Planning and Pacing Guide

Grade 1

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Advocates for Excellence To develop Into Math , we listened to teachers like you from across Florida, who told us about their unique classroom challenges. Thanks to their voices, Into Math is more than just aligned with Florida standards; it was built specifically to help you and your students succeed in the classroom and on the FSA.

Into Math was developed by a team of esteemed researchers and practitioners. These leaders work tirelessly to evolve instructional practices and advocate for more clear, holistic, flexible and active methodology in the classroom.

Edward B. Burger, Ph.D., is a mathematician who is also the president of Southwestern University in Georgetown, Texas. He is a former Francis Christopher Oakley Third Century Professor of Mathematics at Williams College, and a former vice provost at Baylor University. He has authored or coauthored numerous articles, books, and video series; delivered many addresses and workshops throughout the world; and made many radio and television appearances. He has earned many national honors, including the Robert Foster Cherry Award for Great Teaching. In 2013, he was inducted as one of the first fellows of the American Mathematical Society.

Juli K. Dixon, Ph.D., is a Professor of Mathematics Education at the University of Central Florida (UCF). She has taught mathematics in urban schools at the elementary, middle, secondary, and post-secondary levels. She is a prolific writer who has published books, textbooks, book chapters, and articles. A sought-after speaker, Dr. Dixon has delivered keynotes and other presentations throughout the United States. Key areas of focus are deepening teachers’ content knowledge and communicating and justifying mathematical ideas. She is a past chair of the National Council of Teachers of Mathematics (NCTM) Student Explorations in Mathematics Editorial Panel and a member of the Board of Directors for the Association of Mathematics Teacher Educators.

Timothy D. Kanold, Ph.D., is an award-winning international educator, author, and consultant. He is a former superintendent and director of mathematics and science at Adlai E. Stevenson High School District 125 in Lincolnshire, Illinois. He is a past president of the National Council of Supervisors of Mathematics (NCSM) and the Council for the Presidential Awardees of Mathematics (CPAM). He has served on several writing and leadership commissions for NCTM during the past two decades, including the Teaching Performance Standards task force. He presents motivational professional development seminars worldwide with a focus on developing professional learning communities (PLCs) to improve teaching, assessing, and learning of all students. He has recently authored nationally recognized articles, books, and textbooks for mathematics education and school leadership, including What Every Principal Needs to Know about the Teaching and Learning of Mathematics and HEART: Fully Forming Your Professional Life as a Teacher and Leader.


Planning and Pacing Guide

Matthew R. Larson, Ph.D., is a past president of the National Council of Teachers of Mathematics (NCTM). Prior to serving as president of NCTM, he was the K-12 mathematics curriculum specialist for the Lincoln Public Schools (Nebraska), where he currently serves as Director of Elementary Education. A prolific speaker and writer, he is the co-author of more than a dozen professional books. He was a member of the writing teams for the major publications Principles to Actions: Ensuring Mathematical Success for All (2014) and Catalyzing Change in High School Mathematics: Initiating Critical Conversations (2018). Key areas of focus include access and equity and effective stakeholder communication. He has taught mathematics at the secondary and college levels and held an appointment as an honorary visiting associate professor at Teachers College, Columbia University.

Steven J. Leinwand is a Principal Research Analyst at the American Institutes for Research (AIR) in Washington, D.C., and has nearly 40 years in leadership positions in mathematics education. He is a past president of the National Council of Supervisors of Mathematics and served on the NCTM Board of Directors. He is the author of numerous articles, books, and textbooks and has made countless presentations with topics including student achievement, reasoning, effective assessment, and successful implementation of standards.


Program Consultant David Dockterman, Ph.D., operates at the intersection of research and practice. A member of the faculty at the Harvard Graduate School of Education, he provides expertise in curriculum development, adaptive learning, professional development, and growth mindset.

English Language Development Consultant Harold Asturias is the Director, Center for Mathematics Excellence and Equity at the Lawrence Hall of Science, University of California. He specializes in connecting mathematics and English language development as well as equity in mathematics education.


Planning and Pacing Guide

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Ericka François Pineloch Elementary Orange County Public Schools Orlando, Florida Erin Gallagher Cheney Elementary Orange County Public Schools Orlando, Florida Francine Harvey New Heights Elementary Pinellas County Schools St. Petersburg, Florida Melissa McCullough James Tillman Elementary Manatee County Schools Palmetto, Florida Stephanie McNamee Math/Science Instructional Coach Ivey Lane School Orange County Public Schools Orlando, Florida

Stacey Beavin Windermere Elementary Orange County Public Schools Windermere, Florida Analysse Bobek Sunrise Elementary Orange County Public Schools Orlando, Florida Amber Chieffe Robert Louis Stevenson Elementary Rachel M. Dagan Audubon Park Elementary Orange County Public Schools Orlando, Florida Valarie Davis Wolf Lake Middle School Orange County Public Schools Apopka, Florida Sabrina Edwards Moss Park Elementary Orange County Public Schools Orlando, Florida Brevard Public Schools Merritt Island, Florida

Nancy Rivera Andover Elementary Orange County Public Schools Orlando, Florida Nuria Suarez Curriculum Coach Sea Castle Elementary Broward County Public Schools Miramar, Florida Kathryn Tobon Staff Developer Broward County Public Schools Ft. Lauderdale, Florida ChristinaWitherspoon Midway Elementary Seminole County Public Schools Sanford, Florida

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Planning and Pacing Guide

Table of Contents

Welcome to Into Math .


