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 Everyday Mathematics 4 Kindergarten meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focus by assessing grade-level content and spend approximately 71% of instructional time on the major work of the grade. The instructional materials meet expectations for being coherent and consistent with the standards.
Criterion 1.1: Focus
The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assessing grade-level content. The instructional materials do not assess topics before the grade level in which they should be introduced.
Indicator 1a
The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assessing grade-level content. Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year.
Examples of aligned assessment items include but are not limited to:
- Beginning-of-Year Assessment, Item 6, “Give children a bag with 20 connecting cubes. Say, ‘Show me 5 cubes.’ Note whether children count out 5 cubes and the strategies they use to keep track of their counting. You may wish to repeat with other numbers of cubes (up to 20) until the task becomes too challenging.” (K.CC.5)
- Mid-Year Assessment, Item 1B, “Prompt children to count by 10’s. Stop them when they reach 100 or when their counting becomes erratic. Look for children to count by 10’s through 50.” (K.CC.1)
- End-of-Year Assessment, Item 15, “Give children a bag with 15 craft sticks and tell them how many sticks it contains. First ask them to predict how many bundles of 10 and how many single sticks they will have if they bundle the sticks in groups of 10. Then have them bundle the sticks in this way and write a number sentence to describe their grouping. Look for children to predict that they can decompose 15 into a group of 10 ones and 5 more ones and then bundle the craft sticks to show this decomposition. Also, look for them to record this grouping with an equation: 15 = 10 + 5 or 10 + 5 = 15.” (K.NBT.1)
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 Everyday Mathematics 4 Kindergarten meet expectations for spending the majority of time on major work of the grade. The instructional materials, when used as designed, spend approximately 71% of instructional time on the major work of the grade, or supporting work connected to major work 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 Everyday Mathematics 4 Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.
- There are 9 instructional sections, of which 7 sections address major work of the grade or supporting work connected to major work of the grade, approximately 78%.
- There are 117 lessons, of which 83 address major work of the grade or supporting work connected to the major work of the grade, approximately 71%.
- In total, there are 170 days of instruction (125 days of lessons and 45 flex days), of which 86 days address major work of the grade or supporting work connected to the major work of the grade, approximately 51%.
- Within the 45 Flex days, the percentage of major work or supporting work connected to major work could not be calculated because the materials suggested list of differentiated activities do not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.
The number of lessons devoted to major work is most representative of the instructional materials. As a result, approximately 71% 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 Everyday Mathematics 4 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 and content designated for one grade level that is viable for one school year. The instructional materials are partially consistent with the progressions in the standards, and the materials foster 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 Everyday Mathematics 4 Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Examples of supporting standards/clusters connected to the major standards/clusters of the grade include but are not limited to:
- In Lesson 1-2, Focus: Exploring Pattern Blocks, students are introduced to 6 pattern blocks. The teacher asks, “How many sides does the square have? Name or point to another shape with four sides. Do all the shapes with fours sides look the same?” This connects supporting standard K.G.2, “Correctly name shapes regardless of their orientations or overall size,” to the major work of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
- In Lesson 2-7, Focus: Solving the Open Response Problem, students sort a collection of items according to attributes into different categories and then count the items. This connects the supporting work of K.MD.1, “Describe measurable attributes of objects, such as length and weight. Describe several measurable attributes of a single object,” to the major work of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
- In Lesson 3-1, Focus: Graphing Pattern Blocks, students sort pattern blocks into different categories and then compare the categories by answering questions involving fewer and greater. This connects the supporting work of K.MD.3, “Classify objects into given categories; count the numbers of objects in a category,” to the major work of K.CC.6, “Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.”
- In Lesson 4-1, Focus: Exploring Attribute Blocks, students classify and sort attribute blocks by their shape and size and count and compare the number of blocks in each group. This connects the supporting work of K.MD.3, “Classify objects into given categories; count the numbers of objects in a category” and K.G.2 “Correctly name shapes regardless of their orientations or overall size,” to the major work of K.CC.6, “Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.”
- In Lesson 9-4, Focus: Measuring and Comparing Backpacks, students compare the heights of two different backpacks using connecting cubes to measure. This connects the supporting work of K.MD.1, “Describe measurable attributes of objects, such as length and weight. Describe several measurable attributes of a single object,” to the major work of K.CC.7, “Compare two numbers between 1 and 10 presented as written numerals.”
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 reviewed for Everyday Mathematics 4 Kindergarten meet expectations that the amount of content designated for one grade level is viable for one year.
Recommended pacing information is found on page xxii of the Teacher’s Lesson Guide and online in the Instructional Pacing Recommendations. The instructional materials include pacing for 170 days of instruction:
- There are 9 instructional sections with 117 lessons. Beginning in Section 2, Open Response/Reengagement lessons require 2 days of instruction adding 8 additional lesson days.
