Alignment: Overall Summary

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for alignment to the CCSSM. In Gateway 1, the instructional materials meet the expectations for focus as they assess grade-level standards and devote at least 65% of instructional time to the major work of the grade. For coherence, the instructional materials are not coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year, but the materials partially, or do not, meet expectations for the remainder of the indicators within coherence. In Gateway 2, the instructional materials do not meet the expectations for rigor and balance, and they do not meet the expectations for practice-content connections. Since the materials do not meet the expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.

See Rating Scale
Understanding Gateways

Alignment

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Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
9
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
4
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

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Gateway One Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition partially meet expectations for focus and coherence in Gateway 1. For focus, the instructional materials meet the expectations for assessing grade-level standards, and the amount of time devoted to the major work of the grade is at least 65 percent. For coherence, the instructional materials are not coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year, but the materials partially, or do not, meet expectations for the remainder of the indicators within coherence.

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 forEarlybird Kindergarten Mathematics Common Core Edition meet expectations for not assessing topics before the grade level in which the topic should be introduced. The instructional materials include assessment items that primarily align to grade-level standards.

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 for Earlybird Kindergarten Mathematics Common Core Edition meet expectations for assessing grade-level content. Assessment items primarily align to grade-level standards. In instances where items align to standards above grade level, the items could be omitted and the materials adapted without affecting the underlying structure of the materials. Unit 15 requires more significant changes, as students are reading and writing numbers to 100 throughout the assessment.

Examples of assessment items aligned to the grade level include:

  • Unit 1, Student Textbook A, pages 19-20 assess K.MD.B. Students classify and count objects into categories.
  • Unit 4, Student Textbook A, pages 84-87 assess K.CC.A. Students count to build the relationship between numbers and quantities.
  • Unit 7, Student Textbook A, pages 168-169 assess K.CC.C. Students compare two groups of objects using a matching strategy to determine which group has more or less.
  • Unit 9, Student Textbook B, pages 13-14 assess K.CC.A, K.CC.B, K.CC.C. Students count and identify groups of numbers that are greater or less.

Examples of assessment items aligned to standards above grade level include:

  • In Unit 2, Student Textbook B, pages 52-53, students read a picture graph and record the number of objects. Picture graphs are aligned to 1.MD.4, and picture graphs with four categories of data align to 2.MD.10.
  • In Unit 15, Student Textbook B, pages 113-114, students write numbers from 0-100, which aligns to 1.NBT.A. For K.CC.A, students write numbers from 0-20.

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 Earlybird Kindergarten Mathematics Common Core Edition meet expectations for devoting the large majority of class time to the major work of the grade. The instructional materials spend at least 65% of instructional time on the major work 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 Earlybird Kindergarten Mathematics Common Core Edition 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 11 out of 15, which is approximately 73 percent.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 103 out of 147, which is approximately 70 percent.
  • The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is 20 out of 29, which is approximately 69 percent.

A lesson-level analysis is most representative of the instructional materials because it represents the total amount of class time that addresses major work. As a result, approximately 70 percent 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.
3/8
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Criterion Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition do meet expectations for being coherent and consistent with the Standards. The instructional materials have an amount of content designated for one grade level that is viable for one school year. However, the instructional materials miss connections between two or more clusters in a domain or two or more domains, and they do not engage students in the major work of the grade through supporting content, do not identify content from future grades, and do not give students extensive grade-level problems.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
0/2
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Indicator Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards are taught in isolation, and examples of missed connections between supporting and major standards include:

