GK Overview CC 2021

ZEARN OVERVIEW KINDERGARTEN

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Kindergarten: Missions The table outlines the missions, lessons, and estimated duration of Kindergarten content on Zearn.

Mission Title Lessons Weeks

1 Numbers to 10 37 9 2 Two-Dimensional & Three-Dimensional Shapes 10 2

3 Comparison of Length, Weight, Capacity, & Numbers to 10 32 8

4 Number Pairs, Addition & Subtraction to 10 41 9 5 Numbers 10–20 & Counting to 100 24 6 6 Analyzing, Comparing, & Composing Shapes 8 2

Totals 152 36 Kindergarten: Standards The tables show where the new Kindergarten standards are covered on Zearn.

Counting & Cardinality STANDARD MISSION

K.CC.1 5 K.CC.2 1, 5 K.CC.3 1, 5 K.CC.4 1, 4

K.CC.5 1, 5 K.CC.6 3 K.CC.7 3

Operations & Algebraic Thinking

STANDARD MISSION

K.OA.1 4 K.OA.2 4 K.OA.3 1, 4 K.OA.4 4 K.OA.5 4

Numbers & Operations in Base 10

STANDARD MISSION K.NBT.1 5

Geometry STANDARD MISSION

K.G.1 2 K.G.2 2 K.G.3 2 K.G.4 2, 6 K.G.5 6 K.G.6 6

Measurement & Data

STANDARD MISSION K.MD.1 3 K.MD.2 3 K.MD.3 1, 2

© 2020 Zearn Portions of this work, Zearn Math, are derivative of Eureka Math and licensed by Great Minds. © 2020 Great Minds. All rights reserved.

Eureka Math was created by Great Minds in partnership with the New York State Education Department and also released as EngageNY.


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Summary Kindergarten mathematics is about:

1. Representing, relating, and operating on whole numbers, initially with sets of objects

2. Describing shapes and space More learning time in Kindergarten should be devoted to numbers than to other topics. Key Areas of Focus for Grades K-2: Addition and subtraction—concepts, skills, and problem solving Required Fluency: K.OA.5 Add and subtract within 5 Standards for Mathematical Practice: Each Standard for Mathematical Practice is integrated into the design of Zearn Math: MP.1 Make sense of problems and persevere in solving them. An explicit way in which the curriculum integrates this standard is through its commitment to consistently engaging students in solving multi-step problems. Purposeful integration of a variety of problem types that range in complexity naturally invites children to analyze givens, constraints, relationships, and goals. Problems require students to organize their thinking through drawing and modeling, which necessitates critical self-reflection on the actions they take to problem-solve. On a more foundational level, concept sequence, activities, and lesson structure present information from a variety of novel perspectives. The question, “How can I look at this differently?” undergirds the organization of the curriculum, each of its components, and the design of every problem.

Note: In Zearn Math Kindergarten, after Teacher-Led Instruction, students split into two groups for Independent Practice centers. After completing Independent Practice, students complete Paper Exit Tickets from Teacher Materials. See more in the schedule below.

MP.2 Reason abstractly and quantitatively. The use of tape diagrams is one way in which Zearn Math provides students with opportunities to reason abstractly and quantitatively. For example, consider the following problem: A cook has a bag of rice that weighs 50 pounds. The cook buys another bag of rice that weighs 25 pounds more than the first bag. How many pounds of rice does the cook have?


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To solve this problem, a student uses a tape diagram to abstractly represent the first bag of rice. To make a tape diagram for the second bag, the student reasons to decide whether the next bag is bigger, smaller, or the same size—and then must decide by how much. Once the student has drawn the models on paper, the fact that these quantities are presented as bags in the problem becomes irrelevant as children shift their focus to manipulating the units to get the total. The unit has— appropriately—taken over the thought process necessary for solving the problem. Quantitative reasoning also permeates the curriculum as students focus in on units. Consider the problem 6 sevens plus 2 sevens is equal to 8 sevens. The unit being manipulated in this sequence is sevens MP.3 Construct viable arguments and critique the reasoning of others. Time for “debriefing” is included in every daily lesson plan and represents one way in which the curriculum integrates this standard. During debriefs, teachers lead students in discussions or writing exercises that prompt children to analyze and explain their work, reflect on their own learning, and make connections between concepts. In addition to debriefs, “turn and talks” and “rally robins” are woven throughout lessons to create ongoing, frequent opportunities for students to develop this mathematical practice. Students use drawings, models and numeric representations, and precise language to make their learning and thinking understood by others. MP.4 Model with mathematics. A first grade student represents “3 students were playing. Some more came. Then there were 10. How many students came?” with the number sentence 3 + ☐ = 10. A fourth grade student represents a drawing of 5 halves of apples with an expression and writes 5 × ½. Both these students are modeling with mathematics. Students write both “situation equations” and “solution equations” when solving word problems. In doing so, they are modeling MP.2.

Note: In Zearn Math Kindergarten, this is happening daily in the opening routine with word problems and should be a part of the independent centers that occur daily.

