Alignment: Overall Summary

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for alignment to the CCSSM. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and the materials partially connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

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

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

Criterion 1a

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

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 Math Expressions Kindergarten meet expectations that they assess grade-level content.

The materials provide an Assessment Guide for summative assessments. Within the Assessment Guide there is a Prerequisite Skills Inventory Test and Beginning of Year Test. Each of the assessments contain a correlations document between standard and question number. Within each Unit, there is a Test Form A and Test Form B with a correlations document, and a Performance Assessment with a grading rubric and sample student responses. A Middle of Year Test is located at the end of Unit 4 and an End of Year Test at the end of Unit 8, contain correlation documents. Additionally, the Student Activity Book contains Unit Quick Quizzes and Unit Reviews.

Assessment items containing grade level content include, but are not limited to:

  • Unit 1, Form A, Questions 1 and 2, students “ring” groups of a given number and mark an X on groups that are not the number. For example, in Question 1, students see the number 3 and then a group of 4 dots, a group of 3 dots, a group of 2 dots, and another group of 3 dots. (K.CC.4)
  • Unit 4, Performance Assessment 4, Grocery Store Fun, Part A, students are given 10 blocks where 7 are shaded and 3 are not shaded. Students write the number sentence represented by the blocks: 7 + 3 = 10. Students make up an addition story and drawing to show the story problem. (K.OA.1, K.OA.2, and K.OA.3)
  • Middle of Year Test, Question 4, students circle the numbers that are in order when counting a group of apples. (K.CC.3)

Some above grade-level assessment item are included, but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Assessment items containing above grade-level content include:

  • Unit 3, Form A, Question 5; Unit 5, Form A, Question 7; and Unit 5, Review Test, Question 7 students count items and circle the sign equal or not equal to. (1.OA.7)

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
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

Indicator 1b

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.

  • The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 5, 100%.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 96 out of 104, approximately 92%.
  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 138 out of 150, approximately 92%.

A number of days level analysis is most representative of the instructional materials because some lessons require two days of instruction. As a result, approximately 92% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade; content designated for one grade level that is viable for one school year; and coherence through connections at a single grade.

Indicator 1c

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major work of the grade. In the Teacher’s Edition, the Day at a Glance for each lesson contains a bubble identifying the mathematical content standards and mathematical practices addressed in the lesson, and can include connections between supporting and major work standards.

Examples include, but are not limited to:

  • In Unit 1, Lesson 7, students sort objects into categories, count each set, and compare the findings. This connects the supporting standard classify into given categories (K.MD.3) to the major work of count to answer “how many”. (K.CC.5)
  • In Unit 2, Lesson 13, students count the sides and corners of several shapes to name the shape they see. This connects supporting standard classify objects into given categories (K.MD.3) to the major work of count to answer “how many”. (K.CC.5)
  • In Unit 4, Lesson 14, students count the number of faces, count the number of corners, and determine the name of the shape. This connects supporting standard correctly name shapes (K.G.2) with the major work of count to answer “how many”. (K.CC.5)

Supporting standard K.MD.3 connects to K.OA.3 (decompose numbers less than or equal to 10 into pairs in more than one way and record each with a drawing or equation) through natural connections. For example:  

  • In Unit 4, Lesson 2, students start with 10 bugs total, and then proceed to decompose the group of 10 into two groups: sleeping bugs and awake bugs, thereby creating combinations of 10 and recording them as equations.  
  • In Unit 5 Lesson 2, a night sky display is created with big and little stars grouped in sets of ten. Students see all of the combinations of ten displayed, for example, a set of ten is shown with two big stars and eight little stars. In Lesson 3, students match equation strips to the correct display of stars.

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
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 120 days, not including lessons that take two days. Significant modifications would need to be made to make the curriculum viable for one school year as written. The Pacing Guide can be found on page I18 in the Teacher Edition.

  • There are 104 lessons, and most lessons require one day of instruction.
  • The Pacing Guide notes lessons that may take two days, but this is not noted in the Day at a Glance for each lesson.
  • The five units designate two days for Unit Assessments.
  • Unit 1 designates two days for the Prerequisite Skills Inventory Test.
  • Units 4 and 5 designate two days for Strategy/Fluency Checks in the Students Activity Book for each Big Idea.

Materials indicate a teacher will need to spend more than 60 minutes providing math instruction daily. Teaching the lesson is comprised of several activities with estimated time ranging from a total of 20- 60 minutes.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten partially meet expectations for the materials being consistent with the progressions in the Standards.

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. The Teacher Edition (page I19) states, “Standards are designed around coherent progressions from grade to grade. Standards are not stand alone events; they form cohesive links to major work within and across grade levels,” in the Teacher’s Edition (page I12) there is a chart, A Path to Fluency: Kindergarten through Grade 6 to “help students achieve fluency as described in the Common Core State Standards.” Each unit contains a Math Background section referencing the standards progressions in text boxes, and how they relate to work of the grade. Each Unit Overview lays out how the progression of the grade moves towards standards in future grades. Examples of grade level progressions include, but are not limited to:

  • Teacher Edition, Unit 4, Unit Overview states, “In Grade K, children will recognize that a collection of objects is composed of two subcollections and combine their cardinalities to find the cardinality of the collection (conceptual subitizing). In Grade 1, children will see the first addend as embedded in the total, using counting on as a strategy.”
  • Teacher Edition, Path to Fluency, Kindergarten chart states, “Fluently add and subtract within 5 (K.OA.5)” and in Grade 1 students, “Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 (1.OA.6).”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The structure of the Math Expressions program provides a variety of learning opportunities for students to master the grade level curriculum and provide extensive work with grade-level problems. Knead Knowledge through Practice ensures students gain understanding and fluency with desired methods. Daily Routines, Quick Practice, Student Practice, Homework Practice, Remembering, and Math Activity Centers support the classroom learning in every lesson. There are some instances where the full intent of the standard is not met, and there are some lessons that would need to be omitted as they attend to future grade standards. Examples of materials meeting full intent of the standards include, but are not limited to:

  • Unit 2, Lessons 2 through 10, Quick Practice, students show on their fingers the numbers 6-10 as a five and some ones and say the number aloud while the student leader points to the Number Parade (K.CC.1).
  • Unit 4, Lesson 1, Math Activity Center, includes on-level, challenge, and intervention work. On-Level Resources include Activity Card 4-1 which has students work together with advertisements to make up math stories about the items and share them with the class. Challenge Resources include Activity Card 4-1 which has students work together with Grocery ads, cutting items, and putting them together to make pictures and mathematical equations to represent the pictures. Both activities reinforce understanding of word problems as students create and solve addition and subtraction word problems. Students needing intervention complete Reteach 4-1, counting pictures of fruit and solving one addition word problem (K.OA.4).

Instances where full intent of the standard is not met:

  • In the Teacher Edition, Common Core State Standards for Mathematical Content, the publisher notes 31 lessons are aligned to count forward beginning from a given number within the known sequence (K.CC.2). Evidence for this standard in lessons noted was not found.