  • In Unit 1, Matching and Sorting, there are missed natural opportunities to connect supporting standard K.MD.3 to major work K.CC.C (comparing numbers). In Textbook A, pages 15-18 and 21, students sort pictures into two categories. The opportunity to compare the groups after they are sorted is missed. For example, on page 18 students sort objects into boxes based on color. No follow- up questions comparing the number of objects are provided. The directions state, “Tell the students to sort the toys on the cards according to color. Repeat this activity, but allow students to decide the criteria for sorting the toys. Accept any reasonable method of sorting. Ask them to describe their method.”
  • In Lesson 5.4, students identify rectangular prisms in different orientations. This lesson aligns to supporting standard K.G.4 (Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). In Textbook A, page 118 (Teacher’s Guide page 109), students identify the rectangular prism from different 3-D shapes. The teacher is directed to ask the following questions: “Are the objects you named earlier on this page?” “What shape do they all have?” A natural connection to the major work of counting and cardinality is missed, as the students do not count the number of sides or corners of the shapes.
  • In Lesson 5.13, page 34, students identify triangles and use triangles to compose squares. The lesson supports the K.G supporting standard for analyzing, comparing, creating and composing shapes. The lesson does not make a connection to the major work of counting and cardinality.
  • In Lesson 5.14, connections are missed as students work with shapes, supporting standards K.G.2 and K.G.4. For example, on Teacher’s Guide page 125, the teacher is directed to, “Pick out a yellow piece. Say, ‘This is a hexagon.’ Have students repeat after you. Have students trace the outline of the hexagon with their index finger. Have students work in pairs to create a hexagon using other-shaped pieces.” Students do not count the number of sides and corners, a missed connection to counting. A natural connection to compare numbers is also missed due to lack of counting. Activity Book A has one activity on pages 42-43 where students count the objects and write the number. This connects supporting standard K.G.2 to major work K.CC.3, however this is not present in the rest of Unit 5.

Indicator 1d

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

Instructional materials for Earlybird Kindergarten Mathematics Common Core Edition meet expectations that the amount of content designated for one grade level is viable for one year.

  • Instructional materials can be completed in 147 days.
  • The suggested pacing from the publisher is one day per lesson. Each lesson is 60 minutes.
  • Materials include 132 instructional days and 15 days for review/assessment, totaling 147 days.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
0/2
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Indicator Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for the materials being consistent with the progressions in the standards. Content from prior or future grades is not clearly identified in the materials and does not support the progressions of the grade-level standards.

Examples of prior or future work that is not identified:

  • Unit 2, Lesson 6 is aligned to 1.MD.4. Students organize and interpret data with three or more categories.
  • Unit 8, Lesson 6 goes beyond K.MD.2 (directly compare two objects). Students compare three objects. (1.MD.1)
  • Unit 15 is aligned to 1.NBT. Students extend the counting sequence in Lessons 2 and 4 as they write numerals beyond 20.
  • Teacher’s Guide, Lesson 15.3, page 138 states, "Before playing the game, have students look on textbook page 107 and ask them if they notice any pattern(s) formed by the numbers. Point out to them that the numbers in the same column have the same value for the ones place, while the numbers in the same row have the same tens place, except the last number, which has the next higher tens place." In Kindergarten, students work with numbers 11-19 to gain foundations for place value. (K.NBT) In Grade 1, students understand place value (1.NBT.B). Standard K.CC.1, Count to 100 by ones and tens, is identified for this lesson.

Additionally, Earlybird Kindergarten Mathematics Common Core Edition materials do not provide all students extensive work with grade-level problems. For example:

  • Textbook A, page 21, (K.MD.3), Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Students are given pictures of animals and vehicles and directed to, "Sort these things by putting them in the correct box." However, the full depth of the standard is not met. Students are not given the opportunity to "count the number of objects in each category and sort the categories by count."
  • K.CC.7 Compare two numbers between 1 and 10 presented as written numerals. Students are not given enough opportunities to compare numerals. In the textbook and activity book, pictures of objects are shown to accompany the numerals.
  • K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. A Put Together/Take Apart Both Addends Missing situation is not practiced (CCSSM, Table 1, Common Addition and Subtraction Situations, page 88.). Students have opportunities to decompose numbers in different ways; however, it is not in the context of word problems. For example, in Activity Book B, page 58, students are shown different pictures of 10 birds sitting on a brick wall. For each picture, their task is to identify the number of birds on the wall and the number of birds that are flying. Students see different combinations, but the answers are in the picture.

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.
1/2
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Indicator Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition partially meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

The materials include learning objectives that are not consistently shaped by CCSSM cluster headings. Additionally, the cluster headings are not explicitly identified within the materials.

