Kindergarten Program Tools
All students must have access to high-quality, rigorous mathematics instruction. The Exemplary Elementary Mathematics Program document Links to an external site. identifies how the ideas of exemplary mathematics align to Planning and Preparation, Classroom Environment, Instruction, and Professional Responsibilities as related to the Danielson Framework.
Daily mathematics instruction
- is provided for 60 minutes each day for Kindergarten;
- begins with a brief (10 minute) Number Talk for developing fluency or a number routine for developing number sense and numeracy;
- features a high-quality, standards-based instructional task;
- leverages an appropriate grouping structure that maximizes instructional time, student collaboration, engagement, and discussion;
- provides students with opportunity to work with concepts, procedures, and problems before explicit instruction;
- promotes diverse strategies, interpretations, and representations so that students develop their understanding;
- makes use of and connects representations of content;
- is rich meaningful discourse;
- provides appropriate, responsible practice for retaining understanding and using skills efficiently; and
- is evidence of effective teaching practices for equitable mathematics.
Daily high-quality first instruction is described in greater detail on the tab below. Other headings below provide information, resources, and/or links for implementation of the Exemplary Elementary Mathematics Program.
Click on one of the headings below to access information, resources, and/or links for implementation of the Exemplary Elementary Mathematics Program.
Articulation Guidance
Linked below are articulation recommendations from the Elementary Mathematics Office. Adjustments may be needed for varied reasons such as resource allocation, scheduling challenges, or departmentalization models. NOTE: Title I schools also have their own requirements.
Community and Identity
Math Identity
A mathematics identity is the deeply held belief or disposition one has about math and their ability to do math. Our role as teachers is to cultivate and nurture positive math identities. Our work is to make sure we continually learn about who are students are as individuals and how they see themselves as mathematicians. There are a variety of ways to learn about students' identities. Some of those activities are baked into module 1. Others are part of the community activities below.
JOURNAL PROMPTS about DISPOSITION
Remember that these works shouldn't be graded. Grammar, spelling, and punctuation shouldn't matter either. Instead, leave a response to students to let them know you read it and you hear them. To manage work load, rotate the entries you read. Keep in mind this isn't something you need to do daily. Journal prompts could be done once a week or once every two weeks.
Below are a collection of prompts from Productive Math Struggle (Corwin, 2020) for you to choose from but feel free to create your own.
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STUDENT SURVEYS
Surveying students about their thoughts and beliefs about mathematics provides valuable insight to guide your work. Surveys can be given at various times during the year to see how students are growing and changing. A scale response works well and for young students you might choose to use a smiley face, a frowny face, and a neutral face. Below are questions you might include in your survey. They come from Productive Math Struggle (Corwin, 2020). Questions on the left are intended for younger students and questions on the right are intended for older students. You can add to or change questions as you see fit.
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DEAR MATH LETTERS
Engage your class in a conversation using the prompts below (from Dear Math: Why Kids Hate Math and What Teachers Can Do About It by Strong and Butterfield). Then ask students to write a "Dear Math" letter. Depending on the grade level, provide appropriate writing supports. The goal is to encourage thinking about/talking about math identity and provide teachers with insights about how their students feel about themselves as mathematicians.
- Tell me about a time when you felt successful in math class? What happened?
- Tell me about a time when you struggled in math class? What happened?
- When your friends talk about math, what do they say or do?
- What is one way math has helped you grow?
- What can you thank math for?
- How would you change math classrooms?
- What would you like more of in math class?
COMMUNITY
A classroom community is built and maintained throughout the year. A nurturing classroom community is one built on trust and safety. Students share their ideas freely and listen to the ideas of others. They work collaboratively. They know and respect one another. The activities below can be used to learn about student identity while also building toward a stronger math classroom community. You can use these activities at any time during the year.
Number Quilt: A number quilt gives students an opportunity to show who they are through numbers. Each student writes a number on a small rectangular piece of colored construction paper. They attach it to a larger piece of white construction paper with a line of glue at the top. The piece of paper can be lifted up to reveal a picture or words that describe what the number represents about the student.