MP.5 Use appropriate tools strategically. Building students’ independence with the use of models is a key feature of Zearn Math, and our approach to empowering students to use strategic learning tools is systematic. Models are introduced and used continuously, so that eventually students use them automatically. The depth of familiarity that students have with the models not only ensures that they naturally become a part of students’ schema, but also facilitates a more rapid and deeper understanding of new concepts as they are introduced. Aside from models, tools are introduced in Kindergarten and reappear throughout the curriculum in every concept. For example, rulers are tools that students in Kindergarten


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use to create straight edges that organize their work and evenly divide their papers, and they will continue to use them through Grade 5. MP.6 Attend to precision. In every lesson of every mission across the curriculum, students are manipulating, relating, and converting units and are challenged not only to use units in these ways, but also to specify which unit they are using. Literally anything that can be counted by can be a unit: There might be 3 frogs, 6 apples, 2 fours, 5 tens, 4 fifths, 9 cups, or 7 inches. Students use precise language to describe their work: “We used a paper clip as a unit of length.” Understanding of the unit is fundamental to their precise, conceptual manipulation. For example, 27 times 3 is not simply 2 times 3 and 7 times 3, rather it should be thought of as 2 tens times 3 and 7 ones times 3. Specificity and precision with the unit is paramount to conceptual coherence and unity. MP.7 Look for and make use of structure. There are several ways in which Zearn Math weaves this standard into the content of the curriculum. One way is through daily fluency practice. Sprints, for example, are fluency activities that are intentionally patterned. Students analyze the pattern of the Sprint and use its discovery to assist them with automaticity. For example, “Is the pattern adding one, or adding ten? How does knowing the pattern help me get faster?” MP.8 Look for and express regularity in repeated reasoning. Mental math is one way in which Zearn Math brings this standard to life. It begins as early as first grade, when students start to make tens. Making ten becomes both a general method and a pathway for quickly manipulating units through addition and subtraction. For example, to mentally solve 12 + 3, students identify the 1 ten and add 10 + (2 + 3). Isolating or using ten as a reference point becomes a form of repeated reasoning that allows students to quickly and efficiently manipulate units.

Note: In Zearn Math Kindergarten, this mathematical practice is also present in the Daily Digital Activities as students work on counting, counting on, decomposition and composition.


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Zearn Math Implementation

Core Instructional Shifts in Mathematics Students learning with Zearn Math develop a deep understanding of key grade-level math concepts, can connect those concepts to prior learnings, and are able to apply their knowledge flexibly and accurately when encountering new situations, contexts, and problems. All curricular materials reflect the core instructional shifts of mathematics— focus, coherence, and rigor—which are research-based and internationally benchmarked. These shifts ensure K–5 students build the critical arithmetic foundations that prepare them to extend algebraic thinking in middle school and explore more advanced mathematics in later grades.

Learning Principles In conjunction with the core instructional shifts in mathematics, a set of foundational learning principles guides the design of Zearn Math. These principles are grounded in teacher practice, education research, and brain science. Together, they enable the daily differentiation and engagement essential to helping all students love learning math. Everyone belongs and all math brains can grow. A sense of belonging in the math classroom and community is a precursor to engagement and learning. Zearn Math’s commitment to inclusion and emphasis on positive math mindsets helps teachers create learning environments where all students feel welcome and mistakes are viewed as opportunities for reflection and growth. The Zearn Math classroom model creates numerous opportunities for all students to participate in math discussions, shifting math dialogue from answer-getting to a participatory discussion. Daily Lessons also provide teachers with opportunities to build a deep understanding of each student and facilitate math discussions where students can bring their own learnings and frames of reference into the classroom. A strong classroom community enhances collective learning possibilities and ensures each and every student is able to engage in meaningful learning.

Flexible learning environments deepen engagement and understanding. Zearn Math is built on the Universal Design for Learning (UDL) framework, a set of research-based guidelines designed to create flexible learning environments that accommodate individual learning differences and ensure all students can access and participate in learning opportunities. Zearn Math aligns with UDL principles by providing students with multiple ways to engage in learning, acquire knowledge, and demonstrate understanding. Each day with Zearn Math, students learn independently on software-based lessons and in small groups with their teacher and peers. Across these learning experiences, students have opportunities to engage with the same math content in multiple ways using multiple modalities. All students build a deep understanding of grade-level content through this multimodality learning, as they engage with math ideas through words, texts, pictures, discussions, and concrete examples.


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Zearn Math’s flexible approach accommodates learning differences, encourages curiosity and exploration, and builds a participatory math dialogue.

Feedback, while learning, is precise, timely, supportive, and safe. Zearn Math instructional materials prompt teachers to provide direct feedback during moments of misconception. Throughout Lessons, teachers can assess individual student understanding as students model their math using concrete manipulatives, share their reasoning aloud, and problem solve. These moments of feedback provide all students with valuable, in-the-moment support and remediation from their teacher, allowing them to correct misconceptions so students can continue learning. Listening to students’ thinking during discussions can serve as a formative assessment that can inform teachers’ instructional decisions. When students learn in this type of feedback-rich and supportive environment, they become resilient, self-directed learners and can love learning math.