Content Architecture


The Learning Arc and Focus, Coherence, and Rigor .

PG10 PG12 PG14 PG16 PG18 PG20 PG22 PG24 PG26 PG28 PG30 PG32 PG34

Lesson Design .

Promoting Conceptual Understanding .

Real-World Relevance and Mathematical Practices .

Language Development .

Assessments, Data, and Reports Assessment Overview .

Your Friend in Learning and the Interim Growth Measure . Module Assessments and Grouping Recommendations .

Lesson Practice and Homework .

Teacher Support

Supporting Best Practices . Professional Learning .

Building a Culture of Professional Growth .

Learning Mindset .

Unpacking Standards and Algebra Readiness .

Planning and Pacing Guide .


End-of-Year Options .



PG49 PG52 PG54 PG54

Mathematics Florida Standards .

Mathematical Practices .

English Language Arts Florida Standards . English Language Development Standards .

Into Math Solutions and Components .


Professional Learning References .


Academic Notebooks and Math Journals .

PG60 PG61 PG80

My Learning Summary Anchor Charts .

Interactive Glossary .

Index .



Planning and Pacing Guide

Welcome to

Perseverance Powers Student Growth Designed from the ground up to meet the high expectations of the Math Florida Standards, Into Math is the only solution built to track, predict, and propel growth for all of your students in Kindergarten through Grade 8.

The Outcomes You Want The Into Math system produces measurable outcomes:

• Students who have mastered rigorous standards, equipped with skills to persevere when presented with challenging, real-world problems • Teachers who grow as professionals, able to apply current research-based strategies and best practices • Educators who leverage data to differentiate and adapt, ensuring FSA success • Families that use accessible tools to support learning at home


Planning and Pacing Guide

What Makes Into Math Students Unstoppable? The Into Math system maximizes student growth by helping teachers deliver high quality instruction while monitoring every student’s success.

Focused and Purposeful Carefully crafted mathematical tasks, differentiated resources, and clear instructional support help teachers put every student front and center. See pp. PG6–PG15.

Content Architecture


Teacher Support

Assessments, Data, and Reports

Ongoing and Relevant Embedded support, classroom videos, resource libraries, and coaching provide learning opportunities for teachers of all levels. See pp. PG16–PG23.

Integrated and Actionable Auto-scored assignments and assessments help educators make informed instructional decisions. See pp. PG24–PG33.


Planning and Pacing Guide

Content Architecture

Focus, Coherence, and Rigor Into Math breaks down the Math Florida Standards (MAFS) into a coherent progression of concepts and skills that match the cognitive complexity expectations for each standard. A learning arc exists across units and modules, ensuring that a strong foundation of conceptual understanding is built before students learn mathematical procedures.






Build Understanding

Connect Concepts and Skills

Apply and Practice

The number and type of lessons in a module is based on the expectations of the MAFS.

Three types of lessons, each with a different purpose, help teachers know where they are in the arc of instruction.

Build Understanding

Apply and Practice

Connect Concepts and Skills

Conceptual Lessons  These lessons begin with a carefully crafted Spark Your Learning task in which students choose strategies and develop reasoning to make sense of problems. By the end of the lesson, students apply their understanding as they justify their reasoning while solving problems.

Procedural Lessons   These lessons help students understand the steps in a procedure and when the procedure should be used. Students begin to build fluency, learning to choose from multiple available strategies, and relying on the conceptual understanding they developed previously to solve rigorous tasks.

Bridging Lessons  These lessons begin with a conceptual understanding task that sets the foundation for procedural understanding. Students evaluate solution strategies and generalize which strategy or procedure works best for each task. Students apply strategies and procedures as they solve problems.


Planning and Pacing Guide

Content Architecture

Juli K. Dixon, Ph.D. Professor, Mathematics Education University of Central Florida Orlando, Florida

Creating a Learning Arc Teaching with Coherence

Name For students to make the most of their mathematics education, topics should be taught with coherence. This means that topics should be taught as connected ideas rather than within individual silos. Consider multi-digit multiplication. Linking the area model with the partial products algorithm provides a visual representation for this important topic (see Figure 1), setting the stage for finding areas of rectangles and combined rectangles. A benefit of making connections within different mathematical topics Figure 1

Step It Out 2

is that students have multiple pathways to retrieve what they learned, therefore relying less on rote memorization. For example, students can make sense of multi- digit multiplication by recalling their work with area and linking it to partial products. Connecting Concepts and Procedures Rigor describes the important balance between concepts and procedures. While balance is important, so is the order with which these are addressed.

In the storage closet, there are 17 different types of paint brushes with 23 of each type. How many paint brushes are there?