My Favorite Number: Students can create name tents and add their favorite number to the name tent. On the inside, students write about why the number is their favorite. Students then use the name tents to introduce themselves to new partners and groups.
Myself in Numbers: Students identify numbers that describe them and record them on a lap board or something similar. Classmates guess what the numbers might represent about the student. The student shares and classmates earn points for how many guesses they got right.
Picture is Worth 1,000 Numbers: Students bring a picture from home or draw something about their lives. Students then use numbers to describe the picture and why it (or the topic) is important to them.
My Math Biography: Students write their math biographies. They discuss how they use math in their everyday lives. They can also discuss experiences they have had in math in the past and goals they have for working with math in the future.
My Math Superpower: Students create themselves as a "math superhero." They identify what they do well in math and announce those as the superpowers of their superhero selves.
My Summer in Numbers: Students use numbers to describe themselves and their experiences over the summer. This activity could be easily modified to describe family events, holidays, and so on.
Closure
The linked page provides descriptions and videos of closure activities. “Closure in a lesson does not mean to pack up and move on. Rather, it is a cognitive activity that helps students focus on what learned and whether it made sense and had meaning.” How the Brain Learns Mathematics (2007) P. 104.
Daily High-Quality First Instruction
High-quality first instruction is an expectation for each and every student, each and every day. It nurtures student identity, agency, and self-efficacy. First instruction creates an opportunity for students to develop conceptual understanding, build procedural fluency, and apply their learning to solve authentic problems. High-quality first instruction is grounded in evidence-based, effective teaching practices (NCTM, 2014). High-quality math instruction should occur everyday for 75 minutes. The link below outlines the expectations and provides related resources.
Daily High-Quality First Instruction
Family Communication and Support
The linked page provides to access to a variety of resources for supporting parents.
HCPSS Family Math Support Center: This site provides information about grade level topics, vocabulary, practice materials, and related videos.
Math in Minutes: These district-created videos can be used to help families with skills and concepts in your course.
- Decomposition of Numbers Links to an external site.
- Addition With A Number Chart Links to an external site.
- Subtraction With A Number Chart Links to an external site.
- Addition On A Number Line Links to an external site.
- Addition: Partial Sums Links to an external site.
- Subtraction: Take Away and Difference Links to an external site.
- Selecting Appropriate Mathematics Tools Links to an external site.
Math Milestones: These video clips give parents an idea of what mastery of important concepts looks like at each grade level.
Module Overviews for Families: Link to import from Commons *remember to have Commons already open in a different tab for this link to work
Grade Level Readiness Assessments
Grade Level Readiness Assessments can be useful in determining student understanding of foundational number concepts needed for grade level instruction. They should be administered in an interview or small group setting.
Grade Level Readiness Assessment FAQs Links to an external site.
| Grade 1 | Grade 2 |
|---|---|
| All Materials PDF Links to an external site. | All Materials PDF Links to an external site. |
Investigations
In order to teach the Maryland College and Career-Ready Standards Links to an external site., teachers will use resources provided by the Early Childhood and Elementary Mathematics Office. Recommended resources, aligned to each standard, can be found in the standards page. These include Investigations in Data and Space, Teaching Student-Centered Mathematics K-3, Developing Number Concepts, Hands-On Standards, Super Source K-2, and Math Intervention: Building Number Power.
The questioning and modeling practices highlighted in the Investigations program align with principles of developmentally appropriate practice, rigorous instructional pedagogy, and components of the Danielson Framework.
Investigations Alignment & Condensing Documents
Investigations Alignment Download Investigations Alignment
Additional Investigations Content Extension Download Additional Investigations Content Extension
Investigations Correlation to CCSS Download Investigations Correlation to CCSS
Unit 3 Condensing Guide Download Unit 3 Condensing Guide
Unit 4 Condensing Guide Download Unit 4 Condensing Guide
Investigations Unit 4 Extension Download Investigations Unit 4 Extension (zip)
Investigations Unit 6 Extension Download Investigations Unit 6 Extension (zip)
Literature
A comprehensive list of suggested titles, sorted by standards, can be found in the document below. Titles with complimentary lessons or activities are also indicated. Check your school library or Howard County Library System for availability, or purchase using Materials of Instruction (MOI) funds.
