Alignment: Overall Summary

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 partially meet expectations for alignment to the CCSSM. The materials meet expectations for Gateway 1, focus and coherence. The instructional materials meet expectations for not assessing topics before the grade level in which the topic should be introduced, spend approximately 70% of instructional time on the major work of the grade, and are coherent and consistent with the standards. The instructional materials partially meet expectations for Gateway 2, rigor and the Mathematical Practices. The instructional materials meet expectations for rigor, attending to procedural skill and fluency and conceptual understanding, and they do not always treat the three aspects of rigor together or separately. The instructional materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, but do not provide students with opportunities to meet the full intent of all MPs. The instructional materials meet expectations for students constructing viable arguments and analyzing the arguments of others and also for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others.

See Rating Scale Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
15
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focus by assessing grade-level content and spend approximately 70% of instructional time on the major work of the grade. The instructional materials meet expectations for being coherent and consistent with the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
+
-
Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for assessing grade-level content. 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. 

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
-
Indicator Rating Details

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)

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
+
-
Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for spending the majority of time on major work of the grade. The instructional materials, when used as designed, spend approximately 70% of instructional time on the major work of the grade, or supporting work connected to major work of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
+
-
Indicator Rating Details

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.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
+
-
Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are consistent with the progressions in the standards and foster coherence through connections at a single grade.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
+
-
Indicator Rating Details

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.”

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
+
-
Indicator Rating Details

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.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
+
-
Indicator Rating Details

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.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials 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.
2/2
+
-
Indicator Rating Details

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.”

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials for Everyday Mathematics 4 Grade 2 partially meet expectations for Gateway 2, rigor and the Mathematical Practices. The instructional materials meet expectations for rigor, attending to procedural skill and fluency and conceptual understanding, and they do not always treat the three aspects of rigor together or separately. The instructional materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, but do not provide students with opportunities to meet the full intent of all MPs. The instructional materials meet expectations for students constructing viable arguments and analyzing the arguments of others and also for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others. The instructional materials partially attend to the specialized language of mathematics.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for rigor and balance. The materials attend to procedural skill and fluency and conceptual understanding, and they partially attend to application. The materials do not always treat the three aspects of rigor together or separately.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade level. The Focus portion of the lesson provides opportunities for students to explore, engage in, and discuss conceptual understanding of mathematical content. Examples include:

  • In Lesson 1-4, Focus: Exploring Patterns on the Number Grid, students describe and explore patterns on a number grid. Students are expected to observe such things as every other number on the grid is odd and all of the numbers in the far right column end in a 0. Next, the teacher leads the students in using the chart to skip count by 2s, 5s, and 10s. This activity supports conceptual understanding of 2.NBT.2, “Count within 1000, skip-count by 5s, 10s, and 100s.”
  • In Lesson 2-5, Focus: Discussing the Near-Doubles Strategy, the teacher leads a discussion about how using a near doubles fact can help find the answer to a more difficult problem. “Display problems 5 + 7 = ? and 6 + 4 = ? and tell partners to use their knowledge of doubles facts to solve them. After a few minutes, invite volunteers to share their strategies. These may include adding or subtracting 2 from a double (for example, 5 + 7 = 5 + 5 + 2 = 12) or ‘sharing’ (for example, taking 1 from 7 and giving it to 5 to make the double 6 + 6).” This activity supports the conceptual understanding of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.”
  • In Lesson 4-4, Focus: Reviewing Values of Digits, “Display a cube, a long, and a flat. Remind children that these are called base-10 blocks. Hold up a cube.  Say: This is a base-10 cube. It represents 1. Then hold up a long and say: This is a long. It represents 10. Ask children to explain why a long represents 10. Hold up a flat and say: This is a flat. It represents 100. Ask children to explain why a flat represents 100.” This class discussion supports students in developing conceptual understanding of 2.NBT.1, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.”
  • In Lesson 5-5, Focus: Introducing Arrays, students make arrays and write number models to represent them. Students should determine that organizing dots in rows makes it easier to skip count to find the total. This activity supports conceptual understanding of 2.OA.4, “Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns, write an equation to express the total as a sum of equal addends.”
  • In Lesson 9-5, Focus: Comparing Multidigit Numbers, the teacher leads a discussion about expanding three-digit numbers and asks, “How can we use the expanded form of each number to help us compare them? Sample answer: First we can look at the hundreds. Both numbers have 2 hundreds, or 200, so next we look at the tens. We see that 292 has 9 tens, or 90, but 289 has 8 tens, or 80. So we know 292 is larger.” Then the teacher asks, “Do we need to look at the ones?” Students may answer, “No. The tens told us that 292 is larger.” The teacher repeats this activity with other pairs of 3-digit numbers as needed. This activity supports conceptual understanding of 2.NBT.4, “Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record results of comparisons.”