The following lessons address above grade level content and would need to be omitted:

  • Unit 2, Lesson 7 and Unit 3, Lesson 14, students are introduced to the not equal sign to relate two visual representations of a number. This is a Grade 1 standard (1.OA.7) and it is not clearly identified as future grade level content. This symbol is used in subsequent lessons throughout the units.
  • Unit 4, Lesson 1, students solve story problems including comparisons. For example, “How many more pieces of fruit did Amy buy than John? and How many fewer pieces of fruit did John buy than Amy?” Comparison story problems are a Grade 1 standard (1.OA.1), but it is not identified as future grade content. This type of questioning is not found in other activities or assessments.
  • Daily Routines, Use the Counting Tens and Ones Flipchart: each day students add a new counter to the number from the day before on a chart organized into groups of ten. Students proceed to record the numbers using the equation 10 + 10 + 9 = 29. They also use Giant Number Cards 20 and 9 to create the number 29, clearly showing that 20 + 9 = 29. These activities continue everyday through Units 1, 2 and 3. Work with tens and ones is a Grade 1 standard (1.NBT.2), but is not identified as future grade content.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Learning paths are identified at the beginning of each unit relating grade-level concepts to prior knowledge from earlier lessons. For example, The Learning Path for Unit 5 states, “Children in Math Expressions have been building their knowledge of the relations greater than, equal to, and less than throughout the year. They began by matching and counting small sets of objects and moved to larger sets. They later made math drawings to compare two numbers. In Unit 5, they continue to build on this earlier knowledge by practicing comparing numbers between 1 and 10 presented as written numerals.”

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
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

The instructional materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives visibly shaped by CCSSM cluster headings, and provide problems and activities connecting two or more clusters in a domain or two or more domains when the connections are natural and important. ​

Examples where materials include learning objectives visibly shaped by CCSSM cluster headings include, but are not limited to:

  • Each unit is broken into several “Big Ideas” shaped by the CCSSM cluster headings. For example, Unit 1, Understand Numbers 1 - 10 contains four Big Ideas:
    • Big Idea 1: Counting and Cardinality 1 - 5, is shaped by K.CC.B: Count to tell the number of objects.
    • Big Idea 2: Adding, Subtracting, and Comparing Through 5, is shaped by K.CC.C: Compare Numbers and K.OA.A: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
    • Big Idea 3: Show Numbers 1 - 10, is shaped by K.CC.A: Know number names and the count sequence.
    • Big Idea 4: Practice Numbers 1 - 10 is shaped by K.CC.C: Compare Numbers.
  • The Teacher Edition Planning Chart for each unit identifies the Big Ideas, CCSSM Domains, Clusters, and Standards for each lesson.
  • Unit 4, Big Idea 1, is designed around Grade K cluster heading: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from (K.OA). In Lesson 1, students represent addition and subtraction by creating stories. In Lesson 4, students compose/decompose partners of 10 in multiple ways using “bug partners” (K.CC).

Examples of connections between clusters and/or domains include, but are not limited to:

  • Unit 1, Lesson 10, connects supporting cluster K.G.A. to supporting cluster K.MD.B, as students sort shapes into two categories: circles and not circles. Students also count the shapes in each category and compare the numbers to see which shape has more, connecting to the major work of K.CC.5 and K.CC.6.
  • Unit 4, Lessons 4 and 5 connect K.OA.A: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from, to K.NBT.A: Work with numbers 11-19 to gain foundations for place value. In Lesson 4, students decompose numbers to 10 in different ways and in Lesson 5 students learn to decompose teen numbers into a ten and some ones.
  • Unit 5, Lesson 7, connects K.CC.A: Know number names and the count sequence, to K.NBT.A: Work with numbers 11-19 to gain foundations for place value. Students model the numbers 1 - 20 and put them in the correct sequence.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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.
8/8
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

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
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Materials include problems and questions that develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade where called for in the standards. The Teacher Edition states, “Through using objects, drawings, conceptual language, and real-world situations, students build mathematical ideas that make sense to them.”

Materials utilize MathBoards (laminated boards) for students to make their own drawings to communicate their conceptual understanding. Students have access to iTools to model conceptual understanding. Math Talk activities provide “frequent opportunities for students to explain their mathematical thinking and to ask questions of other explainers deepens their understanding of concepts.” Additionally, “What’s The Error” activities with the Puzzled Penguin provide students the opportunity to identify errors, discuss why it is incorrect, and how to correct it. Finally, Learning Paths, found in each unit, explain how students will build understanding of concepts throughout the unit.

Examples include but are not limited to:

  • In Unit 2, Lesson 2, in the Student Activity Book, students identify a number (6-10) and look at a finger representation showing a group of 5 fingers on one hand and then identifying the additional number of fingers shown on the second hand to complete a “5 + ___” addition equation (K.OA.1).  
  • Unit 2, Lesson 19, “What’s The Error,” Puzzled Penguin uses a 10 strip to order numbers 1-10 incorrectly. He asks, “Did I make a mistake?” and students write the numbers in the correct order (K.CC.2).
  • In Unit 3, Lessons 2, 5, 6, 8, 13, 15, and 17 through 20, students count a teen number of objects, then group 10 objects as a 10-group and see how many more ones are in the number. Students use a 10-Counter Strip to represent 10 ones or one 10, and use Number Tiles to make a number with tens and ones. Students use a 10-Counter Strip to represent 10 ones or one ten, and use Number Tiles to make a number with tens and ones. For example, to make 12, students place a 2 tile over the 0 on the 10 tile to show 12 consists of 10 and 2. A classroom Teen Display is created with an equation “14 = 10 + 4” and students use stickers or simple drawings to represent the equation as a group of 10 and a group of 4 (K.NBT.1).
  • In Unit 3, Lesson 3, students use Break-Apart Sticks and square tiles to find all the partners of the numbers 2 through 6, then write the equation for the total and the partners. In the Student Activity Book, students find various decompositions of 4, 5 and 6 using illustrated tiles pictured (K.OA.3).
  • Unit 3, Lesson 16, Math Talk, students play Unknown Partners game for 6 and 7. Student pairs sit beside each other and face their workspace which contains a Counting Mat, Number Tiles, and Operation Tiles. A number is called out. One partner uses centimeter cubes to represent the number, then removes break apart sticks leaving the remaining cubes in place. The partner opens their eyes and must identify the break apart partner that was removed (K.OA.1).
  • The Unit 4, Learning Path, explains how students continue to build understanding of addition and subtraction. “Children also continue to build their understanding of adding and subtracting by telling and solving such problems with larger numbers in the class grocery store and by solving addition equations without a given scenario” (K.OA.2).

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
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop and provide independent opportunities for procedural skill and fluency throughout the grade-level. Math Expressions includes a Path to Fluency for each grade level. “This plan provides targeted practice in the Student Activity Books, Teacher Editions, Teacher Resource Books, Math Activity Centers, as well as Fluency Checks in the Student Activity Books” (TE I12). In Kindergarten the fluency plan contains practice problems in the Student Activity Book identified by a Path to Fluency icon, Fluency Checks beginning in Unit 4, Reteach and Practice sheets, Daily Quick Practice Routines, and online resources. Examples include but are not limited to:

  • Unit 2, Lesson 6, Student Activity Book, Connect the Dot activities help students recognize and order numbers (K.CC.2).
  • Unit 3, Lessons 16-21, Daily Quick Practice Routines, students complete +1 in Addition Stories. Students use the strategy of adding a one to quickly find sums (K.OA.A).
  • Unit 3, Lessons 4, 5, 6, 7, 12, 14, 18, and 19, Student Activity Book, students begin regular practice to fluently add and subtract within 5. Students add or subtract numbers as shown in equation form (K.OA.5).
  • Unit 4, Lesson 17, Homework 4-17, Practice Sheets, students add within ten. These Homework workbook pages found throughout the series spiral back to prior work and help build fluency (K.OA.5).
  • Fluency Checks, Volume 2, Fluency Check 5, page 326, students add and subtract within 5 (K.OA.5).
  • Online Resource, Poggles MX, interactive game providing addition and subtraction fluency practice.

