Kindergarten - Gateway 1

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that they assess grade-level content. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The series is divided into topics with an assessment for each topic that can be delivered online and/or paper and pencil, and a topic performance assessment. Additional assessments include a Kindergarten Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-11, and 1-14. Assessments can be found in the Assessment Resource Book online or in print. The materials also include an ExamView Test Generator. Examples of grade-level assessment items include:

• Topic 1, Performance Task, Item 1, “Karen’s family sells fruit from a fruit cart. Have students count how many of each kind of fruit, and then write the numbers to tell how many.”  (K.CC.3, K.CC.5)
• Topic 3, Topic  Assessment, Item 5, students “Read the number (9) and then draw toys to show how many.” (K.CC.4)
• Topics 1-4, Cumulative  Assessment, Item 13, “Joanie has 2 toy bears and 4 toy lions. Color the cubes to show how many of each type of toy and then draw a circle around the cube train that is greater than the other cube train.”  Students are given a picture with 2 bears and 4 lions. Next to each group of animals is a train of 5 cubes to be colored to match the number of animals. (K.CC.5, K.CC.6)
• Topic 8, Topic Assessment, Item 2, “Count the fruits, draw counters to show how many more fruits are needed to make 10, and write the number that tells how many.”  (K.OA.4)
• Topic 9, Topic Assessment, Item 2, students identify which of the 4 pictures shown, has 12 feathers. (K.CC.5)
• Topic 10, Topic Assessment, Item 5, students view the number 14 and a double ten frame with 10 counters in the top frame. Students “draw counters to make 14, and then complete the equation to match the picture.” (K.NBT.1)

Examples of above grade level assessment items that could be modified or omitted:

• Topic 11, Topic Assessment, Item 2, students count 78 beads and choose the correct answer from the following choices: 78, 79, 88, and 89.  In K.CC.1, students count to 100, but they do not have to recognize the standard form of the number (1.NBT.1).
• Topic 14, Topic  Assessment, Item 5 , students are shown a picture of a fishbowl with 1 connecting cube beside it and asked to “find about how many cubes high the fish bowl is.”  (The fishbowl appears to be equivalent in height to 2 cubes.) Students choose the correct answer from the following choices: 1, 2, 4, and 6. (1.MD.2)
• Topics 1-14 Cumulative/Benchmark Assessment, Item 15, students “Mark all the objects that can be measured with the tool shown.” The tool shown is a measuring cup. In Kindergarten, the focus of standard K.MD.1 focuses on describing measurable attributes such as length or weight, not to identify a tool to use to find an exact measurement.

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. The evidence was collected from Topics, Performance Tasks, Topic Assessments, Benchmarks, Centers, and 3-Act activities.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 10 out of 14, which is 71%. 
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 73 out of 96, which is approximately 76%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 108 out of 145, which is approximately 74%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 76% of the instructional materials focus on major work of the grade.

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work in the Topic Planner pages in the Teacher Edition. For example:

Topic 5 addresses supporting standard K.MD.3 (classify objects and count the number of objects in each category) connected to the major work of standards K.CC.5 (count to answer “how many?” questions), K.CC.C (compare numbers).

• Lesson 5-1, Solve and Share, students solve, “Carlos’s kindergarten class is having a pet fair. The pets need to be put into two tents. One tent is for pets with 4 legs. The other tent is for pets that do NOT have 4 legs. Draw pictures of 5 pets. How many animals are in the 4 legs tent? How many animals are in the NOT 4 legs tent?” Students count the number of animals in each category, and the number of legs on each animal. (K.CC.5)
• Lesson 5-2, Solve and Share, students are shown a picture of animals on the ground and not on the ground. Students answer, “How many creatures does he see on the ground? How many does he see that are NOT on the ground? Tell how you know you counted all the creatures.”  After counting the creatures in each group, students write the numeral to represent that quantity. (K.CC.5)
• Lesson 5-3, Independent Practice, Item 5, students look at a picture of pencils of different lengths and “Sort the pencils into pencils that are short and pencils that are NOT short, and then write numbers in the chart to tell how many.” Students then draw a circle around the category that has greater in number of pencils, and tell how they know. (K.CC.C)
• Lesson 5-4, Share and Solve, students view a picture of blue, yellow, and green cubes and solve, “Carlos says that the number of blue cubes is equal to the number of cubes that are NOT blue. Does his answer make sense?” Using a counting strategy, students decide if the groups are equal and explain their reasoning using numbers, pictures, or words. (K.CC.6)

Topic 13 addresses supporting cluster K.G.B (analyze, compare, create and compose shapes) which is connected to major work of K.CC.B (count to tell the number of objects), 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.CC.3 (represent a number of objects with a written numeral 0 - 20). 

