Kindergarten - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
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 1.1: Focus
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 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 1.2: Coherence
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.
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.
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 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
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.
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.
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.
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.
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.