lesson 2 homework k.5

IM K–5 Math™ certified by Illustrative Mathematics ®

Im k–5 math.

Meets all expectations in all three EdReports Gateways

Learn more about IM K–5 Math v.I with this in-depth look at our new K–5 curriculum. Tour the teacher materials, demonstrate the lesson structure from warm-up to cool down, and see how centers support math fluency.

See why educators love IM K–5 Math.

This curriculum has taken all of the fantastic instructional routines teachers were pulling from multiple sources and tied them up with a great big bow into a rigorous, coherent curriculum resource! Students are talking about math like they never have before, and students who would typically not speak up in math class now join the conversation.

— Catherine Castillo, Elementary Numeracy Coordinator for Springfield Public Schools, MO

As a teacher of 25 years, I always worked on creating a strong class community. I had never considered nor had the tools to develop a safe, supportive, inclusive mathematical community until I used IM K–5  in the alpha and beta pilots. IM K–5 changed my math instruction and changed the way my students see themselves. They see themselves as mathematicians who are enjoying doing and talking about math. 

— Maureen O’Connell, Math Specialist, Ipswich Public Schools, MA

Here’s what students from a grade 4 class at Wanda Gray Elementary said:

“The fractions are so much fun.”

“My favorite part of math this year is everything.”

“I like working with a partner.”

“I like figuring out what mistake the students in the book made (error analysis).”

“Working with a partner helps me get to know them better and we understand more when we work together.”

— Students at Wanda Gray Elementary, Springfield, MO

With IM K–5 every single student can access grade-level math. Students don’t get pulled out for math anymore. They get to be part of the classroom because the curriculum is designed to invite all learners into the lesson with multiple opportunities to use manipulatives, have conversations, share their thinking, and explore the mathematics. It is the most inviting, rigorous, and exciting curriculum I’ve ever taught and it’s amazing how much students can learn and feel successful in math.

— Nancy Sirois, K–5 Math Coach, Gerald E. Talbot Community School in Portland, ME

What makes IM K–5 unique for teachers is that it is an educative curriculum. Teachers are learning so much right along with their students. There are so many layers to it. . . community and equity, mathematical understandings, the Five Practices, language routines, and more. I feel like there are years worth of professional learning and development built right into what is presented, and we can put it into practice as we learn together. It’s amazing.

— Ann Neely, Elementary Program Coordinator, Mathematics, South Williamsport, PA

Ready to get started with IM K–5 Math ™ ?

IM K–5 Math Design Features

IM K–5 Math supports :

A coherent progression of learning.

IM K–12 Math™ is fully aligned to the focus, rigor, and coherence of the standards, and has been given the stamp of approval by EdReports, earning perfect scores in the areas of Focus & Coherence and Rigor & Mathematical Practices. The scope and sequence of units, activities, and representations are designed to help students develop a deep understanding of mathematical concepts, build fluency with procedures, and solve mathematical problems that reflect their lived experiences.

Academic language development

Math vocabulary is developed through the process of actively exploring and learning mathematics. Students make sense of mathematical concepts using informal language before academic terms are introduced. Embedded within the curriculum are Mathematical Language Routines to support academic language development for all learners. These routines also provide opportunities for English Learners to engage in the specialized academic language demands of reading, writing, speaking, listening, conversing, and representing in math.

Culturally responsive pedagogy

Materials are designed to affirm students as they build positive mathematical identities. Units and lessons begin by inviting students to use their prior mathematical knowledge, funds of knowledge, language, and culture to make sense of new mathematical concepts. Activities offer collaborative learning opportunities and instructional routines that center student thinking and encourage students to bring their whole selves to math class. Grades K–5 courses (and coming soon to 6–12 courses) include problem-solving contexts that positively reflect ethnically diverse cultures and support the implementation of culturally relevant and responsive pedagogy.

Teacher learning

Units and lessons include narratives that describe the mathematical work that will unfold, and activities and lessons include a synthesis that assists the teacher with ways to help students incorporate new insights gained into their big-picture understanding. Formative assessments help create clear pathways to address student outcomes. Teacher-facing materials support teachers to develop, refine, and reflect on instructional practices.

