Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 1 partially meet the expectations for alignment to the CCSSM. The materials meet the expectations for focus and coherence in Gateway 1, and they partially meet the expectations for rigor and the mathematical practices in Gateway 2. Since the materials partially meet the expectations for alignment, evidence concerning instructional supports and usability indicators in Gateway 3 was not collected.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
14
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
0
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 Grade 1 meet the expectations for focus on major work and coherence. The instructional materials meet the expectations for focus through their assessments and design concerning class time spent on major work. The instructional materials partially meet the expectations for coherence, and they show strengths in having an amount of content that is viable for one school year and fostering coherence through connections within the grade.

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 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are no assessment items that align to topics beyond Grade 1.

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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 1 meet the expectation for assessing grade-level content. There are no above grade-level assessment questions, and the assessments include material that is appropriate for Grade 1. Probability, statistical distributions, similarity, transformations and congruence do not appear in the assessments.

In the teacher’s edition, assessments for each unit are listed including portfolio opportunities recommending which student work would be appropriate. Assessments are found in the Assessment Sourcebook.

Examples of quality assessments include:

  • On Unit 2 Session 2.4 Assessment Sourcebook page A16, Quiz 2 assesses students on being able to distinguish between defining and non-defining attributes of shapes (1.G.1). Problem 1 asks students to select the triangle out of 4 choices. One of the incorrect choices is a three-sided figure that is not closed, and another incorrect choice is a three-sided figure that is closed with one slightly-curved side.
  • On Unit 7 Session 1.8 Assessment Sourcebook pages A50-51, Quiz 1 assesses students on being able to recognize how many tens are in a number that is a multiple of 10 (1.NBT.2c) and subtracting multiples of 10 from a multiple of 10 (1.NBT.6). The quiz has items that involve almost all multiples of 10 between 10 and 90, and for items aligned to 1.NBT.6, the quiz contains pictures of base-10 blocks so that students can use them when subtracting.

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 meet the expectation for students and teachers devoting the large majority of class time to the major work of the grade when the materials are used as designed. Overall, the materials spend at least 65% of class time on the major work of Grade 1.

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 Grade 1 meet the expectations for spending the majority of class time on the major clusters of the grade. Approximately 74 percent of class time is spent on major work of the grade.

The instructional materials are separated into eight units. Each unit is composed of one, two, three, or four investigations, and each investigation is divided into sessions. The Implementing Investigations guide states in Part 4 (Classroom Routines) within the Overview that each session includes a Classroom Routine activity that is “introduced as a session activity and are then used outside of math time (e.g., during morning meeting, just before or after lunch or recess, or at the beginning or end of the day) or integrated into the math lesson as the first 10 minutes of a 70-minute math block.” The Classroom Routine activity requires 10-15 minutes which provides daily practice and review of previously learned skills. Each session requires sixty minutes. Three perspectives were used when calculating major work of the grade: number of units, number of investigations, and number of sessions.

  • Approximately 5 of the 8 units focus on major work of the grade. This represents approximately 63 percent of the units.
  • Approximately 15 of the 20 investigations focus on major work of the grade. This represents approximately 75 percent of the investigations.
  • Approximately 103 of 140 sessions focus on or support the major work of the grade. This represents approximately 74 percent of the sessions.

The third perspective, number of sessions, is the most reflective of the instructional materials because it is based on the sessions which includes the instructional activities, review, and practice. As a result, approximately 74 percent of the materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 1 partially meet the expectations for being coherent and consistent with the Standards. The instructional materials show strength in having an amount of content that is viable for one school year, but due to not always identifying work that is off grade-level, the materials are not always consistent with the progressions in the Standards. The materials do foster coherence through connections within the grade, but few of those connections are between major work of the grade and supporting work.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 1 partially meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Throughout the instructional materials, major work of the grade is sometimes supported by non-major work. However, there are some missed natural connections, and the supporting standards occasionally appear in lessons with few connections to the major work of the grade.

Although some attempts to connect supporting work to major work are made, students can often complete problems aligned to supporting work without engaging in the major work of the grade.

