2nd Grade - Gateway 1

The materials reviewed for Everyday Mathematics 4, Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year. Unit Assessments found at the end of each unit assess the standards of focus for the unit. Open Response Assessments found at the end of odd-numbered units provide tasks addressing one or more content standards. Cumulative Assessments found at the end of even-numbered units include items addressing standards from prior units.

Materials assess grade-level standards. Examples include:

• 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)

Materials assess above-grade assessment items that could be removed or modified without impacting the structure or intent of the materials. Examples 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 11a, “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 materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials engage all students in extensive work with grade-level problems. Each lesson provides opportunities during Warm Up, Focus Activities, and Practice. Examples include:

• Lesson 2-2, Addition Number Stories, Focus: Writing Number Stories, Math Journal 1, students look at a picture and write a number story to represent it, “Write an equation to represent the story, and solve, using the terminology “Parts and Total” and “Change-to-More” to describe the problem-solving situations.” Unit 2, Lesson 7, students continue to write number stories and models, “Write a number model for this number story. Jessica has 2 dogs and 8 goldfish. How many pets does she have in all?” In Unit 3, Lesson 2, students share subtraction number stories, “Make up a story for the number sentence 10-3=7.” Lesson 3-8, students use a variety of subtraction strategies while solving number stories for context, “Write a number model for this story: Hayden is riding in the elevator of his apartment building. He gets on the elevator at floor 16. He rides down 7 floors to his aunt’s apartments. On what floor is his aunt’s apartment?” In lesson 6-2, students solve comparison number stories, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.” Lesson 6-3, students determine the kind of problem-solving situation used to solve a number story; “Change Situation, Comparison Situation, or Parts-and-Total Situation”, “Show children how different diagrams can be used to organize the information in Problem 1 [Rushing Waters now has 26 water slides. That is 9 more than last year. How many water slides were there last year?], which can be interpreted as a change situation, a comparison situation, and a parts-and-total situation?” After the situations are described, “Encourage children to share strategies, making sure to demonstrate how to organize the information in a diagram.” Students engage in extensive work with grade-level problems for 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.” 

• Lesson 4-4, Numeration and Place Value, Focus: Matching Numbers to Base-10 Block Representations, students use base-ten blocks to represent 3-digit numbers, “Display 3 flats and 4 cubes and ask children to show the number with number cards on their Place-Value Mats. Some children will leave the Tens column empty. Others will put a 1. Write 34 and 304 on the board. Ask, Which number matches the base-10 blocks? Why? Which digit in 304 shows that there are no longs (or no tens)? Students continue to represent numbers with base-10 blocks in Unit 4, Lessons 5 and 6. In Unit 5, Lessons 4, 5, and 10, students solve problems in their Math Journal to practice representing numbers with place value understanding. Math Journal 2, Problem 1, “In the number 300 there are ___ hundreds, ___ tens, ___ones. Students engage in extensive work with grade-level problems for 2.NBT.1, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g.,706 equals 7 hundreds, 0 tens, and 6 ones.”

• Lesson 4-8, How Big is a Foot? Focus: Measuring with a Foot-Long Foot, students measure classroom objects, “Children work in partnerships to measure the lengths of a few objects around the room. Children measure the objects independently and then collaborate with their partners to agree on an approximate number of feet for each object.” Lesson 4-9, Math Journal 1, students are introduced to the inch and taught how to use a ruler to measure objects to the nearest inch, “...use a 12-inch ruler to measure the length of each object. Record the measures.” Lesson 4-10, Math Journal 1, students measure objects in centimeters using a ruler, “Pick short objects to measure. Write the name of each object or draw a picture of it. Then measure the objects in inches and centimeters. Record your measures.” Lesson 7-4, Math Journal 2, Problem 1, students measure in yards, “Find things that are about 1 inch long, about 1 foot long, and about 1 yard long. Use a ruler, a tape measure, or a yardstick to help you.” Lesson 7-5, Math Journal 2, students measure in meters, “Find things that are about 1 centimeter long, about 10 centimeters long, and about 1 meter long. Use a ruler, a tape measure, or a meterstick to help you. List them below.” Students engage in extensive work with grade-level problems for 2.MD.1, “Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.”