Games, Daily Routines, and Math Journals provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

  • In Routine 2: Attendance Routine, students count the number of total students and the number of students present. This information is recorded on the attendance chart and students determine how many children were absent. This activity provides continuous conceptual understanding practice 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 4-5, Game: Introducing Number Top-It, students and a partner are given a game mat with rectangles labeled with place value levels to thousands. Using a deck of digit cards, students take turns drawing cards until each player has three cards. Students use their cards to make a 3-digit number, read the number, and compare the number to their partner’s. The player with the larger number for the round scores 1 point, and the player with the smaller number scores 2 points. Students play five rounds, and the player with the fewest points at the end of five rounds wins the game. This activity provides practice of conceptual understanding of 2.NBT.4, “Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, or < symbols to record the results of comparisons.” 
  • In Lesson 1-3, Math Journal, students find the total value of coin combinations. For example, Question 3 shows 4 dimes and 1 nickel. This practice activity supports conceptual understanding of 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately.”
  • In Lesson 2-8, Math Journal, students use number lines provided to find sums. For example, Question 1, “Show 62 + 10 on the number line below.” Then students record their answers. This practice activity supports the conceptual understanding of 2.NBT.1, “Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.”
  • In Lesson 4-5, Math Journal, students write numbers in expanded form to compare them. For example, Question 2 asks students to compare 42 and 48. Students write 40 + 2 and 40 + 8 so they can use the ones to make a comparison. This practice activity supports conceptual understanding of 2.NBT.3, “Read and write numbers to 1000 using base-10 numerals, number names, and expanded form.”

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade level. The Section Organizer provides information on which part of each lesson develops procedural skill and fluency. Opportunities are found in the Daily Routines and Focus portions of the lesson. Examples include:

  • In Lesson 2-3, Focus: Using Double Ten Frames, “Flash each Quick Look Card for 2 to 3 seconds before removing it from view or covering it. Always allow a second look and follow up by asking children both what they saw and how they saw it. Asking such questions will allow a variety of strategies to emerge. Encourage children to share multiple strategies but focus attention to those that involve doubles and combinations of 10.” This activity provides an opportunity for students to develop fluency of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.”
  • In Lesson 5-7, Focus: Introducing Open Number Lines, students use mental strategies to solve addition number stories and record their thinking on open number lines. For example, “Peter has 64 blocks in his toy box and 30 blocks on the table. How many blocks does he have in all?” This activity provides an opportunity for students to develop fluency 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 7-3, Focus: Introducing Basketball Addition, students play in teams of 3 to 5 players. Teams roll a 20-sided polyhedral die and a 6-sided die and find their sum. Teams add the sum to their team’s total score. The team with the most points wins. This activity provides an opportunity for students to develop fluency 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 Routine 3: Attendance Routine, students use data from the attendance chart to tell number stories such as, “Today, 23 children are here. If 2 more children arrive, how many will be present? There are 24 children here today. If 6 go to the library, how many are left?” This activity provides continuous opportunities for students to develop fluency 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.”