  • In Unit 2 none of the sessions in Investigation 1 or 2 connect the supporting content of comparing and combining shapes (1.G.2) to the major work of the grade. There are some activities within the sessions that contain major work, but these are taught as a classroom routine and not as anything connected to the Geometry standards.
  • In Unit 6 Sessions 1.1, 1.2, and 2.1 address supporting work of the grade using data to create representations (1.MD.4). It is a missed opportunity to connect measurement and data to major work with adding and subtracting in Grade 1.
  • In Unit 6 Sessions 1.4, 1.5, and 1.6 address data displays and representations (1.MD.4) and provide students with one opportunity to incorporate major work. This is a missed opportunity to connect measurement and data to major work with adding and subtracting in Grade 1.

Occasionally supporting standards are used to support the major work of the grade.

  • In Unit 6 Session 1.3 students are organizing data (1.MD.4) by counting left-handed and right-handed classmates, counting on by 5’s (1.OA.5). Students organize data for an "Eagle or Whale?" assignment and write addition equations with data.
  • In Unit 6 Session 1.8 students organize data (1.MD.4) with a "Slide or Swings?" activity and include a subtraction equation (1.OA.8).

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 Grade 1 meet the expectations for the amount of content being viable for one school year.

  • The instructional materials are divided into 8 units that have a total of 140 sessions.
  • Assessments are done during sessions and are not counted as extra days.
  • Each session is designed to be completed in 60-70 minutes with the majority of the sessions being 70 minutes. Each session is accompanied by a Ten-Minute Math activity that is designed to be completed in 10 minutes outside of math time.
  • Each unit takes between 2 to 5.5 weeks to complete according to the “Grade 1 Curriculum Units and Pacing Chart” on page 9 of the Implementing Investigations in Grade 1 guide. Each unit includes an additional day beyond the days required to finish the sessions. This day could be used to complete the Intervention, Practice, and/or Extension activities that are included at the end of each investigation.
  • The pacing chart on page 9 of the Implementing Investigations In Grade 1 guide suggests a total of approximately 28.5-32.5 weeks or 140-165 days.

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.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 1 partially meet the expectations for being consistent with the progressions in the Standards. In general, the materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. The materials provide extensive work with grade-level problems for most standards, but the materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials develop according to the grade-by-grade progressions in the Standards, but content from future grades is not clearly identified. Examples of unclear identification include:

  • In Unit 4 Session 1.3, students measure partial units (3.MD.4).
  • In Unit 7 Sessions 1.1 and 1.2, students skip count by 5’s (2.NBT.2).
  • In Unit 7 Session 1.8, Resource masters S100 and S101 ask students to add and subtract multiples of 100 with numbers larger than 100 (2.NBT.8).
  • In Unit 3 Session 4.1 students sort data by the different number of tiles in a footprint. This activity sorts the data into as many categories as needed for each students footprint length. The example for this activity shows six categories which is above grade-level (3.MD.3).

Some of the above grade-level content is identified as above grade-level.

  • Unit 7 says that the unit lays the foundation for work in Grade 2 with number and operations and place value.
  • Unit 8 says that in Grade 2 students continue to develop and refine many of the ideas and concepts from this unit. Students expand their understanding of 2-D shapes by considering not only the number of sides as a defining attribute, but also the number and type of angles with a specific focus on quadrilaterals and rectangles.

The materials often give all students extensive work with grade-level problems.

  • Recommendations for differentiation allow students to primarily work with grade-level tasks.
  • The standards are addressed throughout the entire series, and no standards were completely omitted. Overall, the materials were on grade-level, and students had a variety of opportunities to engage in grade-level problems.
  • The materials give students extensive work with most domains. However, 1.MD.1 is found in Unit 4 in three sessions. These sessions may not allow all students to develop an understanding of ordering three objects by length or comparing the lengths of two objects indirectly by using a third object.
  • Standard 1.NBT.6 is found in Unit 7 in 5 sessions. This may not provide enough explicit instruction or extensive practice with subtraction for all students.

The materials do not consistently relate grade-level concepts explicitly to prior knowledge from earlier grades. The scope and sequence found in the Implementing Investigations book gives some limited information relating to knowledge from earlier and future grades by listing major topics and which units in prior and future grades address those topics. Each unit has a “Connections: Looking Back” section at the beginning of the unit. Several units specifically refer to work from prior grades without providing explicit connections to specific standards.