IM K–5 Math MeetsExpectationsin All EdReports Gateways

The IM K–5 Math certified curriculum is rigorous, problem-based, and fully aligned to the standards, with coherence across grade bands.

The curriculum is available in both print and digital versions. IM K–5 Math is highly rated by EdReports for meeting all expectations across all three review gateways. Read the full analysis for Kendall Hunt and Imagine Learning .

Ready to Get Started with the IM Certified Experience?

Already using IM, but want to learn more?

Reach out to your IM Certified partner to schedule professional learning , order print materials or digital subscriptions.

IM K–5 MATH FEATURED CONTENT

Featured IM K–5 Math Blog Posts

With that e-mail, we were off and running in the most exciting race of my professional career. We later agreed to deliver a pilot-ready version of grades 6–8 for the 2016–17 school year, rolling out units just in time as the year progressed, and delivered a final version in the summer of 2017, along with aligned professional learning. 

Amanda Gorman recited her poem, “The Hill We Climb,” on Inauguration Day. Her words were not only inspiring, but a piercing call to action. I thought about my work at IM and wondered what a commitment to “all cultures, colors, characters, and conditions of man” meant in my role.

We are never more “on” than when we are teaching a lesson. All of our senses are heightened and all of our energy is focused on understanding students and being understood by the students we are teaching.

IM K–5 Blog Posts From the Authors

Many people have an aversion to word problems. They cringe at the mention of them. In elementary classrooms, teachers often report that this is what their students struggle with most.

What do we do with curious students who are ready, willing, and able to go further with math ideas? Some students cannot wait to dig deeper into the mathematics they are studying in class.

From the start of the year, we want students to know they are capable of engaging in grade-level mathematics. In the Opportunity Myth (2018), data shows that there is an opportunity gap for historically marginalized students to engage with this content in their math classes.

IM K–5 Math Blog Posts From the IM Community

When we consider early childhood mathematics this familiar song comes to mind. In our hurried society where more is more, childhood expectations have been pushed to earlier and earlier ages.

One way is through instructional routines like “Which One Doesn’t Belong” and “Notice and Wonder.” These routines give structure to time and interactions. Within the structure, there are opportunities to have time to think deeply and a predictable way to share and deepen thinking with partners and the whole class.

Last spring, I was approached by our Math Coordinator and asked about piloting a new math program. I knew my staff was ready for building-wide consistency and we were ready to try something new. I easily said yes!

IM K–5 Math Blog Post Series

What does it mean to know mathematics?

A world where all learners know, use, and enjoy mathematics. Perhaps the most mysterious verb in the IM vision—a world where all learners know, use, and enjoy mathematics—is the first one: know.

What Does It Mean to Use Mathematics?

Our vision at Illustrative Mathematics is a world where all learners know, use, and enjoy mathematics. In my last post I picked up that first verb and talked about what it means to know mathematics.

What does it mean to enjoy mathematics?

When I started this series of blog posts on what it means to know, use, and enjoy mathematics, I thought this one would be the easiest. Math is fun, right? How could you not enjoy mathematics? I certainly do—

Fluency Development Within and Across the Grades in IM K–5 Math™, part 1: Addition and Subtraction

“When do students practice their math facts? How is math fluency assessed?” We appreciate these questions for a couple of reasons…

Fluency Development Within and Across the Grades in IM K-5 Math™, part 2: Addition and Subtraction

Because of the problem-based structure of our curriculum, students’ ideas play an integral role in the progression of learning in IM K–5 Math™.

Fluency Development Within and Across the Grades in IM K–5 Math™, part 3: Multiplication and Division

When designing IM K–5 Math™, we thought deeply about the potential impact of our curriculum on students’ mathematical identities.

Fluency Development Within and Across the Grades in IM K–5 Math™, part 4: Multiplication and Division

As a problem-based curriculum, IM K–5 Math™ aims to offer all students opportunities to problem-solve and think critically about new learning.

