Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Kindergarten 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
13
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 Kindergarten 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 Kindergarten.

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 Kindergarten meet the expectations for assessing grade-level content. The assessments include material that is appropriate for Kindergarten. Probability, statistical distributions, similarity, transformations and congruence do not appear in the assessments.

Assessments considered during the review for this indicator include the Assessment Activity and the Assessment Checklists which accompany them.

Kindergarten Investigations uses Benchmarks, “clear mathematical expectations for what students should know and be able to do” (Teacher’s Edition Unit 3 page 10). Each Benchmark has an accompanying Assessment Checklist; therefore, observing students’ work and engaging them in conversation about their ideas is the primary means of assessing mathematical understanding. Assessments are found in the Assessment Sourcebook.

Examples of quality assessments include:

  • Unit 1 Assessment Checklist: Counting. This assessment checklist assesses many aspects of counting such as knowing the names of numbers in order (rote sequence), one-to-one correspondence, knowing how many in a group, and double-checking counting for accuracy.
  • Unit 2 Assessment Checklist: Counting and MP4 and MP8. This assessment has students counting objects to 10. First they are given just ten cubes to count. The teacher watches to see if the student knows the names and sequence of numbers, counts each object once and only once, and double-checks.
  • Unit 3 Assessment Checklist: Describing 2-D Shapes. This assessment is used to assess if students can identify and describe the overall size, shape, and features of familiar 2-D shapes. The teacher uses shape cards to assess each student’s ability to describe 2-D Shapes. The teacher re-orients shapes to see if the student can still identify.

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 Kindergarten.

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 Kindergarten meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, approximately 88 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, or three 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 18 of the 20 investigations focus on major work of the grade. This represents approximately 90 percent of the investigations.
  • Approximately 123 of 140 sessions focus on or support the major work of the grade. This represents approximately 88 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 88 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 Kindergarten 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 Kindergarten 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 3 Session 2.3 students play the game “Fill the Hexagons.” Students roll a pattern block cube and then place that pattern block into the hexagon outline (K.G.A) on their game board. This continues until one player covers all of the hexagons. This work is taught separately and is repeated throughout the session within the math workshop.
  • In Unit 5, all sessions, students are working on comparing and composing/creating shapes (K.G.B). This work is taught separately, and major work is found within the Counting Jar activity in each session, which is a 10 minute counting activity separate from the supporting work.
  • In Unit 5 Session 1.4 the activity “Introducing Making Clay Shapes” has students creating a cylinder (K.G.5) from clay to match the cylinder from a set of Geoblocks. This work is taught separately and is repeated throughout the session within the math workshop.

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

  • In Unit 2, Sessions 2.1 and 2.2 during math workshop activities direct students to measure objects by comparing them to towers of 10 cubes (K.MD.2), which the students must count (K.CC.5). Students also count how many items were longer than the tower.
  • In Unit 3 Session 1.3 students are counting sides on triangles and squares. (K.CC.5 and K.G.4)
  • In Unit 7 Investigation 2 all three sessions connect survey data (K.MD.3) to counting totals. (K.CC.5)

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 Kindergarten 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.
  • Each session is designed to be completed in 45-60 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 weeks to complete according to the “Kindergarten Curriculum Units and Pacing Chart” on page 9 of the Implementing Investigations In Kindergarten 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 Kindergarten guide suggests a total of approximately 28-32 weeks or 140-160 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 Kindergarten 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 7 Session 3.1 students record the number of students in class on ten frames. This activity is related to the grade-level work of K.CC.5. This is grade-level work if the total number of students in class is less than 20 and would be aligned to 1.NBT.1 if the class had greater than 20 students. In Session 3.3 students are asked to count pairs of eyes (1.OA.2). This is related to the grade-level work of K.CC.2, counting forward beginning from a given number within the known sequence. In Sessions 3.3 through 3.8, students skip count by 5’s (2.NBT.2). This is related to the grade-level work of K.CC.2, counting forward beginning from a given number within the known sequence.
  • Unit 8 says that this unit lays the foundation for the work students do in Grade 1 with counting, addition and subtraction, and place value.
  • There is a heavy emphasis on data collection repeated throughout the units by a component called “Today’s Question.” The standard K.MD.3, which specifies that the category counts be less than or equal to 10, is listed for “Today’s Question.” However, the categories could end with number counts of more than 10 depending on how many students are in the class and how they answer “Today’s Question.” For example, in Unit 1 Session 3.1 students count and record how many boys and girls are in the class. In the sample given, there are 12 girls in the class.

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, within the domain of Operations and Algebraic Thinking, the standard K.OA.4 is found in Unit 8 in four sessions. These sessions may not allow all students to develop an understanding of finding a number that makes 10 when added to the given number.