  • A Grade K cluster heading is Compare Numbers. Teacher’s Guide, Unit 9 page 1 is devoted to comparing numbers to 10.
  • The Grade K NBT cluster heading is: Work with numbers 11 - 19 to gain foundations for place value.” Some math in Unit 10 works towards this goal. For example, in lesson 10.3, Teacher’s Guide page 28 and Textbook page 19, students begin to work with a group of 10 linking cubes and some extra cubes. Students also use number cards to show that a teen number is 10 and some ones.
  • Learning objectives for Chapters 2-4 are shaped by cluster headings. For example, the objective for Lesson 3.7 is, “Students will be able to count up to eight and represent the numbers 1 - 8 in writing.” This connects K.CC.A to K.CC.B.
  • In Unit 6 on patterns, the publisher connects to K.G standards, but patterning is not a CCSSM standard.
  • In Textbook B, Lesson 10.1 pages 15-16, students place objects into a container with ten slots or circle a group of ten items, building the understanding that teen numbers are ten ones and some more ones. This supports the cluster heading, "Work with numbers 11-19 to gain a foundation for place value."
  • Objectives in Unit 11 are not visibly shaped by the cluster headings. For example, the objective for Teacher’s Guide, Lesson 11.5 page 56 is “using number bonds to 7.” This represents a specific strategy to solve an addition or subtraction problem.

Materials sometimes include problems and activities that serve to connect two or more clusters in a domain; however, important connections are missed.

  • Units 2 - 4: Connections are made between the CC cluster headings, “Know number names and the count sequence,” and “Count to tell the number of objects.” Students count, write numerals, and order the numerals. For example, in Textbook A page 42, students count the number of fish in the tank and count the number of dots in the square. Next, students put 4 counters on a five frame and write the number 4.
  • Unit 5: Shapes misses natural opportunities throughout the unit to connect K.G.B standard with K.CC.A by counting the number of sides on shapes. For example, in Textbook A, Lesson 5.11 page 131, the directions say, "Show the students some cutouts and say, 'This is/not a rectangle.' Paste a rectangle on the board and say, 'This is a rectangle.' Have the students look at this page. Tell them to point out all the rectangles in the picture. Have them use their index fingers to trace the rectangles. Give the students several objects. Have them say which objects have rectangles on them. Have the students use their fingers to trace the rectangles. Encourage them to use the word ‘rectangle.’"
  • Unit 7: Connections are made between K.CC.6 (identifying whether the number of objects in one group are greater than, less than, equal to) and standards in K.CC.A and K.CC.B (counting and writing numbers 0-20). For example, in Lesson 7.7, the objectives are, “Students will be able to say which group has more/fewer. Students will be able to say which group has a greater number/fewer number.”
  • Unit 7: Connections are made between K.CC.C.6 and standards in K.CC.A and K.CC.B. For example, in lesson 7.7, the objectives are, “Students will be able to say which group has more/fewer. Students will be able to say which group has a greater number/fewer number.” In contrast to this, too many connections are made for K.CC.C.7 where students compare two numbers between 1 and 10 presented as written numerals. Students are not given the opportunity to compare numerals; rather, the numerals always include objects to count.
  • Unit 10: Connections are evident between K.NBT.1 and K.CC.A and K.CC.B. Students count to 20, write numbers to 20, and group objects as a group of ten and some ones. The objective for Teacher’s Guide, Lesson 10.6 page 33 is, “Represent the numerals 16 - 19 as a filled ten frame and a few more and write them as two-digit numbers.”
  • Unit 11: Connections are made between K.CC.A, K.CC.B, and K.OA.1. For example, in Student Activity Book B page 30, students are shown five sheep. The Teacher’s Guide directions on page 56 state, “Color some sheep blue. Color the rest green. Write the numbers.” Students count and write numbers (K.CC.A and K.CC.B). Students classify objects into given categories and count the numbers of objects in each category (K.MD.3), and they represent addition through drawings (K.OA.1).
  • Units 12 - 14: Connections are made between K.CC.A, K.CC.B, K.OA.1, K.OA.2, and K.OA.5. For example, in Teacher’s Guide page 125, Let’s Do It! section, teachers are guided to, “Have students create their own simple word problem by drawing creatively. Have them write the addition/subtraction equation accordingly."

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

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Gateway Two Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for rigor and the mathematical practices in Gateway 2. The instructional materials partially develop conceptual understanding, procedural skill and fluency, and balance, but the instructional materials do not develop application for students. Also, the instructional materials partially identify the mathematical practices through Singapore’s Math Framework, but the instructional materials do not meet expectations for any of the other indicators within practice-content connections.

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.
3/8
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Criterion Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for rigor and balance. The instructional materials partially develop conceptual understanding and procedural skill and fluency, and the materials are partially balanced because there is an under-emphasis on application. The instructional materials do not develop application for students.

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.
1/2
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Indicator Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition partially meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Materials lack conceptual problems and conceptual discussion questions. The exercises are routine addition and subtraction problems and are procedural in nature. Many addition situations are part-part-whole.