IM K–5 Math On-Demand Webinars

Family Engagement, Collaboration, and Support

Families play a crucial role in student learning, and at IM, we believe that students should be empowered to recognize and explore math in the world...

Access to Mathematics through Language

In IM K–5 Math™, vocabulary is formally introduced after students have had time to make sense of mathematical ideas and learn new concepts. Join us...

Racial Justice in Math Education

Join our distinguished panel of scholars and educators as they examine ways to disrupt patterns of racial inequity in mathematics education and...

Experience IM K–5 Math: A Focus on Student Thinking

At IM, we built our curriculum on the principle that all students are capable of using what they know to learn and solve problems. Students learn...

Experience IM K–5 Math: A Roundtable Celebration with the Authors

Celebrate with Illustrative Mathematics’s CEO William McCallum and the authors of IM K-5 Math at an extraordinary event, where they reunite and...

Comparing IM K–5 Math and IM 6–12 Math — What’s New?

While IM K–5 Math shares many similarities with our 6–8 and 9–12 curricula, all of the units have been geared towards meeting the unique needs of...

Advancing English Learners in IM K–5 Math

Join Erin Smith, advisor and lead for supports for English learners, to take a look at enhancements included in the IM K–5 Math designed to advance...

IM K–5 Math as a Support for Culturally Responsive Pedagogy

When developing IM K–5 Math, the authors wanted to make sure that all students—regardless of race, ethnicity, language, gender, ability, and...

Learn All About IM K–5 Math v.I

Learn more about IM K–5 Math v.I with this in-depth look at our new K–5 curriculum. Tour of the teacher materials, demonstrate the lesson structure...

Imagine IM, from Imagine Learning, offers the comprehensive IM® v.360 curriculum with enhanced resources. Imagine IM includes classroom-ready print books designed for usability. The digital experience offers customizable lessons, interactive tools, assessments, and exclusive features like digital centers and videos. Imagine Learning is IM’s original premium partner and supports districts to ensure implementation with integrity.

Kendall Hunt is an IM Certified Partner and print provider of the upgraded IM® v.360 curriculum. The Kendall Hunt version will be the pure, untouched print version – one that is unaltered, unedited, and aligns directly with IM’s free digital version. In addition to this upgraded print version, Kendall Hunt offers professional learning opportunities aligned with customer needs.

IM® v.360 powered by Kiddom unites ground-breaking technology with Illustrative Mathematics’ high-quality curriculum.  Kiddom empowers educators to customize, implement, and measure the impact of IM® v.360 on a simple, powerful platform. A full suite of digital tools and functionality creates dynamic, engaging learning experiences for students, while real-time data supports informed instructional choices.

Kristin Gray

K–5 Director of Curriculum and Professional Learning, IM K–5 Math v.I

Kristin’s continuous curiosity around students’ mathematical ideas drives her work in writing instructional materials that create a coherent mathematical story for all students. She is a National Board Certified 22-year veteran teacher of grades 5, 7, and 8, and was a Teaching Channel Laureate. 

Kristin has a B.S. in Elementary Education with a concentration in Mathematics from the University of Delaware, an M.Ed. in Applied Technology in Education, and is the 2014 Presidential Awardee for Excellence in Mathematics and Science Teaching.

Having served as a curriculum writer on IM 6–8 Math, and as the IM K–5 Math Director of Curriculum and Professional Learning, she is committed to providing opportunities for teachers and students to find joy in learning.

Marni Greenstein

Grade K–3 Lead, IM K–5 Math v.I

Marni has also worked with UnboundEd as a facilitator, supporting teachers and leaders to address systemic racism and disrupt patterns of injustice in mathematics education through strong curriculum, deep content knowledge, and belief in students.

Dionne Aminata

Grade 2–5 Lead, IM K–5 Math v.I

Dionne began her career in education in 2001 as an elementary teacher at LAUSD in Los Angeles, CA, then taught middle school math in Brooklyn, NY, and later served as an instructional coach to new teachers with New York City Teaching Fellows. 

Dionne then spent six years as a math content specialist with Aspire Public Schools in Los Angeles, where she led K–8 teachers and leaders through the transition to Common Core State Standards, the adoption of a new math curriculum, and the implementation of equitable teaching practices in mathematics.