The materials do not 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 prior knowledge by listing major topics and which units 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 learning without providing explicit connections to specific standards.

  • Unit 3 states that the unit "builds on students’ emerging knowledge of shapes, and the work they did identifying attributes of pattern blocks, Geoblocks, and other objects in Unit 1, to further develop their spatial sense and deepen their understanding of the geometrical world in which they live."
  • Unit 4 describes how the unit builds mainly on the work in Unit 2, where students had many opportunities to develop their sense of numbers and quantities; connect number names, numerals, and quantities; count, compare, and order amounts; and directly compare the length of two or more objects.

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 Kindergarten 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 Kindergarten.

  • In Unit 3 Session 2.3 the Math Focus Point is “Combining smaller shapes to make larger shapes.” This is visibly shaped by cluster K.G.B- Analyze, compare, create, and compose shapes.
  • In Unit 6 Session 1.8 the Math Focus Points are “Connecting number names, numerals, and quantities" and "Counting a set of up to 20 objects.” These are visibly shaped by cluster K.CC.B, Count to tell the number of objects.
  • In Unit 7 Session 2.2 the Math Focus Points are “Collecting, recording, and keeping track of and interpreting data," "Counting and ordering a sort by the number of items in each group," and "Identifying an attribute that two or more objects have in common.” These are visibly shaped by cluster K.MD.B, Classify objects and count the number of objects in each category.

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

  • In Unit 6, Sessions 2.1 through 2.3, 2.7, and 2.8 connect K.CC.A, K.CC.B, K.CC.C, and K.OA.A as students count sets of up to 20 objects, decompose the numbers to 10, and solve addition and subtraction story problems.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Kindergarten partially meet the expectations for rigor and the mathematical practices. The materials partially meet the expectations for rigor as they help students develop conceptual understanding and procedural skill and fluency. Also, 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.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for rigor and the mathematical practices. The materials partially meet the expectations for rigor as they help students develop conceptual understanding and procedural skill and fluency. Also, 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 Kindergarten 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 2.1 students develop an understanding of the relationship between numbers and quantities (K.CC.4). In this activity, students count groups of items to put in the “Counting Jar,” and then they make a matching group to put outside the the jar. By Unit 1 Session 3.2 students use the “Counting Jar” activity to not only count groups of numbers but also to start recording how many they have counted. This activity is available to students several times in math workshop throughout the year.
  • In Unit 2 Session 1.7 students develop an understanding of the relationship between numbers and quantities (K.CC.4). In this activity, students choose a number card. They then have to count that many pennies and place them in a Ten Frame making sure to fill in a row of five before placing any counter on the second row.
  • In Unit 4 Session 3.2 students develop conceptual understanding of addition and subtraction (K.OA.1) using an activity called Build It/Change It. In this activity, students choose a number card, build that number with counters in a Ten Frame, and then decide whether to add or subtract to get to the number 6.
  • In Unit 4 Session 3.4 students develop conceptual understanding of addition and subtraction (K.OA.1) using an activity called Toss the Chips. In this activity, students have a cup with counters that have two different colored sides. Students dump the cup. They count how many of each color they have and then add the two numbers together.
  • In Unit 8 Session 2.8 students develop conceptual understanding of composing numbers between 11 and 19 (K.NBT.1) in an activity called Build It, Then Race to the top. Students work in partners. They draw two cards and decide how many dots they need to add to their Ten Frames.

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 Kindergarten 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, Practice, Homework, and Games.

Standard K.OA.5 requires students to fluently add and subtract within 5.

  • In Unit 4 Session 1.9 students use Resource Master-G22 to complete the activity “Roll and Record 2.” Students roll two dot cubes, add the numbers, and record the total on the sheet.
  • In Unit 6 Session 2.1 students use Resource Master-G47 to complete the math workshop activity “Roll and Record 3.” Students roll two dot cubes, add the numbers, and record the total on the sheet. Dot cubes with 0-3 could be used as in previous explorations of this game within prior units.
  • In Unit 8 Sessions 1.2 and 1.3 students use Resource Master-C10 “Fluency within Five Cards” to make up word problems that represents their card. For example, students create a word problem for a card that reads "4-1."
  • In Unit 8 Session 1.4 students use Resource Master-C10 “Fluency within Five Cards” to play the Race to the Sun game.
  • In Unit 8 Session 1.5 students use Resource Master-C10 “Fluency within Five Cards” to complete “Counting Jar” activities and a “Fill the Treasure Chest” activity.
  • Although standard K.OA.5 is addressed in Unit 4, Unit 6, and Unit 8, the games and activities that are provided rarely include the addition and subtraction of expressions involving zero.