On-ramps, remediation, and pedagogical content PD allow all children to access grade-level math. Zearn Math recognizes that all students may not be on grade level at all times and provides on-ramps and remediation support for areas of unfinished learning. Zearn Math Teacher Materials include embedded strategies for teachers to utilize regarding errors and misconceptions when students are struggling with a concept. Zearn Math also provides pedagogical content PD that supports teachers as they address the needs of all the learners in their classroom.

Concept exploration begins in the concrete. As students learn new concepts with Zearn Math, they progress from using concrete materials to pictorial representations to abstract symbols, and they move back and forth between each stage to ensure concepts are reinforced. Through this approach, all students build a deep and sustainable understanding of math as new, abstract concepts are introduced in tangible and concrete ways. This approach also supports students’ language development, as students make connections across representations and describe their thinking aloud during each phase of math learning.

Problem solving starts with visualization and drawing a picture. Zearn Math teaches students to problem solve by first drawing a picture that models their understanding of the mathematics after they read a problem. Drawing a picture helps students make meaning of problems and understand which models or operations may or may not work for problem solving. This approach, which emphasizes careful reading and visualization, helps all students build flexible and accurate solving skills that they can apply across different problem contexts. Students are also introduced to the language used in mathematics and exposed to grade-appropriate, complex texts as they problem solve.

Learning math is coherent and fun. Children who love math describe the curiosity and joy of exploring connections between concepts and working through problems. Zearn Math allows students to access math


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understanding—and have fun along the way—by teaching math as a progression of coherent ideas rather than as disconnected procedures.

Zearn Math Kindergarten Schedule Daily Teacher-Led Instruction Every day, teachers lead Fluency, Word Problems, and Lessons from Teacher Materials. Teachers may choose to deliver instruction in stations or as a whole group. Daily Teacher-Led Instruction builds number sense with concrete manipulatives, pictorial representations, and discussion. Throughout Teacher-Led Instruction, students are provided opportunities to solve word problems independently, share their strategies aloud, and discuss classmates’ problems solving strategies. Using the question prompts in Teacher Materials, teachers facilitate thoughtful mathematical discussions between students that allow learners to refer to and build on each other’s ideas.

Two Stations After Teacher-Led Instruction, students split into two groups for practice and teachers circulate between stations to provide feedback and support. After independent practice, teachers guide students in conversation in the Student Debrief. In Missions 5 and 6, students then complete Paper Exit Tickets, available in Teacher Materials.

• Digital Activities: Each student works through Digital Activities that help students independently practice counting, addition, embedded numbers, and decomposing and composing numbers up to 20 using interactive five frames, ten frames, and number bonds. Students should complete four Digital Activities each week. Teachers should monitor progress in the Zearn Math Activity Tracker. For students struggling to progress through Digital Activities and not meeting their weekly goal, teachers should use the questions provided in the Mission Overview as a way to support progress.

• Problem Sets: Each student works through the Paper Problem Set to independently solve problems flexibly using a range of strategies in a variety of contexts. The primary goal of the Problem Set is for students to apply the conceptual understanding(s) learned during the lesson. Students are encouraged to choose their own strategy and/or representation as appropriate. Teachers should circulate during this time to monitor for different strategies used, use the Notes in the Lesson to support students who may need further scaffolding with a concrete manipulative or an alternative representation, and provide feedback to further student thinking. Teachers can print Problem Sets from Teacher Materials.


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Implementing Digital Activities in Kindergarten Zearn Math for Kindergarten includes developmentally appropriate Digital Activities, which are short, engaging, and designed to build number sense. During the Digital Activities, students build number sense at their own pace through an intentional progression from Numbers to 5 to Numbers to 20, and receive precise digital feedback at the moment of misconception. Students complete each Digital Activity independently through their Zearn account. When students log in, they are directed to their personal Student Feed, where they can see their currently assigned Digital Activity. Students can only access the next Digital Activity in the sequence once they complete their currently assigned activity. Each activity takes about ten minutes. Students advance through activities at their own pace and can revisit activities for additional practice. Embedded supports in the Digital Activities precisely address misconceptions in real time and give all students opportunities to try again. The concrete to pictorial to abstract learning approach serves as the foundation for all Digital Activities, in order to create access by visually supporting developing understanding. Each Mission Overview has specific guiding questions for teachers to support students’ mathematical development in the Digital Activity station. It is recommended that before teaching with Zearn Math Kindergarten, teachers try out each type of Digital Activity, making sure to get a few answers incorrect to experience the embedded and precise feedback. Activities can be previewed in Teacher Accounts, or through the links below:

The Counting Train® The Counting Train activity prompts students to choose different balloons on screen that are each filled with a different number of colorful and fun animals. Students count the objects and select the train car number that matches the total. Try The Counting Train ➜