A. Break each factor into tens and ones. 17 = + 23 = + B. Label the area model with the factors broken into tens and ones. C. Use the Distributive Property to find the partial products. 20 10 7 3










× ) + ( 20




× ) + ( 20


× ) 3

× ) + (


10 × 2 tens 7 × 3 ones D. Add the partial products to find the whole product. 10 × 3 ones 7 × 2 tens

10 3 prior to understanding why, then students may make the error of adding both the numerators and the denominators if they confuse the rules. In contrast, if students make sense of describing fractions with the same-sized pieces in order to combine them prior to learning the standard algorithm for adding fractions, the students are less likely to make errors with the procedures because they understand the reasoning behind the process. The learning arc is complete when concepts are taught first and then those concepts are linked to more efficient processes before the procedures are practiced and applied. E. There are Concepts must be taught before procedures; otherwise, there is no motivation to make sense of the mathematics prior to using more efficient processes. Consider adding fractions with unlike denominators. If students are taught the procedure to • find a common denominator, • create equivalent fractions using that denominator, and • add the numerators of the equivalent fractions Check Understanding Find the product. 1 13 × 16 = + + + 208 200 30 391 140 Module 8 • Lesson 3 4_mflese492760_m08l03.indd 201




paint brushes in the storage closet.

Turn and Talk How does the area model show that the sum of the partial products is the product?








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Planning and Pacing Guide

Content Architecture

Lesson Design Into Math classrooms are different.  Lessons are designed to help you incorporate research-based best practices into your instruction. This design is found in the print student books and in the interactive digital lessons, enabling you to utilize either pathway or a blended approach.




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Spark Your Learning  Teachers guide student discussions and help students persevere as they work together on a mathematical task, working to build shared under- standing by selecting students to explain their reasoning.


Learn Together

ConnectConcepts and Skills

Name Represent Difference Unknown Problems with a Visual Model Essential ? Howdoyou solvewordproblems bycomparing to find thedifference usingavisualmodel? Spark Your Learning Howcanyou showaway to solve theproblem? Lesson 4

MP.2 Reason.


Build Understanding

Build Understanding A In theclass thereare8girlsand 14boys.Howmanymoreboys are there thangirls? Use thebarmodelandwriteanequation.

MOTIVATE > Set the Stage Read theproblemaloud.Askchildrenwhat theyknow aboutzooanimals. SUPPORTSENSEMAKING ThreeReads Havechildrenuse this routine tobreakapart the information in theproblem. PERSEVERE >Think itThrough Ifchildrenneedsupport,guide thembyasking: Q What informationprovided in thewordproblem is important to show thisproblem? Elicit fromchildren theproblem tells them thereare12 sealsand5 lions. Q Whatwillyoudraw to show theproblem? Possible answer: Idraw12circles to show the seals,and then I crossout5circles to show the lions. Q What isanefficientway to show thedifference? Possibleanswer: Idrawacirclearound the7 seals that don’thaveXs; Iwrite thenumber7next to thedrawing. TurnandTalk Ifchildrenarehaving trouble, ask them to subtract the lowernumber from thehighernumber,or suggest theycountonorback from5. BUILD SHARED UNDERSTANDING > Let'sTalk Look forchildrenwhodemonstratevarious strategies ofhow to show thisdifferenceunknownproblem. Have thesechildrenpresent their findings to theclass tohelpotherchildrenunderstandhow to show this problem type.Verifychildrenunderstand thedifference isequal to seven.

Task1 Read thewordproblemaloud.Guidechildren to solvedifferenceunknownproblem typesusingadrawing. SampleGuidedDiscussion: Q What information in theproblemshelpsyouknow if youshouldaddorsubtract? Childrenmay suggest howmanymore means it isan subtractionproblem. Read the secondwordproblem for the taskaloud. SampleGuidedDiscussion: Q How is thiswordproblemdifferent from the first problemon thissamepage? Elicit fromchildren this problemuses theword fewer . TurnandTalk Howdoyouknowwhich number to takeaway fromwhen subtracting? Children should reason they takeaway from thegreater number. OPTIMIZEOUTPUT StrongerandClearer Havechildren share theirTurnandTalk responseswitha partner.Remindchildren toaskquestionsofeachother that focusondescribingmathematical ideasclearly to determinewhichnumber to takeaway from.Then,have them refine theiranswers.

Possibleequation: 14  8 = 6; 8 + 6 = 14

Math Board

boys girls








B In theotherclass thereare6boysand13girls. Howmany fewerboysare there thangirls? Usethebarmodelandwriteanequation.

Math Board

Possibleequation: 13  6 = 7; 6 + 7 = 13

girls boys


Math Board


Learn Together  Teachers facilitate learning during whole- group instruction, ensuring students continue to play an active role in sharing their reasoning and understanding. In Step It Out features, students connect important processes and procedures to mathematical concepts.




more seals.



Read theproblem. At the zoo, thereare 12 sealsand5 lions.Howmanymore sealsare there than lions? Have children solve theproblem.

TurnandTalk Whathelpedyou to setupyour barmodel?

MAFS MAFS.1.OA.1.1 Useadditionand subtractionwithin20 to solvewordproblems . . .


