Kindergarten - Gateway 1

The materials reviewed for STEMscopes Math Kindergarten meet expectations for assessing grade- level content and, if applicable, content from earlier grades.

The curriculum is divided into 11 Scopes, and each Scope contains a Show-and-Tell used to assess what students have learned throughout the Scope. Examples from Show-and-Tell assessments include:

• Scope 3: Represent Numbers to 10, Evaluate, Show-and-Tell, Teacher Prompt Card 2, Question 4, “Direct the student’s attention to the smiley faces on Student Card 1. Ask the student to count and write the number on the line in the box.” (K.CC.3)

• Scope 5: Join and Separate, Evaluate, Show-and-Tell, Teacher Prompt Card 2, Question 2, “Say, ‘Sally has 4 green bears and 2 blue bears. How many total bears does Sally have? Use the bears to model and draw a picture to solve the problem. Can you explain your thinking?’” (K.OA.2)

• Scope 6: Represent Numbers to at Least 20, Evaluate, Show-and-Tell, Teacher Prompt Card 4, Questions 2 and 3, “2. Ask the students to place the objects into the ten frame so that there is a full ten frame and some further ones. 3. Ask the student, ‘How many groups of ten? How many ones?’” (K.NBT.1)

• Scope 9: Create and Compose 2-D Shapes and 3-D Solids, Evaluate, Show and Tell, Teacher Prompt Card 2, Question 4, “Ask, ‘Can you use these shapes to make a large triangle?’” (K.G.6)

• Scope 10: Measurement, Evaluate, Show and Tell, Teacher Prompt Card 1, Question 1, “Place modeling clay on a balance, and ask the student, ‘By placing the modeling clay on the balance, what attribute am I measuring?’” (K.MD.1)

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

The materials provide extensive work in Kindergarten as students engage with all CCSSM standards within a consistent daily lesson structure, including Engage, Explore, Explain, Elaborate, and Evaluate. Intervention and Acceleration sections are also included in every lesson. Examples of extensive work to meet the full intent of standards include:

• Scope 4: Compare Numbers to 10, Explore, Explore 2 - Compare Sets and Explore 3 - Compare Numerals, engages students in extensive work to meet the full intent 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 Explore 2-Compare Sets, Procedure and Facilitation Points, students are assigned to a station around the room, provided with two sets of “boxes” that they count and compare the number of “boxes” at their station. “1. Read the following scenario: Lela went on a field trip to the local post office. She got to help the workers sort the small and large boxes that were being shipped. She had to count how many small and large boxes were in each crate and determine which crate had more boxes to be shipped. Can you help her count and compare the boxes? 2. Explain to students they will pretend the linking cubes are small boxes and the large cube blocks are large boxes. … 4. Instruct students to count how many boxes are in Set 1 and Set 2 in the crate. Encourage students to use matching and/or counting strategies they learned in the Skill Basic lesson prior to this Explore. 5. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK–1 How many small boxes are there? b. DOK–1 How many large boxes are there? c. DOK–1 Which set of boxes has more? d. DOK–1 Which set of boxes has less? e. DOK–2 Is there anything about the sets of boxes that is the same/equal? f. DOK–3 How did you figure that out? 6. Ask students to draw a picture to show how many boxes there are in each set they counted in the Student Journal. Have them write the numeral for this amount. Then, have them circle the set that has more boxes. 7. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK–1 How did you represent the small boxes? b. DOK–1 How did you represent the large boxes? c. DOK–1 Why did you circle that set? d. DOK–2 How do you know?” In Explore 3-Comparing Numerals, Exit Ticket, students compare sets of objects and numbers and determine which is greater. In the first section, students see a stack of six blocks and a stack of nine blocks. In the second section, students are shown four pairs of numbers to compare. “Write the number for how many (blocks) tall the building is and circle the number that is more. ___ is more than ___. ___ is less than ___. Circle the number that is less in each pair below. 10 6, 1 5, 2 8, 0 4.”