  • Materials move quickly from concrete to pictorial representations. For example, in Teacher’s Guide, Lesson 13.1 pages 88 – 91, the initial lesson on subtraction, the teacher shows the class four strawberries. Then the teacher takes away one strawberry, and students count how many strawberries are left. Next, the teacher shows students five balloons. Two students each burst a balloon, and students identify how many balloons are left. Following this, students move to the textbook where they look at pictures, cover the object that is either left or was taken away, and count the number of objects left. In the conclusion of the lesson, students play a game in pairs. The first player holds up a specified number of fingers. The second player turns away, and player one “takes away” some of the fingers. Partner two turns back around and identifies how many fingers were taken away. Students are not given the opportunity to model subtraction with a concrete model. Students watch the teacher model subtraction; then they move quickly to pictorial examples and to missing addend/subtraction with change unknown problems.
  • In Teacher’s Guide B, Lesson 14.1 pages 112 -114, the objective reads: Developing different addition facts based on the same situation. The lesson begins with the students making an animal mask of their favorite animal (blackline master 14.1 a – c). Additional materials include: linking cubes, magnetic counters, and blackline master 14.1d. The lesson begins with the students making a mask of their favorite animal. When the masks are complete, students create groups and use the magnetic counters to model the problem created by the masks on the display board. The consolidation of the lesson includes using the textbook page to highlight how ‘5’ can be decomposed into different versions of addition equations. The conclusion of the lesson has students showing pictures of zoo animals and working in groups to select an animal they like. The directions state, “Have them start off with five of that chosen animal and imagine what can happen next to split them into two groups. For example, ‘There are 5 giraffes. Of them, 3 are eating their food from a tree and 2 are resting. 5 is 3 and 2. 3 and 2 make 5’. Write the different addition equation that make 5 on the board.” This lesson does not include instructional materials that lead to conceptual understanding. The creation of the student masks does not allow for the students to build their understanding of the math concept identified as developing different addition facts based on the same situation.
  • In Teacher’s Guide B, Lesson 14.3 page 118 and Textbook, page 92, students are shown pictures of groups of coins. The teacher is directed to "Have students look at the first situation on Textbook, page 92. Ask them, 'How many coins are there?' Have them use five coins to model the situation. Then ask, 'How many coins are needed to make a total of 10?'"
  • There are some opportunities for students to use manipulatives to build concrete understanding. In the Introduction section of the Teacher’s Guide, page 73, the teacher is directed to “Give students copies of BLM 12.3 Birds (instruct students) to cut out the birds. Have them use the cutouts to form number bonds to show the number of birds they have altogether.”
  • In Teacher’s Guide, Lesson 11.7 page 61, and Workbook page 47, students are shown a picture of nine dots. In number one, the dots are divided into a group of three and a group of six. Underneath the picture is a number bond with the number nine written in the circle for the total. Students work with the teacher to fill in the number bond circles for three and six.
  • Students are not encouraged to use different methods of representation as suggested by K.OA.1. Number bonds are the major strategy addressed.

There is little opportunity for students to demonstrate conceptual understanding independently.

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.
1/2
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Indicator Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition partially meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

Materials provide limited opportunities to develop fluency, but do encourage students to develop procedural skill. For example:

  • Opportunities are not present throughout the year to practice addition and subtraction fluency. Addition and subtraction problems that are given without the support of pictures occur in the last 6 problems within the Review, Textbook B, page 102. Additionally, these review questions still do not address fluency, stating, “Add or subtract. Show using counters.”
  • Students have limited opportunities to develop addition and subtraction skills. Procedures for addition and subtraction are not introduced until Unit 11.
  • Standard K.OA.4 - “For any number from 1 to 9, find the number that makes 10 when added to the given number,” is addressed in 2 lessons where students make a 10.
  • In Unit 11, Lesson 11.3, students use number bonds to represent 5. “Students use linking cubes to represent the lions. Lead them saying _____ and _____ make 5.”
  • Addition strategies practiced in Textbook B, Lessons 12.3-12.5 pages 55-60 include “count on.” On page 55 the directions state, “Say, 'There are 5 birds. Then, 3 birds joined them. How many birds are there altogether?’ Lead the class to count on, ‘6, 7, 8.'”

