The instructional materials for Into Math Florida Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

Each module contains two types of lessons specifically designed to engage students with conceptual understanding, Spark Your Learning and Bridging Lessons. The instructional materials present multiple opportunities for students to develop and independently demonstrate conceptual understanding, and examples include:

• In Lesson 2.3, Read and Write 4 and 5, Spark Your Learning includes the teacher modeling the number four with counters, and students show four with crayons (to correspond to counters). Students answer, “How many crayons did you use? What items do we have four of in the classroom?” During Learn Together, students build understanding with counting, one to one correspondence, identify four and five, and write the corresponding numerals. In Independent Practice, students show what they know about the numbers four and five and how the two numbers are different from each other. Students count and circle the picture that represents five swimmers and draw what they know about four and five. (K.CC.1.3)
• In Lesson 11.3, students solve addition problems within 10 by counting the number of objects in the picture. Spark Your Learning includes questions to further develop understanding depending on if students modeled adding two groups, showed one group, and common errors students might make. (K.OA.1.1, K.OA.1.2)
• In Lesson 11.5, students count how many objects are in each group in a picture and write a corresponding addition equation. (K.OA.1.1, K.OA.1.2)
• In Lesson 12.3, Small Group includes three options to develop students’ conceptual understanding of put together problems within 10. Students use two color counters and crayons to create word problems putting together two groups and writing an equation. (K.OA.1.2)
• In Lesson 17.1, Problem 1, students use 10 cubes and draw some more ones to show the number. Students write the number to show how many more ones, and a picture of 10 cubes at the top of the page represents ten ones. (K.NBT.1.1)
• In Lesson 17.2, Build Understanding, there are ten connecting cubes at the top of the page. Students answer “How many more cubes do you need to make fifteen?” and “describe the number 15” using tens and ones. Students draw a picture and fill in the blank to tell how many ones are needed to make 14 and 15. (K.NBT.1.1)

Every lesson also has an optional Sharpen Skills activity to build conceptual understanding. For example, Lesson 5.1, Act Out Addition Problems Within 5, students act out and tell a story about a picture shown and write numbers to show how many children are in each group.  

The instructional materials for Into Math Florida Kindergarten meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

Students develop procedural skills and fluencies throughout the grade level, and each module contains procedural lessons that help students develop the steps in a procedure and determine when the procedure should be used. Module and Lesson components that specifically attend to student’s developing and independently demonstrating procedural skill and fluency include:

• In Module Planning: Teaching for Success, Teacher to Teacher notes include advice for teachers on how to question the student in order to build procedural fluency. For example, in Module 12, Teacher to Teacher suggests having students visualize six, draw six, and then talk about a part-part-whole relationship to make the connections about part-whole relationships. (K.OA.1.5)
• Activating Prior Knowledge is included in lessons. For example, in Lesson 5.1 students use 5 frames and determine the number shown and “how many more” needed to make five. This supports fluency with addition within 5. (K.OA.1.5)

Students develop fluency with K.OA.1.5 in Modules 5 and 6. Specific lesson components, Step it Out and More Practice/Homework, include opportunities for students to engage in procedural skill and fluency. In addition, Reteach opportunities provide additional fluency practice. For example:

• In Lesson 5.3, ReTeach includes independent practice for students to build fluency of addition within five. Additionally, the More Practice/Homework and Test Prep sections provide students with independent practice of adding within five.
• In Lesson 5.4, Step It Out, On My Own, and More Practice/Homework, students independently practice take from problems within five. Test Prep extends independent practice by having students use pictures to demonstrate fluency of take from problems within five.
• In Lesson 5.6, Step It Out, students use pictures to create matching subtraction equations to practice fluency within five. During On My Own, students independently practice within five. The More Practice/Homework provides students with additional practice opportunities to build subtraction skills.
• In Lesson 6.3, Practice and Homework Journal, students write subtraction equations and solve based off a story problem, “Molly has five cars. Two of the cars are yellow. The rest are blue. How many cars are blue?”.