Dionne has also worked as a facilitator at UnboundEd’s Standards Institutes, helping teachers and leaders from across the country deepen their understanding of the Common Core Standards and engage in critical conversations about systemic bias and racism in math education. 

Dionne successfully supported implementation of the IM K–5 Math beta pilot at LAUSD in 2020–21. She earned her undergraduate degree in Sociology and Business at UCLA. She has an MBA in Entrepreneurship and Global Marketing from Babson College, and a Masters in Math Education from CUNY Brooklyn College.

Alex Clayton

Kindergarten Lead, IM K–5 Math v.I

Alex believes that both teachers and instructional materials should empower students to develop their ideas and mathematical identities. She worked as a kindergarten teacher in New Orleans before joining the IM team as the kindergarten lead. 

Brianne Durst

Grade K–2 Writer and Coherence Reviewer, IM K–5 Math v.I

Brianne believes that all students deserve the chance to learn mathematics as a subject that makes sense, that this sense-making should be done individually as well as within a math community, and that students need to believe in the value of sharing and reflecting upon their ideas as well as the ideas of others in their math community.

She was a classroom teacher in grades 2 and 4 for a total of 12 years before becoming a math coach. She spent 5 years as a math coach and interventionist for grades K–2 at Community Roots Charter School in Brooklyn, NY. She is also a member of the Math Collective, a group that offers professional learning materials and experiences to teachers in New York City.

Brianne led the Grade 1 revisions for v.I and continues to work at IM as a K–5 Curriculum Specialist. Through her work with IM, she is able to help provide students with a mathematics experience that makes sense and encourages learning with a community of peers.

Sara Baranauskas

Grade 1 Lead, IM K–5 Math v.I

Sara began her career as a grade 6 language arts teacher. When she transitioned to grade 5, her love of teaching mathematics blossomed. With decades of educational experience, Sara is now the K–12 STEM coordinator for two districts in Connecticut. In 2015, she was selected as a LearnZillion National Dream Team Coach, where she collaborated with teachers to develop units for grades 1 and 2.

Deborah Peart

Grade 2 Lead, IM K–5 Math v.I

Now based in Florida, Deborah taught for over 25 years in New York, Connecticut, and Georgia in the public and private sectors. Deborah is the founder of My Mathematical Mind and speaks on a variety of topics related to math identity and literacy connections to mathematics. 

Blending her training in yoga and mindfulness with mathematics instruction, Deborah advocates for a mindful approach to teaching mathematics in order to address math anxiety, build confidence, and support the development of positive math identities. She has dedicated her career to helping other educators approach teaching in innovative ways that allow students to see themselves as valued mathematical thinkers and lifelong learners.

Grade 3 Lead, IM K–5 Math v.I

Zack spent 16 years as a teacher and instructional coach with Pinellas County Schools in Florida, where he coached and presented professional development at the district, state, and national levels. He currently serves on the board of directors for the Florida Council of Teachers of Mathematics (FCTM) and was the lead writer on the FCTM Access and Equity Position Statement .

Zack’s work on the IM K–5 curriculum leveraged both his extensive background in mathematics education and his dedication to ensuring quality instruction for every student.

Kaneka Turner

Grade 4 Lead, IM K–5 Math v.I

Kaneka has been a leader inside and outside of the classroom for decades. Her journey as an educator includes experience as a classroom teacher, teacher of gifted education, elementary math coach, Title I elementary math specialist, and district math specialist. In addition to her work in local school districts, she has also served teachers as an author facilitator of math professional learning for more than 18 years.

Her work on the IM K–5 curriculum amplified her dedication to changing lives through teaching, coaching, curriculum development, and professional learning.

Yenche Tioanda

Grade 3–4 Writer and Coherence Reviewer, IM K–5 Math v.I

Yenche is passionate about learning and helping others learn. Her adventures in mathematics education began in Philadelphia, where she taught high school students as a member of Teach For America and later served as a founding teacher of Science Leadership Academy. 