The materials provide opportunities for all students to engage with the full intent of Grade 2 standards through a consistent lesson structure. According to the Teacher’s Lesson Guide, Problem-based Instruction “Everyday Mathematics builds problem-solving into every lesson. Problem-solving is in everything they do. Warm-up Activity- Lessons begin with a quick, scaffolded Mental Math and Fluency exercise. Daily Routines - Reinforce and apply concepts and skills with daily activities. Math Message - Engage in high cognitive demand problem-solving activities that encourage productive struggle. Focus Activities - Introduce new content with group problem-solving activities and classroom discussion. Summarize - Discuss and make connections to themes of the focus activity. Practice Activities - Lessons end with spiraled review of content from past lessons.” Examples of full intent include:

• Lesson 1-9, Even and Odd Number Patterns, Focus: Introducing Even and Odd Numbers, students identify even and odd by making pairs, “Discuss the following points: Whenever each child standing can be paired with another child, the total number standing is called an even number. Whenever one child cannot be paired with another child, the total number standing is called an odd number.” Routine 2, Calendar Routine: Using the Calendar Routine, “Determine whether there has been an odd or an even number of days in the month so far. Ask: What happens if we try to break the days that have passed into two equal groups? Does the result tell us whether the number is even or odd?” Students engage in the full intent of 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.”

• Lesson 5-6, Mentally Adding and Subtracting 10 and 100, Focus: Adding and Subtracting 10 and 100, students use calculators to add and subtract 10 from 3-digit numbers, “Next have children use their calculators to count back by 10s from 547 to 477. Ask: What patterns do you notice? Ask: How is counting by 10s similar to adding or subtracting 10s? Dictate 2- and 3-digit numbers and have children apply the rules generated by the class to mentally add or subtract 10 and 100. They record their answers on slates. Include a variety of numbers.” Lesson 5-6, Home Link, students solve problems adding and subtracting 10 or 100, “Solve mentally. Tell someone at home about the rules you used.” Problem 2, “58 - 10 = ___, Problem 5, “___ = 786 + 100.” Routine 1, Using the Number of the Day, students add and subtract 10s or 100s, “Ask children to tell 10-more, 10-less, 100-more, and 100-less number stories using the number of the day.” Students engage in the full intent of 2.NBT.8, “Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.”

• Lesson 7-9, Exploring Shape Attributes, Graphs, and Measurements, Math Journal 2, students sort shapes by attribute, then trace the shapes, “Trace 3 shapes from a different sort. Write a name that describes the sort.” Lesson 8-2, Core Activities: Focus, Identifying Attributes, students complete sentence frames for students to describe shapes, “This is a _____. It has ____ sides. It has ____ vertices. It has ____ angles.” Students engage in the full intent of 2.G.1, “Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.”

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade.

• 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.

A lesson analysis is most representative of the materials. As a result, approximately 70% of the materials focus on the major work of the grade.

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

Digital materials’ Main Menu links to the “Spiral Tracker” which provides a view of how the standards spiral throughout the curriculum. The Lesson Landing Page contains a Standards section noting standards covered by the lesson. Teacher Edition contains “Correlation to the Standards for Mathematics” listing all grade-level standards and correlating lessons. Examples include:

• Lesson 1-3, Math Tools, Focus: Examining the Nickel, students use skip counting to find the total value of coin combinations, “Ask: If every child in our class had 1 nickel, how much money would we have in all? Record children’s estimates of the total; then count all the nickels together by 5s and record the counts on the board. Discuss with the class what patterns they notice as they count by 5s.” 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.”

• Lesson 4-2, Telling Time to the Nearest 5 Minutes, 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, “Display 9:00 on the clock and ask children what time it shows. Move the minute hand slowly forward, to 9:20, pausing on each number 1 through 4. If needed, adjust the hour hand. At each pause, ask: What time is it now? Say the times with the class: 5 minutes after 9, 10 minutes after 9, 15 minutes after 9, 20 minutes after 9.” 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.”

• Lesson 7-7, Representing Data: Standing Jumps, Focus: Making a Class Line Plot, students make a line plot using standing-jump data and answer questions to interpret the data, “Label the shortest and longest lengths on the line plot. Ask children questions about the set of data displayed in the line plot: What does it mean when there are a lot of Xs above a number? How many children have a jump of 42 inches?” 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.”