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. The Section Organizer provides information on which part of each lesson develops procedural skill and fluency. Opportunities are found in the Practice portions of the lesson, Math Journal, and Math Masters. Examples include:

  • In Lesson 2-4, Math Journal 1, students use double ten frames to make 10, find the sum, and write a combination of 10 that helped them solve. In Question 1, students are shown 9 and 5. The suggested answer is, “The combination of 10 that helped: 9 + 1 = 10 and fact 9 + 5 = 10”. This activity provides an opportunity for students to independently demonstrate the procedural skill of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.”
  • In Lesson 4-11, Math Journal 1, students match subtraction facts to strategies they could use to solve them in their journal. Students then discuss their reasoning for their pairings in small groups, focusing on how they matched facts and strategies. This activity provides an opportunity for students to independently demonstrate the procedural skill 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 5-7, Math Journal 2, students use Open Number Lines to record their thinking when adding two 2-digit numbers. In Question 2, “You build the second tower with 37 red blocks and 32 blue blocks. How many blocks did you use?” This activity provides an opportunity for students to independently demonstrate the procedural skill 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 9-7, Math Journal, students are given a subtraction problem and find a ballpark estimate, write each number in expanded form, and solve. In Question 3, “72 - 49 = ?” This activity provides an opportunity for students to independently demonstrate the procedural skill 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.”

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The materials do not provide opportunities for students to independently engage in non-routine applications of mathematics throughout the grade level.

Examples of students engaging in routine application of mathematics include:

  • In Lesson 3-9, Focus: Math Message, students write a number model for a subtraction 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 apartment. On what floor is his aunt’s apartment?” Students share their models with classmates. Students apply their understanding 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.”
  • In Lesson 5-3, Focus: Making Change, students count up from the cost of an item to the amount paid. Students use Pine School’s Fruit and Vegetable Sale in their journal to answer, “I am buying an orange. I give the clerk two dimes. How much change should the clerk give back?” Students apply their understanding of 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately.”
  • In Lesson 6-4, Focus: Solving Silly Animal Stories, students use an animal heights/lengths poster to solve number stories such as, “How much longer is the blue whale than the white rhinoceros? How many feet would the giant squid have to grow to be as long as the blue whale?” Students apply their understanding of 2.MD.5, “Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.”
  • In Lesson 8-8, Focus: Math Message, students discuss equal-groups and array number stories such as, “Jane bought 3 packs of gum. There are 5 sticks of gum in each pack. How many sticks of gum did she buy? Draw pictures to help you find the answer. Students share their drawings and solutions with classmates. Students apply their understanding of 2.OA.4, “Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.”

The materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. Examples include:

  • In Lesson 2-3, Mental Math and Fluency, students solve number stories such as, “Abby’s crayon box has two rows of crayons. The second row has 8 crayons. Abby’s crayon box has 16 crayons in all. How many crayons are in the first row?” This activity provides the opportunity for students to independently demonstrate 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.”
  • In Lesson 6-7, Practice: Solving Number Stories, students practice writing number stories using the ? for the unknown to solve number stories. For example, “Emma found two leaves. One leaf was 9 centimeters longer than the other. The longer leaf was 20 centimeters long. How long was the shorter leaf?” This activity provides the opportunity for students to independently demonstrate 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.”
  • In Lesson 7-2, Focus: Solving the Open Response Problem, students solve a number story with four two-digit addends, “A theater has 100 seats. Four schools are sending children to a puppet show at the same theater. The first school will send 21 children. The second will send 13. The third will send 42, and the fourth will send 19. Are there enough seats in the theater for all of the children?” This activity provides the opportunity for students to independently demonstrate 2.NBT.6, “Add up to four two-digit numbers using strategies based on place value and properties of operations.”

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the program materials. 

The materials attend to conceptual understanding. Examples include:

  • In Lesson 4-4, Focus: Matching Numbers to Base-10 Block Representations, students represent 3-digit numbers with number cards, base-10 blocks, and expanded form, “Display a Place-Value Mat and place 3 flats, 5 longs, and 2 cubes. Tell children that the collection of blocks represents a number. Ask: How many hundreds are in this number? What is the value of the 3? How many tens are in this number? What is the value of the 5? How many ones are in this number? What is the value of the 2?” This activity develops conceptual understanding of 2.NBT.1, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.”
  • In Lesson 9-6, Focus: Representing Subtraction with Trades, students use base-10 blocks to subtract with trades, “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. 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?” The children make the trade with their base-10 blocks. The teacher represents the trade on the sketch by crossing out 1 long and adding 10 cubes. The class repeats the activity with other subtraction problems. This activity develops conceptual understanding of 2.NBT.7, “Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”