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 instructional materials for Math Expressions Kindergarten meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level and to independently demonstrate the use of mathematics flexibly in a variety of contexts. Opportunities for contextual problem solving and non-routine problems are found in Math Talks. Students are provided real-world problem scenarios throughout each lesson. Performance Tasks at the end of each unit, provide students the opportunity to solve real world situations. Also, Math Readers embed math learning in a context appropriate story. Finally, online games provide problem solving practice. For example:

  • Math Talks provide opportunities for students to engage with more detailed problems. For example, in Unit 2, Lesson 3, the teacher introduces verbal math story problems about real things that happen with families, such as setting the table for dinner and foods eaten for dinner. Students then tell stories about a meal and create and answer addition and subtraction questions from their story.
  • In Unit 3, Lesson 1, students solve “what if” story problems set in a park. “There is 1 child playing with some balls. Imagine that more children come to play. What if 5 more children come? How many children are playing with the balls now?” Students are expected to make math drawings and to begin using symbols to write expressions and equations to match (K.OA.2).
  • Performance Tasks at the end of each unit, provide students with the opportunity to solve a real world task. For example, on the Unit 4 Performance Task, students “show a set of partners for 10, use the partners to make up an addition story problem about the grocery store, make a drawing to show the story problem, and write the numbers in the boxes to show the addition equation.” Next, they show a different set of partners for 10 and create subtraction story problem.
  • Online activities provide additional opportunities for students to apply mathematical knowledge and skills to real-world contexts. For example, for the In-Depth Inquiry Based Task in Unit 4, Stock and Shop, students create a grocery store, sort and count the items, and create subtraction word problems related to the items in the store.
  • Students create their own story problems. For example, in Unit 5, Lesson 2, students create their own addition and subtraction story problems. Students start by using numbers for adding and subtracting within five and towards the end of the unit create for within 10.
  • Math Readers provide opportunities for students to solve word problems in a variety of contexts. Unit 5’s Reader, “Under the Umbrellas” includes addition and subtraction story problems based on the pictures in the story.

Indicator 2d

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

The instructional materials for Math Expressions Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently to develop students’ mathematical understanding of a single topic/unit of study throughout the grade level materials. The three aspects of rigor can be found separately and together in the Daily Routines, Quick Practice, Math Talks, Fluency Checks, Puzzled Penguin, Lessons, and Homework. For example:

  • Fluency can be found in any of the 6 Fluency Checks. For example, Fluency Check 5 has students adding and subtracting within 5 (K.OA.5).
  • Conceptual Understanding can be found in any of the Puzzled Penguins, “What’s the Error?” Questions. For example, in Unit 4, Lesson 19, Student Activity Book, page 254, students must look at what Puzzled Penguin wrote, “6 = 4 - 2” help him, and discuss with classmates how he wrote the equation incorrectly.
  • Application can be found in Math Talk in Action activities. For example, in Unit 4, Lesson 4, teachers present the following Math Talk problem, “The fruit bowl has 7 bananas. Jeff takes out 3 bananas to peel. How many bananas are in the fruit bowl now? Ask children how they might solve this problem and what tools, if any they would use to help them.” (TE 380)

Examples where the aspects of rigor are treated together include, but are not limited to:

  • In Unit 2, Lesson 5, students act out addition and subtraction stories from family experiences. Students build a conceptual understanding by discussing addition and subtraction using familiar scenarios. The remaining lesson involves procedural skill as students practice writing the number six and drawing groups of six.
  • In Unit 3, Lesson 1, students observe a park scene and use procedural skill to identify groups of 1-10 objects and color them with one color. Students use conceptual understanding to see how objects are arranged in the picture and identify partners for each number (nine birds total are pictured as a group of four and a group of five). Students use pictures and apply their learning to create story problems, such as, “There is 1 child playing with some balls. What if 5 more children come? How many children are playing with balls now?”
  • In Unit 4, Lesson 2, students’ fluency prior knowledge is activated through Partner Practice with Finger Wiggles and review on how to find partners and record them with an equation. Conceptual understanding is built using centimeter cubes, number tiles, and the plus sign in the Unknown Partner game for six or seven. Students use a break-apart stick to find the partners of six and then record the expression using the plus sign. Next, within the context of sleeping/awake bugs students use inch tiles to apply their learning and find partners of 10. Lastly, the activities progress to more of a skill-oriented activity where students find partners of 10 and record them as equations in their Student Activity Book.

Criterion 2e - 2g.iii

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

The instructional materials reviewed for Math Expressions Kindergarten partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified, but the materials partially attend to the full meaning of each MP. The instructional materials also partially support the standards’ emphasis on mathematical reasoning.

Indicator 2e

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level; however there are instances when the Mathematical Practices are over-identified.

Materials clearly identify Mathematical Practices being used in each lesson and are embedded in the content to enrich the mathematics. Instructions are provided for teachers on how to implement Mathematical Practices within the lesson. While Mathematical Practices are not identified in the student materials, the Teacher Edition does provide highlighted narratives for Mathematical Practice activities found in the Student Activity Book.

Examples include, but are not limited to:

  • The Teacher Edition provides guidance on how to implement the Mathematical Practices in the Student Activity Book. For example, in the Student Activity Book, Unit 3, Lesson 13, students identify the error the Puzzled Penguin made as he circled groups of five (MP3).
  • All Mathematical Practices identified in the materials have notes for the teacher. For example, Unit 2, Lesson 1, Activity 2, teacher notes include, "MP6 Attend to Precision. In this unit, children will focus on numbers 6 through 10. Children will draw scenes with groups of a specified number (6, 7, 8, 9, 10) for homework. Children can add to their scenes by drawing groups of small things.”  
  • Focus on the Mathematical Practices lessons are the last lesson in each unit. These lessons engage students in all eight practices, however, the practices are often over-identified. For example, in Unit 4, Lesson 22, Focus on the Mathematical Practices, students engage with MP8 as they describe the attributes of objects they find, and MP3 as they justify the attributes of the objects they circled.
  • The Overview of every unit contains “Common Core State Standards for Mathematical Practices in this Unit”.  A table is provided listing every Mathematical Practice along with corresponding lessons where the practice is embedded.
  • The “Using the Common Core Standards for Mathematical Practice” section contains a description of the Mathematical Practice along with examples of where to find it within the unit. For example in Unit 2, Lesson 2-5, MP1 Make Sense of Problems: Act It Out. “Act out another story about a meal in someone’s family. Ask, “Who can tell a story about a family dinner?  Then we’ll find some math in the story.” “Focus children’s attention on the addition found in the story. Act out the situation in the front of the room. Show the adding with fingers. Lead children to see partner sets of numbers, saying 4 is 2 and 2 or 3 and 1.” Additional examples are provided for each Mathematical Practice.
  • Every lesson identifies and provides explanations for the Mathematical Practice addressed in the lesson.  For example, Unit 4, Lesson 4-7, “MP7 Look for Structure | Identify Relationships After children have placed 10-sticks and centimeter cubes under all of the numbers, ask them to discuss different things they notice about the board. MP8 Use Repeated Reasoning | Generalize, There are many observations that the class can make. For example, children may notice that each of the teen numbers has one 10-stick. They may see that each number has one more cube than the number before it. Children might also discern that the number in the right column matches the number of centimeter cubes and the number in the left column matches the number of 10-sticks. Elicit as many observations from them as you can.”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Kindergarten partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The instructional materials attend to all eight Mathematical Practices. However, the instructional materials do not address the full meaning of Standard MP5 as tools are chosen for students, and there are few opportunities for students to choose tools strategically. For example:

  • In Unit 3, Lesson 21, Activity 2, students sort shapes into categories. MP5 Use Appropriate Tools is identified and explained in the teacher notes as, “Children will be sorting shapes into two groups by given attributes. Distribute the shapes and a sheet of paper to each child. Demonstrate folding the paper in half, so that children have two boxes in which to sort. On the board, draw a right triangle, equilateral triangle, square, rectangle, hexagon, and circle. Below, draw a table with two columns.” Students are not given the opportunity to choose the tools or how they will represent their thinking, but rather are told which tools to use.
  • In Unit 5, Lesson 19, Student Activity Book, “Draw circles to show each number. Write ten and the extra ones under the circles.” MP5 is identified in the teacher notes and states, “They can draw circles, dots, triangles, or anything they wish in the 10-sticks.” Students are given pictures of 10-sticks in their Student Activity Books limiting their ability to choose tools strategically.