  • Unit 1 describes the unit building on work students did in the Kindergarten Number and Operations units.
  • Unit 4 states that the unit builds on the work students did in Kindergarten describing measurable attributes of objects, directly comparing the length of two or more objects, describing them as longer or shorter than, and developing strategies for measuring.

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 Grade 1 meets the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials begin each investigation with a planner that lists objectives for each session, and in the session materials, Math Focus points are listed at the beginning of each session. The instructional materials include objectives and Math Focus points that are visibly shaped by the CCSSM cluster headings for Grade 1.

  • In Unit 1 Session 2.1 the Math Focus Point is “Relating adding 1 or 2 to counting on”. This is visibly shaped by cluster 1.OA.C, Add and subtract within 20.
  • In Unit 5 Session 3.5 the Math Focus Points are “Solving story problems about unknown change" and "Using standard notation (+, -, =) to represent situations with unknown change." These are visibly shaped by cluster 1.OA.A, Represent and solve problems involving addition and subtraction.
  • During Unit 7 Session 3.5, in Math Workshop students play a game that involves representing two 2-digit number with cubes, bundling 10 cubes as a ten, and then finding the total of the two numbers (1.NBT.B and 1.NBT.C).

The instructional materials include problems and activities that connect two or more clusters in a domain or two or more domains.

  • In Unit 2, Sessions 2.1, 2.2, and 2.4 connect 1.G.A and 1.MD.C as students observe and describe defining attributes of 2-D shapes, use those attributes to build, compare, and sort 2-D shapes, and compose and decompose 2-D shapes. It includes activities and routines that develop concepts mainly from the Geometry Domain; however, some connections are made to the Measurement and Data Domain.
  • In Unit 4, Sessions 1.5 through 1.8 connect 1.OA.A, 1.OA.B, 1.OA.C, 1.OA.D, and 1.MD.A as students measure lengths indirectly and by iterating length units and use their measuring skills to solve problems that involve adding and subtracting while writing equations and using the properties of operations to solve.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 1 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others.

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 Grade 1 partially meet the expectations for rigor and the mathematical practices. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. However, the materials partially meet the expectations for mathematical practices as they do not attend to the full meaning for each of the MPs and rarely prompt, or have the teachers prompt, students to analyze the arguments of others.

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 materials reviewed for Grade 1 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. In the instructional materials visual representations, verbal explanations, and written equations are used to develop conceptual understanding.

  • In Unit 1 Session 3.4 students are engaged in solving subtraction story problems (1.OA.1) through modeling the use of number lines, student drawings, and written equations.
  • In Unit 7 Session 1.3 students develop conceptual understanding of counting by tens (1.NBT.2c) by using the concrete model of human fingers to count groups of ten. Also in this session, students build towers of ten cubes and count those by tens.
  • In Unit 7 Session 1.6 students develop the conceptual understanding of finding ten more or ten less (1.NBT.5) without having to count. Students play a game called How Many Now? with cubes. Students use towers of ten and add or subtract by towers of tens without having to count.
  • In Unit 7 Session 2.1 students develop conceptual understanding that 10 can be thought of as a bundle of ten ones (1.NBT.2a). Students learn this through a game called Roll Tens. Students roll dice and collect cubes and place them in groups of tens.

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 materials reviewed for Grade 1 meet the expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The materials include opportunities to review and practice in order to build procedural skill and fluency in the Classroom Routines, Daily Practice, Homework, and Games.

Standard 1.OA.6 requires students to fluently add and subtract within 10.

  • In Unit 1 Session 2.1 students use Resource Master-G5 to complete the activity “One or Two More” to practice their procedural skills and fluency for addition.
  • In Unit 1 Session 2.3 students can use Resource Master-G9 to complete the activity “Five-in-a-Row.” This activity is like Bingo, where students roll 2 dice, get a total, and find the number on the board.
  • In Unit 1 Session 2.5 students use Resource Master-G10 to complete the activity “Roll and Record.” Students roll two dot cubes, add the numbers, and record the total on the sheet.
  • In Unit 1 Session 3.1 students use Resource Master-G15 to complete the activity “One or Two Less” to practice subtraction.
  • In Unit 5 Session 1.4 students use Resource Masters G45-G46 to complete the activity “Tens Go Fish.” Students practice pairing number cards that make 10.