Since then, she has strived to create meaningful learning experiences—in mathematics and beyond—as a curriculum designer, leader of professional learning communities, academic director, and consultant to schools and non-profit organizations.

Yenche served as the lead author of the grade 6 course in the IM 6–8 curriculum, the lead for Algebra 1 in the IM 9–12 curriculum, and a writer for the IM K–5 curriculum.

Yenche holds a BA in Architecture from Washington University in Saint Louis, an MArch from Harvard Design School, and an MS in Education from the University of Pennsylvania. 

Sarah Caban

Grade 5 Lead, IM K–5 Math v.I

Sarah started her teaching career on an island off the coast of Maine, teaching in a K–8 one-room schoolhouse, then she spent four years teaching grade 4. Since 2001, she has been a K–12 math coach and coordinator. She also presents professional development at local, state, and national conferences.

Sarah facilitated professional learning for the IM middle school curriculum, and her work as a grade 5 lead puts her passion for listening and collaboration at the heart of every lesson she designs, teaches, and places in a teacher’s hand. She believes that all students learn math by doing math together, and sees great value in listening to students’ ideas.

Noelle Conforti Preszler

Grade K–5 Writer and Coherence Reviewer, Managing Editor, IM K–5 Math v.I

Noelle values students’ experiences with mathematics and works to create classrooms where students feel they belong and know their mathematical ideas are honored.

She is a mathematics educator with a Ph.D. from the University of Washington and over 10 years of undergraduate teaching experience, including 8 years teaching pre-service teachers in K–8 math content courses.

Along with writing and reviewing lessons across K–5 at IM, Noelle served as the Instructional Designer for the project. Her work focused on thinking carefully about the educative aspects of IM K–5 and its coherence across grades. Noelle led the final content and print book reviews for IM K–5 Math v.I. She continues her work at IM as Managing Editor, K–5 Curriculum. 

Michael Nakamaye

IM Mathematician in Residence, IM K–5 Math v.I

Mike is Mathematician in Residence at Illustrative Mathematics. He is the only author who has written classroom materials for every grade of IM curricula. 

He has a BA in French from Gonzaga University and PhD in Mathematics from Yale. He taught mathematics at Harvard and the University of New Mexico for over 20 years, including pre-service elementary and secondary teacher courses. 

Mike still loves French literature as well as cycling and the music of Rossini. His ideal time is attending the Rossini Opera Festival (by night), biking along the beautiful Italian coast (by morning), and taking a nap or dreaming about mathematical ideas (in the afternoon).

Liz Ramirez

VP of Implementation Programs

Liz unequivocally believes that education is an essential means of empowerment. This conviction guides her passion for advancing access and equity in the field of mathematics education for students and for teachers.

Liz led the strategic direction and development of IM’s research-based frameworks for enhancing access for both English learners and students with disabilities within IM K–12 math. The associated resources and professional learning have equipped IM teachers with math language routines that facilitate discourse and language development, as well as access-supporting instructional strategies grounded in the Universal Design for Learning guidelines. 

Liz also managed several projects focused on the development of tools, resources, and guidance to help districts establish the conditions necessary to successfully implement the IM curriculum.

As the vice president of implementation programs, Liz leads the strategy and development of IM programs for teachers, coaches, instructional leaders, and partner organizations. Liz and her team are committed to the continued advancement of IM’s professional learning for teachers and support for the districts and organizations that serve them.

William G. McCallum

CEO and Cofounder

Bill McCallum has dedicated his life to helping teachers, educators, mathematicians, and policymakers show fidelity to both mathematical coherence and student learning.

He is an Emeritus Distinguished Professor of Mathematics at The University of Arizona, where he researches number theory and arithmetical algebraic geometry, authors textbooks, and advises researchers and policymakers. Bill’s work as a lead writer of the Common Core State Standards in Mathematics earned him the Award for Distinguished Public Service from the American Mathematical Society and the Dolciani Award from the Mathematical Association of America.

As CEO and cofounder of Illustrative Mathematics, Bill chairs the organization’s board of directors, helping craft IM’s strategic direction and contributing to the curricula. He also represents IM to funders, at speaking events, and in workshops.