The instructional materials attend to the full meaning of MP1, MP2, MP4, MP6, MP7, and MP8. Examples where materials attend to the full meaning of Mathematical Practices:

  • In Unit 5, Lesson 17, Math Talk in Action, “What are different ways we can compare groups of objects?” “What is another way to compare groups?” “Now let’s talk about comparing numbers when we don’t see the groups.”
  • In Unit 3, Lesson 11, Activity 1, students tell story problems with totals of 6 through 10. Other students retell the story in their own words, visualize the actions, decontextualize it, then use fingers or square tiles to solve it. They also use number tiles and operation symbols to represent the problem with an expression, connecting written symbols and models. (MP2)
  • In Unit 2, Lesson 10, Activity 1, students act out and tell math stories. Students write an equation to summarize the story, applying math to a given real-world situation. Acting out, telling stories and writing equations are all models students can use in real-world mathematical problems. (MP4)
  • In Unit 4, Lesson 15, Activity 2, students solve addition equations. MP6 is identified in the teacher notes, “Attend to Precision/Describe Methods: What methods could you use for solving this problem?” Possible student responses are “I could use my fingers; I already know that 5 and 5 are partners of 10; I just know the answer; I would draw 5 circles and 5 more circles, and count them all.” This activity requires students to attend to precision in calculations and language. 
  • In Unit 2, Lesson 13, Student Activity Book page 93, students look for structure as they identify shapes in the real-world objects, such as a door and window shown on the page. (MP7)
  • In Unit 5, Lesson 20, “MP8: Use Repeated Reasoning | Conclude, the goal is for children to realize that they can make two groups equal by taking away from the larger group or by adding to the smaller group.”

There is one instance in the materials where MP4 is misidentified: in Unit 3, Lesson 21, Activity 2, students sort 2D shapes into categories. The teacher notes for this activity state, “MP1, MP4 Make Sense of Problems/Model with Mathematics. Explain to children that they will be sorting the shapes in several different ways. Tell them they will be using the two boxes on their paper to show the categories each time they sort” (TE page 347). In this activity, students do not model with mathematics.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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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.
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Indicator Rating Details

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

Math Talk is a critical component of the instructional materials and presents opportunities for students to use a consistent structure: Solve, Explain, Question, and Justify. Math Talk activities are identified in the Teacher Edition, and the structure is a familiar routine for students. In addition, students are presented with opportunities to use pictures to create math stories. Students need to explain how their story represents the picture. Examples include but are not limited to: 

  • In Unit 2, Lesson 11, Tell A Math Story, The Neighborhood Garden presents a picture of a garden in which there are birds, pears on a tree and on the ground, rabbits, tulips, carrots, tomatoes, and flowers. Students use a variety of math strategies to add, choose to count on, combine quantities, etc. to tell their story.
  • In Unit 5, Lesson 23, students compare heights of animals. This is extended to compare other attributes. Students use the attributes of shapes and length to construct arguments as they compare. 
  • In Unit 3, Lesson 3, students work with partners of numbers that make a larger number; for example 2 and 2 are partners of 4. MP3 is identified and students discuss their partners. “Which group of children was able to show the most partners? Which group showed the fewest partners? Why do you think this is true?” Students need to construct an argument to explain why. 

Puzzled Penguin problems are found throughout the materials and provide students an opportunity to correct errors in the penguin’s work. These tasks focus on error analysis, and many of the errors presented are procedural. Examples of Puzzled Penguin problems include:

  • In Unit 1, Lesson 6, Puzzled Penguin “Am I correct?” students look at a picture of three dogs and answer “How many cats are there?” The Puzzled Penguin writes 1 cat. Students “Count the cats. Ring the number of cats.” (either 0 or 2.) “Count the dogs. Ring the number of dogs.” (either 3 or 5).
  • Unit 3, Lesson 11, Puzzled Penguin. “Help Puzzled Penguin. Look at Puzzled Penguin’s answers. Am I correct?” There are five diagrams with circles inside of a rectangular box. Students count the number in each box and identify the error. 
  • In Unit 4, Lesson 17, MP3 Construct Viable Arguments | Critique the Reasoning of Others, Puzzled Penguin, “Look at what the Puzzled Penguin wrote. Help Puzzled Penguin.” The Puzzled Penguin wrote the number sentence 4 + 1 = 3. Students use a picture of four apples and one apple to find 4 + 1 = 5. They explain that the Puzzled Penguin subtracted instead of adding.

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.
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Kindergarten partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

Missed opportunities include, but are not limited to:

  • In Unit 2,  Lesson 16, Student Activity Book page 100, the teacher notes state, “Explain how to solve a  - 1 equation. ‘8 - 1=7’ Children’s explanations should demonstrate their understanding of how to subtract 1.”  These notes do not help the teacher guide students to construct viable arguments.
  • In Unit 2, Lesson 17, Math Talk Activity, the teacher notes identify MP3 and teachers are prompted to ask, “How many sides does it have? How many corners does it have? Are all the side equal in length?”  These questions do not help teachers guide students to construct viable arguments.
  • In Unit 4, Lesson 13 the teacher notes state, “Encourage children to share what they remember about the similar pages in previous lessons and about the Tiny Tumblers. As children complete the top section of the page by drawing the partners, have pairs of children check each other’s pages.” This activity does not provide an opportunity to construct viable arguments.
  • In Unit 5, Lesson 1, students complete the first row of exercises by writing the addition expression for the Partners of 10 that are modeled in the pictures. MP3 is identified in the lesson narrative for this activity and the teacher notes state, “Complete the row together in this manner. When everyone has finished, ask what is the same and what is different in the first three rows. Then continue to guide children as they write the partners for the remaining rows.” Math is not needed to identify the similarities and differences, and students do not need to construct an argument to critique each other’s work.
  • In Unit 5, Lesson 16, students are asked to decide if the Puzzled Penguin’s number comparisons are correct or not.  The MP3 teacher notes state, “Let’s look at Puzzled Penguin’s work. For each pair of groups, we should check that both the counting and comparison are correct. Count the number of objects in both rows of Exercise 7. Did Puzzled Penguin count correctly? Did Puzzled Penguin correctly show which number is greater and which is less? Ask a volunteer to say the two comparisons. Now cross out the extra object to make the groups equal.” These questions do not prompt students to construct viable arguments.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Kindergarten meet expectations that materials use accurate mathematical terminology.

There are instances where materials use “A classroom research-based term developed for Math Expressions.” These terms are used in the Student Activity Book. Examples include but are not limited to: 

  • “Break-Apart Stick” is a simple stick, such as a coffee stirrer, that children can use to help break apart numbers. Children lay out a certain number of counters and then use the Break-Apart Stick to separate the counters into two groups.
  • “Math Mountains” are used to represent a total number and its decomposition into number partners. The total appears at the top, and the two partners that are added to produce the total are below to the right and left.
  • “Number Parade” is a large connected sequence of numbers from 1 to 10 that is displayed permanently in the classroom. Above each number is a 5-structured grouping of dots.
  • “Switch the Partners” refers to changing the order of the partners in an addition equation (commutative property).