- There are 45 Flex Days that can be used for lesson extension, extra game time, differentiation, or connection activities; however, explicit teacher instructions are not provided.
- There are 3 embedded face-to-face assessments, Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment, spanning multiple days.
The materials note that lessons are 45-60 minutes and consist of 3 components: Daily Routine: 10-15 minutes; Core Activity: Focus; 20-30 minutes; and Core Activity: Practice: 10-15 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 reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for being consistent with the progressions in the Standards. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades, but there are some lessons that contain content from future grades that is not identified as such. There are also standards for which the materials do not present extensive work.
The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past”. This section describes “how standards addressed in the Focus parts of the lessons link to the mathematics that children have done in the past.” Examples include:
- Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Past” for K.CC.1, “In PreK, children learned and practiced the count sequence through 10 (and beyond as ready) through playful counting games, songs, and movement activities.”
- Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Past” for K.OA.1, “In Pre-K, children represented addition and subtraction by acting out number stories either physically or concretely with manipulatives.”
- Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Past” for K.MD.1, “Children described lengths of objects in Kindergarten lessons 1-1 and 3-5. In Pre-K, children used the terms big and small to describe measurable attributes and began to learn about different size dimensions, such as length and weight.”
- Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Past” for K.NBT.1, “Children informally explored numbers 11 through 20 earlier in Kindergarten and in PreK, through various oral and rational counting activities.”
- Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Past” for K.G.3, “In PreK, children explored both 2-dimensional and 3-dimensional shapes in a variety of tactile, kinesthetic, and visual ways.”
The instructional materials relate grade-level concepts with work in future grades. Each Section Organizer contains a Coherence section with “Links to the Future”. This section identifies what students “will do in the future.” Examples include:
- Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Future” for K.CC.1, “Children will continue to extend their knowledge of the count sequence across the year through a variety of oral counting activities and as they count objects in sets of increasing sizes. They will learn to count by 10s beginning in Section 4. In Grade 1, they will extend their knowledge of the oral count sequence to at least 120.”
- Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Future” for K.OA.2, “Throughout the year, children will solve addition and subtraction problems within 10 in a variety of contexts, including number stories, domino and dice games, as well as other activities. In Grade 1, children will model and solve problems involving addition or subtraction of two numbers within 20.”
- Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Future” for K.MD.1, “In Kindergarten Sections 4 through 9, children will practice observing and describing an object's length, weight, and capacity, as well as describing several measurable attributes of a single object. In Grade 1, children will quantify length measurements as the number of same-size units that span a distance.”
- Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Future” for K.NBT.1, “In Section 5, children compose and decompose numbers 11 through 19 on double ten frames and with partners using two pairs of hands. In Sections 7 and 8, they record these types of decompositions with drawings and equations. In Grade 1, children will apply this concept as they extend their understanding of place value to include all 2-digit numbers.”
- Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Future” for K.G.3, “In Section 6, children learn the difference between 2- and 3-dimensional shapes as they assemble and analyze objects for the Solid-Shapes Museum, and stamp different 2-dimensional faces of 3-dimensional shapes onto paper. They will continue to explore and compare 2-D and 3-D shapes, and the relationships between them, as they play Solid-Shapes Match Up in Section 7 and as they create both 2-D and 3-D shapes from marshmallows and toothpicks in Section 8.”
In some lessons, the instructional materials contain content from future grades that is not clearly identified as such. Examples include:
- Lesson 4-3, Focus: Graphing Favorite Colors, “Model how to label the axes on the graph with the color names and a number of children who chose the color as their favorite. Explain that this is sometimes called a bar graph, and ask why it might have that name.” Students can choose from 6 colors, making 6 categories on the graph. This lesson is labeled K.MD.3, “Classify objects into given categories; count the number of objects in each category and sort the categories by count.” Using a bar graph with up to three categories is a Grade 1 standard (1.MD.4, “Organize, represent, and interpret data with up to three categories…”)
- In Lesson 5-6, Practice: Solving Number Stories, students solve problems in their journals. Sample problem, “I saw some children swinging. One more child joined them. Then there were 9 children swinging. How many children were swinging at the beginning?” This lesson is labeled K.CC.5, “Count to answer ‘how many’ questions.” Starting with an unknown in a problem-solving situation is a Grade 1 standard (1.OA.1, “Use addition and subtraction within 20 to solve word problems with unknowns in all positions”).
- In Lesson 5-9, Focus: Introducing the Equal Symbol, students use their fingers to show different representations of the numbers 3, 4, and 5. The teacher is instructed to “Introduce the word equal as a way to describe two quantities that are the same. Explain that there is also a symbol that means equal. Write the word equal, draw the equal symbol on the board, and have children make the symbol using two fingers on opposite hands. Explain that this means that the total on both sides of the symbol is the same: 5 is equal to 5. Mention that another way to say equal symbol is equal sign.” This lesson is labeled as K.CC.5, “Count to answer ‘how many’ questions”; K.CC.6, “Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group”; and K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.” Understanding the meaning of the equal sign and determining if equations involving addition and subtraction are true or false is aligned to a Grade 1 standard (1.OA.7, “Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false”).