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
2/2
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-
Indicator Rating Details

The materials reviewed for Grade 1 meet the expectations for teachers and students spending sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Practice with application of the major work in addition and subtraction is found throughout five units of instruction. Students have many opportunities to work with cluster 1.OA.A, represent and solve problems involving addition and subtraction that involve take from with result unknown, add to with result unknown, put together/take apart with both addends unknown, comparison problems with the difference unknown, put together/take apart with one addend unknown, add to and take from with unknown change, and comparison problems with bigger or change unknown. These opportunities can be seen in whole-group activities, discussions, and independent math workshops.

In Unit 1, students solve addition and subtraction word problems within a whole group, with partners, and in their student activity book. They also have discussions about the strategies they used to solve the problems. In Unit 3, students apply decomposing strategies for a given number by solving word problems with both addends unknown. Students also begin to label a word problem with an equation. In Unit 4 students also solve word problems involving measurement, including comparison problems. In Unit 5 students apply decomposing to a word problem with both addends unknown such as “How many of Each?” In Unit 6, students apply addition and subtraction to answer questions about survey data.

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.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 1 partially meet the expectations for balance of the three aspects of rigor within a grade. Although the instructional materials meet expectations for each aspect of rigor, these aspects of rigor are often addressed in separate parts of the Sessions. Materials targeting application are often scaffolded, detracting from the balance of rigor. Overall, the three aspects of rigor are most commonly treated separately.

In general, conceptual understanding, procedural skill and fluency, and application are addressed in the Sessions; however, for the most part they are addressed in separate sections of the instructional materials. Conceptual understanding is typically addressed in the Discussion and Math Workshop portions of the Sessions. Procedural skill and fluency is typically introduced in separate Sessions and then practiced in the Daily Practice portion of sessions. Application consists of routine word problems in the instructional materials. As a result, all aspects of rigor are almost always treated separately within the curriculum including within and during Sessions, Practice, and Homework.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
7/10
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 1 partially meet the expectations for practice-content connections. Overall, the materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialize language of mathematics. However, the materials do not always attend to the full meaning of each MP, and there are few opportunities for students to analyze the arguments of others either through prompts from the materials or from their teachers.

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 for Grade 1 meet the expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich the mathematical content. The MPs are clearly identified in Implementing Investigations on page 44 and can also be found in each unit. The instructional materials highlight two MPs in every Unit. During the sessions, Math Practice Notes dialogue boxes are given to provide tips to the teacher on how to engage students in the MPs. Additionally, Math Practice Notes are provided for the MPs that are not highlighted so students continue to work on the practices all year.

The Introduction and Overview of each unit includes a “Mathematical Practices in this Unit” section. This section of each unit highlights the two MPs that are the focus of the unit. The MPs are described and examples from the unit are provided. A chart showing where Mathematical Practice Notes occur and when the MP is assessed is also included in this section.

  • The Unit 1 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP1 and MP8. An example of MP1 from the story problem routine that will be introduced in the unit is included.
  • The Unit 5 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP3 and MP7. An example of MP7 from the activity “Ten Plus” is included.

Math Practice Notes are provided in sessions alongside content. Math Practice notes are provided for the MPs highlighted within the unit and MPs that are not the highlighted practices for the unit.