• Lesson 7-8, Representing Data: Arm Span, 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, “Determine who has the shortest and longest arm spans and what their lengths are. Tape an actual tape measure to the board and mark the longest and shortest arm spans. Draw a comparison diagram on the board, filling in the known quantities and writing a question mark for the difference. With the class, find the difference between the two arm spans. Explain that children will use the class arm span data to make a frequency table and 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.”

• Lesson 8-8, Equal-Groups and Array Number Stories, Focus: Solving Equal-Groups and Array Number Stories, students solve array number stories, “Pose number stories involving equal groups or arrays of objects. Tell children to work with their partners and use drawings to model and solve each problem. After each number story, have volunteers share their strategies.” This connects the major work of 2.OA.A, “Represent and solve problems involving addition and subtraction.” to 2.OA.C, “Work with equal groups of objects to gain foundations for multiplication.”

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The Teacher Edition contains a Focus section in each Section Organizer identifying major and supporting clusters covered. Materials do not contain connections of supporting work to supporting work. There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Lesson 1-2, Number Lines and Partnership Principles, 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, “Have children solve the following number story using one of the number lines on the inside back cover of their journals: Angela had $14. She earned $5 more. How much money does Angela have now?” This connects the major work of 2.OA.B, “Add and subtract within 20” to the major work of 2.MD.B, “Relate addition and subtraction to length.”

• Lesson 2-9, Even Numbers and Equal Addends, Warm-Up: Mental Math and Fluency, teachers pose number stories to students, and they share their solutions and strategies, “Pose number stories and have children share their solutions and strategies.” This connects the major work of 2.OA.B, “Add and subtract within 20” to the major work of 2.OA.A, “Represent and solve problems involving addition and subtraction.”

• Lesson 3-3, Fact Families, Focus: Discussing Fact Families, students use fact triangles to name 3 numbers that make addition and subtraction facts, “Ask a volunteer to name another group of three numbers that are related by addition and subtraction. Write these numbers in the corners of the triangle and have children write the fact family for these numbers on their slates.” This connects the major work of 2.OA.B, “Add and subtract within 20” to the major work of 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.”

• Lesson 6-4, Animal Number Stories, 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, “Tell the class they will use the data from the Animal Heights and Lengths Poster on journal page 146 to make up and solve their own number stories. Have children share their solution strategies.” This connects the major work of 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.” to the major work of 2.MD.B, “Relate addition and subtraction to length.”

• Lesson 7-1, Playing Hit the Target, Practice: Bamboo Plant Number Stories, students solve problems in Math Journal 2, p. 166-167. Students are given a chart of bamboo growth each day for a week measured in inches, ranging from 12 inches to 99 inches. “Use the information above to solve the following number stories.” Problem 1, “How many inches did the bamboo plant grow from Tuesday to Friday? Number Model: ______ Answer: ____ inches.” This connects the major work of 2.OA.A, “Represent and solve problems involving addition and subtraction.” to the major work of 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.”

• Lesson 9-6, Expand-And-Trade Subtraction Part 1, Focus: Representing Subtraction with Trades, students represent numbers using base-ten blocks and sketches of place value, then use to subtract, “Tell children they will now use their base-10 blocks to solve 53-37. Ask children to represent 53 with base-10 blocks. When they have finished, record a sketch of 5 longs and 3 cubes. Ask: Are there enough longs and cubes for me to remove 3 longs and 7 cubes? How can I get more cubes so I can remove 7 cubes? Have the children make the trade with their base-10 blocks. Represent this trade on your sketch by crossing out 1 long and adding 10 cubes.” This connects the major work of 2.NBT.A, “Understand place value,” to the major work of 2.NBT.B “Use place value understanding and properties of operations to add and subtract.”

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Materials relate grade-level concepts to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past” containing information about how focus standards developed in prior units and grades. Examples include:

• 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 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.”

Materials relate grade-level concepts to future work. Each Section Organizer contains a Coherence section with “Links to the Future” containing information about how focus standards lay the foundation for future lessons. Examples include:

• 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 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.”

Materials contain content from future grades in some lessons that is not clearly identified. Examples include:

• Lesson 1-10, Skip-Counting Patterns, 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, the students 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, Representing Data: Standing Jumps, 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 the 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, Fractional Units of Length, 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 \frac{1}{2} inch throughout the lesson and on page 227 f 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”).