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 materials reviewed for Kindergarten partially 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. Overall, the materials reviewed partially engage students in activities that require application.

Practice with the application of the major work of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10, by using objects or drawings to represent the problem, can be found in 2 units of instruction.

  • Unit 4 Session 2.2 during “Two Story Problems” students visualize, represent, and solve addition and subtraction story problems with result unknown; however, it is scaffolded with the teacher directing the students through this entire activity. During Session 2.3 “Acting Out Story Problems” students act out word problems and use strategies to solve. After solving both problems, they are asked to compare what is the same about the two problems and what is different. This session asks the students to apply their understanding of addition or subtraction by having them compare two word problems. During Session 2.5 “More or Less at the End” students visualize, represent, and solve addition and subtraction story problems with result unknown; however, it is scaffolded with the teacher directing the students through this discussion.
  • Unit 6 Session 2.2 includes a whole-group classroom routine called “Story Problems.” This classroom routine requires students to apply what they know in order to solve the word problems. Students compare what is the same and different. The Focus Points of the routine are visualizing, representing, and solving addition word problems with result unknown and solving a set of related problems. Students are presented with two different word problems one at a time. Students are not told whether or not the word problem involves combining or removing. After solving the problem, students are asked, “Is this a problem about separating or taking away one group from another?” After solving both problems, they are also asked to compare what is the same about the two problems and what is different.

Some sessions listed as addressing K.OA.2 in the Content Guide do not require students to solve addition and subtraction word problems. This is found in Unit 4 Sessions 1.6, 1.7, 1.8, 1.9, 1.10, and 2.4. Also, the word problems that are given throughout the material are often routine.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for balance of the three aspects of rigor within a grade. Although the instructional materials meet expectations for conceptual understanding and procedural skill and fluency, the three aspects of rigor are often addressed in separate parts of the Sessions. Materials addressing 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 all 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 Sessions. Procedural skill and fluency is typically introduced in separate Sessions and then practiced in the 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 Kindergarten 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 Kindergarten 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 that 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 MP5. An example of MP5 from Session 1.5 is included.
  • The Unit 8 “Mathematical Practices in this Unit” is found on pages 8-11. This unit focuses on MP8 and MP7. An example of MP8 from the activity “Race to the Top” 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 1.1 includes a Math Practice Note for MP7, a practice not highlighted in the unit. Students are counting the number of students in attendance in order to build their understanding of the basic structure of the whole number system.
  • Unit 4 Session 1.1 includes a Math Practice Note for MP5, a practice not highlighted in the unit. The note discusses the students using a familiar tool in a new way. It also includes a Math Practice Note for MP6, a practice highlighted in the unit. Students use precision to correctly measure length.
  • Unit 6 Session 2.2 includes a Math Practice Note for MP3 and MP8. MP3 is a practice highlighted in the unit, and the note states that the students are exposed to new ways of thinking through listening to other students reasoning. MP8 is not a practice highlighted in the unit. The note discusses how the teacher can present the students with another example of a problem and ask if it fits the pattern.
  • Unit 8 Session 2.3 includes a Math Practice Note for MP8, a practice highlighted in the unit. Students are working with problems that emphasize the relationship between addition and subtraction.

Indicator 2f

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

The instructional materials reviewed for Kindergarten 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.

The following are examples of how the materials do not develop the full meaning of some MPs:

  • The Unit 1 Session 3.1 Math Practice Note lists MP1 and has students matching attributes. Students are asked to look at a chart asking “Are you a girl or boy?” The teacher walks them through counting the number of boys and girls in the class. The Math Practice Note states that developing the habit of double-checking will serve students throughout their mathematical studies. This session guides students through checking to make sure the information makes sense but does not have them persevere through a problem.
  • The Unit 2 Session 1.7 Math Practice Note lists MP5 and has students play a game to be introduced to the Ten Frame. The Math Practice Note talks specifically about the introduction of the Ten Frame and how this tool will allow students to become familiar with numbers less than 10. This activity only has students learning about Ten Frames and does not allow them to choose any other tool.
  • The Unit 4 Session 2.3 Math Practice Note lists MP4 and has students playing a one more or one less game with pennies and a number cube. Though they are using money, which is a real-world concept, the game itself is not actually modeling a real-world problem that could arise in everyday life, society, or the workplace.
  • In Unit 5 Session 1.1 students are looking at 3-D shapes. The students are only using the set of eight shapes that the teacher has been informed to assemble. This session does not allow them to choose any other tool as is intended by MP5.