  • Unit 1 Session 1.3 includes a Math Practice Note for MP5 and MP2, practices that are not highlighted in the unit. The note for MP5 states that students are using a Ten Frame to create compositions of 10. The note for MP2 discusses how students must connect numerals and number names with the quantities they represent.
  • Unit 4 Session 2.1 includes a Math Practice Note for MP4, a practice highlighted in the unit. The note discusses students modeling one-half. It also includes a Math Practice Note for MP6, a practice not highlighted in the unit. The note discusses a more precise meaning of the mathematical term “one half.”
  • Unit 5 Session 3.6 includes a Math Practice Note for MP1, a practice not highlighted in the unit. The note discusses how students practice the activity of breaking down what is known in a problem as a first step toward solving the problem on their own.
  • Unit 7 Session 2.1 includes a Math Practice Note for MP3 and MP7, practices not highlighted in the unit. Students are asked to explain why the count of cubes is the same no matter what strategy is used to count in the note for MP3. The note for MP7 discusses students rewriting a sum between 11 and 19 as a sum of 10 and a one-digit number.

Indicator 2f

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

The instructional materials reviewed for Grade 1 partially meet expectations that materials carefully attend to the full meaning of each practice standard (MP). Although the instructional materials attend to the full meaning of some of the MPs, there are some MPs for which the full meaning is not developed.

At times, the instructional materials only attend superficially to MPs. The following are examples:

  • The Unit 1 Session 1.1 Math Practice Note lists MP1 and has students learn the activity "Start With/Get To." The students are being shown a strategy to help them through making sense of a problem; however, the students are never actually having to engage in any of the MP themselves.
  • The Unit 1 Session 2.3 Math Practice Note lists MP1 and is introducing students to story problems and is establishing the routine for working on them in the whole group. The Math Practice Note states that story problems will be a central component of students’ mathematical studies for many years and that this session students learn how to enter into a problem. This session does allow students to make sense of certain problems, but it does not have them persevere through any.
  • The Unit 2 Session 2.2 Math Practice Note lists MP5 and has students play a game called Triangle Connect-the-Dots. This game has students draw triangles on dot paper. Students are not able to choose a tool in this session.
  • The Unit 8 Session 1.1 Math Practice Note lists MP5 and has students look at a set of geometric solids while the teacher explains that the shapes are 3-dimensional. In this session students are not able to choose a specific tool, only looking at the given geometric solids and a chart with 2-dimensional flats.

At times, the instructional materials fully attend to a specific MP. The following are examples:

  • The Unit 6 Session 2.2 Math Practice Note lists MP4 and has students representing and interpreting data in three categories. Students take a survey on which they like the best. The teacher models how the responses will be recorded, and there is a brief discussion on the results. Then students complete an activity on their own in the Student Activity Book making sure to ask themselves if the representation communicates the information appropriately. The students are working with a real-world problem and making a model of their choice to represent the information.
  • The Unit 7 Session 3.1 Math Practice Note lists MP5 and has students playing a game that introduces adding tens. The students are only using cubes in tower form and have the ability to use Ten Frame Cards if they choose. The Math Practice Notes say that students can represent the numbers with either cubes in towers of 10 or Ten Frame Cards. In this session students are able to choose between the two different tools which at this grade level is appropriate.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 1 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

When MP3 is referenced, students are often asked to solve and share solutions. The independent work of the student is most often about finding the solution to a problem without creating a viable argument. Students often listen to peer solutions without being asked to critique the reasoning of the other student. Much of the student engagement in the class discussion is teacher prompted without giving students the opportunity to create their own authentic inquiry into the thinking of others.

  • In Unit 1 Session 3.2 students are asked to compare their strategy for solving a problem to others that are shared with the class, and the students are asked to raise their hand for the strategy that was closest to their own. There are no prompts or questions for students to construct their own argument or to analyze the strategies presented that are different from theirs.
  • In Unit 3 Session 4.6 the students discuss with a partner, before joining a whole-class discussion, what the missing number could be when playing a game. Some students share their explanations with the class, but all students do not get to necessarily share their argument. There are no prompts or questions for students to analyze the arguments of others.
  • In Unit 8 Session 1.4 students are asked to pick blocks that match pictures presented to them. After viewing other students’ selections, students can change their original picks. Students are asked how they made their final decision, but there are no specific prompts that have them analyze the selections of other students.

There are a few places where the materials prompt students to construct viable arguments and analyze the arguments of others.

  • In Unit 6 Session 1.3 students are prompted with a set of questions to help them make sure they have a viable representation of a set of data. Then the students participate in a whole-class discussion and are instructed to “Look at your classmates’ representations. What do you notice that is the same or similar in many of your representations? How are your representations different?”

