Kindergarten - Gateway 1

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

The curriculum is divided into nine units with one assessment per unit, except for Units 3 and 9. Unit 3 includes two Summative Assessments that assess Lessons 3.1 - 3.5 and Lessons 3.6 - 3.11. Unit 9 includes two Summative Assessments that assess Lessons 9.1 - 9.6 and Lessons 9.7 - 9.13. Assessments include Unit Summative Assessments and formative assessments. Examples include:

• Unit 2: Numbers to 10, Assessment: Lessons 2.1 - 2.9, Exercise 6a, students compare two numbers. “Put in order from less to more. (7,6,9).” (K.CC.7)

• Unit 3: Numbers to 20, Assessment: Lessons 3.1 - 3.5, Exercise 1a, students are given a picture of ten fingers and two more fingers. Students choose from numbers 11-19 to identify the number of fingers. (K.NBT.1)

• Unit 7: Addition and Subtraction Strategies, Assessment: 7.1 - 7.9, Exercise 4c, students use an equation to decompose numbers less than ten. “$$2+?=9$$.” Students choose the correct answer “1, 2, 3, 4, 5, 6, 7, 8, 9, 10.” (K.OA.3)

• Unit 8: Measurement and Data, Assessment: 8.1 - 8.7, Exercise 3c, students describe and compare two objects.“The house is…the tree.” Students choose the correct phrase “shorter than, as tall as, taller than.” (K.MD.2)

• Unit 9: Geometry, Assessment: 9.1 - 9.6, Exercise 1d, students describe the relative positions of books. Students “Drag the book to the shelf below the glue.” (K.G.1)

Materials include above-grade assessment items that are mathematically reasonable and could be removed or modified without impacting the structure of the materials. Examples include:

• Unit 3: Numbers to 20, Assessment: Lessons 3.1 - 3.5, Exercise 1b, students are given a box with the numeral “10” on it and “1 ten” written below it. Next to the box are 3 individual candies with a blank answer box labeled “and ___ ones” below it. Students drag a number tile from 1-9 into the ones box and solve, “How many?” by tapping on the choices 13, 15 or 17. This problem is aligned to K.NBT.1 in the materials (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 (e.g., 18=10+8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.) This problem better aligns to 1.NBT.2a (10 can be thought of as a bundle of ten ones — called a "ten.”) 

• Unit 3: Numbers to 20 Assessment: Lessons 3.6 - 3.11, Exercise 1b, students read and write numbers to 20. “17, 1 ten and 7 ones, 19, sixteen, 1 ten and 8 ones, seventeen. Tap on the three boxes that have the same number.” This problem is aligned to K.CC.3 in the materials (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects.)) This problem better aligns to 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones.)

The materials reviewed for Snappet 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 present opportunities for students to engage with the full intent of grade-level standards through a consistent lesson structure. According to the Snappet Teacher Manual, 3. Lesson Structure, “Snappet lessons are organized by learning objective and focus on one learning objective per lesson. Each lesson consists of three parts: Instruction and guided practice, Independent and adaptive practice, and Small group instruction.” Within Instruction and guided practice, “The teacher introduces the learning goal, activates prior knowledge, delivers the lesson, and monitors guided practice.” Within Independent and adaptive practice, students work independently “while receiving immediate feedback, and are continuously challenged at their own level while working in adaptive practice.” Within Small group instruction, “The teacher can help students who need additional support with these extension exercises.” Examples of full intent include:

• Unit 3: Numbers to 20, Lesson 3.1 engage students in the full intent with K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones and record each composition or decomposition by a drawing or equation; understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones). Instruction & guided practice, Exercise 1c, students decompose and compose 11-19 in multiple ways. “Game: more than 10 fingers? Rules of the Game: The teacher selects a student, asking him/her to show 10 fingers and to stand up. The teacher says the number 11 and asks, “How many more fingers does the student need to make 11?” “One.” Another student is selected to stand next to the first student, raising 1 finger so that the total number of fingers is 11. The teacher repeats the process using numbers 11-19.” Instruction & guided practice, Exercise 1q, “$$10+$$___ ones = ___.” Teacher tip, “Point out that an abacus can be used to show numbers between 10 and 20. Ask: How many beads are shown on the top row? [10] What do you notice about the top row? [Sample answer: The beads are all together.] How many beads are shown on the bottom row? [10] What do you notice about the bottom row? [2 beads are below the 10 from the top row and 8 are to the right.] What do you think this means? [The abacus shows 1 ten and 2 ones.]” Independent practice, Exercise 2i, The number 14 is decomposed into 10 and an empty box. Students select the correct answer. 