The materials attend to procedural skill and fluency. Examples include:

  • In Lesson 1-8, Warm Up, Mental Math and Fluency, students solve addition facts using Quick Looks, “Always allow children a second look and follow up by asking both what they saw and how they saw it.” The teacher shows the Quick Look Card 79 which shows a double ten frame with four dots at the bottom of each ten frame, “Sample answer: I saw 4 and 4. I know that 4 + 4 = 8.” This activity develops the procedural skill of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.”
  • In Lesson 3-2, Focus: Generating Related Addition and Subtraction Facts, students generate related addition and subtraction facts based on dominoes, “Display a domino with 5 dots on one side and 4 dots on the other, Help children discover the addition facts and subtraction facts it shows. Ask: Which addition facts describe the domino? If needed, remind children about using the turn-around rule to generate related addition facts. Which subtraction facts describe this domino?” Students repeat the activity with other dominos. This activity develops the procedural skill 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.”

The materials attend to application. Examples include: 

  • In Lesson 2-2, Focus: Creating and Solving Addition Number Stories, students make up and solve number stories, “1. Display the story or draw a picture that illustrates the story but doesn't suggest a solution strategy. 2. Draw an empty unit box below the story. 3. Have children write a label in the unit box and share how they would answer the question in the story. 4. Ask a volunteer to write a number model for the story. 5. Ask another volunteer to explain how the numbers in the number model connect to the story.” This activity provides the opportunity to apply understanding 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.”
  • In Lesson 6-2, Focus: Math Message, students solve comparison number stories, “Fish A is 14 inches long. Fish B is 6 inches long. How many inches longer is Fish A than Fish B?” Students solve several other comparison number stories. This activity provides the opportunity to apply understanding of 2.MD.5, “Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.”

Multiple aspects of rigor are engaged in simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

  • In Lesson 4-7, Focus: Playing Target to 50, students add and subtract using base-10 blocks, “Players take turns. When it is your turn, do the following: Turn over 2 cards. You may either use one card to make a 1-digit number or both cards to make a 2-digit number. Model your number with base-10 blocks. Put these blocks just below your Target Game Mat but not on the mat. You now have two choices: Choice 1: Add all of the base-10 blocks below the mat to the blocks already on your Target Game Mat. Choice 2: Subtract all of the blocks below the mat from the blocks already on your Target Game Mat. If you decide to subtract, you may first have to make exchanges on the mat.” The first player to have a mat with a value of exactly 50 wins. Students develop conceptual understanding of 2.NBT.1, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones,” and procedural skill with 2.NBT.7, “Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.”
  • In Lesson 4-11, Focus: Exploration A: Matching Facts with Strategies, students match subtraction facts to possible solution strategies, “Children independently match subtraction facts from Math Masters, page 110 to strategies they could use to solve them on journal page 89. In small groups children discuss their reasoning for their pairings, focusing especially on differences in how they matched facts and strategies.” Students develop procedural skill with 2.OA.2, “Fluently add and subtract within 20 using mental strategies,” and conceptual understanding 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 6-4, Focus: Solving Silly Animal Stories and Writing Silly Animal Stories, students solve number stories comparing the heights and lengths of various animals, “Have children share the names and lengths of the longest animal and the shortest animal.” Then students write and solve their own number stories, “Children write two number stories. In each story they compare or add the lengths in feet of two animals from journal page 146.” Students develop procedural skill with 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,” and application 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.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
+
-
Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 partially meet expectations for practice-content connections. The instructional materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, but do not provide students with opportunities to meet the full intent of MP5, choose tools strategically. The instructional materials meet expectations for students constructing viable arguments and analyzing the arguments of others and also for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of othersThe instructional materials partially attend to the specialized language of mathematics.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level.