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
0/2
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Indicator Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition do not 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 do not include non-routine problems. Students do not have the opportunity to demonstrate the use of mathematics flexibly. Pictures accompany word problems, and students are prompted often to use specific methods, such as number bonds, to solve the problems. For example:

  • In Activity Book B, Lesson 12.4 pages 44-46 there are six story problems. Each of these problems are partially illustrated for the student. The first group is depicted in the illustration. The students use cutouts to add to the picture in order to find the total. Students use the model to solve routine problems.
  • In Textbook B, Lesson 12.6 page 61, students make up a story to describe the picture on the page. The picture shows a fox eating and a fox with no food.
  • In Textbook B,Lesson 13.1 page 69, the teacher gives situations for each of three problems. “Ask, ‘There were 5 balloons. 1 burst. How many balloons are still here?’” Each problem is illustrated with the original number of balloons. Students cross out the burst balloons and write the answer in the box. This is a routine application problem.
  • In Activity Book B, Lesson 13.2 pages 51-52, there are four story problems centered around the nursery rhyme, Jack and Jill. All the rhymes start with “Jack and Jill went up the hill to fetch (total number of pails of water). Jack carried (set number) of pails. How many pails did Jill carry?”
  • In Textbook B, Lesson 13.8 page 83, the Development section states, “Give each student linking cubes in two different colors. Tell the students to form a rod using two colors. Tell them they must use eight cubes altogether. Ask, 'How many cubes are there altogether? How many of them are red? How many of them are blue?'” This is the one opportunity students are provided for both addends in an unknown problem type.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
1/2
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Indicator Rating Details

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

All three aspects of rigor are present in program materials, but there is an under-emphasis on application.

  • Conceptual understanding and procedural skill are present in Textbook pages 42-43, Lesson 2.11, where students represent the numeral 4 in writing (K.CC.3). Students count the number of objects in a picture, trace and write the numeral 4. This the first time that students write the numeral 4, thus developing their understanding of numbers and the count sequence. At the same time, students are building procedural fluency as they practice counting the groups of objects in the pictures. (K.CC.5)
  • Conceptual understanding and procedural skill are present in Textbook, Lesson 13.6 page 79, students represent subtraction with objects and drawings. (K.OA.1) In the Teacher’s Guide, page 102, the teacher is directed to ask, “How many apples are there at first? How many apples does the boy eat? How many apples are there now?” After the Textbook activity, students build conceptual understanding of subtraction using buttons and paper plates. Students are also building procedural fluency with counting and the relationship between numbers and quantities. (K.CC.5, K.CC.4)
  • Procedural skill and fluency are attended to in Lesson 15.1, where students count to 100 by tens. (K.CC.1) In the Teacher’s Guide page 133, Textbook page 104, students are shown a hundreds chart. The teacher is directed to “have students count in tens as they point to the last number in each row.”

Materials under-emphasize application. Students are directed to use specific methods to solve problems. For example, in Teacher’s Guide, Lesson 12.2 pages 70 - 71, and Activity book pages 38 - 41, students are shown a picture of birds sitting on a wall and one more bird flying in to join the group. Students are prompted to “add by relating pictures to number bonds and addition equations.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
1/10
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Criterion Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for practice-content connections. The instructional materials partially identify the mathematical practices through Singapore’s Math Framework, but the instructional materials do not meet expectations for any of the other indicators within this criterion.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

Overall, the materials lack identification of several MPs. Additionally, there is no guidance provided as to how the MPs enrich the content.

  • MPs 6, 7, and 8 are not explicitly listed in the materials. However, in Unit 11, students are making use of structures and look for and express regularity in repeated reasoning by using number bonds.
  • Identification of MPs is located at the beginning of each lesson. There is no specific guidance within lessons around the MPs.
  • In the Teacher’s Guide, page vi of the introduction provides a correlation between Singapore’s Math Framework and the MPs.
  • Whole chapters address a particular MP. For example, Chapters 1 - 6 primarily address MP2, and Chapters 9 -15 primarily address MP1. Chapters 7, 12, 13, and 14 also address MP4, and Chapter 11 addresses MP5.