• Scope 5: Join and Separate, Skill Basics- Representing Addition and Subtraction with Objects, Fingers, Mental Images, Drawings, and Sounds, engages students in extensive work 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.) Story Problem Card 4, “Tasha had 5 markers in the box. Janie gave her 4 more. How many markers does Tasha have now?” Teacher Guide, Procedure and Facilitation Points, “1. Explain to students that they are to use some similar story problems to the ones they acted out in the previous lesson, but this time they use other strategies to explain what is happening in the story problems, in addition to using objects and drawing pictures. They may use their fingers, clap their hands, or use mental images to solve the problems. … 4. Read the first story problem aloud to the class, and use questioning to guide students: a. Aden had 5 books. Suzy gave him 3 more books. b. Visualize what action is happening in this story. What image do you picture in your mind? … c. Continue reading the story problem, ‘How many books does Aden have now?’ d. Instruct students to use the Drawing Models Work Mat to draw pictures to represent the problem, or they may use mental images. e. How would you solve to find the total number of books when Aden started with 5 books and he joined/added 3 more? f. Say, ‘Let’s clap out how many books Aden had.’ First clap 5 saying, ‘One, two, three, four, five.’ Then say, ‘We have to clap 3 more from five. Six, seven, eight.’ 5. Explain to students that we use different strategies to solve word problems. Sometimes we use objects or drawings, sometimes we count on our fingers, and sometimes we clap out the number of items to help us count. Some people think it is helpful to visualize the image of the problem in their minds…” Story Problem Card 6, “Ruby had a stack of 3 cubes. She added 7 more cubes to her stack. How many cubes are stacked together now?”

• Scope 6: Represent Numbers to at Least 20, Explore, Explore 3 - Generating a Set of Objects, engages students in extensive work to meet the full intent of K.NBT.1. (Compose and decompose numbers from 11 to 19 into ten ones and some further ones…) Student Journal, Generating a Set of Objects, Question 1, students are given a picture of a bowl with the number 14. “Draw O to match the number of crackers in the bowl. Circle groups of ten. Decompose the total into ten and ones. Write the equation. 10 and ___ equals ___. ___ is the same as 10 and ___. ___ =10+ ___” Explore 4 - Composing Tens and Ones, Teacher Guide, Procedure and Facilitation Points, “1. Read the following scenario: Tasty Treats Bakery needs your help sorting through some of their online cupcake orders. The bakery owner needs you to look at each online order, fill the boxes with cupcakes, and determine how many total cupcakes are in each order. This will help the bakery owner determine how much customers owe when they come to pick up their sweet treats! 2. Direct students’ attention to the bags of Cupcake Cutouts and Cupcake Ten Frames. Give each student a copy of the Student Journal. 3. Instruct students to find Online Order 1. Read aloud the online order and ask: a. DOK–1 What did the customer order? b. DOK–2 How can the Cupcake Ten Frames help us organize the order? 4. Encourage students to use the Cupcake Cutouts and Cupcake Ten Frames to find the total number of cupcakes in each order. Once they have completed the concrete model with their partners, have students draw pictorial models using the ten frames on their Student Journals. Have them find the total and complete the equations below the ten frames. Ask partners to count and check the equations to make sure their partners are on the right track.” Student Journal, Composing Tens and Ones, “Online order 2: 8 lemon, 5 vanilla, 4 red velvet.” Students are given workspace with 2 ten frames, “$$10+$$ ___ = ___,   ___ =10+ ___”

• Scope 7: Two-Dimensional Shapes and Scope 8: Three-Dimensional Solids engages students in extensive work to meet the full intent 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…) Scope 7: Two-Dimensional Shapes, Explore, Skill Basics - Identifying Shapes and Their Attributes Using Formal and Informal Geometric Language, Plane Shapes Town Poem, “Have you ever heard of Plane Shapes Town? It has a perfect circle Sun, no points, just round. Triangle roofs have 3 vertices and 3 sides. Rectangle streets make for perfect rides. Square-shaped houses have 4 same-sized walls. And one more shape, a hexagon, on a tree so tall; 6 sides and 6 vertices, I hope it won’t fall.” Teacher Guide, Procedure and Facilitation Points. “6. Tell students that you are going to reread the poem, but this time, they are to trace around the shapes on their copy of the Student Handout as you read the poem. 7. Reread the poem. Pause after reading each line to make sure students have time to trace the shapes and they are tracing the correct shape. a. Explain any vocabulary, such as sides and vertices.” Explore 2 - Classifying and Identifying 2-D Shapes, Teacher Guide, Procedure and Facilitation Points, “1. Read the following scenario: Joy loves to play with her paper dolls. Her grandmother bought her a paper dollhouse kit for her birthday. There is one big problem, though. The directions mention the names of shapes, and she has not learned about shapes in pre-K. Can you help her match the name of the shape with the correct dollhouse piece so she can make her paper dollhouse? 2.Pass out bags to each set of partners. Direct students’ attention to the bag of dollhouse pieces and explain what the bags contain - dollhouse pieces and shapes. Allow students a few moments to discover the manipulatives and experience how to work with their partners. … 4. Instruct students to match the correct shape with the correct dollhouse piece. … 7. Have students move on to the last page of the Student Journal. Have them look at groups of dollhouse pieces and circle the 2 pieces that have similar attributes. 8. After students have completed the Student Journal, bring the class together as a whole group. 9. After the Explore, invite the students to a Math Chat to share their observations and learning.” Scope 8: Three-Dimensional Solids, Skill Basics - Comparing 2-D Shapes and 3-D Solids, Teacher Guide, Procedure and Facilitation, “Part II. 1. Give each student a bag of dough and allow time for students to explore the manipulative. 2. Instruct students to flatten out the dough on the table, then take each of the three-dimensional solid manipulatives and press into the dough. 3. Ask the following questions: a. What do you notice about the shape that is left in the dough after pressing the 3-D solid into it? Answers will vary. When I press this 3-D solid into the dough, it makes a 2-D shape. b. What happens to the shape when you turn the 3-D solid in different ways before pressing it into the dough? Answers will vary. The shape in the dough stays the same, it is just facing different directions. c.What is the name of this 2-D shape? Answers will vary. This shape is called a square. 4. Continue to add to the chart paper and rephrase student responses to encourage use of content vocabulary. 5. When this activity is complete, move on to Explore 2 for students to apply their knowledge of the skills they just learned.” 