- In Lesson 9-4, Focus: Measuring and Comparing Backpacks, students use connecting cubes to measure the height and width of their backpack and that of a partner. The teacher is prompted to, “introduce the term area as the amount of flat space that is taken up by the front, the back surface, or side, of the backpack. Explain that children can trace the outline of a backpack on large paper to help them see and compare the area of one side. Ask: Which backpack takes up more space (has a larger area)?” This lesson is labeled K.MD.1, “Describe measurable attributes of objects such as length or weight.” Recognizing area as an attribute of plane figures and understand concepts of area measurement is a Grade 3 standard (3.MD.5, “Recognize area as an attribute of plane figures and understand concepts of area measurement”).
The instructional materials do not present sufficient opportunities to meet the full intent of standards K.NBT.1 and K.G.5. Examples include:
- K.NBT.1, “Compose and decompose numbers from 11 to 19 into ten ones and some further ones,” is addressed in the Focus section of Lessons of 5-6, 5-8, 7-3, 8-6, and 8-13. K.NBT.1 is also embedded in Routine 1: Number of the Day, where students track the number of days in school on a Growing Number Line, and represent the number of the day with objects. These opportunities are not sufficient for students to meet the full intent of K.NBT.1.
- K.G.5, “Model shapes in the world by building shapes from components,” is taught in the Focus section of lessons 3-3, 5-4, 8-2, 9-7, 9-12, and 9-13.
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 reviewed for Everyday Mathematics 4 Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.
Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Focus and Supporting Clusters addressed in each section are found in the Table of Contents, the Focus portion of each Section Organizer, and in the Focus portion of each lesson. Examples include:
- Lesson 1-9, Focus: Representing 5 is shaped by K.OA.A, “Understand addition as putting together and adding to, and subtraction as taking apart and taking from.” The featured number of the day is 5. Students show different ways to represent 5.
- Lesson 2-8, Focus: Getting to Know Circles is shaped by K.G.A, “Identify and describe shapes.” Students look at a circle and describe its attributes; they then look around the room to find other circles.
- Lesson 5-1, Focus: Celebrating the 100th Day is shaped by K.CC.A, “Know number names and the count sequence.” Students share and compare the collections of 100 they brought to school.
- Lesson 6-2, Focus: Ordering Straws by Length is shaped by K.MD.A, “Describe and compare measurable attributes.” Students work with a partner to order a set of 5 straws by length.
- Lesson 8-6, Focus: Bundling Craft Sticks is shaped by K.NBT.A, “Work with numbers 11-19 to gain foundations for place value.” Students take 15 craft sticks and bundle them into a group of 10 and a leftover group of 5.
The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:
- In Lesson 1-8, Focus: Making an Age Graph, students practice counting the number of students in different age groups and then discuss which line has more and less people. K.CC.A, “Know number names and the count sequence” is connected to K.CC.C, “Compare numbers.”
- In Lesson 2-9, Focus: Exploring Ten Frames, students represent 10 and 5 counters on a ten frame and share their representations. K.CC.B, “Count to tell the number of objects” is connected to K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
- In Lesson 2-12, Practice: Revisiting Shape Collages, students sort shape cards onto the proper collage and describe their sorting attributes. Cluster K.G.A, “Identify and describe shapes” is connected to K.G.B, “Analyze, compare, create, and compose shapes.”
- In Lesson 3-2, Focus: Finding Combinations of Ten, students use two-colored beans to fill in a ten frame, and then color a ten frame to match the combination. K.CC.B, “Count to tell the number of objects” is connected to K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
- In Lesson 4-1, Focus: Exploring Attribute Blocks, students work in groups to describe the blocks and then sort them. Cluster K.MD.A, “Describe and compare measurable attributes” is connected to K.MD.B, “Classify objects and count the number of objects in each category.”
- In Lesson 5-8, Focus: Playing Teens on Double Ten Frames, students take turns spinning on a 10-20 Spinner and placing the number of counters on their double ten frame. Students compare their double ten frames and the student with the largest number wins the round. K.CC.C, “Compare numbers” is connected to K.NBT.A, “Work with numbers 11-19 to gain foundations for place value.”
- In Lesson 6-9, Focus: Playing Disappearing Train, students roll a subtraction die marked with -1, -2, and -3. Students roll the die and use a snap cube train to take away the matching number of cubes. K.CC.B, “Count to tell the number of objects” is connected to K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
- In Lesson 8-2, Focus: Modeling Shapes, students create 2-D and 3-D shapes with toothpicks and marshmallows. K.G.B, “Analyze, compare, create, and compose shapes” is connected to K.MD.A, “Describe and compare measurable attributes.”