In addition, every lesson has an optional Sharpen Skills activity to build skill and fluency. For example, in Module 5 Lesson 3, students use connecting cubes of two different colors while articulating sentences using addition vocabulary. “I am joining 3 blue and 2 red. The total number is 5. I am adding 2 red cubes to 3 blue cubes. Three plus 2 is equal to 5.” (K.OA.1.5)

The instructional materials for Into Math Florida Kindergarten meet expectations for teachers and students spending sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Students engage in routine application problems throughout the grade level. In Independent Practice and On My Own, students apply what they have learned to solve real world problems independently. For example:

• In Lesson 5.1, students “act out and tell a story about the picture. Write the numbers that show how many children are in each group.” Guided questions throughout the activity prompt students to apply their understanding of addition to find a total unknown. “How many children are sitting on the rug? How many children come? What happens to the group when one child joins them? How can you find the total number of children there now? What groups are you adding?” (K.OA.1.2).
• In Module 5, Test Form A, Item 5, students apply mathematics to a real-world context, “Ben and Lisa are playing in the park. Their friends Matt and Kate join them. How many friends are in the park now?”
• In Lesson 11.1, Spark Your Learning begins with a story problem and picture to show how many backpacks are in a truck. Students consider, “How can you act out the backpacks in the truck? How many backpacks does the girl bring? How can you act out the backpacks that girl brings? Now how many backpacks are there altogether?” During Learn Together, students use counters, cubes, or pictures and write an addition problem for story problems. During On My Own, students act out an addition story about camping by a lake within 10, draw to show the story, and write a matching equation. (K.OA.1.5a)
• In Lesson 12.5, Step It Out and On My Own, students create picture models and equations to solve addition word problems, and in More Practice/Homework, students solve word problems within 10 in a variety of contexts. (K.OA.1.2)
• In Lesson 13.3, students listen to a story problem and use objects and drawing to solve addition equations within 10. (K.OA.1.1)

Students engage with non-routine application of the mathematics throughout the materials when they create story problems for pictures and number sentences. For example:

• In Lesson 5.6, students “Tell a subtraction word problem about the picture. Mark an X to show what is being taken away from the group. Write an equation to model the problem.” (K.OA.1.2)
• In Lesson 6.1, students represent addition problems within five using objects and drawings. During Spark Your Learning, students respond to, “Look at the picture. What addition story can you tell about the cat and dogs? Write how many total pets?” Students create their own story problem based on the picture of 4 pets. (K.OA.1.2)
• In Lesson 6.7, students “Tell your own addition word problem within 5. Draw to represent your story. Write the equation to model your story” (Both addends unknown). (K.OA.1.2)
• In Lesson 12.1, Spark Your Learning, students look at a picture of dogs. “What addition story can you tell about the small dogs and the big dogs? Complete the equation to show how many dogs in total.” Students count the small dogs and place a red counter on them while counting aloud. Students count the large dogs and place a yellow counter on them while counting aloud and then are asked, “How can you decide how many dogs there are in all?” (By counting all the counters). Students add the small (red counters) and large dogs (yellow counters) and write a corresponding equation. Throughout the lesson, students model a story problem with counters, write a corresponding addition sentence using the correct numbers, plus sign, equal sign, and find the total sum. (K.OA.1.1)

The instructional materials for Into Math Florida Kindergarten meet expectations for the three aspects of rigor not always being treated together and not always being treated separately. In general, two or all three, of the aspects are interwoven throughout each module.

All three aspects of rigor are present independently throughout the program materials. Examples include:

• Lessons 1.1-1.3 address developing conceptual understanding of numbers to five where students use counters to represent numbers. Students listen to stories and show the number using counters. “Maria went to the park. She saw three squirrels in the tree. There were also four ducks under the tree.” 
• In Lesson 2.4, Step It Out, students develop procedural skill and fluency as they count the flowers in each vase to count and write the number. (K.CC.1.3)
• In Lesson 5.2, students use pictorial representations to demonstrate story problems to show subtraction within five. (K.OA.1.5)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

• In Lesson 9.3, students apply what they know about counting to understand how to count on from any given number in a counting sequence. (K.CC.1.2)
• In Lesson 10.1, students develop conceptual understanding by using counters, pictures, or connecting cubes to compare two groups of objects within 10. Students practice procedural skill by drawing lines to match the objects in each group. Students draw a group greater than the picture shown and circle the group that has a number of objects greater than the other group. (K.CC.3.6)

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for carefully attending to the full meaning of each practice standard (MP). 