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.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 1 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, teachers are instructed to have students share or explain their solutions and occasionally ask questions of other students, but these questions or prompts generally do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

  • In Unit 2 Session 2.4 students examine six shapes in order to determine how each of them may or may not be grouped with two triangles. The teacher is prompted to “encourage students to share their thinking and to respectfully disagree with one another, insisting that they explain their reasoning as they are trying to name shapes.” This assistance prompts students to construct an argument, but there are no other questions or prompts to help students who are not able to construct an argument. There are also no questions or prompts for students to analyze the arguments of others.
  • In Unit 5 Session 1.4 students are playing a game called Tens Go Fish, and the teacher is reminded to “ask students to share their strategies for playing the game. Then have students use cubes to model their strategies for classmates.” This prompt is one method for the teacher to assist students in constructing an argument, but no other possible methods are discussed. There are also no questions or prompts for students to analyze the arguments of others.
  • In Unit 7 Session 2.1 teachers are prompted to say, “Does it make sense that (two students) got the same number even though they counted in different ways?” This question could prompt a student to construct an argument, but there is no other assistance for teachers if students don’t answer on their own. The teachers are also reminded to ask their students if they agree with their classmates explanations, but there are no other questions or prompts to assist in analyzing those arguments.

There are a few places where the materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

  • In Unit 3 Session 3.6 the teacher leads a whole group discussion about determining which equations are true and which ones are false. As students give their explanations, the teacher is prompted to encourage kids to think about what mistakes the students could have made and share their thoughts. The teacher is also provided with possible explanations that students could give which would assist students in analyzing the arguments of others.

Indicator 2g.iii

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

The instructional materials reviewed for Grade 1 meet the expectations for explicitly attending to the specialized language of mathematics.

The instructional materials provide opportunities for teachers to say mathematical terms to students during the whole group portion of the lessons. The materials use precise and accurate terminology when describing mathematics. New terminology is introduced on the summary page of the TE at the beginning of the session where it will first be used. The mathematical terminology is highlighted in italics throughout the sessions within the TE. There is also an index at the end of each unit manual in which math terms are listed for the unit.

  • In Unit 2 Session 1.2 students are discussing the attributes of several different shapes. The materials prompt the teacher to state, “Many people call this shape a diamond, but mathematicians have a different name for it. They call it a rhombus. How many sides does a rhombus have? What else do you notice about the sides? How is the rhombus the same as or different from other shapes on our shape posters?”
  • In Unit 2 Session 2.3 students are discussing the attributes of a quadrilateral. The materials prompt the teacher to state, “How many points or corners are there on your quadrilaterals? Remember that mathematicians call these vertices.”
  • In Unit 7 Session 1.4 students are recording the number of fingers in a group of students. The teacher is prompted to state, “The 7 in 70 means that there are 7 groups of ten or 7 tens. The zero in 70 means that all the fingers were counted and there are no leftovers, so there are zero ones.”

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

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.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

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.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

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.
0/2

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.
0/2

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.
0/2

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).
0/0

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.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

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.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

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).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

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.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

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.
0/0

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.).
0/0

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.
0/0

Additional Publication Details

Report Published Date: Fri Feb 10 00:00:00 UTC 2017

Report Edition: 2017

Title ISBN Edition Publisher Year
Investigations 3 Common Core Standards Practice Workbook Grade 1 (Student) 978-0-328-75684-1 Pearson 2017
Investigations 3 Common Core Standards Practice Workbook (Teacher Guide) 978-0-328-75691-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 1 978-0-328-85898-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 2 978-0-328-85899-6 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 3 978-0-328-85900-9 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 4 978-0-328-85901-6 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 5 978-0-328-85902-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 6 978-0-328-85903-0 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 7 978-0-328-85904-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade 1 Unit 8 978-0-328-85905-4 Pearson 2017
Implementing Investigations in Grade 1 978-0-328-85940-5 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade 1 978-0-328-85964-1 Pearson 2017
Investigations and the Common Core Content Guide Grade 1 978-0-328-85970-2 Pearson 2017

About Publishers Responses

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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.

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