Math Journals
Students need many opportunities to write in mathematics. Journaling can be done as a warmup, independent work, closing, or homework activity. The linked page below provides resources for using math journals in your class.
Mobile Apps
iPads have been provided to every kindergarten teacher for classroom use. An assortment of apps that support kindergarten standards can be found at the Domain-Specific Resources page.
Vocabulary cards, web-based games, and other domain-specific resources can also be found at this page.
In addition, the linked page below provides access to a variety of student-facing web-based games, organized by math domain.
Planning for Advanced Learners
The following document is intended to give all Kindergarten teachers guidance on how to identify students who are ready to receive instruction on first grade mathematics standards. A paper-pencil placement test is NOT appropriate. The guidelines below will provide teams/teachers with a developmentally appropriate method to gather the data needed to identify students.
Scope and Sequence for Kindergarten Advanced Mathematics Links to an external site. (above guidance needs to be followed before use)
Kindergarten to First Grade Standard Alignment Links to an external site.
Mathematics Learning Behaviors Download Mathematics Learning Behaviors
Planning for Mathematics
what is collaborative planning in Elementary mathematics (HCPSS)?
Collaborative planning can be done with or without a Math Coach. Participants discuss upcoming math standards and make purposeful selections of instructional material.
Collaborative planning…
- Is intentional and purposeful.
- Is a shared responsibility.
- Is time to discuss upcoming standards and learning targets, that were reviewed by all before the collaborative planning meeting.
- Confirms the meaning of the mathematics inherent in the standard and considers “what comes before” and “what comes after” within the grade and across grades.
- Identifies and selects tasks that promote student reasoning and that are aligned with the established mathematical goal(s).
- Is a time to do the selected task.
- Is an opportunity to anticipate student responses and misconceptions.
- Discusses which representations and strategies are appropriate to highlight and what connections students might make between representations.
- Identifies what manipulatives may be needed to support student understanding.
- Considers which grouping structure to select based on the task and purpose of the day.
- Includes discussions about purposeful questions to ask students in order to advance students’ reasoning and sense making.
- Complements provided timelines by considering evidence of student progress and understanding
- Can include professional development “shorts” provided by Math Coach to enhance understanding of standards.
Collaborative planning is not...
- Providing all of the activities to the entire group by one individual (ITL, Math Coach, or any teacher)
- Grabbing activities or finding worksheets so that copies can be made
- Filling in a plan book for five or more full days of instruction. The process (in column to left) takes time.
- Dividing to conquer the task where one person plans all the homework for the team, one person plans all the routines for the team, or in which each person plans a different day of the week. More ideally, each teacher brings a few instructional ideas (for the standard(s)) and collaboratively the team discusses which order, which structure, etc. for the instructional materials brought to the planning table.
planning for task implementation
Planning for a task is different than selecting materials for copying and preparing. There a few steps that we may not be familiar with. These steps are critical for being well-prepared for a rich mathematics class. Keep in mind that none of these steps should take more than a few moments but can have far-reaching implications on the orchestration and intentionality of a lesson.
Do the Task Yourself
Take a few moments to complete the task ourselves. This helps us consider how we would prefer the task to be solved. It also gives us an idea about possible missteps or even shortcuts that students might take.
How Might They Solve It?
After doing the task, we have a sense of what they might do to solve the problem or complete the task. Anticipating what they might do helps us consider what questions to ask, what strategies might be highlighted, and what representations might be used.
What Might They Misunderstand?
Learning mathematics is grounded in making mistakes and proving that misconceptions are just that. Doing the task helps us anticipate what students might do. It also helps us consider what misconceptions they might have and how they might be countered. Misconceptions and errors are not a bad thing. They can be leveraged to develop a deep understanding of the mathematics.
What Misconceptions Might I Have?