• Scope 10: Measurement, Explore 2, 3 and 5, engages students in extensive work 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 Explore 2-Comparing Length, Procedure and Facilitation Points, students use linking cubes to compare six different suspect footprints. “5. Instruct students to measure the length of the Evidence Footprint and each Suspect’s Footprint using their linking cubes. Model how to do this in a whole-group setting. Explain to students how to record the final measurement on the first page of their Student Journal. If the length of a footprint is not an exact number of cubes, show students how to round up or down to the next unit depending on how much of the cube is covering the end of the footprint. 6. Once all footprint lengths have been recorded, have students place suspect 1’s footprint beside the Evidence Footprint to begin comparing. First, have them determine if suspect 1’s footprint is shorter than, longer than, or equal to the Evidence Footprint. Then, have them determine how many cubes shorter or longer than the evidence footprint it is, unless it is equal to the evidence footprint. They will use the word bank to complete the comparison statements for each suspect. Assist with reading if needed. 7. Repeat step 6 for the remaining Suspect Footprints. 8. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK–1 How many cubes long is the Evidence Footprint? b. DOK–1 How many cubes long is suspect ___’s footprint? c. DOK–2 What do you notice about the length of the Evidence Footprint and each suspect’s footprint? d. DOK–3 How can you determine if a suspect’s footprint is longer or shorter than the Evidence Footprint? e. DOK–3 How can you determine how many cubes shorter than/longer than/equal to a suspect’s footprint is compared to the Evidence Footprint? f. DOK–3 How can we determine which suspect matches the evidence?...” In Explore 3-Measurement, Exit Ticket, students identify which of two images is taller. In the first section, students see a child four handprints tall and another six handprints tall. “Count how many handprints tall each child is. Circle the child who is the shortest.” In the next section, images of two trees, two chairs, two flags, and two giraffes are shown. “Circle your answers. Which tree is taller? Which chair is shorter? Which flag is shorter? Which giraffe is taller?” In Explore 3-Comparing Height, Procedure and Facilitation Points, students work in groups, and with teacher guidance, to measure heights of students using non-standard measurement. “1. Read the scenario: The choir teacher is finalizing plans for the kindergarten spring program. Sonja, Henry, Anika, Roberto, and Emily will be singing the final song in the program. The choir teacher wants these students to stand on the steps of the stage. She needs our help to figure out each child’s height and arrange them in order from shortest to tallest. Can you help the choir teacher measure the height of these students? 2. Divide the class into five groups. 3. Distribute one piece of butcher paper with a child’s name and outline and 10 Handprint Cutouts to each group. 4. Direct students’ attention to the set of Handprint Cutouts and traced images on butcher paper. Allow students a few moments to discover the manipulatives and experience how they work with their groups. 5. Distribute a Student Journal to each student. 6. Encourage students to discuss what they think height means and how they will measure the height of the child. Ask the following questions: a. DOK–1 How does the choir teacher need us to help her? b. DOK–1 What do you think height measures? c. DOK–2 Show me how you could use your Handprint Cutouts to measure the height of the child’s outline on your butcher paper. 7. Instruct students to measure the height of the child’s outline on their butcher paper using their set of Handprint Cutouts. They will record the number of handprints tall the child is on their Student Journals. 8. Monitor and talk with students as needed to check for understanding by using the following guiding questions: a. DOK–2 Explain how you are measuring ___ (child’s name from scenario) height. b. DOK–1 How many handprints tall is the child you are measuring? c. DOK–3 What do you notice about the height of ___ compared to the height of ___? d. DOK–2 How can you determine which child is the shortest/tallest? I can put their heights in order from least to greatest. e. DOK–3 What strategy can you use to determine how many handprints shorter/taller one child is compared to another child? 9. Rotate the pieces of butcher paper until each group has measured and recorded the height for all 5 traced outlines. 10. Once all heights have been recorded, students will complete the comparison statements at the bottom of their Student Journals. They will determine how many handprints shorter or taller one child is compared to another. They will use the word bank to complete the comparison statements… 11. After students have completed the Student Journal, bring the class together as a whole group.” Finally, in Explore 5-Comparing Weight, Exit Ticket, students determine which of a pair of animals weighs more. A balance scale is provided in each picture to help determine the heavier/lighter animal. Students see four balance scales with different animals on each scale. “Circle the animal that is heavier.” Students see an elephant and a mouse. “Circle the animal that weighs the least.” Students see an ant and a rabbit. “Circle the animals that weigh the same.” Students see two scales. One has a cat and a rhino. The other has a cat and a dog weighing the same amount.