• Unit 4: Numbers to 100, Lessons 4.1 and 4.2 engage students in the full intent of K.CC.1 (Count to 100 by ones and tens.), and K.CC.2 (Count forward beginning from a given number within the known sequence (instead of having to begin at 1).), as students count numbers within 100. In Lesson 4.1, Instruction & Guided Practice, Exercise 1d, students are given a sequence of numbers, counted by one, and asked to continue the sequence. Students see the sequence 1-22 (grouped in tens) with the spaces for 23-30 blurred. “Say the numbers in the bottom row together. How did you do? How do the numbers in the top and middle rows help you with the bottom row?” In Lesson 4.2, Independent Practice, Exercise 2c, students see five bags with a tennis ball and the number ten on each bag. (Each bag represents 10 tennis balls.) Students count by ten to determine how many tennis balls are in all the bags together. “How many balls? 10, 20, 30, 40, 50, 60, 70, 80, 90, 100”

• Unit 8: Measurement and Data, Lessons 8.3, and Lesson 8.4 engage students with the full intent of K.MD.2 (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.) In Lesson 8.3, Instruction & Guided Practice, Exercise 1e, students compare the width of two objects. “How does the width of the paper clip compare to the ruler?” Independent practice, Exercise 2a, students compare the height of lighthouses. “Choose the taller one.” In Lesson 8.4, Independent Practice, Exercise 2i, students compare the weight of objects. A picture shows a balanced scale with a birthday hat on the left side, “How do you know which object goes on the right side of the scale?” Students choose from balloons or a birthday cake.

• Unit 9: Geometry, Lesson 9.10, Instruction & guided practice, engage students with the full intent of K.G.5 (Model shapes in the world by building shapes from components [e.g., sticks and clay balls] and drawing shapes). In Exercise 1c, students model and draw two- dimensional shapes. “Let’s make 2-D shapes! Explanation: Students work in pairs to create the following 2-D shapes: triangle, square, rectangle, and circle using the set of straws, pipe cleaners, and clay/play dough. The clay/play dough are used to as a way to attach the straws together as students make slides and corners. Pipe cleaners are best used for creating circles. Keep the slide up for students as they work to create their shapes. Encourage students to look at each other’s shapes, name the shapes, and talk to each other.” In Independent practice, Exercise 2f, “Draw a rectangle.”

The materials present opportunities for students to engage with extensive work with grade-level problems. Examples of extensive work include:

• Unit 1: Numbers to 5, Lesson 1.10, Unit 2: Numbers to 10, Lesson 2.7, and Unit 3: Numbers to 20, Lesson 3.6 engage students in extensive work with K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20.) Unit 1: Numbers to 5, Lesson 1.10, Instruction & guided practice, Exercise 1b, students write numerals from a given picture of 2 pencils. “How many? Write the number.” Unit 2: Numbers to 10, Lesson 2.7, Independent practice, Exercise 2i, students use the picture of a rectangle with 4 flowers and a rectangle with 8 flowers to write numbers. “Which has more? Write the number.” Unit 3: Numbers to 20, Lesson 3.6, Instruction & guided practice, Exercise 1v, students write the number of insects. “How many? Write the number 3 times.” Throughout Kindergarten, students write numbers from 0 to 20.

• Unit 3: Numbers to 20, Lesson 3.9, and Unit 4: Numbers to 100, Lesson 4.2, students engage with extensive work with K.CC.2 (Count forward beginning from a given number within the known sequence). In Unit 3: Numbers to 20, Lesson 3.9, Instruction & guided practice, Exercise 1c, students count from a given number. “The teacher points to a student to start the game. The first student says, “one” and claps their hands once. The teacher then points to another student, who claps twice and says “two.” The number of claps increases by 1 each time the teacher chooses another student. The game continues until a student gets to 20. The teacher changes the game so that she/he begins with a number other than 1 and students count up from that number. The game continues with counting up from any number (0-20).” In Unit 4: Numbers to 100, Lesson 4.2 Independent practice, Exercise 2h, students count on when given a number, “Count by 10s. What comes next? 30, 40, ?, ?, ? (50, 60, 70), (10,20, 30), (50, 70, 90).”