We all have perspectives of mathematics. It's possible that as adults we have incomplete thoughts about concepts or possible misconceptions. This usually results in a focus on procedure so that the misconception or misunderstanding doesn't arise. This is completely natural. It's important to check in with MSTs and colleagues to confirm ideas about upcoming standards. This is just part of the importance of collaborative planning.
What Will I Circle Back To?
What in the task will I use to circle back to other ideas? What connections will I make to other ideas that students have already learned? Like any other content, mathematics is not an isolated collection of ideas. Each task and activity is an opportunity to make connections. Students who make connections have a deeper understanding that they can apply and transfer more easily.
A lesson Plan organizer
Planning for mathematics has many parts. The lesson planning templates provided below are recommended but not required. The template aligns with the concepts of Understanding by Design in that we plan with the end in mind. The template also helps teachers think about what students might do during the mathematics lesson and plan for questions to react to student thinking and guide the discussion. The electronic version can be copied into your Google account and completed there.
Daily Planning Organizer Links to an external site. (electronic version)
Daily Planning Organizer Links to an external site. (print version)
This template focuses on the planning of the mathematics. It is not the traditional "teacher-centered" form. Instead, it asks for us to think about intended outcomes, assessment of those outcomes, task selection, and anticipation of student understanding. It also asks for teachers to select both a routine and a structure for the class that day. The upper righthand section of the template prompts for "teacher moves." Those actions are general academic strategies or approaches for introducing, managing, or engaging students in the task or discussion. Some moves are listed below. Not all are intended to be recorded. Teachers should highlight the big ideas that need to be kept in mind. The moves include:
Teacher Moves:
How will I
- Give directions or introduce the task?
- Scaffold student support?
- Monitor student thinking during the task?
- Work or visit with small groups during the task?
- Facilitate discussion?
- Record or chart ideas?
- Sequence student work?
Talk Moves:
How will I use
- Think, Pair, Share?
- Turn and Talk?
- Use wait time?
- Whole group or small-group discussion?
- Partner talk?
- Revoicing (“So you’re saying that it’s an odd number”)?
- Student revoicing (students revoicing ideas of classmates)?
- Prompt for further participation or discussion. (“Would someone like to add on?”)
Problem Solving
Problem solving is not an isolated activity. It doesn't occur every Friday. Instead problem solving is a skill that favors every mathematics lesson. Problem solving is more than just one-step word problems. Problem solving should feature rich tasks, authentic purposes, and multiple ways to be solved. This linked page offers suggestions and resources for developing your students' problem solving capabilities.
Rekenreks
The Rekenrek, or arithmetic rack, was designed by Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, to support the natural development of number sense in children. The downloadable files are resources to assist in using Rekenreks with your students.
HCPSS Adapted Resources (zip) Download HCPSS Adapted Resources (zip)
K-5 Math Teaching Resources: Rekenrek Resources Links to an external site.
Resource Bank
The linked page includes non-editable pdfs of templates resources that you can use with lessons, centers, or other instructional activities as well as links to a variety of web-based manipulatives and tools that you can use for demonstrations, lessons, centers, or more.
Routines
Routines are a desirable way to begin math class. They develop number sense by connecting critical math concepts on a daily basis. They should be used in place of a traditional warm-up or reviewing homework. This linked page provides descriptions, examples, and videos of routines.
SBIR (Standards Based Instruction and Reporting)
Measurement Topics and Instructional Standards Crosswalk
This file aligns instructional standards with the measurement topic that they roll up to. It also identifies the instructional quarter that each measurement topic is reported.
Mathematics Measurement Topics Crosswalk Links to an external site.
Report Card Comments Bank by Quarter
This is the collection of prepared report card comments in Synergy. Teachers can use these comments and/or write their own. Reminder: A comment is needed for students learning standards from the next grade.
Mathematics Report Card Bank Links to an external site.
SBIR Canvas Course
This course houses a collection of SBIR information including directions for using the Canvas grade book, SBIR FAQs, and other resources.
SBIR Family Canvas Course
This course houses a collection of resources to help parents understand Standards Based Instruction and Reporting.
SBIR CANVAS COSBIR Family Canvas Course
August SBIR Professional Learning Session
PL Session from August 23rd Links to an external site.