Students do have opportunities to engage with MP4 in Chapters 12, 13, and 14. For example, on Activity Book page 44, students solve this problem: “Two little dicky birds, sitting on a wall. Four more come to join them all. ____ birds all together.” Students are shown two birds in their book; they model the four that join and the total amount of birds.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2
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Indicator Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

  • In Teacher’s Guide, Lesson 2.4 pages 29-30, MP3 is identified. However, when following the lesson plan, there is no opportunity for students to “construct a viable argument or critique the reasoning of others.” Students are instructed to work with others in the conclusion of the lesson. The directions state, “Have students work in groups to create a story that has sets of 1, 2, 3, 4 and 5 objects. Students can then share or act out their story to the rest of the class.”
  • In Teacher’s Guide B, Lesson 11.2 page 49, MP1 and MP5 are listed in the Lesson Plans. When following the Lesson Plan, there is no opportunity for students to choose appropriate tools.
  • MP1 is identified in Lesson 9.1. Students are given few opportunities to make sense of problems on their own. In the Textbook, page 2, the teacher is instructed, “Direct students’ attention to the first triangle in the top row on Textbook, page 2. 'What number is 1 more than 3?' Have them count the dots in the next triangle to confirm the answer. Guide them to say, “1 more than 3 is 4.”
  • MP5 is identified in Chapter 11. In these lessons, students connect cubes and number bonds. The Teacher’s Guide does not identify opportunities for students to choose their own tools; rather, they are guided by the teacher and the drawings in the Textbook and Activity book to use specific tools. For example, in Teacher’s Guide, Lesson 11.3 page 51, and Textbook page 39, the teacher is directed, “Provide five linking cubes, two blue, and three red for each student. Have them use the cubes to show the number of lions and lionesses.” On Textbook page 39, students are shown two lions and three lionesses and a number bond that shows two connecting cubes in one part, three connecting cubes in the other part, and five connecting cubes in the whole.

Indicator 2g

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

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2
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Indicator Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The student edition textbook and activity book do not have questions or problems where students justify their conclusions, communicate them to others, and respond to the arguments of others. Many questions presented in the content elicit one answer.

There are few prompts for students to construct viable arguments.

  • MP3 is identified in Lesson 1.1. In this lesson, students compare objects to determine if they are the same or different (teacher edition page 3). The teacher is directed to “Show students the red and blue cup. Ask, ‘What can you tell me about these?’ Have students use their own words before modeling the language structure, ‘They are not exactly the same.’ Have students tell you why the cups are not exactly the same."
  • MP3 is identified in Teacher’s Guide A, Lesson 1.2 page 6. The teacher asks the question, “Are these the same?” In the conclusion, the students are to “tell their partner about objects in the classroom that are the same but are placed differently.”
  • MP3 is identified in Teacher’s Guide A, Lesson 1.5 pages 11-12. In Activity Book A, page 6, students choose one animal out of a line of four that is different from the others. Students are to give their reasons for their answers. Students explain their reason for picking an animal, but there is no mathematical reasoning required.
  • MP3 is identified in Teacher’s Guide, Lesson 7.7 pages 158-159. Students use sentence frames to compare the number of shoes in the picture. “Guide students to say, ’The number of shoes with buckles is greater/fewer than the number of shoes with laces.’ and ‘There are more/fewer shoes with buckles than shoes with laces.’” There is no evidence of students constructing a viable argument or critiquing the reasoning of others in this lesson.

Students are not given opportunities to look at another student’s work and critique their solution or strategy. There are also no opportunities for students to look at two samples of work and justify which is correct.

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.
0/2
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Indicator Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not 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.

Teacher directions do not include prompts to lead discussions around the construction of viable arguments or to analyze the arguments of others. Materials do not give opportunities for teachers to present problems to the class that require students to develop arguments.

  • Other than listing the Mathematical Practice in the beginning of these lessons, there is no other specific instruction to help the teacher engage students in constructing viable arguments or critique the reasoning of others.
  • Teacher’s Guide A, Lesson 1.1 page 3 lists MP3 as the Mathematical Practice focused on in the lesson. The directions in the Teacher’s Guide state, “Ask, ‘What can you tell me about these?’ Have students use their own words before modeling the language structure, ‘They are not exactly the same.’“ These questions do not lend themselves to students justifying their mathematical thinking.
  • Teacher’s Guide A, Lesson 1.5 pages 11-12 identifies MP3. “Teachers ask, ‘Are these two colored the same way?” Elicit the response, ‘No.'” Follow-up questions for teachers are not provided nor is there an opportunity for students to share their thinking.
  • Teacher’s Guide A, Lesson 2.5 page 31 identifies MP3. Students show five fingers then bend some fingers. Teachers are prompted to ask, “'Are all their fingers different? Do any of them have the same finger form?' Elicit responses from students using ‘same’ and ‘different.’” No prompts are provided for the teacher to lead the students in a mathematical discussion.
  • In Teacher’s Guide A, Lesson 8.10 page 180, students compare objects that are heavy and light. The teacher holds a dictionary in one hand and a pencil in the other. The teacher is prompted to, “Ask, ‘Which do you think is more difficult to carry?’ Say, ‘The dictionary is more difficult to carry. It is heavy.’ Guide students to say, ‘The dictionary is heavy.’ Say, ‘The pencil is easier to carry. It is light.’ Guide students to say, ‘The pencil is light.’" Students are prompted to give specific answers, and the teacher explains most concepts to the students.
  • In Teacher’s Guide B, Lesson 13.7 page 104, the teacher asks, “How many insects are there altogether? How many of them are red? How many of them are green?” There is no follow-up question that asks students to justify their reasoning.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
0/2
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Indicator Rating Details

