Kindergarten - Gateway 1

The materials reviewed for enVision Mathematics Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Above-grade-level assessment items are present but could be modified or omitted without significantly impacting the underlying structure of the instructional materials.

The series is divided into topics that include a Topic Assessment, available for online and/or paper and pencil delivery, and a Topic Performance Task. Additional assessments include a Kindergarten Readiness Test; Basic-Facts Timed Tests; four Cumulative/Benchmark Assessments addressing Topics 1–4, 1–8, 1–11, and 1–14; and Progress Monitoring Assessments A–C. Assessments can be found in the digital teacher interface and the Assessment Sourcebook online or in print. The materials include an ExamView Test Generator allowing teachers to build customized tests.

Examples of items that assess grade-level content include:

• Topic 8, Assessment, Problem 2, “Directions Have Students: count the fruits, draw counters to show how many more fruits are needed to make 10, and write the number that tells how many.” A picture of eight pears is provided. (K.OA.4)

• Topic 10, Assessment, Problem 5, “Directions Have students: draw counters to make 14, and then complete the equation to match the picture.” Students engage with two ten-frames, with 10 counters in the top frame with the bottom frame empty, and the equation 14 = __+__ . (K.NBT.1)

• Topic 12, Performance Task, Problem 1 presents images such as a basketball, a trash can, a crate, and a pennant. Students identify shapes by drawing circles around objects that look like cylinders and marking an “X” on other objects that look like spheres. Problem 1, “Directions Carnival Time! Say: Miguel and his friends go to a carnival. Have Students: 1 draw a circle around the objects that look like a cylinder. Then have them mark an X on the objects that look like a sphere.”  Students view images of a megaphone, soccer ball, crate, bottle, cone, empty cage,  trash can, and basketball. (K.G.2)

• Topics 1–4, Cumulative/Benchmark Assessment, Problem 13, “Directions Say: 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 view images of two bears and four lions and engage with two five-cube trains. (K.CC.5 and K.CC.6)

Examples of above grade-level assessment items that could be modified or omitted include, but are not limited to:

• Topic 11, Assessment, Problem 2, students count 78 beads and choose the correct answer from the following choices: 78, 79, 88, and 89. This question requires students to recognize the standard form of the number. (1.NBT.1)

• Topics 1–14, Cumulative/Benchmark Assessment, Problem 15, “Directions Have students: mark all the objects that can be measured with the tool shown.” This question requires students to identify a tool to find an exact measurement. (2.MD.1)

The materials reviewed for enVision Mathematics Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The 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. During Independent Practice, students work with problems in various formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• In Topic 3, Lessons 3-1 and 3-5 and Topic 9, Lessons 9-3 and 9-4, students engage in extensive work with grade-level problems to meet the full intent of K.CC.5 (Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects). In Lesson 3-1, Quick Check, students count out a specified number of objects. Problem 1 asks, “Which shows 6 muffins?” Pictured are four choices of rows of muffins. Problem 4 asks, “Which shows 7 balls?” Pictured are four choices of rows of balls. In Lesson 3-5, Enrichment, students count how many birds, nests, apples, flowers, bees, and skunks up to 10. “Directions Have children count each item in the nature picture and draw counters to show how many of each item.” Pictured is a nature scene with scattered images of the above-mentioned items. In Lesson 9-3, Guided Practice, Problems 1 and 2 students count two groups of piggy banks up to 16 and 17, respectively. “Directions 1 and 2 Have students count the piggy banks in each group; use cubes to show how many, and then practice writing the number that tells how many.” Provided is a picture of 16 piggy banks in a rectangular array and 17 piggy banks in a row. In Lesson 9-4, Reteach to Build Understanding, Problem 2, students count fish up to 19. “Directions Say: 2. Let’s count the fish. There are 19 fish. Practice writing the number 19.” Pictured are 19 fish arranged in a circle. 