Sum Snacks® Sum Snacks asks students to give playful, on-screen animals fruit to eat, prompting them to count each additional piece of fruit. As the student increases the amount of fruit, numbers appear below each piece of fruit to help count on to the total and begin to build number sense around embedded numbers and addition. Try Sum Snacks ➜

https://www.zearn.org/k_activities/11



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Hop Skip Splash!® Hop Skip Splash prompts students to count additional objects needed to help the frog hop across a stream. Students are asked to both count up and count down for each problem, solidifying their understanding of the counting sequence. Try Hop Skip Splash! ➜ Make and Break® Make and Break asks students to decompose and compose numbers 5 to 20 using interactive five frames, ten frames and number bonds. Students are prompted to complete addition or subtraction sentences, reinforcing how their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers connects to solving addition and subtraction equations. Try Make and Break ➜

Next Stop Top® Next Stop Top asks students to decompose and compose numbers 5 to 20 using interactive number bonds that prompt students to practice identifying 5 and 10 as embedded numbers. The activity engages students by having them work their way up to the top of a building, stopping at each floor to decompose and compose colorful ten frames (depicted as large windows!). Try Next Stop Top ➜

Many teachers introduce their kindergarten students to Zearn Math Digital Activities by modeling the student experience together. The Zearn Help Center includes a short video to help teachers orient their students to the digital experience. It is recommended that teachers whole class model one Digital Activity each day during the first week of instruction, making sure to show students how to: • Sign-in: Log in as a student, and show students where to put their username and password,

and how to click the blue button to begin. • Start an activity: Show students that clicking the blue Start button on the top card in their

Next Up feed will start the activity. Once in the activity, start by pressing the green play button.

• Press the text to speech button: Digital Activities are designed with minimal instructional prompts to support young learners. All instructional prompts students see in Digital Activities have audio support through either recorded audio or Zearn’s text-to-speech feature. Students can click on the audio button next to text questions or prompts to hear the words spoken aloud. These accessibility features are particularly important for students with cognitive impairments, students with learning differences, and English Language Learners. Ensure all students know where to find this button by whole class modeling the






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text to speech function. If English Language Learners need instructional prompts read out loud to them in another language, it is recommended that students use the Google Chrome browser and use the Dictation plug-in. Instructions for teachers on how to use this plug-in can be found in the Zearn Help Center.

• Show the on-screen keypad: When students complete questions on Zearn, they have the option to use Zearn’s on-screen keypad, rather than a computer keyboard, to type and submit their answers. This accessibility feature is particularly important for tablet users and young students who may not know how to use a computer keyboard. Teachers should orient all students to this feature to show them how to use it. Instructions for using the keypad can be found in the Zearn Help Center.

• Complete an activity: Complete the full activity and end the activity by clicking the blue Done button.

• Use the feed: Show students that the next activity is on the top of their Next Up feed. • Log out: Show students how to click the log-out button when they are done Zearning! After week 1, students should independently work through Digital Activities. As students work through Digital Activities, the Zearn Math Activity Tracker provides teachers with real-time data for student progress through the sequence of Digital Activities. Teachers should check the Activity Tracker twice weekly to monitor student progress in their digital fluency work. If students are not completing four activities per week, teachers should check in with students during station time and use the guiding questions provided in each Mission Overview to support students’ mathematical development in each type of fluency activity. Additionally, as teachers are circulating through the Problem Set station, they should periodically circulate through the Digital Activity station to ensure students are making progress, using the questions provided in the Mission Overview as a way to check for understanding.

Assessments The Zearn Math curriculum includes a series of formative assessments designed to provide teachers with precise and actionable feedback they can use to inform instruction and respond to the needs of each student. Assessments focus on the big ideas of mathematics and allow students to demonstrate their understanding across multiple modalities through a thoughtful balance of software- and paper-based experiences. Zearn Math offers daily, lesson-level assessments—the Tower of Power (available for 1st–5th grades) and Exit Tickets—along with Mid- and End-of-Mission assessments that are more comprehensive and administered roughly biweekly. All assessments are designed to fit into the classroom model and enhance, rather than distract from, instruction.

Diagnostic Assessment Zearn Math is designed so that all students work on grade-level content. There is no diagnostic assessment for placement. It is recommended that all students begin on Mission 1 Lesson 1 of their grade-level and work through the same scope and sequence. This ensures students spend the majority of time on the major clusters of each grade. Teachers have the opportunity to


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provide targeted support during daily centers, and the Zearn Daily Digital Activities will provide targeted remediation when students need it.

Exit Tickets Exit Tickets are un-scaffolded practice problems that allow students to transfer their learning to paper and demonstrate their understanding of the content of the lesson. Teachers can use Exit Tickets as formative assessments to identify students who may need extra help with a particular concept and provide appropriate support.

Note: In Zearn Math Kindergarten, the beginning Missions do not include Exit Tickets to allow K students to focus on concrete learning. During these Missions, teachers should use the problem set as an opportunity to informally assess. These assignments are done independently. The primary goal of the problem set is for students to apply the conceptual understanding(s) learned during the lesson. Students transition to more independent work throughout the year and then will begin to complete Exit Tickets.