220 two hundred twenty

Module 7 • Lesson4

two hundrednineteen

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Tellchildren to read thequestion stem three timesandprompt themwithadifferent questioneach time. 1 FirstRead:What is the situationabout? Thereare sealsand lions.How can I findhow manymore seals than lions thereare? 2 SecondRead:Whatare thequantities in the situation? Thereare12 sealsand5 lions. 3 ThirdRead:Whatare thepossiblemathematical questions thatwe couldask for this situation?

DepthofKnowledge (DOK)



CognitiveComplexity1 Recall

Children’sanswers to thisquestionwilldemonstrate if they can showhow to solvewordproblems for differenceunknown comparingmoreobjects.

Carloshas6baseballs.Roberthas13baseballs.How manymoredoesRoberthave thanCarlos? Howcanyoudrawapicture toshow this? 7more;Children's drawingsshouldshow13baseballswith6crossedout. Carloshas6baseballs.Roberthas13baseballs.How manymoredoesRoberthave thanCarlos? 13 − 6 = 7 Roberthas7morebaseballs. Carloshas6baseballs.Roberthas13baseballs.How manymoredoesRoberthave thanCarlos? Writeanaddition to show theaction in theproblem,and thenwritea subtractionequation to find the solution. 6 + 7 = 13 13 − 6 = 7 Roberthas7morebaseballs.

CognitiveComplexity2 BasicApplicationofSkills &Concepts* CognitiveComplexity3 StrategicThinking& ComplexReasoning

Children’sanswers to thisquestionwilldemonstrate that theyunderstandhowshowadifferenceunknown foramoresituationusinganumbersentence. Children’sanswers to thisquestionwilldemonstrate that theyunderstandhow tomatchnumber sentenceswith situationsand solutions.

Possiblequestions:Howmany sealsare there?Howmany lionsare there?How canyou findhowmanymore seals than lions thereare?Whatoperationdoyouuse?

*Expected levelof complexity forMAFS.1.OA.1.1





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Planning and Pacing Guide


Digital and interactive versions of resources are available on Ed: Your Friend in Learning.







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Differentiation Options Teachers utilize the Check Understanding as a formative assessment to determine whether students have mastered lesson content. A variety of leveled resources are available to help teachers differentiate early and effectively.

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Homework & Test Prep


LESSON 7.4 More Practice/ Homework





Represent Difference Unknown Problems with a Visual Model Complete thebarmodel. Writeanequation. 1 Roycebuys11pears.Hebuys8plums.How many fewerplums thanpearsdoeshebuy?

Use these teacher-guidedactivitieswithpulled smallgroupsat the teacher table. Small-Group Options

Represent Difference Unknown Problems with aVisual Model Problem1 provideschildren theopportunity towritean equation to solve theproblem.






Materials: worksheetwithbarmodel templates

Materials: worksheetwithbarmodel templates

Materials: worksheetwithbarmodel templates


Mathon theSpot



Encouragechildren tocomplete Problem2and then review their workwitha familymemberby watchingMathon theSpotvideo.


Provideadditionalwordproblems, so thesechildrencancontinuepracticing makingbarmodelsasa tool to solve unknowndifferenceproblems formore objectsand fewerobjects.Alsohave thesechildrencreatedrawingsand number sentences simultaneously to show these sameproblems.

Toprovidepractice fordifference unknownproblemswithmoreobjects and fewerobjects,havechildrenmake barmodels, illustrations,andnumber sentences to show theactionand solve theproblem.

Have thesechildrenwrite theirownword problems foramoreanda fewer situation,butuse the same fact family for bothproblems.Discusswithchildrenhow the twoproblemsdifferwhile thebar diagram to showbothproblems remains the same. Write thewordproblemsandbarmodels ondrawingpaper tocreateavisual model todisplay in theclassroom.

8 + 3 = 11or11 – 8 = 3

Equation: Roycebuys


fewerplums thanpears.

Put It inWriting What isanobjectyouhave severalof?Drawapicture to showanumber fewer thanyouhave. I Can Scales toTrackLearningGoals The scalesbelowcanhelpyouandyourchildren understand theirprogressona learninggoal.

2 MathontheSpot Pamhas4marbles. Rickhas10marbles.Howmany fewer marblesdoesPamhave thanRick?



Teacher TabletopFlipchart: Lesson7.4




10 – 4 = 6




fewermarbles thanRick.


Module 7 • Lesson 4

Icanuseabarchart to solvedifferenceunknown formoreor fewerobjects.


1_mflepb526670_m07l04p.indd 83 Thechartbelow indicateswhichproblemsareassociatedwith tasks in theLearn Together.Assigndailyhomework for taskscompleted.

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Math Center Options

Ican solveaproblem to findhowmany thereare when therearemoreor fewerofanobjectwhen compared toanotherquantity.


MorePractice/HomeworkProblems LearnTogetherTasks

Use these children self-directedactivitiesat centersor stations.



Icandrawapicture to show thedifferencebetween twonumbers.



Ready forMore




Wrap-Up  Teachers bring the class together to summarize, using the provided exit tickets, “I Can” scales, journal writing activities, or anchor charts.

● MyLearningSummary ● InteractiveOnMyOwn

● Reteach7.4

● Challenge7.4 ● UnitProjects,G1,Unit2




Icancompare thenumberofobjects.