All MPs are clearly identified throughout the materials, with few or no exceptions. Examples include:

  • The mathematical practices are listed on pages xxxvi-xxxix in the Grade 2, Volume I Teacher’s Lesson Guide as “Correlation to the Mathematical Process and Practices” which states, “Everyday Mathematics is a standards-based curriculum engineered to focus on specific mathematical content, processes, and practices in every lesson and activity. The chart below shows complete coverage of each mathematical process and practice in the core program throughout the grade level.” 
  • Each Unit Organizer contains a Mathematical Background: Processes and Practices component identifying the MPs addressed in the section and in individual lessons. Additionally, “The authors created Goals for Mathematical Practice (GMP) that unpack the practice standards, operationalizing them in ways that are appropriate for elementary students.” 
  • Within each lesson description, GMPs appear in bold print and teacher side notes identify the MPs that are addressed in the lesson.

The majority of the time the MPs are used to enrich the mathematical content. Examples include:

  • In Lesson 2-4, Focus: Exploring the Making-10 Strategy, students use the making-10 strategy to determine the number of dots in ten frames, “Remind children that Quick Look activities help us think about addition strategies. Flash Quick Look cards 95 and 98 in sequence. Have children write words or number sentences on their slates to record how they figured out the total number of dots on each card.” The mathematical content in this activity is enriched by MP2.
  • In Lesson 3-10, Focus: Summarizing Subtraction Strategies, students discuss subtraction strategies used to solve problems, “Have partners discuss the following questions: If you want to solve a subtraction fact that you don’t know, what strategies could you use? Pose a few subtraction facts to provide a context, such as 12 - 6, 15 - 8, and 16 - 7. Encourage children to refer to their My Subtraction Fact Strategies table on journal page 48. As volunteers share their ideas, record their strategies on the Class Data Pad and lead a class discussion about the similarities and the differences between the strategies.” The mathematical content in this activity is enriched by MP1.
  • In Lesson 6-5, Focus: Solving Two-Step Number Stories, students solve two-step number stories, “Display and fill in a change diagram to model the first step. Write 9 in the Start box, + 12 on the Change line, and ? in the End box (see margin). Tell children that the ? represents the number of shells Anabelle has after adding 12 more to her collection. Have children suggest a number model with ? to represent the first step. Write the number model below the change diagram (see margin).” The mathematical content in this activity is enriched by MP4.
  • In Lesson 8-3, Focus: Comparing Triangles, students compare triangles and discuss polygons, “Compare some of the different triangles, focusing on the sides and the angles. Be sure to display one triangle with a right angle and one with all equal-length sides and discuss these attributes.” The mathematical content in this activity is enriched by MP7.
  • In Lesson 9-10, Focus: Connecting Doubles and Equal Groups, students use doubles facts to solve equal-groups stories, “After all 10 possible arrays have been recorded, have children examine the list. Ask: What patterns do you notice? Referring to the two lists of possible number models, discuss the idea that when children need to find the total number of objects in 2 equal groups (or multiply by 2), they can use addition doubles. Ask: How can we use doubles facts to help us solve number stories about 2 equal groups?” The mathematical content in this activity is enriched by MP8.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials attend to the full meaning of most of the MPs, but they do not attend to the full meaning of MP5 as students do not get to choose tools strategically.

Examples of the materials attending to the full meaning of most MPs include:

  • MP1: In Lesson 3-4, Focus: Introducing and Playing Salute!, students play a game to practice adding and finding missing addends, “Circulate among the groups as they play. Whenever possible, encourage children to reflect on and discuss strategies they think would have been more efficient for a given round. Have them resolve any discrepancies between their answers.”
  • MP2: In Lesson 7-8, Focus: Making a Line Plot of Arm Span Data, students make a line plot of students’ arm span and then answer questions about the data collected, “To make sure that all of the data from the class are represented, prompt children to count the number of Xs and compare the total to the number of children in the class. Discuss children’s completed line plots. Ask: What does it mean when there are a lot of Xs above a number? Which arm span is the most common? What do you know about the numbers that have no Xs above them? How many children have an arm span of 51 inches? Of 46 inches?” 
  • MP4: In Lesson 9-3, Focus: Solving the Open Response Problem, students show how to divide muffins equally among two and four children, describing each child’s share. “Distribute Math Masters, pages 254-255 to all children. Read the problem as a class and ask partners to discuss what the problem asks them to do. Encourage children to refer to the Equal Shares posters and use fraction vocabulary like that on the poster as they talk about and write responses to the problem. Review the terms one-half, two-halves, one-fourth, and four-fourths. Tell children that an important part of the task is to write how much muffin is in one child’s share. Circulate as children work. Ask children to explain their drawings and descriptions of one child’s share and encourage them to add details to clarify their responses. You may also want to make notes about children’s strategies. Ask: How did you show your work and thinking for this problem? Did you use words, symbols, or anything else?”
  • MP6: In Lesson 4-3, Focus: Exploring a 24-Hour Timeline, students help create a 24-hour timeline, “Invite volunteers to talk about events that usually occur during the day, such as getting up for school, beginning the school day, and eating dinner. Children may refer to the Class Schedule for regular school-day events. Each volunteer says a time, including A.M. or P.M., and finds it on the timeline, while the rest of the class sets their toolkit clocks to the time.” 
  • MP7: In Lesson 7-2, Focus: Counting Pencils, students discuss strategies for solving a number story with three addends, “Were any of the three ways easier for you to find the sum? Why? Does it make a difference in what order the three numbers are added? Why? If no child mentions the turn-around rule, ask: How do you think this is related to the turn-around rule for addition?”
  • MP8: In Lesson 3-6, Focus: Discussing the -0 and -1 Strategies, students develop rules for solving -0 and -1 facts, “Ask children to copy the facts onto their slates and solve. Prompt them to describe how to find the answers to -0 facts and -1 facts. Encourage children to look at the facts to find patterns and determine rules for solving these types of facts. Sample answers: If 0 is subtracted from any number, that number does not change. If 1 is subtracted from any number, the result is the next smaller number.”

Examples of the materials not attending to the full meaning of MP5 because students do not get to choose tools strategically include:

  • In Lesson 2-8, Exploration A: Using Tools to Add, students find sums using number lines and number grids, “Use the number lines below to find the sums. Then find the sums using the Number Grid page. Show 62 + 10 on the number line below. Show 62 + 10 on the number grid. Draw arrows to show your counts.” 
  • In Lesson 3-3, Focus: Introducing the Fact Triangles Routine, students generate sets of related facts for numbers shown on Fact Triangles, “Demonstrate the procedure for fact practice using an actual Fact Triangle of the one shown on Math Masters, page TA16. Have partners follow these steps to practice their facts with each other: Partner A covers one corner of a Fact Triangle with a finger or a thumb, concealing part of an addition or subtraction fact. Partner B says the complete fact. Partners trade roles and repeat.” 
  • In Lesson 7-6, Focus: Measuring Arm Spans, students measure each others’ arm spans in centimeters and inches, “The second helper then holds the tape at the tip of the volunteer's left middle finger and reads the tape to the nearest inch. Turn the tape over, repeat the procedure, and have the second helper read the tape to the nearest centimeter.”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Student materials consistently prompt students to construct viable arguments and analyze the arguments of others. Lessons offer Differentiated Options where students work in small groups or with partners as teachers facilitate discussions so students have opportunities to construct viable arguments and critique the reasoning of others. Open Response and Reengagement Lessons provide opportunities for students to critique the open response answers of other students. 

Students construct arguments. Examples include:

  • In Lesson 5-2, Focus: Math Message and Finding the Total, students find the total value of specified toolkit coins and share their strategies for counting their coins, “Take 10 pennies, 6 nickels, 6 dimes and 4 quarters from your toolkit. How much money is that? Ask children to share their strategies and justify their answer for finding the total value of the coins.”
  • In Lesson 7-3, Focus: Introducing Basketball Addition, students learn a game for adding three or more numbers, “At halftime, invite children to examine the scoreboard. Ask: Is it possible for the team that is behind to win? Yes. Why or why not? Sample answer: In the second half, the team that is behind could roll a lot of large numbers, and the team that is ahead could roll a lot of small numbers.”
  • In Lesson 8-4, Focus: Setting Expectations, students discuss solutions to the Open Response Problem and revise their solutions, “Review the open response problem from Day 1. Ask: What do you think a complete answer to this problem needs to include? Sample answer: It needs drawings of gardens for Juan and Linda and an explanation for why the circled shape has the attributes for Linda’s plan.”