Mid-Mission and End-of-Mission Assessments Mid-Mission and End-of-Mission assessments are formative assessments administered roughly halfway through the Mission and at the conclusion of the Mission respectively. For 1st–5th grades, these paper assessments consist of open response items that require students to show their work or explain their thinking in a variety of ways, including drawing models and writing explanations. In Kindergarten, each paper-based assessment is designed to be administered interview-style where teachers record their observations of the student’s work and thinking. The assessment items vary in their focus, ranging from items that highlight a student’s understanding of a big mathematical idea to items that are more focused on students’ procedural fluency.

English Language Learner Support Zearn Math is designed so that language learners of all levels can and should engage with grade-level math content that is scaffolded with the appropriate amount of linguistic support. Instructional materials foster the side-by-side development of math understanding and language competence, as students are provided with opportunities to both access mathematics using existing language skills and extend their language development in the context of mathematical sense-making. While these features of Zearn Math support all students in building a deep understanding of grade-level mathematics, they are particularly critical for meeting the needs of English Learners, who are simultaneously learning math and acquiring language. In each Mission Overview, there is guidance with strategies for meeting the needs of a range of learners, and in particular, support, accommodations, and modifications for English Language Learners in both Teacher-Led Instruction and Digital Activities. It is also recommended that all teachers orient English Language Learners to the Digital Activities as outlined in the “Implementing Digital Activities in Kindergarten” section above.


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Parent/Caregiver Resources Zearn Math provides resources for informing parents or caregivers about the mathematics program and suggestions for how they can support their child’s progress with Zearn Math. Zearn’s Help Center offers Parent Orientation Resources such as downloadable Parent Letters and Zearn Helpers, which provide families with strategies and tips to engage with their child’s math learning. Zearn’s website includes a web page designed for parents with orientation webinars for families, available in both English and Spanish. Read our Approach to Teaching & Learning to learn more about how Zearn Math supports a love of learning math for all students and ask further implementation questions in Zearn Math’s Help Center.

https://help.zearn.org/hc/en-us/articles/360052425953-Parent-orientation-resources

https://about.zearn.org/remote-zearning

https://webassets.zearn.org/resources/zearn_math_teaching_and_learning_approach.pdf

https://help.zearn.org/hc/en-us/categories/115000937227-Implementation-Resources

https://help.zearn.org/hc/en-us/categories/115000937227-Implementation-Resources


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Mission 1

Numbers to 10 OVERVIEW The first day of Kindergarten is long anticipated by parents and young students. Students expect school to be a dynamic and safe place to learn, an objective that is realized immediately by their involvement in purposeful and meaningful action.

In Topics A and B, classification activities allow students to analyze and observe their world and articulate their observations. Reasoning and dialogue begin immediately. “These balloons are exactly the same.” “These are the same but a different size.” As Topic B closes, students recognize cardinalities as yet one more lens for classification (K.MD.3). “I put a pencil, a book, and an eraser, three things, in the backpack for school.” “I put five toys in the closet to keep at home.” From the moment students enter school, they practice the counting sequence so that when counting a set of objects, their attention can be on matching one count to one object, rather than on retrieving the number words (K.CC.4a).

In Topics C, D, E, and F, students order, count (K.CC.1), and write (K.CC.3) up to ten objects to answer how many questions from linear, to array, to circular, and finally to scattered configurations wherein they must devise a path through the objects as they count. Students use their understanding of numbers and matching numbers with objects to answer how many questions about a variety of objects, pictures, and drawings (K.CC.5).

They learn that the last number name said tells the number of objects counted (K.CC.4b). Daily, they engage in mathematical dialogue. They might compare their seven objects to a friend’s. For example, “My cotton balls are bigger than your cubes, but when we count them, we both have seven!”

Very basic expressions and equations are introduced early in order to ensure students’ familiarity with numbers throughout the entire year so that they exit fluent in sums and differences to 5 (K.OA.5). Decomposition is modeled with small numbers with materials and drawings and as addition equations. Students see that both the expression 2 + 1 (Topic C) and the equation 3 = 2 + 1 (Topic D) describe a stick of three cubes decomposed into two parts (K.OA.3). Emphasis is not placed on the expressions and equations or using them in isolation from the concrete and pictorial—they are simply included to show another representation of decompositions alongside counters and drawings.

In Topics G and H, students use their understanding of relationships between numbers to recognize that each successive number name refers to a quantity that is one greater and that the number before is one less (K.CC.4c). This important insight leads students to use the Level 2 strategy of counting on rather than counting all, later in the year and on into Grade 1.

In this mission, daily fluency activities with concentration and emphasis on counting (K.CC.4ab, K.CC.5) are integrated throughout the lesson: “I


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counted six beans in a row. I counted six beans in a circle and then squished them together and counted again. There were still six!” “I can make my six beans into rows, and there are no extras.” Students complete units of five using the fingers of their left hand and 5-groups. The numbers 6, 7, 8, and 9 are introduced relative to the number 5: “Five fingers and ____ more.” Students also explore numbers 5 to 9 in relation to 10, or two complete fives: “Nine is missing one to be ten or two fives.” (K.OA.4)

As students begin to master writing numbers to 10, they practice with paper and pencil. This is a critical daily fluency that may work well to close lessons, since management of young students is generally harder toward the end of math time. The paper and pencil work is calming, though energized.