Print&OnlineAssets OnlineAssets





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Planning and Pacing Guide

Content Architecture

Promoting Conceptual Understanding Not All Tasks Are Equal.  The Spark Your Learning tasks were carefully crafted to promote reasoning and problem solving. The tasks have a low floor and a high ceiling as well as varied solution strategies, ensuring every student can make progress and build mathematical understanding.

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Teachers begin a Spark Your Learning task by setting goals and using language development routines to help students understand the task, if needed.

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Name Identify Even and Odd Numbers Essential ? Howareevennumbersand oddnumbersdifferent? Spark Your Learning Howcanyou show thepaintbrushesat theartcenters? Lesson 1 BuildUnderstanding


MOTIVATE > Set the Stage Askchildrenwhat theyknowaboutpairsofobjects. Havechildren shareobjects thatcome inpairs. SUPPORTSENSEMAKING ThreeReads Havechildrenuse this routine tobreakapart the information in theproblem. PERSEVERE > Think It Through Ifchildrenneedsupport,guide thembyasking: Q Howcanyouuse tools to show1pairofbrushes? Icanuse2counters to show1pairofbrushes. Q Howcanyouuse tools to show3pairsofbrushes? Icanuse6counters,putting2counters together foreachpair. TurnandTalk Howdidyouuse tools to show 3pairsofbrushes? Possibleanswer: Iused 2counters foreachpairofbrushes.Thereare3pairs in 6counters. BUILD SHARED UNDERSTANDING > Let's Talk Havechildrenexplainhow theyare thinking to solve the task.Thenaskchildren touseanagree sign tocritique the reasoningofothers. Q Howmanybrushesare in1pair? 2

Teachers support productive perseverance and foster a growth mindset as student work through the task. The Teacher Edition includes student work samples and support to help connect mathematical representations and correct common errors. The Talk Moves routines help teachers elicit reasoning and guide students.


Checkchildren’swork.Children should show 2paintbrushesateachof3artcenters.

Read the following: Jimmyhelpspassout supplies for the3art centers inhis class.Hehas6paintbrushes.Eachart centerneeds2paintbrushes. How can you show thepaintbrushesat theart centers? Have children discuss how their concretemodelsordrawingswould change ifJimmy had 7paintbrushes topassout.

MAFS MAFS.2.OA.3.3 Determinewhetheragroupofobjects (up to20)hasanoddorevennumberofmembers,e.g.,bypairingobjectsor counting themby2s;writean equation toexpressanevennumberasa sumof twoequaladdends.


Module 2 • Lesson1


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Tellchildren to read thequestion stem three timesandprompt themwitha differentquestioneach time. 1 What is the situationabout? Jimmypassesoutart supplies. 2 Whatare thequantities in the situation? Hehas6paintbrushes inall.Eachart centerneeds2paintbrushes. 3 Whatare thepossiblemathematicalquestions thatwe couldask for this situation? Possiblequestions:Howmanypaintbrushesare there inall?Howmanydoes eachart centerneed?Howmanyart centerswill receivepaintbrushes?How can you countby twos to solve theproblem?What if Jimmyhas7brushes?How does this changeyouranswer?

A Spark Your Learning task is complete when the class comes to shared understanding and the teacher celebrates student success.



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See It In Action  Professional Learning

support includes classroom videos with hints, tips, and commentary from experts and authors.


Planning and Pacing Guide

Content Architecture

Juli K. Dixon, Ph.D. Professor, Mathematics Education University of Central Florida Orlando, Florida

Promoting Perseverance Rigorous Tasks

There is little argument that students need to learn to persevere. Where the struggle exists is in determining the pathway to this important outcome. It begins with a good task. Good tasks are rigorous. Providing rigorous tasks sets the stage for students to engage in worthwhile activity around learning mathematics. Good tasks have “low floors” and “high ceilings” so that students have access to the content regardless of their prior achievement. A rigorous task is one that supports students to do the sense making. A goal might be to make connections between concepts and procedures or possibly to determine a solution process when a procedure for the solution has not yet been introduced. Students are expected to explain and justify their thinking. Rigorous tasks afford students the opportunity to develop productive habits of mind around mathematical problem solving. Just-in-Time Scaffolding All too often, with best intentions, teachers or resources undermine the value of a good task by providing scaffolding too early. It is tempting to provide scaffolding to students at the first sign of struggle or even in anticipation of student struggle. However, if the struggle is productive, this scaffolding should be withheld. Instead of providing scaffolding just in case students might need it, scaffolding should be offered just in time, when there is evidence that the student’s struggle is no longer productive. While the opportunity to develop perseverance is reliant on access to good tasks, it is supported during instruction by effective teaching. In order for students to develop perseverance, they must engage in productive struggle. This means that scaffolding, on the student page or from the teacher, needs to be managed in a way that supports students to do the sense making. Scaffolding should be provided when students’ engagement with the task is no longer productive or when the student work is not leading to the learning objective. A key to effective teaching is to know when to provide the scaffolding and to know when to step aside to allow students to persevere.