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for attending to the specialized language of mathematics.

  • Materials do not always use accurate vocabulary. For example, in Teacher’s Guide, Lesson 8.9 page 179 and Student Materials page 186, students compare three bears using the terms big, bigger than, and biggest, and small, smaller than, and smallest. Another example can be found in Teacher’s Guide, Lesson 5.4 page 108. A rectangular prism is referred to as a rectangular block.
  • Vocabulary words are listed at the beginning of each lesson but are not always explained/used within the lesson. For example, in Teacher’s Guide, Lesson 8.2 page 165, students compare the length of objects using the terms short and long. The words length, long, and short are not explained within the lesson nor in the previous lesson. Workbook page 67, which corresponds to Lesson 8.2, uses the words height and tall, and these words are also not explained.
  • Vocabulary is not introduced in the chapters on addition and subtraction. Addition is introduced in Unit 11: Number Bonds. There is one vocabulary word included in this unit, which is number bond in theTeacher’s Guide, Lesson 11.3 page 51. Vocabulary such as add, addition, total, and sum are not included in the unit.
  • Unit 12 introduces students to equations and the + and = symbols. This is not labeled as vocabulary within the lesson plans or introduced to the students within the lesson plan script. There is one vocabulary word included in this unit within Lesson 12.5, number line on page 79.
  • Teachers Guide B, Unit 12, Lesson 1 page 67 states, “Have the students say, ‘2 and 3 make 5’ while you point at the numeral 2, then +, 3, and =. Hence, write the number 5 in the addition equation.“ Correct vocabulary is not shared with or explained to the students.
  • In Teacher’s Guide, Unit 13, Lesson 13.5 page 99, subtraction sign and subtraction equation are listed in the lesson plans. Instruction is not given to the teacher or students for these vocabulary words. Show students three balloons. Write the numeral '3' on the board. Have a student burst two balloons. Then, write the subtraction sign and ‘2’ to show ‘3-2’ on the board. Ask, “how many balloons are left? As you point to the remaining balloon. Finally, complete the subtraction equation to show 3 - 2 = 1

An example where vocabulary is introduced and explained is in Unit 5. Unit 5 introduces students to cubes, cones, rectangular blocks, spheres, cylinders, circles, rectangles, squares, triangles, and hexagons.

Gateway Three

Usability

Not Rated

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

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3z - 3ad

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

Indicator 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ad

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

Additional Publication Details

Report Published Date: 11/12/2018

Report Edition: 2014

Title ISBN Edition Publisher Year
Earlybird Kindergarten Mathematics Common Core Edition Textbook A 978-981-01-8976-1 Marshall Cavendish Education Pte Ltd 2014
Earlybird Kindergarten Mathematics Common Core Edition Textbook B 978-981-01-8977-8 Marshall Cavendish Education Pte Ltd 2014
Earlybird Kindergarten Mathematics Common Core Edition Activity Book A 978-981-01-9839-8 Marshall Cavendish Education Pte Ltd 2014
Earlybird Kindergarten Mathematics Common Core Edition Activity Book B 978-981-01-9840-4 Marshall Cavendish Education Pte Ltd 2014
Earlybird Kindergarten Mathematics Common Core Edition Teacher's Guide A 978-981-01-9851-0 Marshall Cavendish Education Pte Ltd 2014
Earlybird Kindergarten Mathematics Common Core Edition Teacher's Guide B 978-981-01-9852-7 Marshall Cavendish Education Pte Ltd 2014

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Math K-8 Rubric and Evidence Guides

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

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

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

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