In addition to a Glossary in the Student Activity Book, there are Teaching Notes on vocabulary and language. These are found in Unit 1 as students are introduced to mathematical language. For example:

  • In Unit 1, Lesson 7, Vocabulary includes: “partners, how many, add, subtract.”
  • In Unit 1, Lesson 9, Teaching Note, Language and Vocabulary states “To demonstrate the word horizontal, children can each hold out an arm horizontally. Have them pretend the sun (their other hand made in a fist) is coming over the horizon. Connect the two words. To demonstrate the word vertical, children can each move an arm so it is straight up. Help children visualize things they do horizontally (sleep, lie down on the beach). Also visualize things they do vertically (walk, stand).”

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials distinguish between problems and exercises.

Materials provide the opportunity for students to learn new mathematics through problem solving activities. In a typical lesson, Activity 1 and Activity 2 develop the new math content of the lesson. Lessons are outlined according to an Inquiry Lesson Path based on four phases: Phase 1 Guided Introduction, Phase 2 Learning Unfolds, Phase 3 Knead Knowledge (practice stage), and Phase 4 Maintaining and Integrating Fluency. Students build mastery through practice problems/exercises. In a typical lesson, during Activity 2 and Activity 3, students complete problems in the Student Activity Book which provide practice with the math content. The purpose of each Activity within a unit is explained in the “Teaching the Lesson Section” found on the first page of each lesson.

Examples include but are not limited to:

  • In Unit 2, Lesson 7, Teaching the Lesson Section, Activity 1, Counting Mat Activities with 5-Groups, is stated as being important because “Children build a strong foundation for understanding the concepts of equal and not equal by comparing both numerals to objects and objects to objects. Activity 2, Review Numbers, is stated as being important because “Children practice writing numbers.”
  • In the Student Activity Book, Unit 1, Lesson 6, Activity 1, students observe pictures and count the number of objects in them. They practice visualizing groups of 3 and 4 objects. In Activity 2, students look at a picture of dogs, identify Puzzled Penguin’s counting error, and count the number of cats and dogs in the picture. To deepen their understanding, students draw pictures of 5 hats, 3 cats, 4 stars, and 2 cars.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide tasks in an intentional sequence.

The design of the assignments follows a natural progression, leading to full understanding and mastery of new mathematics. Lessons follow a consistent pattern of two or three activities per lesson. Activity 1 usually focuses on the new learning. This learning is reinforced in Activity 2, and then students practice the new learning by completing Student Activity Book pages during Activity 3. Activity 3 either reinforces the new skill, or it reviews previously learned content.

Examples include but are not limited to:

  • In Unit 1, Lesson 9, students build an understanding of comparing numbers using a vertical Comparing Mat and square tiles to compare the height of the columns of tiles. On Student Activity Book page 27, numbers are represented on pictures of the vertical Comparing Mat with square tiles. On the following page, students color in boxes on blank Comparing Mats to represent the numbers being compared. Numerals are shown for each of the numbers being compared, but students are not expected to write the numbers yet.
  • In Unit 2, Lesson 13, students learn about triangles by exploring models of triangles. After the initial exploration, students practice identifying objects in the classroom that are triangles, and then they identify triangles in pictures in the Student Activity Book.
  • In Unit 4, Lesson 21, Activity 3, students practice combining 3D shapes to make new shapes using cubes, cones, cylinders, and cube-, cone-, and cylinder-shaped objects. Next, students build their own solid shapes using clay and straws and combine the shapes to make a new shape.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide varied opportunities for students to present their mathematical knowledge.

Examples of how students produce answers and solutions include but are not limited to:

  • Coloring groups of objects
  • Identifying the error and correcting it (Puzzled Penguin)
  • Using counters to practice counting to 20
  • Explain their thinking during Math Talk in Action Activities 
  • Modeling addition with fingers
  • Modeling number partners using a Break-Apart Stick and square tiles
  • Acting out problems
  • Model story problems with objects
  • Using Secret Code Cards to represent teen numbers
  • Drawing circles to represent numbers
  • Writing expressions to represent the number of objects in pictures, “11 = 10 + 1”
  • Using 2-D shapes
  • Using sorting cards to classify objects
  • Using base-ten blocks to represent teen numbers
  • Class discussions
  • Fluency Practice in the Student Activity Book
  • Problem Solving exercises in the Student Activity Book

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide virtual and physical manipulatives that are faithful representations of the mathematical objects they represent and are connected to the written material.

Students use a variety of manipulatives including counters, Secret Code Cards, base-ten blocks, 5-Counter Strips, comparing mats, square tiles, Stair Steps, and Math Mountains. Most of these manipulatives are available virtually in the itools found in ThinkCentral. Manipulatives are often connected to written methods when appropriate. 

Examples include but are not limited to:

  • Unit 3 Lesson 6, counters and Break-Apart Sticks are used to model partners of 5. These manipulatives make the decomposition easier for students to see.
  • Unit 3, Lesson 8, Square Tiles and 5-Square Tiles are used to represent the ten and ones in teen numbers. This is connected to pictures found in the Student Activity Book and to equations.

Indicator 3e

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

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the mathematics.

Student Activity Book pages include many exercises per page, but they follow a consistent layout and do not feel cluttered because there are no extra and unnecessary pictures on the pages. Additionally, students are provided ample space to show their work. When needed, models, which are consistent with the materials used in the lesson, are included on the pages. For example, on Student Activity Book page 145, Square-Inch Tiles and 5-Square Tiles are shown, and students write the corresponding numbers. Illustrations, when included, are simple and do not distract from the math.

In the Teacher Guide, lessons follow a consistent layout, moving from one activity to another. Each Activity includes a large blue box that highlights the mathematical content and practice standards, the focus of the lesson, and materials needed. Parts of the lesson, such as MathTalk, are clearly labeled. For example, in Unit 1, Lesson 14, a MathTalk in Action box shows examples of how students might model addition and subtraction stories based on pictures found in the Student Activity Book.

The digital interactive game, Poggles, includes simple, appealing characters that do not distract students as they practice addition and subtraction. Poggles are small squarish characters with animated faces whose appearance can be changed by adding hair and hats to the Poggle squares.

Criterion 3f - 3l

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Examples of teacher support include but are not limited to:

  • Questions for teachers to pose are consistently included in the lesson narrative. They are italicized, making them easily visible. 
  • MathTalk in Action boxes include questions for the teacher to ask and potential student responses. For example, in Unit 3, Lesson 15, the teacher is guided to ask the questions: “What do you see is the same when you look at them (Teen Number Displays)? What do you see that is different? Does it matter what objects you use to show a number?”
  • Teacher Notes are also provided at the bottom of the lesson pages and include questions to deepen students understanding of the mathematics. For example, in Unit 3, Lesson 6, the Learning Community notes provide several probes to promote student thinking and discussion: “How do you know that you need a 5-group and another one to show 6? How do you know how many extra ones you need to draw after the 5-group? What numbers do you want to use for your story? Why?”
  • Teacher Notes at the bottom of lesson pages also include information about best practices to strengthen teachers questioning techniques. For example, in Unit 4, Lesson 1, the MathTalk note provides the following questions for teacher reflection: “What types of questions are you asking your students? Are you asking questions that elicit a short answer, or do you probe to learn more about children’s thinking as they tell about their work?"

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that 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. Materials also, when necessary, provide teacher guidance for the use of embedded technology to support and enhance student learning.