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Mission 2

Two-Dimensional and Three-Dimensional Shapes OVERVIEW 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 this mission, students seek out flat and solid shapes in their world (K.G.1). Empowered by this lens, they begin to make connections between the wheel of a bicycle, the moon, and the top of an ice cream cone. Just as the number 4 allowed them to quantify 4 mountains and 4 mice as equal numbers, learning to identify flats and solids allows them to see the relationship of the simple to the complex, a mountain’s top to a plastic triangle and cone sitting on their desk.

To open Topic A, students find and describe flat shapes in their environment using informal language, without naming them at first (K.G.4). In Lesson 2, they classify the shapes, juxtaposing them with various examples and non-examples. This process further refines their ability to talk about the shapes, for example, as closed or having straight sides. The naming of the flat shape as a triangle is part of that process, not the focus of it (K.G.2, K.G.1).

The same process is then repeated with rectangles in Lesson 3 and hexagons and circles in Lesson 4. In Lesson 5, students manipulate all the flat shapes using position words as the teacher gives directives such as, “Move the closed shape with three straight sides behind the shape with six straight sides.” These positioning words are subsequently woven into the instructional program, at times in math fluency activities, but also throughout the entire school day.

The lessons of Topic B replicate those of Topic A but with solid shapes. In addition, students recognize the presence of the flats within the solids. The mission closes in Topic C with discrimination between flats and solids. A culminating task involves students in creating displays of a given flat shape with counter-examples and showing related solid shapes (K.G.3).

The fluency components in the lessons of Mission 1 included activities wherein students used a variety of triangles and rectangles to practice the decompositions of 3 and 4. Flats and solids will continue to be included in fluency activities in this mission and throughout the year so that students have repeated experiences with shapes, their attributes, and their names. Daily number fluency practice in this new mission is critical. There are two main goals of consistent fluency practice: (1) to solidify the numbers of Mission 1 and (2) to anticipate the numbers of Missions 3, 4, and 5. Therefore, students continue to work extensively with numbers to 10 and fluency with addition and subtraction to 5.

The Kindergarten year closes in Mission 6 with another geometry unit. By that time, having become much more familiar with flats and solids, the students compose new flat shapes (“Can you make a rectangle from these two triangles?”) and build solid shapes from components (“Let’s use these straws to be the edges and these balls of clay to be the corners of a cube!”).


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This mission will allow them to bring together all that they have learned throughout the year as they manipulate shapes and their components (K.G.4, K.G.5).


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Mission 3

Comparison of Length, Weight, Capacity, and Numbers to 10 OVERVIEW Having observed, analyzed, and classified objects by shape into predetermined categories in Mission 2, students now compare and analyze length, weight, capacity, and finally, numbers in Mission 3. Students use language such as longer than, shorter than, as long as; heavier than, lighter than, as heavy as; and more than, less than, the same as. “8 is more than 5.” “5 is less than 8.” “5 is the same as 5.” “2 and 3 is also the same as 5.”

Topics A and B focus on comparison of length, Topic C on comparison of weight, and Topic D on comparison of volume (K.MD.2). Each of these topics opens with an identification of the attribute being compared within the natural context of the lesson (K.MD.1). For example, in Topic A, before exploring length, students realize they could have chosen to compare by a different attribute: weight, length, volume, or numbers (K.MD.1).

T: Students, when you compare and say it is bigger, let’s think about what you mean. (After each question, allow students to have a lively, brief discussion.)

T: Do you mean that it is bigger, like this book is heavier than this ribbon? (Dramatize the weight of the book and ribbon.)

T: Do you mean that it is longer, like this ribbon is longer than this book? (Dramatize the length of the ribbon.)

T: Do you mean that it takes up more space, like this book takes up more space than this ribbon when it is all squished together? (Dramatize.)

T: Do you mean to compare the number of things, like the number of books and ribbons? (Dramatize a count.)

T: So, we can compare things in different ways! Today, let’s compare by thinking about longer than, taller than, or shorter than. (Dramatize.)

After the Mid-Mission Assessment, Topic E begins with an analysis using the question, “Are there enough?” This leads naturally from exploring when and if there is enough space to seeing whether there are enough chairs for a small set of students: “There are fewer chairs than students!” This bridges into Topics F and G, which present a sequence building toward the comparison of numerals (K.CC.7). Topic F begins with counting and matching sets to compare (K.CC.6). The mission culminates in a three-day exploration, one day devoted to each attribute: length, weight, and volume (K.MD.2). The mission closes with a culminating task devoted to distinguishing between the measurable attributes of a set of objects: a water bottle, cup, dropper, and juice box (K.MD.1).

