Kindergarten - Gateway 1

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for assessing grade-level content.

Materials include Mid-Mission Assessments for Missions 1, 3, 4, and 5 and End-of-Mission Assessment Tasks for Missions 1-6. Both assessments include problems from different topics throughout the Mission. A performance task rubric for each Mid-Mission Assessment and End-of-Mission Assessment is provided. Examples include:

• Mission 1, Mid-Mission Assessment Task, Topic C, Numbers to 5 in Different Configurations, Math Drawings, and Expressions states, “(Put 5 loose cubes in front of the student.) Whisper-count as you put the cubes into a line. How many cubes are there? (Move the cubes into a circle.) How many cubes are there? (Scatter the cubes.) How many cubes are there? Please show this (show 2 + 1) using your cubes. (Have the student explain what he does. We might expect the student to make a linking cube stick of 3 and break it into two parts.).” (K.CC.5)
• Mission 2, End-of-Mission Assessment Task, Topic A, Two Dimensional Flat Shapes states, “(Hold up a rectangle. Use different shapes for each student.) Point to something in this room that is the same shape, and use your words to tell me all about it. How do you know they are the same shape? (Place several typical, variant, and distracting shapes on the desk. Be sure to include three or four triangles.) Please put all the triangles in my hand. How can you tell they were all triangles? (Hold up a rectangle.) How is a triangle different from this rectangle? How is it the same? (Place five typical shapes in front of the student.) Put the circle next to the rectangle. Put the square below the hexagon. Put the triangle beside the square.” (K.G.4)
• Mission 3, End-of-Mission Assessment Task, Topic G, Comparison of Numerals states, “(Present a set with 7 cubes and a set with 5 cubes.) Put these objects in lines to match and compare them. Which number is more? Less? (Write the numerals 8 and 4.) Use the words more than to compare these two numerals.” (K.CC.7) 
• Mission 4, Mid-Mission Assessment Task, Topic A, Compositions and Decompositions of 2, 3, 4, and 5 states, “(Put 4 toy animals in the whole’s place on the number bond. Orient the whole toward the top.) Tell me a story about part of the animals going here (point to part of the number bond) and part of the animals going here (point to the other part of the number bond). Move the animals as you tell your story. (Turn the number bond mat so that the parts are on top. Put 3 connected linking cubes and 2 connected linking cubes in the parts of the number bond.) Use these linking cubes (present the tub) to complete this number bond. (Students should put 5 linking cubes into the whole’s place.) Replace your cubes with numbers.” (K.OA.1)
• Mission 5, Mid-Mission Assessment Task, Topic A, Count 10 ones and some ones states, “Count 10 straws into a pile. Whisper while you count so I can hear you. Count 6 more straws into a different pile. Count 10 straws and 6 more straws the Say Ten way (Pause.) How many straws do you have? (If the student says the number the Say Ten way, ask the student to also say it the regular way.)” (K.NBT.1)
• Mission 6, End-of-Mission Assessment Task, Topic A, Building and Drawing Flat and Solid Shapes states, “(Place all the straws and formed clay balls in front of the student.) Build a square. (Place solid shapes in front of the student.) Choose one object that has the shape you just built. (Place pattern blocks template in front of the student horizontally.) The star is the beginning. Point to the third shape. Point to the seventh shape. (Turn the template vertically.) The star is the beginning. Point to the first shape. Point to the ninth shape.” (K.G.5)

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of missions devoted to major work of the grade (including assessments and supporting work connected to the major work) is 4/6, which is approximately 67%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 128.5/162, which is approximately 79%.
• The number of minutes devoted to major work (including assessments and supporting work connected to the major work) is 7670/8925, which is approximately 86%. 

A minute level analysis is most representative of the instructional materials because it takes into account Digital Activities, which are a 10-minute station, following the Daily Teacher-Led Instruction part of the lesson. As a result, approximately 86% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Zearn Math Kindergarten meet expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade. Examples include:

• In Mission 1, Topic B, Lesson 5, Lesson, students classify items into three categories, determine the count in each, and reason about how the last number named determines the total. The materials state, “Today, we are going to do another sorting activity, but this time we are going to look for three different groups to sort things into. We’re going to play a game called Where Do I Belong? I will call one of you up to choose a picture from this bag while the rest of us whisper-count together to 10. (The counting keeps the lesson moving along and speeds the students’ decision times.) You decide if your picture belongs with the sun, the rain, or the snow. After you tell us why you made that choice, we will put it on the board underneath its weather type. Great job! I wonder how many sunny pictures we found? Let’s count them. (Number each picture as it is counted.) How many sunny pictures?” This activity connects the supporting work of K.MD.3, classify objects in given categories, to the major work of K.CC.5, count to answer “how many?” questions about as many as 20 things.
• In Mission 2, Topic A, Lesson 3, Lesson, students sort shapes and non-examples identifying rectangles. As part of the lesson debrief students ”Count how many rectangles you colored. Did your partner color the same number?” This activity connects the supporting work of K.MD.3, classify objects into given categories, to the major work K.CC.5, count to answer “how many?” questions about as many as 20 things.
• In Mission 3, Topic B, Lesson 7, Lesson, students compare linking cube number stairs. The materials state, “Mix up your number stairs on your desk. Find your 5 stick. Look at it carefully. Now, listen to my riddle. We are two different sticks. We are each shorter than the 5-stick, but when you put us together, we are the same length as the 5-stick!” This activity connects the supporting work of K.MD.2, directly compare two objects with a measurable attribute in common, to the major work of K.CC.6, identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. 
• In Mission 4, Topic F, Lesson 30, Lesson, students represent pictorial decomposition and composition addition stories to 10 with 5-group drawings and equations. The materials state, “Ricky had 10 space toys. He had 7 rockets and 3 astronauts. Erase your board. Work with your partner to draw 10 in the 5-group way, and decide how to separate it into two groups. Make two different number sentences about your new picture.” This activity connects the supporting work of K.MD.3, classify objects into given categories, to the major work of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10.
• In Mission 6, Topic A, Lesson 3, Lesson, students use flat squares to construct a cube, “In our last lesson, you made some great shapes out of your straws! I want to use some of the squares you constructed to make a new shape like one of our solids. Does anyone have any ideas? Look at the cube we already have. (Hold it up.) How many squares will I need to use? Let’s count together.” Once the cube is constructed, the class counts the number of faces and edges and determines whether the faces are squares or rectangles. This activity 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.5, count to answer “how many?” questions about as many as 20 things.

The instructional materials for Zearn Math Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year. 

The Kindergarten Overview PDF outlines the number of missions, number of lessons in each mission, and estimated number of weeks needed for each mission based on teaching four lessons per week. As designed, the instructional materials can be completed in 152 days or 36 weeks.

• There are six missions with a total of 152 lessons.
• There are a total of 10 Mid-Mission and End-of Mission Assessments, which adds 10 instructional days.
• According to the Recommended Schedule PDF, Daily Teacher-Led Instruction requires 30-45 minutes divided into three lesson parts to build number sense with concrete manipulatives, pictorial representations, and discussion: Fluency (5-10 minutes), Word Problems (5-10 minutes), and Lessons (20-30 minutes). Following the Teacher-Led Instruction, students split into two groups for practice. Station one is Digital Activities (10 minutes) where students play online games to build number sense and are given the goal of completing four activities per week. Station two is Problem Sets (10 minutes) where students work through Fluency, Word Problems, problems from the lesson, or Problem Sets with the teacher. In Missions 5 and 6, students fill out a Paper Exit Ticket after completing both stations.

The instructional materials for Zearn Math Kindergarten meet expectations for being consistent with the progressions in the Standards. The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. Students are provided extensive work with grade-level problems.

Materials develop according to the grade-by-grade progressions in the Standards and content from prior or future grades is clearly identified in the and related to grade level work. Each Mission and Topic Overview provides information about standards covered and how they are connected to prior and future learning. Examples include:

• The Mission 2 Overview states, “In Mission 1, students began the year observing their world. What is exactly the same? What is the same but…? They matched and sorted according to criteria sequenced from simple to complex. Their perceptions evolved into observations about numbers to 10. ‘4 is missing 1 to make 5.’ ‘4 plus 1 more is 5.’ ‘There are the same number of dogs and flowers, 6.”
• In Mission 3, Topic A, Comparison of Length and Height states, “In Mission 2, students observed, analyzed, and categorized geometric shapes by focusing on their attributes; they now launch into the process of recognizing and comparing these attributes. In Mission 3, comparisons of length, weight, and volume transition into comparisons of numbers: longer than, shorter than, as long as; heavier than, lighter than, as heavy as; more than, less than, the same as. For example, ‘8 is more than 5. 5 is less than 8. 5 is the same as 5.’”
• In Mission 4, Topic A, Compositions and Decompositions of 2, 3, 4, and 5 (K.OA.1,3,5) states, “In Mission 1, students found embedded numbers and experienced decomposition by finding hidden partners. Topic A formally teaches composition and decomposition using number bonds as students explore the relationships between numbers to set the foundation for addition and subtraction.”
• The Mission 6 Overview states, “Composition and decomposition of geometric figures reinforce the idea that smaller units can combine to form larger units. This concept underlies not only area concepts but also the base ten number system. Students leave this mission and the kindergarten year prepared to tackle the mathematical concepts of Grade 1 and beyond.”
• In Mission 6 Overview, Notes on Pacing and Differentiation states, “Addressing ordinal numbers and relative position may not be a standard in some states or districts. Using ordinal words to describe a procedure is included in Lesson 1 and parts of Lesson 5, as well as the Word Problems in Lessons 4, 5, and 6. Consider omitting pertinent lessons partly or entirely. The fluency activity ‘If You’re Happy and You Know It’ in Lesson 1 might be omitted as well, since it prepares students to work with that content.”

Materials give students opportunities to engage in extensive work with grade-level problems. Students engage in grade-level work during Fluency Practice, Word Problem, Lesson, and Problem Set activities. Examples include: 

• In Mission 1, Topic B, Lesson 6, Fluency Practice, Happy Counting within 5, students count up or down and when told to stop have to remember the last number they said within 5. During the lesson students sort treasures in a bag into groups and count the number of objects in groups of 2, 3, or 4 and based on the number total they count put it in a treasure box numbered 2, 3, or 4. The Problem Set has students look at groups of objects and color groups of 2 red, groups of 3 blue, and groups of 4 orange. All three of these activities in Lesson 6 provide extensive work with KCC.2, count forward beginning from a given number within the known sequence.
• In Mission 2, Topic A, Lesson 2, Fluency Practice, Make a Shape, students use a craft stick to create a shape that has three points. During the Word Problem, students draw a pizza, divide it into slices and describe the shape of the slices to a partner. During the lesson, students use geoboards to create different triangles. All three of these activities in Lesson 2 provide extensive work with K.G.4, analyze and compare two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, and parts.
• In Mission 3, Topic B, Lesson 5, Fluency Practice, Show Me Longer and Shorter, students use their hands to show longer and shorter. During the lesson, students use a string and find objects in the classroom that are longer and shorter than the string. During the Problem Set, students cut out a string at the bottom of their worksheet and use it to find pictures on the page that are longer than the string. All three of these activities in Lesson 5 provide extensive work with K.MD.2, directly compare two objects with a measurable attribute in common, to see which object has “more or less of” the attribute, and describe the difference.
• In Mission 4, Topic B, Lesson 13, Fluency Practice, Dot Cards to 6, students are shown a card of dots, state how many dots they see, and break the dots into two parts. In the Word Problem, students solve, “4 silly seals were splashing in the water. Show the silly seals with your linking cubes. 2 more silly seals came to splash. Show the new seals. How many silly seals are splashing in the water now?” The Problem set has students look at a group of objects and fill in number bond sentences, “There are 6 cornstalks. 5 cornstalks are in the first row. 1 cornstalk is in the second.” All three of these activities in Lesson 13 provide extensive work with K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way. 
• In Mission 5, Topic A, Lesson 1, Fluency Practice, 5-Group Flashes: Partners to 5, students are shown a card with dots, state how many dots they see, and tell how many more dots would be needed to make 5. During the lesson, students investigate various bags of materials and count how many using an egg carton to see if there are enough to make 10. During the Problem Set students circle groups of pictures that show 10 ones. All three of these activities in Lesson 1 provide extensive work with K.CC.1, count to 100 by ones and by tens.