Ample guidance is provided in the Teacher Guide for planning. The Pacing Guide provides guidance for each unit. Charts show the Learning Progression for the Content Standards Across Grades for the standards addressed in the Unit. A Planning Chart for each Unit that includes Math Activity Center Resources, Big Idea Resources, and Lesson Resources is provided. The Planning Chart also includes the standards addressed in each lesson, the digital and print resources for each lesson, and the assessments for the Unit. A table of the Standards for Mathematical Practice and the lessons where each is embedded is included. Also, a Table of the Math Content Standards and the lessons where they are taught is provided. Finally, a list of Assessment, Review, and Intervention Resources for the Unit is provided.

Examples include but are not limited to:

  • Each lesson includes guidance on the focus of each Activity and why it is important. For example, in Unit 3, Lesson 6, Activity 1, Show All the Partners of 2 Through 6, is stated as important because “Using number Tiles and +/- Tiles to show expressions is preliminary work before writing them.”
  • Each Activity includes an explanation of what the teacher should do or say and includes possible correct responses to questions posed by the teacher. 
  • Formative Assessment and Check for Understanding questions are highlighted in the Teacher Guide.
  • Math Practices are highlighted in the lesson narratives.
  • A list of questions that can be used to build a Math Talk community is included at the beginning of each Unit. 
  • Notes at the bottom of each page of the lesson narrative give useful suggestions for implementing the lesson, asking questions, acquiring vocabulary, and building concepts. For example, in Unit 1, Lesson 1, the Learning Community note, Building Concepts, an explanation on the use of 5-groups states, “Using the 5-group arrangements repeatedly on the Number Parade helps build recognition of small quantities less than or equal to 5.”
  • Digital Resources for each lesson are highlighted on the first page of the lesson, and itools, which includes virtual manipulatives, are shown in the lesson narrative when it may be beneficial to use them. For example, in Unit 2, Lesson 9, a picture of itools Number Tiles is shown because they may be used in the lesson.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials contain a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

Notes are provided at the bottom of each lesson narrative in the Teacher Edition to deepen teacher understanding of the mathematics and to improve instruction. Math Background Notes provide information about the math topic to deepen teacher’s understanding. Watch For! Notes provide information about potential misconceptions and things to watch for as students complete the lesson. What to Expect from Students notes provide information about how students might engage with the math and why the math is important. Building Concepts notes provide explanations of the math and how students learn.

Examples include but are not limited to:

  • Path to Fluency Charts are provided.
  • Chart of the Addition/Subtraction and Multiplication/Division problem types is provided.
  • Table of the Major Work and Major Clusters of the Grade is provided.
  • Table of the Common Core State Standards for Mathematical Content is provided.
  • Table of the Common Core State Standards for Mathematical Practice with an explanation for each Mathematical Practice is provided.
  • The Putting Research into Practice section at the beginning of each unit provides research about best practices in teaching children mathematics.
  • The Math Background section, prior to each unit, includes sections that deepen teacher knowledge of the math in the unit. Examples include Learning Path in the Common Core Standards, Help Students Avoid Common Errors, Effective Practice Routines, Relate Mathematics to the Real World, and Focus on Mathematical Practices. 
  • The Math Background section, prior to each unit, provides excerpts from the Progressions for the Common Core State Standards.
  • The Mathematical Practices section, prior to each unit, provides information on how students will engage with the Practice Standards throughout the unit.
  • A Teacher Glossary is provided.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials contain a teacher’s edition that explains the role of the specific mathematics standards in the context of the overall series.

A Path to Fluency: Kindergarten through Grade 6 Chart is provided and highlights the fluency requirements of each grade level, activities that target fluency, and interventions for Grades 3, 4, 5, and 6. Also, a Major Work and Major Clusters of the Grade Chart for Grades K-6 is provided. Finally, for each unit, a Learning Progressions for the Common Core State Standards Chart for the domains addressed in the unit, which includes the current, prior, and next grade level standards is provided.

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).
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten provide a list of lessons in the teacher's edition, cross-referencing the standards addressed and providing an estimated instructional time for each lesson, chapter, and unit.

Math Expressions does not include chapters, but rather units which are divided by Big Ideas, which are further divided into lessons. The Pacing Guide provides estimated instructional time for lessons and units. This Pacing Guide provides an estimated number of days for each unit, including lessons that may take two days and the number of days for assessments and quizzes. It should be noted that Lessons identified as taking two days in the Pacing Guide are not identified in the lesson narratives, nor is a breaking point indicated.

Examples include but are not limited to:

  • The Table of Contents provided in the introduction to the materials includes standards for all of the units’ Big Ideas.
  • The Chart of the Common Core State Standards for Mathematical Content provided identifies the lessons in which each standard will be addressed. 
  • The Chart of the Common Core State Standards for Mathematical Practice provided identifies the lessons in which each Mathematical Practice will be addressed. 
  • A Planning Chart is provided in the Overview for each unit that includes the standards that are addressed in each lesson. 
  • Charts of the Math Content Standards and Math Practice Standards are provided in the Overview for each unit. These charts include a list of each standard and the lessons where they are addressed. 
  • The Content and Practice Standards are identified on the first page of each lesson. The standards are also listed for each Activity within a lesson.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Letters for each unit are found in the Student Activity Book. These letters explain content, manipulatives students may use, and an explanation of terminology that may be unfamiliar to parents. Most units include between 1-3 Family Letters. Spanish versions of the letters are also included in the Student Activity Book.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Teacher Edition contains explanations of the program’s instructional approaches and research-based strategies. An Inquiry Learning Path describes the four phases of the Math Expressions classroom: Guided Introduction, Learning Unfolds, Knead Knowledge, and Maintaining and Integrating Fluency. The Putting Research into Practice pages at the beginning of each Unit explain best practices related to the content of the Unit. Excerpts from the Progressions for the Common Core State Standards are included in the Math Background section of each Unit. Research Notes are sometimes included in the Teaching Notes at the bottom of the lesson narrative in the Teacher Edition. For example, the Teaching Notes for Unit 2, Lesson 9, Activity 2 state, “Children in the U.S. are frequently asked to write their numerals very large. However, research shows that children have more control over their smaller motor coordination and find it easier to write smaller numerals.”

Criterion 3m - 3q

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

Indicator 3m

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

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

Examples include but are not limited to:

  • The Assessment Guide contains a 25 question Prerequisite Skills Inventory Test, organized by Domains, and a corresponding Prerequisite Skills Inventory Test Correlation document. The correlation aligns each question with a description of the prerequisite skill addressed, as well as the DoK level of the question. This correlation document is formatted as a table so each student’s performance by question/skill can be recorded. The Prerequisite Skills Inventory Test is designed to be administered at the beginning of the school year.
  • When a student completes practice opportunities and tests in the Personal Math Trainer, all of the performance data and adaptive learning information follows each student to the next grade.
  • Quick Practice activities at the beginning of each lesson are designed to “provide opportunities for students to call to mind their prior understanding of a topic that has already been discussed in class or to begin to build a prerequisite skill for a topic that is to come later” (Teacher Edition page I4).
  • In the Unit 4 Overview, the author discusses developing the prerequisites for Level 2 and Level 3 Methods of Adding and Subtracting. The author states, “Students are working on all the prerequisites for the Level 3 derived fact methods, such as make-a-ten. The prerequisites are: Seeing the tens in teen numbers; knowing all the partners of 10, and knowing all the partners of numbers below 10” (Teacher Edition page MB1-U4).
  • Students take three progress monitoring assessments to assess grade level skills and concepts students have learned. The Beginning of Year test assesses concepts they will learn throughout the year, the Middle of Year Test shows progress made in the first half of the year, and the End of Year Test measures growth throughout the school year. 