Game board link from presentation Links to an external site.
How can I collect evidence of student understanding?
- Observe students during instruction, while they use centers, or while they play games
- Evaluate written work
- Rubric for Tasks Links to an external site.
What can I Use to collect evidence of student understanding?
- Any item found on the Independent Work tab can be used to collect evidence
- Teacher-created items
- Anecdotal notes (Folder containing all grade level Anecdotal Data Collection Tools) Links to an external site.)
- Observation of students working on centers and games from the Independent Work tab
- Items from Module/Canvas assessments that align to this standard
Reminders
- You do not need to grade all of the evidence you collect.
- If a student's work is inconclusive, get more evidence of the individual. You don't need to reassess the entire class.
- Some evidence with be evaluated using the rubric. Other evidence will use percentages.
- The assessments provided by the mathematics office should not be the only evidence used for grading and should not be valued more greatly than other data points.
- Report card comments: Students learning standards from the next grade level must have a comment that stating that. Students with an L must get a comment about their performance in that measurement topic
guidance for determining if students should be instructed on the next grade level's mathematics standards
The following document provides guidance for determining students’ instructional level/which curriculum is appropriate in mathematics. All students should receive instruction at their chronological grade level at a minimum. This document provides guidance in determining if a student is better matched with the next grade level curriculum.
Guidance for determining appropriate instructional math standards Links to an external site.
Standards for Mathematics Practice
The Standards for Mathematical Practice identify the behaviors of mathematically proficient students. The "practices" are not taught in isolation. They are developed intentionally through mathematics instruction. This page identifies student and teacher behaviors of these practices and also provides resources for developing these habits of mind in your students.
Structures for Math Class
The models on the linked page outline options for structuring a kindergarten mathematics class. Your mathematics class is not required to use the same model throughout the year. The model for each day should be selected intentionally to support the needs of your students and the goals of the lesson.
Student Learning Objectives (SLO)
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Reminders about mathematics SLOs.
- Your SLO is determined by you and your principal.
- It is recommended that the SLO focuses on a major work or big idea from a grade level.
Recommended Option 1:
Select a Major Work (topic) from the appropriate mathematics course. Those assessments are linked below and within each grade level course. Note: Major Works Assessments are not available for grade 4 G/T and/or grade 5 GT due to the compaction of grade level standards in these courses.
Recommended Option 2:
Use a math practice rubric with an appropriately aligned task.
Recommended Option 3:
Select a Measurement Topic from your grade level's report card and use the aligned Measurement Topic Assessments from your grade level content. For example, if you select Understanding of Addition in grade 1 you would then use the measurement topic assessments aligned to that topic. NOTE that this would include multiple assessments to pre-test.
Suggested Math Materials
The Office of Early Childhood Programs supplies a variety of math manipulatives and resources for kindergarten teams and classrooms. Please visit the Kindergarten Inventory page for a list of materials.
Vocabulary Cards
These vocabulary cards identify important mathematics vocabulary by quarter. They can be used with mathematics word walls and daily instruction.
Math Learning Center Vocabulary Cards Links to an external site.
Number and Base Ten Vocabulary Cards Links to an external site.
Counting and Cardinality Vocabulary Cards Links to an external site.
Addition and Subtraction Vocabulary Cards Links to an external site.
Geometry Vocabulary Cards Links to an external site.
Measurement and Data Vocabulary Cards Links to an external site.
Primary Math Numbers & Base Ten Vocabulary Cards in Spanish Download Primary Math Numbers & Base Ten Vocabulary Cards in Spanish
Primary Math Geometry Vocabulary Cards in Spanish Download Primary Math Geometry Vocabulary Cards in Spanish
Walkthrough Tools
The folder linked below includes walkthrough tools for administrators and teachers to use when visiting mathematics class. They are designed to look for evidence of high-quality mathematics instruction. These tools are provided as examples. Schools may select the tool that aligns most closely to their School Improvement Plans and/or professional learning activities. Users may choose to focus on a select number of practices for the Effective Teaching Practices tool or the Standards for Mathematical Practice (SMP) tool.