The following are examples of how the materials attend to the full meaning of some MPs:

  • In Unit 6 Session 3.3 the Math Practice Note lists MP5 and has students making the number six. Students are encouraged to use cubes or their fingers to solve the problems given; however, they are not directly told to use any one specific tool and are able to choose a tool that works best for them and the problem.
  • In Unit 7 Session 1.1 the Math Practice Note lists MP1 and has students matching and sorting during their Math Workshop time. Students are working in pairs to find attribute blocks that share at least one attribute. The Math Practice Note informs teachers that if students aren’t making sense of the problem that they should ask them questions to get them started. They are also prompting students to stay with the problem and persevere. This session attends to the full meaning of the MP 1.

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 Kindergarten 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 5 Session 1.2 students work with partners exploring geoblocks, and in the activity, students discuss the size, shape, and position of the geoblocks relative to each other. The teacher is instructed to watch students work to see if students explain their ideas to their partner and then listen to their partner’s ideas. The teacher is instructed to ask other students in the class if their block looks like the chosen block and students answer. There is no direction for the students to explain their own descriptions or to analyze the descriptions of their partners.
  • In Unit 7 Session 1.1 students are supposed to stand next to the teacher based on whether or not they meet a certain characteristic. There are no questions or prompt that have students explain or justify why they did or did not stand next to the teacher, and there are no opportunities for students to analyze the other's arguments.
  • In Unit 8 Session 2.5 students are prompted to explain how they knew to correctly fill in their ten frame card while playing a game. There are no questions or prompts for the students to analyze other students’ explanations when multiple explanations are possible.

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

  • In Unit 4 Session 2.7 students are asked to compare the sums of two pairs of numbers. Students are prompted to explain which sum is bigger, and multiple strategies for explaining their choice are shared throughout the class. All students are asked to analyze the explanations of others as they are prompted to indicate which of the shared strategies theirs is most alike.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten 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 3 Session 2.7 students are playing a game called Fill the Hexagons. Teachers are instructed to tell the students, “Before we discuss what you found out, take a minute to compare the hexagons you made with those of a person sitting near you. Did you find the same combinations? Did you find any that were different?” These instructions assist teachers in starting a dialogue between the students, but there is no specific assistance that could assist students in constructing their own argument about playing the game or analyzing the arguments of others when different combinations are discussed.
  • In Unit 6 Session 1.1 the teacher is instructed to say the following prompt during a class activity that requires the measurement of body parts using cubes: “We found that my hand was nine cubes long, and (Mary’s) hand was five cubes long. Whose hand was longer? How do you know?” There are no questions or prompts that would assist the teacher in engaging students in analyzing the arguments of others.
  • In Unit 8 Session 1.3 the teacher is instructed to say, “We have several different stories for the problem three minus two. Do you think these problems have the same answer or different answers? Why?” These questions prompt 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.

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 2 Session 1.5 the teacher is told to “ask students to describe what they noticed (while the teacher counted) and to suggest strategies that may help (the teacher) count more accurately.”

Indicator 2g.iii

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

The instructional materials reviewed for Kindergarten 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 how many objects a student can pick up in one handful. They estimate the amount and determine if it is more or less than five. The materials prompt the teacher to state, “About how many objects do you think there are in (Kiyo)’s handful? Does it look like five? More than five? Fewer than five?” The math words that are focused on are "more" and "Fewer."
  • In Unit 4 Session 2.3 students are playing a game with the addition and subtraction of 1. The materials prompt the teacher to state, “In this game, partners take turns turning over a number card and building that number on a Ten Frame. This Plus or Minus cube is going to tell you to add one more penny to your Ten Frame or take away one penny from the Ten Frame.”
  • In Unit 7 Session 1.3 students are playing a game where matching at least one attribute of a shape is needed to create a train. The materials prompt the teacher to state, “Remember that blocks match if they have one or more attributes that are the same.” The math word that is the focus is "attribute."

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
Common Core Standards Practice Workbook Grade K (Student Guide) 978-0-328-75683-4 Pearson 2017
Common Core Standards Practice Workbook Grade K (Teacher Guide) 978-0-328-75690-2 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 1 978-0-328-85890-3 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 2 978-0-328-85891-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 3 978-0-328-85892-7 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 4 978-0-328-85893-4 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 5 978-0-328-85894-1 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 6 978-0-328-85895-8 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 7 978-0-328-85896-5 Pearson 2017
Investigations 3 Common Core Curriculum Unit (TE) Grade K Unit 8 978-0-328-85897-2 Pearson 2017
Implementing Investigations in Kindergarten 978-0-328-85939-9 Pearson 2017
Investigations 3 Common Core Assessment Sourcebook Grade K 978-0-328-85963-4 Pearson 2017
Investigations and the Common Core Content Guide Grade K 978-0-328-85969-6 Pearson 2017

About Publishers Responses

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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.

Educator-Led Review Teams

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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.

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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