• In Topics 6 and 7, students engage in extensive work with grade-level problems to meet the full intent of K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations). In Topic 6, Lesson 6-1, Solve & Share, students look at pictures and use counters/fingers to represent addition. “Carlos is thinking about some flowers he picked. Use counters to show how many pink and purple flowers he picked. How many flowers did he pick in all? Think about the problem. Write the number that tells how many. Then use your fingers to show how you know.” In Lesson 6-4, Reteach to Build Understanding, Problem 1, students represent addition using equations. “Directions Say: 1. When you add two groups, you can write an addition sentence that tells how many in all. You can use the plus sign and equal sign to write an addition equation. 3 and 5 is 8 can be written as 3 + 5 = 8. Circle the plus sign and the equal sign.” In Topic 7, The Animated Math Story: Where’s My Fish?, students reason about subtraction given a story. “Zak has 4 fish. Maria wants a fish. So Zak gives her 1 fish. Now Zak has ___ fish.” In Lesson 7-7, Visual Learning Bridge, Problem 2, students use tools to solve subtraction problems posed with a story. “Directions Have students listen to each story, use a tool to help them solve the problem, and then write the equation. Then have them explain whether or not the tool they chose helped to solve the problem. 2. Marta sees 7 seagulls. 4 fly away. How many seagulls are left?”

• In Topics 6 and 7, students engage in extensive work with grade-level problems to meet the full intent of K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10). In Topic 6, Lesson 6-5, Guided Practice, Problems 3 and 4, students use or make pictures to represent word problems and to write addition equations that represent how many in all. “Directions Have students listen to the story, use counters to show the addition, look at or draw a picture, and then write an equation to tell how many in all. 3. 5 squirrels are looking for food. 4 more join them. How many squirrels are there in all? 4. There is 1 turtle on the beach. 5 more walk up. How many turtles are there in all?” Problem 3 provides pictures of the squirrels; Problem 4 provides blank space for student drawings. The worksheet includes a two-lined paper image to guide students' writing and circles to enclose the + and = symbols. In Topic 7, Lesson 7-5, Independent Practice, Problems 7 and 8, students use or make pictures to represent word problems and to write subtraction equations that represent how many are left. “Directions Have students listen to each story, draw a picture to show what is happening, and then write an equation. 7. There are 5 acorns under a tree. A squirrel takes 3 of them. How many acorns are left? 8. Higher Order Thinking Have students listen to the story, draw a circle around the picture that shows the story and tell why the other picture does NOT show the story, and then write an equation. There are 4 ducks in a pond. 1 leaves. How many ducks are left?” Problem 7 provides blank space for student drawings; Problem 8 provides pictures of 9 ducks with an X through 1 duck. The worksheet includes two-lined paper images to guide students’ writing and circles to enclose the + and = symbols.

• In Topic 14, Lessons 14-1 through 14-3, and Lesson 14-5, students engage in extensive work with grade-level problems to meet the full intent of K.MD.1 (Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object). In Lesson 14-1, Independent Practice, Problems 7 and 8, students compare the lengths of two objects to determine which item is longer, shorter, or the same length. “Directions 7 and 8 Have students mark an X on the shorter object and draw a circle around the longer object, or underline the objects if they are the same length.” Provided is a picture of two wrenches and two sneakers. In Lesson 14-2, Additional Practice, Problem 1, students compare objects based on their capacity. “Directions Say: Which bowl holds more? How do you know? Draw a circle around it. Then mark an X on the bowl that holds less. 1. Have students draw a circle around each container that holds more and mark an X on each container that holds less, or underline the containers if they hold the same amount.” Provided is a picture of a room with two buckets below a table, two jars on a table, and two watering cans on a shelf above the table. In Lesson 14-3, Reteach to Build Understanding, Problem 1, students compare items based on weight. “Directions Say: 1. You can use the words same, lighter and heavier to compare how much objects weigh. Look at the apples. Do you think 1 apple is heavier than a basket of apples? Draw a circle around the object you think is heavier. Mark an X on the object that is lighter.” Pictured are a picture of a single apple and a basket of apples. In Lesson 14-5, Guided Practice, Problems 2 and 3, students describe attributes that can be measured. “Directions Have students look at the objects on the left and identify the attributes that can be measured. 2-3 Then have students mark an X on the object that holds less or underline both objects if they can hold the same amount. Say: Which tool can you use to tell about how much the objects hold? Circle this tool. ” Problem 2 shows a bucket and a yellow wagon on the left and a scale and a measuring cup on the right.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for that, when implemented as designed the majority of the materials address the major clusters of each grade. The materials devote at least 65% of instructional time to the major clusters of the grade.