The materials reviewed for STEMscopes Math Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.

The instructional materials devote at least 65% of instructional time to the major clusters of the grade:

• The approximate number of scopes devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 10, approximately 70%.

• The number of lesson days and review days devoted to major work of the grade (including supporting work connected to the major work) is 136 out of 180, approximately 76%.

• The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 136 out of 180, approximately 76%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of lesson days, all assessment days, and review days. As a result, approximately 76% of the instructional materials focus on the major work of the grade.

The materials reviewed for STEMscopes Math 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 supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples of connections include:

• Scope 4: Compare Numbers to 10, Explore, Explore 2–Compare Sets, Exit Ticket, connects the supporting work of K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.) 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, e.g., by using matching and counting strategies.).  Students count two sets of objects and compare the two sets. “Count the (blocks) in each set. Write the number. Compare the numbers.” Students see five blocks and six blocks. “Circle the number that is greater. ___ is greater than ___.”

• Scope 6: Represent Numbers to at Least 20, Explore, Explore 3–Generating a Set of Objects, Procedure and Facilitation Points, connects the supporting work of K.G.A (Identify and describe shapes.) to the major work of K.CC.B (Count to tell the number of objects.)  Students work together to count a set of objects and draw circles to represent the number. “1. Read the following scenario: The cafeteria is going to have soup as a choice for lunch. The cafeteria workers need your help adding different amounts of crackers to each soup bowl. Can you help them count out the crackers? 2. Direct students’ attention to the bag of linking cubes, the Soup Bowl Cards, and the bowl. Explain to students they will be pretending the linking cubes are crackers (unless the teacher chooses to use real crackers). Allow the students a few moments to discover the manipulatives and experience how they work with their partners. 3. Instruct students to take turns taking a Soup Bowl Card out of the bag. They will count out that many linking cubes and place them into the bowl as they are counting. Once they are finished, their partners will count the linking cubes to check to see if their partners are correct. 4. Give each student a copy of the Student Journal. Students will find the same number bowl they just counted on their papers. Instruct students to draw a picture to represent the number of crackers for each bowl. They will circle groups of ten and decompose the total into a group of ten and ones by completing sentence stems and writing an equation…”

• Scope 9: Create and Compose 2-D Shapes and 3-D Solids, Explore, Explore–2: Composing 2-D Shapes, Procedure and Facilitation Points, connects the supporting work of K.G.6 (Compose simple shapes to form larger shapes…) to the major work of K.CC.4b (Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.) Students create larger shapes by combining smaller shapes and counting the number of shapes used. “1. Read the following scenario: The art museum has a new exhibit based on shape art. They want you to create different works of art by composing 2-D shapes you already know. All you have to do is follow the directions. Can you create the art for the museum? 2. Give each student a copy of the Student Journal and divide the class into six groups. Assign each group a station at which to start. There will be two groups at each station. 3. Direct students' attention to the bag of pattern blocks. Allow students a few moments to discover the manipulatives and experience how they work with their group…”

The materials for STEMscopes Math Kindergarten meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Materials are coherent and consistent with the Standards. These connections are sometimes listed for teachers in one or more of the three sections of the materials: Engage, Explore and Explain. Examples of connections include:

• Scope 3: Represent Numbers to 10, Explore, Explore 1–Represent 6 with Objects and Pictures, Exit Ticket, connect the Kindergarten Counting & Cardinality domain to the Operations & Algebraic Thinking domain as students count the given picture of 6 cupcakes. Students count the cupcakes and create an equation. “Color the cupcakes with 2 different colors. I  counted ___ cupcakes. ___ are colored. ___ are  colored. Write an equation. ___ + ___ = ___”

• Scope 5: Join and Separate, Engage, Hook, Part II–Post Explore, connects the Operations & Algebraic Thinking domain to the Kindergarten Counting & Cardinality domain, as students count the objects to represent the crabs they see in the video and then put them together to create an equation and find the sum. “Divide the class into groups of two or three, and give each group the six crab cutouts. Instruct the students to model the solution to the problem by using the cutouts. Call on volunteers to explain the strategy they used to solve the problem.”

• Scope 7: Two-Dimensional Shapes, Explore, Explore–2, Classifying and Identifying 2-D Shapes, Exit Ticket, connects the supporting clusters of K.MD.A (Describe and compare measurable attributes.) and K.MD.B (Classify objects and count the number of objects in each category.) as students count the measurable attribute of the number of vertices to classify  into the given category. Students are given a rectangle, a circle, a hexagon, a triangle, and a square. “Circle the shapes with 3 or more vertices.” 

• Scope 9: Create and Compose 2-D Shapes and 3-D Solids, Engage, Hook–Making Shapes, Part II–Post Explore, connects the Geometry domain to the Measurement & Data domains as students use the shapes in their bags to create a “Rectangle, Hexagon, Square, Triangle.” This is followed by a math chat where students discuss questions about the 2-D shapes they just made: “DOK-2 What do you have to consider when using two-dimensional shapes to compose other two-dimensional shapes? DOK-2 How did the shape you created at station 3 compare to the shapes you used to create it?”

The materials reviewed for STEMscopes Math 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 materials in the Home, Content Support, Background Knowledge, as well as Coming Attractions sections. Information can also be found in the Home, Scope Overview, Teacher Guide, Background Knowledge and Future Expectations sections. 

Examples of connections to future grades include:

• Scope 3: Represent Numbers to 10, Home, Content Support, Coming Attractions connects K.CC.2 (Count forward beginning from a given number within the known sequence (instead of having to begin at 1) to work in grade 3. “In third grade, students find efficient strategies for adding and subtracting within 1,000. They apply strategies based on place value, properties of operations, and the relationship between addition and subtraction. Third-grade students solve multi-step problems involving all 4 operations, and they represent each problem by using an equation with a variable. Students assess the reasonableness of answers using mental computation and estimation strategies, including rounding.”

• Scope 6: Represent Numbers to at Least 20, Home, Scope Overview, Teacher Guide, Future Expectations, connects K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18=10+8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.) to future work in grade 1. “In first grade, students develop an understanding that a unit called a ten is composed of ten ones. They learn to efficiently compose and decompose tens. First-grade students use this knowledge to develop base-ten methods to solve problems involving addition and subtraction within 20.”

• Scope 11: Data Analysis, Home, Scope Overview, Teacher Guide, Future Expectations, links K.MD.3 (Classify objects and count the number of objects in each category) to first grade 1.MD.C (Represent and interpret data). “In first grade, students organize, represent, and interpret data with up to three categories, and they reason about the total number of data points, how many are within each category, and how many more or less are in one category than in another. Students create object and picture charts, as well as Venn diagrams.”

Examples of connections to prior grades include:

• Scope 5: Join and Separate, Engage, Foundation Builder Accessing Prior Knowledge from Pre-K Concepts, connects 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) to work done prior to kindergarten. “Demonstrate an understanding of addition and subtraction by using objects and fingers and by responding to practical situations (e.g., if we have 3 apples and add 2 more, how many apples do we have all together?)”

• Scope 7: Two-Dimensional Shapes, Home, Content Support, Background Knowledge, connects K.G.2 (Correctly name shapes regardless of their orientations or overall size) to work done prior to Kindergarten. “In pre-kindergarten, students may be familiar with the names of basic shapes (squares, circles, triangles, and rectangles). They may be able to analyze, compare, and sort objects by their attributes.”

• Scope 10: Measurement, Home, Content Support, Background Knowledge, linking K.MD.A (Describe and compare measurable attributes.) “By the end of pre-kindergarten, students may be able to recognize and compare the heights or lengths of people and objects. Students may have observed measurement in real-life situations, such as building, cooking, or visiting the doctor for a checkup. Students may be able to identify measurable attributes of objects, such as length and weight, and can describe them using words such as small, big, short, tall, empty, full, heavy, and light.”