 1-2, Focus: Working with a Partner to Add and Subtract on a Number Line, students work with a partner to solve number stories using the number line in the back of their journal. 2.OA.B, “Add and subtract within 20” connects to 2.MD.B, “Relate addition and subtraction to length.”
• In Lesson 1-4, Focus: Exploring Patterns on a Number Grid, students look for and discuss patterns on a number grid and then use it to skip count up and back. 2.NBT.A, “Understand place value” connects to 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.” 
• In Lesson 2-9, Warm-Up: Mental Math and Fluency, teachers pose number stories to students, and they share their solutions and strategies. 2.OA.B, “Add and subtract within 20” connects to 2.OA.A, “Represent and solve problems involving addition and subtraction.”
• In Lesson 3-3, Focus: Discussing Fact Families, students use fact triangles to name 3 numbers that make addition and subtraction facts. 2.OA.B, “Add and subtract within 20” connects to 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.”
• In Lesson 3-9, Focus: Going Back Through 10, students use number lines and the going back-through-10 subtraction strategy to solve problems. 2.OA.B, “Add and subtract within 20” connects to 2.MD.B, “Relate addition and subtraction to length.”
• In Lesson 6-4, Focus: Silly Animal Stories, students use data from the Animal Heights and Lengths Poster from their journal to make up and solve animal number stories. 2.MD.A, “Measure and estimate lengths in standard units” connects to 2.MD.B, “Relate addition and subtraction to length.”
• In Lesson 6-7, Focus: Finding Partial Sums with Base-10 Blocks, students represent addends with base-10 blocks and combine the blocks to find the sum. 2.NBT.A, “Understand place value” connects to 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.”
• In Lesson 7-7, Focus: Discussing the data, students share their jump length data, and work in partners to list the data from shortest to longest and determine the difference between the longest and shortest jump. 2.NBT.B, “Use place value understanding and properties of operations to add and subtract” connects to 2.MD.B, “Relate addition and subtraction to length.”
• In Lesson 9-8, Focus: Making Equivalent Amounts with Coins and Bills, students find two different ways of paying for grocery items. 2.NBT.A, “Understand place value” connects to 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.”