• 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 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 materials focus on the major work of the grade.

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

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher’s Edition, Lesson Overview, Coherence, Cross-Cluster Connections on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed in a document titled “Scope and Sequence.” Examples of connections include:

• Topic 5, Lesson 5-2 connects the supporting work of K.MD.B (Classify objects and count the number of objects in each category) to the major work of K.CC.B (Count to tell the number of objects). In the Visual Learning Bridge, students count objects in a category and sort categories by count. Pictured are images of small creatures: bees, a ladybug, caterpillars, millipedes, and spiders. Classroom Conversation asks students the following questions: “A) What do you see? Which creature has 6 legs? Which has 8 legs? This creature has lots of legs. Does it have more than 6 legs? B) Which category does this show?” Guided Practice, “Directions 1 Have students draw lines in the chart as they count the animals that are in the pond and the animals that are NOT in the pond, and then write the numbers to tell how many in another chart.” A picture of a field is shown with various animals in and out of the pond.

• Topic 12, Lesson 12-2 connects the supporting work of K.G.A (Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)) to the major work of K.CC.A (Know number names and the count sequence). In Solve & Share, students find objects that resemble circles and triangles. “Go on a shape hunt. Find objects in the classroom or outside that look like the shapes shown. Which objects did you find? How are they different? Draw the objects you find in the space below.” In the Visual Learning Bridge, students continue to distinguish between circles and triangles and describe the shapes by their attributes. In addition, students count the sides of the triangle and vertices of the triangle to determine the shape. The teacher asks students the Essential Question, “How do you tell the difference between a circle and a triangle?” Students are shown a visual picture of a girl tracing a circle (Picture A), holding a flying disc (Picture B), tracing a triangle (Picture C), and pointing to a sail on a sailboat (Picture D). Classroom Conversation asks students the following questions: “A) Emily is tracing a shape called a circle. What does a circle look like? B) What is Emily holding? What shape is the flying disc? C) Emily is tracing a shape called a triangle. What does a triangle look like? D) What shape is Emily pointing to on the sailboat? How do you know?” 

• Topic 13, Lesson 13-4 connects the supporting work of 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 and other attributes) to the major work of K.OA.4 (For any number from 1 to 9, find the number that makes 10 when added to the given number). In the Solve & Share, students are given images of ten two- and three-dimensional shapes of different sizes and orientations, students sort shapes into two categories: flat and solid. “ Directions Say: Jackson wants to put flat shapes behind Door 1 and solid figures behind Door 2. Draw a line from each shape to the correct door to show how he should sort the shapes. Count all the shapes on the shelves. Then cover one door. Count the number of shapes that are behind the door you can see. Without counting any shapes, tell how many you think are behind the other door. Then count to check your answer.”

The materials reviewed for enVision Mathematics Kindergarten meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. These connections are listed for teachers in the Topic Overview, Scope and Sequence, and Teacher Guides within each topic. Examples include:

• In Topic 3, Lesson 3-7, Independent Practice, Problems 5 and 6, students write the number (0, 2 or 8, 10) that corresponds to dots shown on cards. “Directions Have students: 5 and 6 count to find the number that is 1 less than and 1 greater than the given number, and then write the numbers.” In Problem 7, students sequence numbers 7–10. Directions, “7 compare the number cards, write the smallest number, and then count forward and write the number that is 1 greater than the number before.” The materials show cards bearing the numbers 10, 8, 7, and 9 in that order. This connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.CC.B (Count to tell the number of objects).  

• In Topic 4, Lesson 4-1, Guided Practice, Problems 1–4, students compare the numbers. The materials show rows of chicks of different colors. “Directions 1 Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group. … 3 and 4 Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is less in number than the other group.” This connects the major work of K.CC.B (Count to tell the number of objects) to the major work of K.CC.C (Compare numbers).