Planning and Pacing Guide

Content Architecture

Real-World Relevance Is your weight on the Moon proportional to your weight on Earth? Am I on track to meet my goal for number of steps walked today? How did people 10,000 years ago incorporate geometric designs into their jewelry? Projects and tasks in Into Math are carefully crafted, not only to ensure they have the appropriate level of rigor, but also to ensure students remain engaged and see the relevance of math in the world around them.

Each unit opens with a career and a project that students can work on throughout the unit.


Learning Mindset Challenge-Seeking MakeDecisions

In thisunit,youwill learnaboutplacevalue relationships inwholenumbers.Youwill learn to read andwrite largenumbers,andhow to regroup themby focusingon thevalueofeachdigit.You’ll learn to compareandordernumbers,and to roundnumbers in order toestimateandassess the reasonablenessof answers. Musician • Didyouknow thathundredsof thousandsof students across thecountryplayan instrumentor sing ina schoolbandorchorus? • Timeand rhythm inmusicalnotationaredoneusing numbersand ratios.All trainedmusiciansusemath. STEMTask Determine throughdiscussionwhatpriorknowledge studentshaveofmusicians. • Ask studentswhoare someof their favoritemusicians. Have theyever seenmusiciansplay live? • Ask students if theyplayan instrumentorknow anyonewhodoes. • Ask studentswhocome fromothercountries,orhave relatives thatcome fromothercountries, if thereare specific instruments thatareprominent in their culture. Unit 1 Project ConcertCalculations Overview: Studentsplana tourwithagoalof reaching amillionpeoplebut spending$300,000or less. Materials: BLMConcert InfoSheet AssessingStudentPerformance: Answerswillvary. Check the totals.

Unit 1

Place Value and Whole-Number Operations

Learning Mindset Challenge-Seeking MakeDecisions

The learningmindsetof thisunit ischallenge-seeking.Challenge- seekingcanbeunfamiliar to some,but it’sawayof fosteringa growthmindset.A fixed-mindsetvoice says thatchallengesare hardandyou shouldavoid themas longaspossible.Agrowth- mindsetvoice sayschallengeswillcomenomatterwhatyoudo, so it isbetter to seek themoutandmeet them than to fear them. Makingdecisions isan importantpartofchallenge-seeking.The morequicklyanddefinitivelyyoumakedecisions themorequickly youcanmove forward.Don’tworry if the firstdecisionyoumake is wrong– justgoon to thenextone.Help students see that seeking challengeswillhelp to fostergrowthmindset. UnderstandingMindsetBeliefs Ask students todiscussa timewhen theyavoidedaddressinga challenge that theyknewmightbedifficult for them.Did ithelp? Ordid thechallenge justcomeanyway?Discuss the importanceof theirattitude,ofembracingchallengeand takingcontrolof the things theyneed toworkon. DevelopingGrowthMindsetBehaviors Ask students to recall times that theycouldn’tmakeadecision.Did theproblem solve itself?Elicit from students times theywereable tomakedecisionsandmove forward.Whatenabled them todo that?What stood in thewayof it?Howcanwecreatecircumstances whereweembracemakingdecisionsand seekingoutchallenges?

In this unit youwill learn to read,write, compare, and order large numbers.You’ll learn to make estimates and assess the reasonableness of answers.Youwill use your understanding of place value to add larger numbers.



Each human culture hasmusic, just as each has language. The Bureau of Labor Statistics summarizes that in 2016 therewere over 170,000 jobs formusicians and singers in the United States alone. If you include people who playmusic just for fun, it's reasonable to assume there aremillions ofmusicians in theworld. It is impossible to know exactly howmany types of instruments there are, but experts believe the number to be in the thousands. Youmight already play, or be thinking about playing, an instrument. There's so much to decide!Which instrumentwill you pick?Howmuchwill you practice?

STEM Task:

Workwith a partner to experimentwith sound. Cut a 4-footpieceof yarn. Tightly tie the handle of ametal spoon in the center of the yarn. Then wrap the two ends of the yarn around your index fingers and hold your fingers against your ears.Have your partner tap the hanging spoonwith a ruler.What happens next may surprise you. Try a larger spoon and other objects. Collect data for each object. What do you and your partner infer about sound?

Picking and accepting any new challenge requires you tomake a lot of decisions.Gathering information is one step in a decision-making process.What information can you gather about instruments before selecting one to study?You can study different types ofmusic.You can try out different instruments before you pick one.You can also evaluate if you have enough time to practice.


Q What evidence about sound did you gather from the experiment? Q How did the decisions youmade aboutmaterials affect the outcomes of the experiment?



Watch for studentswho seem tentative.For these students, suggest strategies suchas: • identify thequestion theyareunsureof • trya strategy • assess if the strategyworked • tryanew strategy ifone isneeded What to Watch For

Have studentsaskeachotherquestions suchas: • Is itbetter toplaymoreconcertsorbiggerconerts? • Areweclearaboutwhatoperation is required foreachcalculation? • Does itmakesense to try to finishonepartof theproblem first, thenworkon the otherpart?

“ If at first you don’t succeed, try, try again. ”

—Thomas H. Palmer





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Cross-curricular tasks are found throughout the program, including STEM problems in each module and STEM- themed unit projects.