Students critique the reasoning of others. Examples include:

  • In Lesson 2-3, Focus: Using Double Ten-Frames, students explore strategies for finding the total number of dots shown on double ten frames, “Have children suggest number sentences that match their strategies and display them for the class. Whenever children’s strategies involve either doubles or filling a frame to make 10, follow up with questions such as the following: Can someone explain Tommy’s strategy or Tommy’s way of thinking for us again? Can you use thinking like Tommy’s on this next example?”
  • In Unit 3 Open Response Assessment, A Subtraction Strategy, “Grace solved 12 - 7 this way: ‘I started at 12 and took away 2 to get to 10. Then I took away 5 more. I ended up at 5. So 12 - 7 = 5.’ Grace solved 13 - 4 this way: ‘I started at 13 and took away 3 to get to 10. Then I took away 1 more. I ended up at 9. So 13 - 4 = 9.’ Show and explain how to use Grace’s subtraction strategy to solve 14 - 8.”
  • In Lesson 4-7, Practice: Practicing Place-Value Concepts, Math Journal Page 79, Item 8, “Marta wrote 24 to describe the number shown by these base-10 blocks: Do you agree with Marta? Explain your answer.”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Examples of assisting teachers in engaging students to construct viable arguments include:

  • In Lesson 3-6, Focus: Discussing the -0 and -1 Strategies, students develop rules for solving -0 and -1 facts, “Display this problem: 87 - 0 = ___. After a volunteer has given the answer, ask another child to explain why this is correct. Sample answer: When we subtract 0, we are not taking anything away. So we still have 87. Ask: Do you think this will always be true? Even with very large numbers? Why? Yes. Sample explanation: It is always true because when we subtract 0 from any number, the number remains the same.”
  • In Lesson 6-7, Focus: Math Message and Sharing Strategies, students solve a 2-digit addition problem and share their strategies for solving, “Solve 37 + 52. Explain your strategy to a partner. Circulate and observe as children solve the Math Message Problem and explain their strategies to their partners. Encourage partners to try using each other’s strategies to solve the problem.”
  • In Unit 7 Organizer, Mathematical Background: Process and Practice, Standard for Mathematical Process and Practice 3, “According to SMP3, mathematically proficient students ‘make conjectures and build a logical progression of statements to explore the truth of their conjectures.’ In Lesson 7-1 children enter a starting number into their calculators and work to change it to a given multiple of 10. For example, they enter 17 and are asked to change it to 40. When children state whether they need to add or subtract and what number they need to add or subtract, they are making conjectures, or educated guesses, based on some given information. When they explain how they determined what number to add or subtract, they are making arguments, or logical progressions of statements, that support their conjectures.”

Materials assist teachers in engaging students to analyze the arguments of others frequently throughout the program. Examples include:

  • In Lesson 1-5, Number-Grid Puzzles, Getting Ready for Day 2, students’ share and discuss their solutions to the Open Response Problem, “Display a response showing a solution to the puzzle that uses counting or operations with patterns on the number grid. Child B shows ‘two moves’ from 78 to 98, explaining that moving down on the number grid is the same as adding 10. A related example could show ‘one move’, in which 88 is left out and the explanation uses the number model 78 + 20 = 98. Encourage children to connect these explanations in the discussion. Ask questions such as: How are these strategies different? Do they both get the correct answer? Why? What’s different about how these children explained their thinking?”
  • In Lesson 5-11, Adding Multidigit Numbers, Getting Ready for Day 2, students share and discuss their solutions to the Open Response Problem, “Display responses that use the same tool but different strategies to find the total. See sample work for Child A and Child B. Have children interpret and compare the strategies. Ask: What tool and strategy do you think Child A used to find the total cost? What could this child do to help us understand the strategy better? How are Child A’s and Child B’s work alike? Different? What could the second child do to help us understand the strategy better?”
  • In Lesson 8-4, Drawing and Reasoning About Quadrilaterals, Reengaging in the Problems, students discuss their drawings and evaluate their written arguments that their drawings have the given attributes, “Children reengage in the problem by analyzing and critiquing other children's work in pairs and in a whole-group discussion. Have children discuss with partners before sharing with the whole group. Guide this discussion based on the decisions you made in Getting Ready for Day 2.”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Grade 2 partially meet expectations for explicitly attending to the specialized language of mathematics. The materials provide explicit instruction on how to communicate mathematical thinking using words, diagrams, and symbols, but there are instances when the materials use mathematical language that is not precise or appropriate for the grade level.