• In Topic 10, Lesson 10-3, Reteach to Build Understanding, Problem 2, students engage with counters organized in ten-frames and write an equation. “Say: How many counters are in the first ten-frame? Draw more counters in the second ten-frame to show how to make 19. How many counters did you draw? Now write an equation to match the picture. The picture and equation show one way to make 19 with 10 ones and some more ones.” This connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.NBT.A (Work with numbers 11–19 to gain foundations for place value). 

• In Topic 12, Lesson 12-1, Independent Practice, Problem 6, students sort various shapes and real-world objects by indicating if they are flat (two-dimensional) or solid (three-dimensional). The directions state, “mark an X on the objects that are solid. Then have them draw a circle around the objects that are flat.” The materials show shapes (circle, square, rectangle, and triangle) and real-world objects (vase, can of beets, and a shoe box). This connects the supporting work of K.MD.B (Classify objects and count the number of objects in each category) to the supporting work of K.G.A (Identify and describe shapes).

The materials reviewed for enVision Mathematics Kindergarten meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

Prior and Future connections are identified within the Teacher Edition Math Background: Focus, Math Background: Coherence, and Lesson Overview. Examples of connections to future grades include:

• Topic 5, Lessons 5-1 - 5-3 connect K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count) to the work of future grades. “In Lesson 5-1, students classify objects into two categories. In Lesson 5-2, they count objects in each category and represent the counts with tally marks and numbers. In Lesson 5-3, they sort categories as defined by comparing or ordering the number of objects in the categories.” In Grade 1, Topic 6, students will “organize data into three categories and will use data to make a typical tally chart and picture-graph representation.”

• Topic 6 connects K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations) to the work of future grades. In Topic 6, “the meaning of addition is illustrated with objects, fingers, claps, mental images, drawings, and acting out situations. Students progress from using addition sentences in Lesson 6-1, 6-2, and 6-3 to using equations in Lesson 6-4 to describe addition situations. In Grade 1, “Topics 1, 2, 3, and 5, students will work on addition within 20. The emphasis will be on strategies and building fluency. Grade 1 students will be expected to become fluent with adding within 10.”

• Topic 10 connects K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones, understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones) to the work of future grades. ”In Lessons 10-1, 10-2, and 10-3, students make teen numbers by putting together 10 ones and some extra ones and then writing the related equation. In Lessons 10-4, 10-5, 10-6, students draw on these understandings to break apart teen numbers into 10 ones and some extra ones and then write the related equation.” In Grade 1, Topic 8, students will “determine how many tens and ones are in 2-digit numbers.”

Examples of connections to prior knowledge include:

• Topic 1 connects K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20) to learning before entering school. “Before entering school … Most young children have memorized a part of the verbal sequence of counting numbers. Many can recite the sequence using numbers 1 to 10.”  In Lesson 1-1, “students count 1, 2, or 3 objects. In Lesson 1-2, students view 1,2, or 3 objects in different arrangements. Then, in Lesson 1-3, they represent these quantities using numerals. This sequencing is repeated in Lessons 1-4 through 1-6 for the quantities of 4 and 5. Students connect representing 0 in Lessons 1-7 and 1-8.”

• Topic 2 connects 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) to learning before entering school. “Before Entering School... Many students come to school with experiences using direct measurement to determine which object is longer or which child is taller. This helps students when they are using a matching strategy to determine which group has the greater number of objects. Students are also likely to have compared numbers when they tell which of two children is older." In this topic, “students use matching to determine whether groups of objects are equal in number. Students then apply the matching technique to help them determine if the number of objects in a given group is greater than, less than, or equal to the number of objects in another group.”

• Topic 7, Lesson 7-5, connects K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10) to learning before entering school. Before entering school, “children understand simple subtraction situations. … (they) know that if one of their toys were taken away, or one of their sandwiches eaten, they would be left with fewer toys or sandwiches.” In this lesson, students “represent different subtraction word problems in multiple ways, including with equations.”