Opportunities, strategies, and support to help students focus on mindset are embedded in every lesson and in the unit-level projects.


Planning and Pacing Guide

Content Architecture

Mathematical Practices Each lesson has a focus Mathematical Practice based on the lesson’s learning goal and the tasks that meet the learning goal. Questions provided in the Teacher’s Edition support teachers in facilitating and guiding student engagement with the Mathematical Practice . Build Understanding lessons always include Spark Your Learning, a productive perseverance task, and are paired with MP.1 (Make sense of problems and persevere in solving them), MP.3 (Construct viable arguments and critique the reasoning of others), and MP.5 (Use appropriate tools strategically). Connect Concepts and Skills lessons focus on MP.7 (Look for and make use of structure) and MP.8 (Look for and express regularity in repeated reasoning) where students connect understanding they have developed with more efficient procedures. These practices help students explain and justify the procedures they use along with MP.4 (Model with Mathematics) when students are connecting their understanding to a procedure. Apply and Practice lessons provide opportunities for MP.2 (Reason abstractly and quantitatively) as well as provide opportunities for MP.6 (Attend to precision) as students apply procedures in practice. While support is provided for specific Mathematical Practices, other Mathematical Practices will be present but not the focus of the learning experience. As students engage in tasks, they will naturally use additional Mathematical Practices, especially when students are provided opportunities to do the sense making and share reasoning with their classmates.

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LESSON 12.4 Solve Take Apart Problems Within 10 Using Objects and Drawings DO NOT EDIT--Changes must be made through "File info" CorrectionKey=FL-A

Major LESSON FOCUS AND COHERENCE Mathematics Florida Standards LESSON FOCUS AND COHERENCE Mathematics Florida Standards ■ MAFS.K.OA.1.2 Solve ad itio an subtraction word probl ms, and add and subtract within 10, e.g., y using bjects or drawings to represe t the problem. Mathematical Practices ■ MAFS.K.OA.1.2 Solveadditionand subtractionwordproblems,and addand subtractwithin10,e.g.,byusingobjectsordrawings to represent theproblem. Mathematical Practices MAFS.K12.MP.2 Reasonabstractlyandquantitatively. MAFS.K12.MP.5 Useappropriate tools strategically. Solve Take Apart Problems Within 10 Using Objects and Drawings ■


● Additional Essential Questi How can you solve tak using objects, drawing Learning Objecti Use objects, drawings, a take apart problems wit Language Objec Use take apart, subtract, equation for drawings an Lesson Materials: two-

■ Supporting

Essential Question Howcanyousolve takeapartproblemswithin10by usingobjects,drawings,andequations? Learning Objective Useobjects,drawings,andequations to solve takeapartproblemswithin10. Language Objective Use takeapart,subtract,minus, isequal to, and equation fordrawingsandequationsshowingsubtraction. LessonMaterials: two-colorcounters,crayons

MAFS.K12.MP.2 Reason abstractly and quantitatively. MAFS.K12.MP.5 Use appropriate tools strategically.

Mathematical Progressions




Children: • solve subtractionproblemswithin5using objects,drawings,actions,andequations. MAFS.K.OA.1.2 GradeKLessons6.4

Children: • solve subtractionproblemswithin10 usingobjects,drawings,actions,and equations. MAFS.K.OA.1.2

Children: • solvewordproblems involvingputting togetherusing subtractionwithin20. • represent subtractionproblemsusing objects,drawings,andequations. MAFS.1.OA.1.1 Grade1Lessons2.2,5.3

Mathematical Progressions

Prior Learning

Current Development

PROFESSIONAL LEARNING Children: • solve subtraction problems within 5 using objects, drawings, actions, and equations. MAFS.K.OA.1.2 Grade K Lessons 6.4 Using Mathematical Practices MAFS.K12.MP.5 Useappropriate tools strategically.

Children: • solve subtraction problems within 10 using objects, drawings, actions, and equati ns. MAFS.K.OA.1.2

Childre • solve togeth • repres object MAFS.1. Grade 1

The tools thatchildrenuse includemanipulativessuchascountersandcubes,crayonsorother writing implements,andeven themselves: theymaycounton their fingersoractoutanaddition orsubtractionproblembymakinggroupswith theirclassmates.Representingsubtractionmay requirespecialattention touseof these tools.Childrenneed reminders that theyareshowing anddiscussinga largergroup thathasbeen takenapart into twosmallergroups.Theymay choose todemonstrate thisbydrawing,usingcounters,using their fingers,oracting itout. Whateverstrategy theychoose foran individualproblem,childrenshouldbeguided to learn how touseaversatilearrayof toolsandstrategies.Althoughchildren’scurrent task, learning to subtractwithin10,canoftenbeaccomplishedbysimplycountingvisibleobjects ina remaining group, thestrategies that they learnwithin these lessonswillcreatea foundation forstrategic choiceandusageof tools for them touseas tasksbecomemoreabstract.



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Using Mathematical Practices MAFS.K12.MP.5 Use appropriate tools strategically.