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each Mission and Topic Overview provides information about standards covered and how they are connected to prior learning. Examples include:

• In Mission 1, Topic E, Working with Numbers 6-8 in Different Configurations states, “As in previous topics, students will count objects and match their count with a digit card to reinforce that the last number said when counting tells the number of objects. Lesson 18 extends the counting of larger numbers by having students count 6 out of a larger set and order numbers 1–6 based on their knowledge that each number represents a quantity of objects. This calls their attention to the concepts of part and whole. Their 6 beans are within the larger amount. Students might say they disappeared or are hiding. They are there, but no longer a distinct set.”
• In Mission 2, Topic B, Three-Dimensional Solid Shapes states, “The lessons of Topic B replicate concepts taught in Topic A but with solid shapes. Lesson 6 begins with students finding solid shapes in their environment. They might find bottles of paint, tissue boxes, balls, or crayons and describe these objects to their neighbor using informal language. ‘My ball is round, and it bounces! This tissue box has a lot of pointy corners.’ Some students might even use the flat shape vocabulary they learned in Topic A to describe their solid shape. ‘There are a lot of rectangles on my tissue box, too.’”
• In Mission 4, Topic B, Decompositions of 6, 7, and 8 into Number Pairs states, “Topic B advances the work of Topic A, building students’ skill with number pairs for 6, 7, and 8, which is cultivated and maintained throughout Topics B and C during Fluency Practice. In the first three lessons of this topic, students decompose 6, 7, and 8. These decompositions are modeled as put together situations and represented as addition expressions (C = + ), as opposed to the take from decomposition type (C – B = ), which is taught in Topic D.”
• The Mission 5 Overview states, “Students have worked intensively within 10 and have often counted to 30 using the Rekenrek during Fluency Practice. This sets the stage for Mission 5, where students clarify the meaning of the 10 ones and some ones within a teen number and extend that understanding to count to 100. In Topic A, students start at the concrete level, counting 10 straws.”
• The Mission 6 Overview states, “As in Mission 2, students explore the relationship between flats and solids, this time using flats to build solids. ‘I made my square into a cube. First, I made another square the same size. Second, I attached the two squares with four straws the same length.’ They also apply their knowledge of ordinal numbers to describe the relative position of shapes within a set. ‘The yellow circle is first, and the red square is tenth.’”

The instructional materials for Zearn Math Grade Kindergarten meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The instructional materials include learning objectives that are visibly shaped by CCSSM cluster headings. Examples include:

• In Mission 1, Topic E, Lesson 20, Lesson Objective states, “Reason about sets of 7 varied objects in circular and scattered configurations. Find a path through the scattered configuration. Write numeral 7.” (K.CC.A,B)
• In Mission 2, Topic B, Lesson 8, Lesson Objective states, “Describe and communicate positions of all solid shapes using the words above, below, beside, in front of, next to, and behind.” (K.G.A)
• In Mission 3, Topic F, Lesson 21, Lesson Objective states, “Compare sets informally using more, less, and fewer.” (K.CC.C)
• In Mission 4, Topic C, Lesson 14, Lesson Objective states, “Represent decomposition and composition addition stories to 7 with drawings and equations with no unknown.” (K.OA.A)
• In Mission 5, Topic B, Lesson 6, Lesson Objective states, “Model with objects and represent numbers 10 to 20 with place value or Hide Zero cards.” (K.NBT.A and K.CC.A) 
• In Mission 6, Topic A, Lesson 3, Lesson Objective states, “Compose solids using flat shapes as a foundation.” (K.G.B)

The instructional materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

• In Mission 1, Topic D, Lesson 15, Lesson, students group objects randomly displayed in a circle into categories, and count to find how many. The materials state, “We are going to play Count, Wait, and Say How Many. Count how many there are in the group I point to. Wait for my magic snap, and then say how many. (Repeat until students demonstrate fluency in counting the groups.)” This activity connects K.CC.A, know number names and the count sequence, to K.CC.B, count to tell the number of objects. 
• In Mission 2, Topic C, Lesson 9, Lesson, students sort an assortment of flat shapes and solids. The materials state, “Do you think we could sort all of the things on your desk? Take a few minutes to look at all of your objects and think about what things they might have in common. (Allow time for thought and experimenting.)” This activity connects K.G.B, analyze, identify and describe shapes, to K.G.A, identify and describe shapes. 
• In Mission 5, Topic A, Lesson 4, Lesson, students count straws the Say Ten Way to 19 making groups of 10. The materials state, “At recess, 17 students were playing, 10 students played handball, while 7 students played tetherball. Draw to show the 17 students as 10 students playing handball and 7 students playing tetherball.” This activity connects K.NBT, numbers and operations in base ten, to K.CC, counting and cardinality.
• In Mission 6, Topic B, Lesson 5, Lesson, students make flat shapes by combining pattern blocks. The materials state, “Place the squares on your personal white board. See if you can make a different rectangle from your squares. (Pause.) Tell me about your work.” This activity connects K.G.A, identify and describe shapes, to K.G.B, analyze, compare, create, and compose shapes.