The mission supports students’ understanding of amounts and their developing number sense. For example, counting how many small cups of rice are contained within a larger quantity provides a foundational concept of place value: Within a larger amount are smaller equal units, which together make up the whole. “4 cups of rice is the same as 1 mug of rice.” Compare that statement to “10 ones is the same as 1 ten” (1.NBT.2a). As students become confident directly comparing the length of a pencil and a crayon with statements such as “The


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pencil is longer than the crayon” (K.MD.2), they will be ready in later grades to indirectly compare using length units with statements such as “The pencil is longer than the crayon because 7 cubes is more than 4 cubes” (1.MD.2).

Additional foundational work for later grades is as follows:

• Foundational work with equivalence. The length of a stick with 5 linking cubes is the same as the length of my cell phone. A pencil weighs the same as a stick with 5 linking cubes. Each mission component on measurement closes with a focus on the same as.

• Foundational work for the precise use and understanding of rulers and number lines. The mission opens with lessons pointing out the importance of aligning endpoints to measure length.

• Foundational understanding of area. At the opening of the second half of the mission, students informally explore area as they see whether a yellow circle fits inside a red square. They then see how many small blue squares will fit inside the red square and, finally, that many beans will cover the same area (pictured to the right).

• Foundational understanding of comparison. As students count to compare the length of linking cube sticks, they are laying the foundation for answering how many more…than/less…than questions in Grade 1 (1.MD.2).


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Mission 4

Number Pairs, Addition and Subtraction to 10 OVERVIEW Mission 4 marks the next exciting step in math for kindergartners—addition and subtraction! Students begin to harness their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers to reason about and solve addition and subtraction expressions and equations (K.OA.1, K.OA.2).

In Topic A, decompositions and compositions of numbers to 5 are revisited to reinforce how a whole can be broken into two parts and how two parts can be joined to make a whole. Decomposition and composition are taught simultaneously using the number bond model, so students begin to understand the relationship between parts and wholes before adding and subtracting, formally addressed in Topics C and D.

Topic B continues with decomposing and composing 6, 7, and 8 using the number bond model. Students systematically work with each quantity, finding all possible number pairs using story situations, objects, sets, arrays, 5 + n patterns, and numerals (K.OA.3).

Topic C introduces addition to totals of 6, 7, and 8 within concrete and pictorial settings, first generating number sentences without unknowns (e.g., 5 + 2 = 7) to develop an understanding of the addition symbol and the referent of each number within the equation. Next, students graduate to working within the addition word problem types taught in kindergarten: add to with result unknown (A + B = ___), put together with total unknown (A + B = ___), and both addends unknown (C = ___ + ___) (K.OA.2). Students draw a box around the total to track the unknown.

Topic D introduces subtraction with 6, 7, and 8 with no unknown. The lessons in Topic D build from the concrete level of students acting out, crossing out objects in a set, and breaking and hiding parts, to more formal representations of decomposition recorded as or matched to equations (C – B = ___).

Topics E, F, and G parallel the first half of the mission with the numbers 9 and 10. Topic E explores composition, decomposition, and number pairs using the number bond model (K.OA.3). It is essential that students build deep understanding and skill with identifying the number pairs of 6 through 10 because this is foundational to Grade 1’s fluency with sums and differences within 10, as well as Grade 2’s fluency with sums and differences to 20. Topics F and G deal with addition and subtraction, respectively. Students are refocused on representing larger numbers by drawing the 5 + n pattern to bridge efficiently from seeing the embedded five to representing that as addition.


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After addition and subtraction have been introduced, Topic H explores the behavior of zero: the additive identity. Students learn that adding or subtracting zero does not change the original quantity. Students also begin to see patterns when adding 1 more and the inverse relationship between addition and subtraction (8 + 2 = 10 and 10 – 2 = 8). Finally, students begin to formally study and explore partners to 10 (K.OA.4), though this essential work has been supported throughout Mission 4 during fluency activities.

The culminating task of this mission asks students to demonstrate their understanding of addition as putting together, or adding to, and subtraction as taking apart, or taking from. Students use mathematical models and equations to teach a small group of students, administrators, family members, or community partners about a decomposition of 10.


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Mission 5

Numbers 10–20 and Counting to 100 OVERVIEW Students have worked intensively within 10 and have often counted to 30 using the Rekenrek during fluency activities. 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.

T: Count straws with me into piles of ten. S: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 1, 2, 3, …, 8, 9, 10. 1, 2, 3, …, 8, 9, 10. T: Let’s count the piles! S: 1 pile, 2 piles, 3 piles, 4 piles.

Thus, Kindergarten students learn to comfortably talk about 10 ones, setting the foundation for the critical Grade 1 step of understanding 1 ten. They next separate 10 objects from within concrete and pictorial counts up to 20, analyzing the total as 10 ones and no ones or 10 ones and some ones (K.CC.1, K.NBT.1). They see two distinct sets which are then counted the Say Ten way: ten 1, ten 2, ten 3, ten 4, ten 5, ten 6, ten 7, ten 8, ten 9, 2 tens. Students hear the separation of the 10 ones and some ones as they count, solidifying their understanding as they also return to regular counting: eleven, twelve, thirteen, …, etc. (K.CC.5)

In Topic B, the two distinct sets of ones are composed, or brought together, through the use of the Hide Zero cards (pictured below) and number bonds. Students represent the whole number numerically while continuing to separate the count of 10 ones from the count of the remaining ones with drawings and materials (K.NBT.1). Emerging from Topic B, students should be able to model and write a teen number without forgetting that the 1 in 13 represents 10 ones (K.CC.3).