• Unit 5: Understand addition within ten, Lesson 5.6; Unit 6: Understand subtraction within ten, Lesson 6.3; and Unit 7: Addition and subtraction strategies, Performance Task, Exercise 1c, engage students with extensive work with K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10.) In Lesson 5.6, Instruction & guided practice, Exercise 1j, students are shown a birthday cake with 3 lit candles and 2 unlit and are asked to create an addition equation to find the total number of candles. “There are a few candles burning. Oliver lights all the candles. How many candles are burning. Find the sum.” In the same lesson, Exercise 2k, students work independently to create an addition equation that adds up to 4. “Grandma and Alex baked 4 cookies. How many cookies did grandma bake and how many cookies did Alex bake? Make a sum. __ + __ = 4"  In Lesson 6.3, Exercise 1i, students see a tray of 6 cookies, two of which are crossed out. They are then asked to find how many cookies remain. “Jasmine baked cookies. She ate some cookies. How many cookies are left? Find the sum.” Later in the same lesson, Exercise 2k, students see a similar picture, but three of the cookies have been eaten. “Jasmin baked cookies. She ate some cookies. How many are left? Find the sum.” In Unit 7: Addition and Subtraction Strategies, Performance Task, Exercise 1c, Problem 8, students solve word problems using addition. “9 fish in a tank. Some have stripes. Some do not. How many have stripes? How many have no stripes?” Students are expected to solve the problem using two different methods.

• Unit 7: Addition and Subtraction Strategies, Lessons 7.1 and 7.2, engage students with extensive work with K.OA.3 (Decompose numbers less than or equal to 10 into pairs in more than one way.) Lesson 7.1, Instruction & guided practice, Exercise 1f, given a number bond with a 4 in the top box and a 1 in one of the bottom boxes, and pictures of 4 fish and 2 fish bowls, students drag the fish to the bowls and “uncover” the number 3 in the other number bond bottom box. Lesson 7.2, Instruction & guided practice, Exercise 1e, given pictures of a hand showing 2 fingers and a girl saying, “I have 2 fingers raised.” “How many more fingers to make 4?” Teacher directions, “(SEL) Encourage students to use their fingers to act out the problem.” The teacher's answer shows a hand with two fingers raised. Within the same lesson, Exercise 1g, “How many balls should we add to the basket to make 4?” given pictures of 1 ball and a basket with 3 balls in it. “$$3+$$___$$= 4$$.”

The materials reviewed for Snappet Math Kindergarten meet expectations that, when implemented as designed, most of the materials address the major clusters of each grade. The materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to the major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 9, approximately 78%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 64 out of 89, approximately 72%. 

• The number of weeks devoted to the major work of the grade (including assessments and supporting work connected to the major work) is 28 out of 35, approximately 80%.

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 unit. As a result, approximately 72% of the materials focus on major work of the grade.

The materials reviewed for Snappet 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 to connect supporting standards/clusters to the grade's major standards/ clusters. These connections are listed for teachers in the Course Overview/Pacing Guide and Teacher Guides within each unit. Examples of connections include:

• Unit 8: Measurement and Data, Lesson 8.6, Instruction & Guided Practice, Exercise 1i, students count the number of strawberries and lemons as they sort them into groups. “How many in each group?” Students count and match the number in each group to a written numeral. This 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.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).

• Unit 8: Measurement and Data, Lesson 8.7, Instruction & Guided Practice, Exercise 1k, students sort three types of flowers and then count the number in each group. “Which has the least?” This connects the supporting work of K.MD.3 (Classify objects into given categories; count the number 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). 

• Unit 9: Geometry, Lesson 9.3, Independent Practice, Exercise 2c, students identify which shapes are triangles and count the total number of triangles. Students see 5 triangles and 3 diamonds and must choose, “How many triangles? 1, 2, 3, 4, 5.” This connects the supporting work of 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.)

The materials reviewed for Snappet Math 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 Course Overview/Pacing Guide and Teacher Guides within each unit. Examples include:

• Unit 2: Numbers to 10, Lesson 2.9, Instruction & Guided Practice, Exercise 1a, students count the number of screws. “How many? Write the number.” This activity 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). 

• Unit 3: Numbers to 20, Lesson 3.1, Independent Practice, Exercise 2j, students represent 17 as a ten and a number of ones. “ ___ + ___ones = 17.” This activity connects the major work of K.OA.A (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from) to the major work of K.NBT.A (Work with numbers 11-19 to gain foundations for place value). 