The Section Organizer provides a vocabulary list of words to be used throughout lesson discussions. Each lesson contains a vocabulary list, Terms to Use, and vocabulary words appear in bold print in the teacher notes. Some lessons incorporate an Academic Language Development component that provides extra support for the teacher and students. Additionally, the Teacher’s Lesson Guide contains a detailed glossary with definitions and images where appropriate. Examples of explicit instruction on how to communicate mathematical thinking include:

  • In Lesson 2-3, Focus: Naming Doubles and Combinations of 10, students sort facts into two groups, doubles and combinations of 10, and record their strategies, “Tell children that combinations of 10 have a sum of 10. If needed, remind children that the sum is the answer to an addition problem”.
  • In Lesson 4-1, Focus: Reviewing Units of Time, students discuss functions of clocks and units of time, “Remind children that a clock with an hour hand, a minute hand, and numbers and marks around the clock face is called an analog clock. Briefly review the clock’s functions and units of time by asking the following questions: How many hours does it take for the hour hand to move from the 1 to the 2? From the 2 to the 3? Emphasize that children should use the unit hour.”
  • In Lesson 5-9, Focus: Introducing the Parts-and-Total Diagram, students use parts-and-total diagrams to find the total number of dots on a domino, “Draw a unit box with the label dots. Display a parts-and-total diagram. Write 8 and 9 in the two boxes labeled Part. Write 17 in the box labeled Total. Tell children that the diagram is a convenient way to represent the domino in the Math Message. The Part boxes show the number of dots on each side of the domino, and the Total box shows the total number of dots on the domino.” 
  • In Lesson 7-5, Focus: Introducing the Meter, students compare a meterstick to a tape measure and a yardstick, “Remind children that inches, feet, and yards are part of the U.S. customary system and centimeters are part of the metric system. In the metric system, the meter is another commonly used standard unit of length. Tell children that the abbreviation for meter is m. Show the class a meterstick. On the Class Data Pad, write ‘A meter stick is 100 centimeters long’.” 
  • In Lesson 9-3, Sharing Muffins, Academic Language Development, “Use of the term ‘equal’ within the context of equal shares may confuse students who often have used ‘equals’ within the context of a number story, such as 3 plus 2 equals 5. It may be helpful to point out the varied uses of the term. In this lesson ‘equal shares’ mean that the shares are the same size.”

Examples of the materials using mathematical language that is not precise or appropriate for the grade level include:

  • In Lesson 2-6, Focus: Exploring the Turn-Around Rule for Addition, students write 2 related addition facts using dominoes, “Label this the turn-around rule and instruct children to add it to their My Addition Fact Strategies list on journal page 22.”
  • In Lesson 3-7, Focus: Introducing “What’s My Rule?”, students fill in a rule for a given table of numbers, “Use children’s answers to fill in the rule box for Table 1. Explain that children will use tables like this to solve problems.” The materials later state, “Explain that these tables are called “What’s My Rule?” tables.”
  • In Lesson 9-7, Focus: Introducing Expand-and-Trade Subtraction, students use expanded form to subtract 2 and 3 digit numbers with and without regrouping, “Tell children that today they will use expanded form to help them think about making trades.” The materials later state, “Tell children that this subtraction method is called expand-and-trade subtraction because children use expanded form to think about whether they need to make trades.”

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
abc123

Additional Publication Details

Report Published Date: 10/29/2020

Report Edition: 2020

Title ISBN Edition Publisher Year
Everyday Math 4 Quick Look Activity Pack 9780076718641 McGraw Hill 2019
Everyday Math 4 Classroom Resource Package 9780077040215 McGraw-Hill 2019
Everyday Math 4 Implementation Guide 9780079049391 McGraw-Hill 2019

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Please note: Reports published after 2021 will be using version 2 of our review tools. Learn more.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways. 

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. 

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

X