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide support for teachers to identify and address common student errors and misconceptions.

Examples include but are not limited to:

  • Common student errors are identified for each Unit Review/Test question along with a direction on how to help students. For example, on the Unit 3 Review/Test, if a student misses Question 3, the common error identified states, “Students may be confused about the objects not in the group of ten.” Teachers are directed to “Encourage children to count ten stars and then ring that group. Then have them count the remaining or extra stars.”
  • The Math Background section of each Unit provides a narrative called “Help Students Avoid Common Errors”. 
  • Puzzled Penguin activities highlight typical student mistakes and misconceptions by challenging students to find the Puzzled Penguin’s mistake and correct it. Teachers are provided questions in order to lead classroom conversations through a MathTalk format that revolve around the mistake and its correction, helping students understand the mathematics.
  • Watch For! are teaching notes periodically found in each unit. These notes alert teachers to common misconceptions they should be on the lookout for. For example, in Unit 3, Lesson 3, the Watch For! note states, “Some children may just move the Break-Apart Stick instead of actually switching partners. Instruct them that they need to change the positions of the solid tile group and dot tile group to show they are the same 2 groups just not shown in different positions.”

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Examples include but are not limited to:

  • Homework and Remembering pages provide a review of recently taught topics as well as a spiral review throughout the year. The Personal Math Trainer online platform allows students to complete homework tasks for each lesson, receive instant feedback, and  step-by-step guidance if needed.
  • Unit Review/Test and Performance Tasks for each unit are found in the Student Activity Book. The author states, You can use this Unit Review/Test as an end-of-unit review to determine if children have mastered the content of the unit. You can assess children’s knowledge with one of the forms of the Unit 1 Test in the Assessment Guide.” Teachers are provided with a Data-Driven Decision Making Table which suggests specific reteaching activities for students who incorrectly answer the correlated questions, as well as suggestions for which Standards Quiz to assign in the Personal Math Trainer which provides a personalized intervention for the student. The Performance Task includes a detailed scoring rubric which can be used to provide feedback to students.
  • The Personal Math Trainer can be used for homework practice, fluency practice, standards practice, unit pre-tests with instant feedback, and step-by-step guidance when needed. Everything a student completes in the platform helps to improve the adaptive workflow (powered by Knewton Adaptivity) for the student throughout the year.  
  • The Knewton Adaptivity, Homework with Daily Intervention and Enrichment can be used in multiple ways in the classroom. A 5-minute Warm-Up provides students with personalized review prior to the assignment. On-level and advanced students may receive less or no warm-up, as determined by Knewton. After the warm-up, the HMH pre-built assignment is given to students. A 10-minute personalized enrichment is provided for students who demonstrate mastery (95% or higher) on the assignment.  Enrichment shows students proximate, forward-looking concepts based on the assignment content.
  • Other Formative Assessment opportunities include: daily Check Understanding tasks on select Student Activity Book pages, daily observation with anecdotal notes, observations during Math Talk conversations, and analyzing student work samples and student responses in the Student Activity Book. Portfolio suggestions are also provided at the end of each unit.

Indicator 3p

Materials offer ongoing formative and summative assessments:
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Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
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Indicator Rating Details

The materials reviewed for Math Expressions Kindergarten meet the expectation for offering ongoing assessments that clearly denote which standards are being emphasized.

Examples include but are not limited to:

  • Every unit includes two versions of a Unit Assessment, Form A and Form B, found in the Assessment Guide. Both assessments provide PARCC and Smarter Balance question formats and a Standards Correlation Document which can be used to collect student performance data. This document also aligns each question to a DoK Level and Standard(s). 
  • Each unit contains a Performance Assessment which can be found in the Assessment Guide. The standards are clearly noted for the assessment as a whole, and not by specific question. 
  • There are three Benchmark Assessments (Beginning of the Year Inventory, Middle of the Year Inventory and End of Year Assessment) found in the Assessment Guide. Standards for these assessments are clearly noted on the Correlation Document and DoK Levels are noted.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Examples include but are not limited to:

  • Scoring Guides are provided for each Unit Performance Assessment found in the Assessment Guide. Each question is assigned a point value and a rubric is provided to determine Performance Levels 0-3 based on the number of points earned. Additionally, each Performance Level is further defined on a task-specific basis and indicates specifics about student understanding to assist teachers in interpreting student work. Sample student work for each Performance Level is also provided in the Assessment Guide. 
  • Answer keys for the Unit Assessments, Form A and Form B, are located in the back of the Assessment Guide. However, no guidance or suggestions for follow-up instruction are included in the Assessment Guide. 
  • The online Personal Math Trainer can be utilized to administer Beginning, Middle and End of Year Tests, Unit Assessments, and Fluency Checks. The data from these assessments is collected and analyzed, and a Personal Study Plan is prescribed through Adaptive Workflow settings (through Knewton Adaptivity) based on the data and the mastery threshold percentage established for the assessment. The primary use is for end of unit assessments, or to provide targeted students with occasional review, intervention, and re-assessment opportunities. Students must complete an initial assignment (test). Students who do not demonstrate mastery receive a Personal Study Plan, consisting of a personalized review and intervention assignment lasting 15 minutes. After completing the Personal Study Plan, the initial assignment is given again, but the numbers in the assessment are changed.

Indicator 3q

Materials encourage students to monitor their own progress.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten do not encourage students to monitor their own progress and do not provide direction for teachers to encourage students to monitor their progress.

Criterion 3r - 3y

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

The instructional materials reviewed for Math Expressions Kindergarten meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Teachers guide students through an inquiry path to become mathematically proficient. The four stages of the path to learning are guided introduction, learning unfolds, knead knowledge through practice, and maintain fluency. As stated by the publisher in the Teacher’s Edition, “Within the curriculum, a series of learning progressions reflect research on students’ natural learning stages when mastering concepts such as computation and problem-solving strategies. These learning stages informed the order of concepts, the sequence of units, and the positioning of topics in Math Expressions.”

Examples include but are not limited to:

  • In Unit 1, Lesson 16, students learn about and write the number 5. Prompts are given for EL students at three different levels: emerging, expanding, and bridging. The prompt states, “Help children think about the number 5. Hold up 1 hand.” Emerging: “What is this? Wiggle your fingers. What are these? How many fingers? 1 hand has 5 fingers. Have children repeat.” Expanding: “Wiggle your fingers. How many fingers are on 1 hand? Ask children to repeat. Draw 5 toes on a foot. Continue.” Bridging: “Have children count their fingers. How many fingers do you have on 1 hand? Have children tell how many toes are on 1 foot.”
  • In Unit 3, Lesson 9, the Watch For! teaching notes state, “Some children may try to use shapes (like squares) that fit inside but leave empty spaces. Remind them that the entire shape must be filled with no empty spaces.”
  • In Unit 5, Lesson 2, the Universal Access/Extra Help differentiated instruction note states, “You can form a group of children who need additional help and solve as many problems with them as necessary. Alternatively, choose some Student Leaders to help those who need assistance, while the rest of the class works on the problems independently.”