• Unit 3: Numbers to 20, Lesson 3.4, Independent Practice, Exercise 2c, students count up to 20 by making groups. “How many flowers?” Students add five flowers to 2 flowers. This activity connects the major work of K.CC.B (Count to tell the number of objects) to the major work of K.CC.A (Know number names and the count sequence).

• Unit 9: Geometry, Lesson 9.9, Instruction & Guided Practice, Exercise 1c, students compare the attributes of three-dimensional shapes and classify objects into categories. “Have students form groups. Provide each group with a bag of three-dimensional shapes. Tell groups to roll the clay on the table so that it is smooth and flat. Ask groups to select the cube and press one side of the cube into the clay. Ask: What shape did the cube make? [square] Have students try the other faces of the cube to discover the shape of the cube’s faces. Allow students to repeat using other shapes. Make sure students choose the flat side of the cylinder.” Exercise 1d, “Divide the class into six groups. Provide each group a number cube. Have one person from each group to come to the front and show the faces with 1–6 dots in numerical order. Discuss that the flat surface is called a face. How many faces does a cube have? [6]”. This activity connects the supporting work of K.G.B (Analyze, compare, create, and compose shapes) to the supporting work of K.MD.B (Classify objects and count the number of objects In each category).

The materials reviewed for Snappet 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 the Pacing Guide and every Lesson Overview. Connections are further described within each Unit Overview embedded in the Learning Progression. 

Examples of connections to future grades include:

• Unit 5: Understand Addition Within 10, Lesson 5.5, Lesson Overview, “In this lesson, students will add within 10 using objects, drawings, and number sentences. (K.OA.A.2) understand that pictures, story problems, and number sentences are related and can display the same meaning. (K.OA.A.1) In future lessons, students will add and subtract within 20 using mental math strategies. (1.NBT.C.4) represent and solve ‘put together’ word problems (1.OA.A.1).”

• Unit 6 Overview: Understand Subtraction Within 10, Learning Progression, “In this grade level, students will subtract amounts using drawings. They will advance to writing subtraction expressions using the minus sign. They will represent and solve ‘take from’ and ‘take apart’ word problems with sums to 10. In future grade levels, students will subtract within 20 using drawings, by counting back, and by counting on. They will relate subtraction to addition and use fact families (1.OA.A.1). They will use the strategies of doubles and near doubles to subtract within 20 (1.OA.C.6). They will use mental math strategies to subtract within 20 (1.NBT.C.4). They will subtract using compensation (2.NBT.B.5). They will find 100 less than a number (2.NBT.B.8). They will subtract three-digit numbers including the use of regrouping and subtracting across zeros (2.NBT.B.7).”

• Unit 9 Overview: Geometry, Learning Progression, “In this grade level, students use words and phrases to describe location and space (K.G.A.1). They name two-dimensional shapes that include squares and rectangles. They name three-dimensional shapes (K.G.A.2). They identify shapes as having two or three dimensions (K.G.A.3). They compare, model, and draw two- and three-dimensional shapes (K.G.B.4, K.G.B.5). In future grade levels, students name and explore the attributes of two-dimensional shapes including circles, triangles, and rectangles. They identify three-dimensional shapes, including pyramids, cones, and cubes (1.G.A.1). They compose and decompose two- and three-dimensional shapes (1.G.A.2). They draw and classify two-dimensional shapes (2.G.A.1).”

Examples of connections to prior knowledge include:

• Unit 3: Numbers to 20, Lesson 3.1, Lesson Overview, “In prior lessons, students have written numbers to 10. (K.CC.A.3) counted numbers to 10 to find how many. (K.CC.B.4, K.CC.B.5) In this lesson, students will represent 11–19 as a ten and a number of ones. (K.NBT.A.1) compose and decompose a number from 11 to 19 (K.NBT.A.1).”

• Unit 6: Understand Subtraction Within 10, Lesson 6.1, Lesson Overview, “In prior lessons, students have counted back from 20. (K.CC.A.2) solved addition word problems. (K.OA.A.2) In this lesson, students will subtract amounts using objects or drawings (K.OA.A.1).”

• Unit 7 Overview: Addition and Subtraction Strategies, Learning Progression, “In prior units, students counted back from 20, added two numbers to 20, and subtracted within 10. In this grade level, students will compose and decompose numbers to 10. They will use these skills to use mental math to add sums to 5. They will use these skills to add and subtract within 5 mentally.”