Kristin Umland

President and Cofounder

Kristin Umland believes that by coordinating the expertise of teachers, mathematicians, mathematics educators, and business professionals, we can help all students realize their mathematical potential.

Before joining the IM team, she was an associate professor in the Department of Mathematics and Statistics at the University of New Mexico (UNM). After joining UNM with a PhD in Mathematics, she carried out research in mathematics education, taught pre-service and in-service elementary and secondary teachers, and conducted education outreach at the local, state, and national level. A recipient of both the Louise Hay Award and the AMS Impact Award, Kristin’s goal has always been to improve the mathematical and pedagogical quality of children’s learning experiences.

Standards Alignment

Assessments, professional learning, family engagement, case studies.

NEW EUREKA MATH 2 ® PILOT PACKAGE

Are you looking for new ways to advance equity and build knowledge in your math classroom with high-quality instructional materials? EdReports recently reviewed Eureka Math 2 . Scan the QR code or access the final report .

Check out our special pilot package for only $10 per student.

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At Great Minds ® , we’re committed to ensuring our curricula are aligned to the latest research on how students best learn to read, write, and build knowledge.

Explore webinars, blogs, research briefs, and more to discover how we incorporate this important body of research.

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At Great Minds®, we’re committed to supporting educators with high-quality curricula and resources.

Explore resources designed to aid students in science and engineering and spark classroom conversation.

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Eureka Math  Print Materials

As the creator of Engage NY Math and Eureka Math , Great Minds is the only place where you can get print editions of the PK–12 curriculum. Our printed materials are available in two configurations: Learn, Practice,   Succeed , or student workbooks, teacher editions, assessment and fluency materials. 

The Learn, Practice, Succeed configuration is available for grades K–8 and offers teachers multiple ways to differentiate instruction, provide practice, and assess student learning. The Learn, Practice, Succeed configurations are also available in the following languages:

• Arabic (K–5)
• Armenian (K–6)
• French (K–6)
• Korean (K–6)
• Traditional Chinese (K–3)
• Simplified Chinese (4–6)
• Spanish (K–8)

In addition to our Learn, Practice, Succeed configuration you can get student workbooks, teacher editions, and assessment and fluency materials for Grades PK–12. These materials are also available in Spanish for Grades K–8.

Along with our curriculum print materials,  Eureka Math   Manipulative Kits   and   Study Guides are available exclusively from our partner, Didax. We also offer specially priced print bundles.

Our sales team is available to help you navigate our offerings and determine the best package for your school or district. 

Learn, Practice, Succeed Configuration: K–5

• Application Problems
• Problem Sets
• Exit Tickets

Practice  Book*

• Sprints & Fluency
• Additional Problems for Homework

Homework Helpers

* The  Learn  and  Practice  books provide all of the printed materials a student uses for core instruction.   

Learn, Practice, Succeed Configuration: 6–8

Learn, Practice, Succeed  Book*

* The same content found in the  Learn ,  Practice ,  Succeed  books but in one book per module.

Original Configuration: PK–12

Student Edition*

Printed Packets

* Available in Spanish (Grades K-8)

NOW AVAILABLE

Eureka Math in Other Languages

Eureka Math is now available in the following languages.

Traditional Chinese

Simplified Chinese

Bundles and Class Sets Available

Bundle options are available for all of our materials (print, digital, PD, etc.). Prices vary by grade and size of class set. Certain grade-levels do not include all packets due to the nature of the grade-level content. Student workbooks are available in class sets of 20, 25, and 30. Prices vary by size of class set.

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Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
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• Main idea & details
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• Conclusions & inferences
• Sounds & phonics
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• Dolch sight words
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• Cursive passages
• Grammar & Writing

Answer Keys for Worksheets

Worksheet answers.

Almost all of our grade 1-6  worksheets   have an answer sheet appended to the worksheet. Only a few of the simplest worksheets do not have answer sheets.

Most of our preschool and kindergarten worksheets do not have answer sheets; the exercises are short and simple enough that they are not usually needed.

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