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Examples include but are not limited to:

  • An explanation of differentiated instruction is provided in the Teacher Edition. 
  • A list of intervention resources is provided for each unit in the Unit Overview Assessment.
  • Math Activity Centers resources for on-level, challenge, and intervention are provided for each unit’s lessons. 
  • Teaching notes for English Learners are provided for emerging, expanding, and bridging students and are provided for each unit’s lessons.
  • Some lessons have Differentiated Instruction notes provided for universal access/extra help.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meets expectations that materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

MathTalks provide “an inquiry environment that encourages constructive discussion of problem-solving methods through well-defined classroom activity structures. . . comprises four components: questioning, explaining math thinking, contributing math ideas, and taking responsibility for learning” (Teacher Edition page I3). Initially, teachers model MathTalks and then students run the MathTalk. For example, in Unit 5, Lesson 2 the MathTalk instructs teachers to “Explain that Puzzled Penguin was asked to write the numbers 14, 17, and 19. Puzzled Penguin is not sure that each number was written correctly. Help Puzzled Penguin look at the first number to see if it is correct.” The teacher is then provided prompts to help guide the student discussion.

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).
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meets expectations that 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.

Examples include but are not limited to:

  • Scaffolding of vocabulary is provided. For example, in Unit 5, Lesson 10, teachers are provided support to explain the word fewer for EL students. Teachers are instructed to “Write ‘fewer’ on the board. Fewer means a smaller amount of something of less. Draw a row of 3 circles above a row of 4 squares. The are fewer circles than squares. Have students repeat.” 
  • Extra support is provided for EL students. For example, in Unit 5, Lesson 13, students count by ones and tens to 100. Teachers are instructed to “Write 100 and one hundred on the board. Display a hundred base ten block. Lead children in counting to one hundred as you point to the ones cube in the hundred block.” 
  • Each unit lesson contains a Math Activity Center with activities and resources for students who are on-level and those needing challenge and intervention.
  • Teaching notes included in some lessons provide specific guidance for teachers to support students who are emerging, expanding, and bridging language acquisition.

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meets expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Examples include but are not limited to:

  • Math Lessons contain Differentiated Instruction Math Activity Centers. Challenge Resources specify which Activity Card will challenge advanced students.
  • The online Personal Math Trainer provides personalized enrichment with learning supports.
  • Challenge worksheets for each lesson are available in print and digitally and are noted on the Differentiated Instruction page for each lesson.
  • Math Readers, books in the Math Activity Center, place math content in the context of stories and support higher levels of critical thinking.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten meets expectations that materials provide a balanced portrayal of various demographic and personal characteristics. 

Examples include but are not limited to:

  • Puzzled Penguin appears throughout the unit to provide opportunities to help students avoid common errors. These errors are presented as letters to students. Students teach Puzzled Penguin the correct way and explain why the penguin is wrong. 
  • Math Readers contain a variety of animals, children, and adults.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten provide opportunities for teachers to use a variety of grouping strategies.

Examples include but are not limited to:

  • Math Activity Centers are provided at the conclusion of each lesson and students can be grouped individually, in pairs, or in groups to complete the Activity Cards. For example, in Unit 2, Lesson 18, Challenge Activity card 2-18, students can work in pairs or groups to make and write the numbers 8 and 9. 
  • Math Writing Prompts are part of the Math Activity Centers and provide opportunities for students to work individually, in pairs, or in groups. For example, in Unit 1, Lesson 6, the On-Level Math Writing Prompt states, “Choose a number. Ask a partner to draw items to match that number.”
  • MathTalks provide various grouping structures. During Solve and Discuss, 4-5 students go to the board and solve the problem while the rest of the class is solving independently or as part of a small group consisting of 2-3 students. During Scenarios, a group of students act out a particular mathematical situation for other students to see.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten sometimes encourage teachers to draw upon home language and culture to facilitate learning.

Family Letters for each unit are found in the Student Activity Book. Spanish versions of these letters are also included in the Student Activity Book. However, instructional materials do not encourage teachers to draw upon home language and culture to facilitate learning. English Learner notes in the Teacher Edition do not reference Spanish vocabulary to facilitate learning.

Criterion 3z - 3ad

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

The instructional materials reviewed for Math Expressions Kindergarten: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Examples include but are not limited to:

  • The Student Activity eBook provides audio, ability to submit answers online, a drawing tool for math drawings, guided practice to help students solve problems, and virtual manipulatives.
  • The Personal Math Trainer is an online adaptive assessment and personalized learning system for students. It analyzes student activity to determine strengths, weaknesses, learning style preferences, and pace. It provides a personalized learning path for students and generates reports for teachers to inform instruction.
  • The online Math Activity Center provides online differentiated instruction opportunities for practice, reteach, and challenge. Teachers can assign RTI assignments to students who struggle on Big Idea Quick Quizzes. Fluency Builders develop students’ basic facts and automaticity.
  • OSMO is an interactive gaming system for iPads to build students’ fluency and problem-solving skills. It offers physical manipulatives and provides immediate feedback.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten are web-based and compatible with multiple internet browsers. In addition, materials are platform neutral and allow the use of tablets and mobile devices.

Web-based instructional materials for both teachers and students can be accessed using multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, both students and teachers can use multiple devices to access instructional materials (desktop computer, tablet, iPad, Smartboard, laptop, or cellphone). Students with disabilities can use mobile devices, assistive technology, or PCs to access materials. For example, non-readers have the option to have the entire text in an audio format. Additionally, the materials are platform-neutral for a variety of operating systems.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten provide opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Online assessments are available. Teachers have the ability to create their own assessments or customize those provided by the program. A variety of assessment types are provided: multi-step, fill in the blank, multiple-choice, or teacher-created questions. For example, teachers giving the computer adaptive test may edit the format and/or values of the text causing the corresponding complexity of the lesson to change accordingly.

The Personal Math Trainer is an online adaptive assessment and learning system of mathematical understanding and procedural skill/fluency. Teachers can identify question types, assignment type, or standard tested. Once students have completed the task or assessment, various charts and graphs can be generated based on standards to inform instruction. Reports are available for individual students and the entire class.

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.
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

Teachers can manipulate the Personal Math Trainer to create learning experiences for students targeting their needs. Additionally, teachers can create lesson materials that are specific to the learning targets for specific unit lessons. For example, in Kindergarten students practice one to one correspondence through the use of math stories and online assignments. Students complete learning tasks on their level, such as adding to 5.

The instructional materials for Math Expressions Kindergarten can be easily customized for local use.

Digital materials include adaptive technological innovations for teachers to personalize learning for students. Digital materials can be differentiated based on individual student’s needs. For example, when using the Personal Math Trainer, teachers can add or modify existing tasks to a student’s personalized learning path. Additionally, adaptive technology allows teachers to provide two flexible differentiated styles (Daily Intervention and Enrichment or Personal Study Plan) for students.

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
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Indicator Rating Details

The instructional materials for Math Expressions Kindergarten do not include reference technology that provides opportunities for teachers and/or students to collaborate with each other.

Materials do not provide opportunities for students and teachers to participate in discussion groups using technology.

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Additional Publication Details

Report Published Date: 09/04/2019

Report Edition: 2018

Title ISBN Edition Publisher Year
CCSS Homework and Remembering BLM Grade K 9781328703552 Houghton Mifflin Harcourt 2018
CCSS Assessment Guide BLM Grade K 9781328703620 Houghton Mifflin Harcourt 2018
Teacher Resource Book Grade K 9781328703699 Houghton Mifflin Harcourt 2018
CCSS Teacher Edition Collection Grade K 9781328741400 Houghton Mifflin Harcourt 2018
CCSS Softcover Consumable Student Activity Book Collection w/Mathboards Grade K 9781328764232 Houghton Mifflin Harcourt 2018

About Publishers Responses

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

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

The publisher has not submitted a response.

Educator-Led Review Teams

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

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

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

Rubric Design

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

Advancing Through Gateways

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

Key Terms Used throughout Review Rubric and Reports

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

Math K-8 Rubric and Evidence Guides

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

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

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

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