Topic C opens with students making a simple Rekenrek to 20 (pictured to the right) and modeling numbers thereon. The tens can be seen both as two lines with a color change at the five or two parallel unicolor fives.

In Topic C, the focus is now on the decomposition of the total teen quantity so that one part is ten ones. This is what makes Topic C a step forward from Topics A and B. Previously, the ten


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and ones were always separated when modeled pictorially or with materials. Now, the entire teen number is a whole quantity represented both concretely and pictorially in different configurations: towers or linear configurations, arrays (including the 10-frame or 5-groups), and circles. Students decompose the total into 10 ones and some ones. Through their experiences with the different configurations, students have practice both separating 10 ones within teen numbers and counting or conservation as they count quantities arranged in different ways and, as always, use math talk to share their observations (K.CC.5). They also come to know each successive teen number as one larger than the previous number (K.CC.4a).

In Topic D, students extend their understanding of counting teen numbers to numbers from 21 to 100. They first count by tens both the Say Ten way—1 ten, 2 tens, 3 tens, 4 tens, etc.—and the regular way: twenty, thirty, forty, etc. They then count by ones to 100, first within a decade and finally across the decade (K.CC.1, K.CC.2). Topic D involves the Grade 1 standard 1.NBT.1 because students also write their numbers from 21 to 100.

The writing of larger numbers has been included because of the range of activities they make possible. The writing of these numbers is not assessed nor emphasized, however. Topic D closes with an optional exploration of numbers on the Rekenrek, bringing together counting with decomposition and finding embedded numbers within larger numbers. This lesson is optional because it does not directly address a particular Kindergarten standard.

In Topic E, students apply their skill with the decomposition and composition of teen numbers. In Lesson 20, they represent both compositions and decompositions as addition statements (K.NBT.1). In Lesson 21, they model teen quantities with materials in a number bond and hide one part. The hidden part is represented as an addition sentence with a hidden part (e.g., 10 + ___ = 13 or 13 = ___ + 3). The missing addend aligns Lesson 21 to the Grade 1 standard 1.OA.8. In Lesson 22, students apply their skill with decomposition into 10 ones and some ones to compare the some ones of two numbers and thus to compare the teen numbers. They stand on the structure of the 10 ones and use what they know of numbers 1–9 (MP.7). Comparison of numbers 1–9 is a Kindergarten standard (K.CC.6, K.CC.7).

In Lesson 23, students reason about situations to determine whether they are decomposing a teen number (as 10 ones and some ones) or composing 10 ones and some ones to find a teen number. They analyze their number sentences that represent each situation to determine if they started with the total or the parts and if they composed or decomposed, for example, 13 = 10 + 3 or 10 + 3 = 13 (K.NBT.1). Throughout the lesson, students draw the number of objects presented in the situation (K.CC.5).

The mission closes with a culminating task, wherein students integrate all the methods they have used up until now to show decomposition. For example, they are instructed, “Open your mystery bag. Show the number of objects in your bag in different ways using the materials you choose” (MP.5). This experience also serves as a part of the End-of-Mission Assessment, allowing students to demonstrate skill and understanding using all they have learned throughout the mission.

Towers Arrays Circles

I have 10 ones and 2 ones. 10 and 2 is ___. 12 = 10 + ___.


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Mission 6

Analyzing, Comparing, and Composing Shapes OVERVIEW The kindergarten chapter of Zearn Math comes to a close with another opportunity for students to explore geometry. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.

Topic A begins with students applying their knowledge of attributes to analyze two- and three-dimensional shapes from the real world and to construct models using straws and clay (K.G.5). “Let’s use the straws to make the sides of the rectangle, and we’ll stick the straws together at each corner using clay!” Students use their understanding of ordination to thirds to share and communicate the systematic construction of flats and solids. “First, I cut four straws to be the same length. Second, I made a square by placing the four straws so they look like a frame. Third, I connected the sides at the corners with four little clay balls” (K.CC.4d).

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 (K.CC.4d). “The yellow circle is first, and the red square is tenth.”

The lessons of Topic B focus on composition and decomposition of flat shapes (K.G.6). Students begin by using flats to compose geometric shapes. “I put two triangles together to make a square.” They then decompose shapes by covering part of a larger shape with a smaller shape and analyzing the remaining space. “When I cover part of my square with this triangle, I can see another triangle in the empty space.”

As they build competence in combining and composing shapes, students build toward more complex pictures and designs. Students progress through stages as they build competence in combining shapes to form pictures, beginning with trial and error and gradually considering the systematic combination of components. “This square fits here because the corners match the puzzle.” The culminating task of this mission is set up as a Math Olympics, a celebration of student learning from the whole year. Students complete tasks related to number, measurement, operations, and geometry.


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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.

Documents

GK Overview CC 2021