The tools that children use include manipulatives such as counters and cubes, crayons or other writing implements, and even themselves: they may count on their fingers or act out an addition or subtraction problem by making groups with their classmates. Representing subtraction may require special attention to use of these tools. Children need reminders that they are showing and discussing a larger group that has been taken apart into two smaller groups. They may choose to demonstrate this by drawing, using counters, using their fingers, or acting it out. Whatever strategy they choose for an individual problem, children should be guided to learn how to use a versatile array of tools and strategies. Although children’s current task, learning to subtract within 10, can often be accomplished by simply counting visible objects in a remaining group, the strategies that they learn within these lessons will create a foundation for strategic choice and usage of tools for them to use as tasks become more abstract.

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Planning and Pacing Guide

Content Architecture

Language Development Language development and development of mathematical understanding are interdependent. All students must be able to listen, speak, read, write, and converse in order to meet the rigorous expectations of Florida’s standards and become fluent problem solvers. Math is a second language for ALL students. Into Math is built upon 4 design principles from the Stanford Center for Assessment, Learning, and Equity (SCALE). These 4 design principles promote the use and development of language as an integral part of instruction.  1 • Principle 1: Support Sense-Making  Scaffold tasks when needed, being sure to amplify (instead of simplify) language for students. • Principle 2: Optimize Output  Help students describe their mathematical reasoning and understanding. • Principle 3: Cultivate Conversation  Facilitate mathematical conversations among students. • Principle 4: Maximize Linguistic and Cognitive Meta-Awareness  Help students evaluate their use of language and see how mathematical ideas, reasoning and language are connected. Language Routines that help teachers embrace these principles during instruction are included in Into Math .

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LANGUAGE DEVELOPMENT • Planning for Instruction

Bygivingallchildren regularexposure to language routines incontext,youwillprovide opportunities forchildren to listen , speak , read ,and write about mathematicalsituation sand developbothmathematical languageandconceptualunderstandingat the same time. Using Language Routines to Develop Understanding Use theProfessionalCards for the following routines toplan foreffective instruction. ThreeReads Lessons1.2,1.3,1.4,1.7 Children readaproblem three timeswitha specific focus. 1stRead What is the situationabout? 2ndRead Whatare thequantities in the situation? 3rdRead Whatare thepossiblemathematicalquestions thatwecouldask for the situation? StrongerandClearer Lessons1.2,1.4,1.5 Childrenwrite their reasoning toaproblem, share,explain their reasoning, listen toand respond to feedback,and thenwriteagain to refine their reasoning. SupportsMathematicalPractice6 Attend toprecision. CompareandConnect Lessons1.1–1.6 Children listen toapartner’s solution strategyand the identify,compare,andcontrast this mathematical strategy. SupportsMathematicalPractice5 Useappropriate toolsstrategically. Critique,Correct,andClarify Lessons1.6,1.7 Childrenconnect thework ina flawedexplanation,argument,or solutionmethodand share withapartnerand refine the samplework. SupportsMathematicalPractice3 Constructviableargumentsandcritiques the reasoningofothers. SupportsMathematicalPractice1 Makesenseofproblemsandpersevere insolving them.

Linguistic Note Manykey phrasesuse familiar words innewcombinations.For example,makea tenanddoubles plus1maybediscernableas individualwords,butEnglish LanguageLearnersmayhave troubleunderstanding these wordsphrases.Promptingprior knowledge isessential tohelp childrenunderstandphrases such as these so theymayapply appropriate strategiesduring this lesson.

Connecting Language to Fluency for Addition and SubtractionWithin 20

Watch forchildren’suseof review terms listedbelowas theyexplain their reasoningwithnew concepts. Ifchildren strugglewith the term counton and countback useahundredchartor number line to show themexamples.

Key AcademicVocabulary

PriorLearning •ReviewVocabulary

CurrentDevelopment •NewVocabulary

counton start fromanumberandcount forward toadd countback start fromanumberandcountback to subtract related fact setof threenumbers thatcanbeaddedand subtracted

addends numbers toadd together inanadditionequation difference the solution toa subtractionequation doubles add the samenumber two times sum thequantityaltogether



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The Language Routines as well as new and review vocabulary are summarized on the Language Development page for each module.

The write-on/wipe-off MathBoard includes a graphic organizer that students can use with the Three Reads routine.

Make Sense of Problems ThreeReads

Read the problem 3 times. With each read, focus on a different question below. Lean el problema 3 veces. Con cada lectura, enfóquense en una pregunta diferente de las siguientes.

The research-based Language Routines in Into Math provide opportunities for all levels of English Learners. Linguistic support and suggestions for effective scaffolding are provided in the Teacher Edition and on Ed: Your Friend in Learning.

FirstRead What is theproblemabout? Primera lectura ¿Dequé trata elproblema?

SecondRead Whatdo eachof the numbersdescribe? Segunda lectura ¿Quédescribe cada unode los números?

ThirdRead Whatmathquestions could youaskabout theproblem? Tercera lectura ¿Quépreguntasmatemáticaspodrías hacer sobre elproblema?

©HoughtonMifflinHarcourtPublishingCompany 978-1-32854-838-2

1) Zwiers, et al. (2017). Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Stanford Center for Assessment, Learning, and Equity.


Planning and Pacing Guide

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