• Lesson 13-1, Solve and Share, students compare shapes and count the number of sides and vertices of each shape. Students classify the shapes into a group that has 4 vertices and a group that does not have 4 vertices. They count the shapes in each group, write the numbers, and circle the greater number. (K.CC.6, K.CC.3)
• Lesson 13-5, Guided Practice, Items 2 and 3, “Have students use the pattern block shown to cover the shape, draw the lines, and then write the number tells how many pattern blocks to use”.  Item 4, “Have students use the pattern blocks shown to create the fish, and then write the number that tells how many of each pattern block to use.” (K.CC.5)
• Lesson 13-6, Teacher Edition, Guided Practice, students use yarn, pipe cleaners, or straws to make a square and a shape that is not a square. They explain why the second shape is not a square. (K.CC.5)

The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. 

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 145 days. Teacher’s Edition Program Overview p.22, “Each core lesson, including differentiation, takes 45-75 minutes.” 

Kindergarten includes 14 topics. Each Topic is broken down into lessons which include additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment (Teacher’s Edition Program Overview, page 22). For example:

• There are 96 Content focused lessons. 
• There are 14 days of Topic Centers 
• There are 7 days for 3-Act Math activities 
• There are 28 days of Topic Reviews and Assessments

Additional Resources that are optional and not counted in the program days include:

• Math Diagnosis and Intervention System
• 10 Step-Up to Grade 1 Lessons to use after the last topic
• Readiness Test; Review What You Know; Cumulative/Benchmark Assessment (4 in all); Progress Monitoring Assessment Forms A, B and C (3 in all)

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet the expectations for being consistent with the progressions in the standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems.

The materials develop according to the grade-by-grade progressions in the standards. The Teacher Edition contains a Topic Overview Coherence: Look Back and Look Ahead, and a Lesson Overview Coherence: Look Back and Look Ahead, which identify connections to content taught in previous grades, indicating the relevant topics and/or lessons. In addition, the sections include connections to content taught in future grades, topics, or lessons. For example: 

The Topic 3, Numbers 6 to 10 Topic, Overview, Coherence:

• Look Back, “In Topic 1, students counted quantities of 1 to 5 objects in different arrangements.  They recognized that each successive number name is one greater, and learned that the last number name in the counting sequence answers the “how many” question.”
• In Topic 3, “The numbers 6-10 are introduced in order, thus reinforcing the understanding students acquired previously that each successive number name refers to a quantity that is one greater.”
• Look Ahead - Later in Kindergarten, “In Topics 9 and 11, students will extend the counting sequence and count to 20 and then 100 using most of the same principles and processes that were incorporated in Topic 3.”
• Look Ahead - Grade 1, students will “relate counting to addition. In Topics 2, 3 and 4, students will use counting on and counting back as strategies for adding and subtracting within 20.”

The lessons support the progression of Kindergarten standards by explicitly stating in the Lesson Overview connections between prior lessons, the current lesson, and future lessons. For example: 

• In Lesson 4-2, the Lesson Overview Look Back, This Lesson, and Look Ahead, “In Lesson 4-1, students used a matching strategy to compare groups of up to 10 objects.” In this lesson, “Students continue to match objects, then also compare the corresponding numbers. In the next lesson, students compare groups of objects by counting.”
• In Lesson 7-1, the Lesson Overview Look Back, This Lesson, and Look Ahead, “Students learned the foundations of addition in Topic 6. In this lesson, students explore various ways to represent subtraction. Later in this Topic, students will use subtraction sentences and equations to represent subtraction.”
• In Lesson 13-2, the Lesson Overview Look Back, This Lesson, and Look Ahead, “In Topic 12, students learned to identify spheres, cylinders, cones, and cubes, and to find objects that have those shapes in the environment. In this lesson, students learn that some attributes of solid figures give objects the ability to roll, stack, or slide. In Lesson 13-3, students will compare 2-D and 3-D shapes.”

The instructional materials support the progressions of grade-level standards, as evidenced by the sequencing of the topics in the curriculum. For example, in developing number concepts:

• Counting and Cardinality clusters are addressed in Topic 1: Numbers 0 to 5; Topic 2: Compare Numbers 0 to 5; Topic 3: Numbers 6 to 10; Topic 4: Compare Numbers 0 to 10;  Topic 9: Count Numbers to 20; and Topic 11: Count Numbers to 100. These concepts are also supported in Topic 5: Classify and Count Data.
• Operations and Algebraic Thinking is addressed in Topic 6: Understand Addition; Topic 7: Understand Subtraction; and Topic 8: More Addition and Subtraction.
• Number & Operations in Base Ten is addressed in Topic 9: Count Numbers to 20 and Topic 10: Compose and Decompose Numbers 11-19.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to the Independent Practice. During Independent Practice, students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example:

• Lesson 2-4, Solve and Share, students solve, “Maria builds a tower with red and blue blocks. Count how many red blocks and how many blue blocks she uses. Write the numbers to show how many. Then draw a circle around the number that is less than the other.” (K.CC.6, K.CC.3, K.CC.5)
• Lesson 4-3, Solve and Share, students solve, “The class aquarium has two kinds of fish, goldfish and tetras. Place counters on the fish as you count how many of each kind. Write numbers to tell how many of each kind. Draw a circle around the fish that has a number greater than the other. Tell how you know you are right.” (K.CC.6,  K.CC.2, K.CC.7)
• Lesson 6-6, Solve and Share, students solve, “Daniel’s teacher is making name tags for her students. She makes 3 name tags for boys. She makes 2 more for girls. Now she has 5 name tags. How does Daniel’s teacher know that she has made 5 name tags? Explain and then show how you know.” (K.OA.2, K.OA.1)
• Lesson 10-1, Guided Practice, Problem 2, students find, “How many?” Students have 11 cubes and use ten frames to find 10 + 1. (K.NBT.1, K.CC.5)

There are two instances where the materials engage students with above grade level work:

• Lesson 14-1, Guided Practice, Problem 6, students compare the lengths of two rulers with the first ruler shown vertically and the second ruler shown on a diagonal. Students are unable to do direct comparison because the objects are not lined up beside each other. This exercise goes beyond directly comparing two objects (K.MD.2) and aligns to 1.MD.1, order three objects by length; compare the lengths of two objects indirectly by using a third object.
• Lesson 14-4, Solve and Share, students see two trays. One has a measuring cup on it, and the other has a train of 6 connecting cubes. Students think about the measuring cup and the train of connecting cubes, as they answer the questions, “What can you measure with the cup? What can you measure with the cube train?” Choosing appropriate tools aligns to 2.MD.1. In kindergarten, students “directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference.” (K.MD.2)

The Topics and Lessons support the progression of Kindergarten standards by explicitly stating connections between prior grades and current grade level work. Each topic contains a Math Background: Coherence document with Look Back narratives that identify connections to what students learned before entering school and concepts previously learned in Kindergarten. 

• Topic 3, Numbers 6-10, Coherence: Look Back, “Earlier in Kindergarten, Count 1 to 5 in Topic 1, students counted quantities of 1 to 5 objects in different arrangements. They recognized that each successive number name is one greater, and learned that the last number name in the counting sequence answers the “how many” question.”
• Lesson 4-3, Coherence: Look Back: “In Lesson 4-2 students wrote numbers to compare groups of up to 10 objects that are aligned.”
• Topic 5, Coherence: Look Back section explains that before entering school most “students have been finding similarities and differences in objects and classifying objects from a very young age.” It also relates to earlier in Kindergarten lessons on counting and comparing 0 - 10.
• Lesson 12-7, Coherence: Look Back, “Previously in this topic, students learned shape and positions words for naming and describing two- and three-dimensional shapes.”

​The instructional materials reviewed for enVision Mathematics Common Core Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• Topic 2, Lessons 2-2, 2-3, and 2-5, Lesson Objectives, “Tell whether one group is greater in number than another group,” “Tell whether one group is less in number than another group,”  and “Use objects, drawings and numbers to compare numbers” respectively. These objectives are shaped by K.CC.C Compare Numbers.
• Topic 6, Lessons 6-2 and 6-3, Lesson Objectives, “Represent addition as adding to a number” and “Represent addition as putting two or more numbers together,” respectively. These objectives are shaped by K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
• Topic 12, Lessons 12-2 and 12-5, Lesson Objectives, “Identify and describe circles, and triangles” and “Describe and identify solid figures,” respectively.  These objectives are shaped by K.G.A, Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres.)

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important. For example:

• Topic 3, Lesson 3-2, Guided Practice, Problem 5, connects K.CC.B, “Count to tell number of objects” to K.CC.A, “Know number names and the count sequence”. Students view a picture of seven sailboats. They “count the objects, and then practice writing the number that tells how many.”
• Topic 4, Lesson 4-2, Independent Practice, Problem 4, connects K.CC.A, “Know number names and the count sequence”, to K.CC.B, “Count to tell the number of objects”, and to K.CC.C, “Compare numbers.” Students view a picture of ten corn seed packets and seven tomato seed packets. They count the number of objects in each group, write the corresponding numbers to tell how many, and identify the number that is less than the other number by crossing it out.
• Topic 10, Lesson 10-3, Guided Practice, Problem 4, connects K.NBT.A, “Work with numbers 11-19 to gain foundations for place value” to K.CC.A, “Know number names and the count sequence.” Students view a picture of a group of ten connected cubes and a group of seven unconnected cubes. They “write an equation to match the counters” and “tell how the picture and equation show 10 ones and some more ones.