The materials attend to the full intent of all eight MPs. In the Teacher’s Edition, the Focus and Coherence for each lesson describes how the MPs are addressed with the lesson. The Planning and Pacing Guides include a description of lesson components that address specific MPs.

• During Spark Your Learning, students encounter a productive perseverance task that engages students with MP.1.1 (Make sense of problems and persevere in solving them), MP.3.1 (Construct viable arguments and critique the reasoning of others), and MP.5.1 (Use appropriate tools strategically).
• Connect Concepts and Skills lessons focus on MP.7.1 (Look for and make use of structure) and MP.8.1 (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.4.1 (Model with Mathematics) when students are connecting their understanding to a procedure. 
• Apply and Practice lessons provide opportunities for MP.2.1 (Reason abstractly and quantitatively) as well as provide opportunities for MP.6.1 (Attend to precision) as students apply procedures in practice.

Examples of the instructional materials attending to the full meaning of the MPs include:

• MP.1.1: In Lesson 11.1 students listen to a story, act it out, and then write an equation to match. “There are six butterflies in the meadow. Four more butterflies join them. How many butterflies are in the meadow now?”
• MP.2.1: In Lesson 12.2, students solve, “There are ten plates on the picnic table. Six are blue. The rest are red. How many are red?”. Students draw a picture to represent the problem and write an equation.
• MP.4.1: In Lesson 6.4, On My Own, students “Make up your own take apart story problem using numbers within 5. Draw to show your problem. Write the equation that matches your story.”
• MP.5.1: In Lesson 10.1 students show which group has a greater number of objects. Students can choose to use counters, connecting cubes, or drawings.
• MP.6.1: In Lesson 19.1, Learn Together, “Leo builds two castles with blocks. He wants to put one of the castles in his bookcase. Use the words taller than, shorter than, or longer than to describe the heights and lengths of the castles. Use red to show the height of each castle. Use blue to show the length of each castle. Circle the castle Leo places on the bookcase.”
• MP.7.1: In Lesson 7.4, Ways to Make Ten, students use two color counters to represent 10, color the ten frame on the page to match their counters, and write in the addition sentence to match.
• MP.8.1: In Lesson 9.2, Step It Out, Task 2, “Have children listen as you read the questions aloud. Explain the pattern: each row of the hundred chart goes up by ten.” “What number should you start with if you want to count by ten? Start with ten and count ten more. How many do you count? Point to the numbers on the chart. Ten more is 20, The one changes to a 2 and the 0 stays the same. Now count ten more. How many do you count? How has the number changed? How do you count to one hundred by tens?”

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Students have opportunities to construct viable arguments through activities such as explaining their thinking or justifying steps, and the materials prompt them to analyze the arguments of others. Examples include:

• In Lesson 5.4, Build Shared Understanding, students explain how they solved a problem, and students are encouraged to ask their classmates what they did first, next, and last.
• In Lesson 8.1, Put It In Writing, students explain how to find whether there are eight or nine objects in each group. 
• In Lesson 9.2, On My Own, students “place rows of numbers as you count by tens to 100. Tell a classmate about counting by tens to 100. What is alike about the numbers? What is different about the numbers?”.
• In Lesson 12.5, students draw representations of word problems and write an equation to model the problem. Students “compare their drawings and talk about how they knew how many cartons of each kind of milk to draw.” 
• In Lesson 14.3, Learning Mindset, Try Again, students discuss, “Which strategies they used? Which they like best? Which were most challenging? Would they try any of the strategies their classmates mentioned?”.
• In Lesson 19.2, On My Own, Problem 3, the materials state, “Look at the rugs. Compare the lengths of the two rugs. Use the words longer than or shorter than to describe the lengths. Draw a circle around to longer rug. Mark an X on the shorter rug. Explain why the two rugs must be at the same starting point to compare the lengths.” 
• In Lesson 19.3, Learning Mindset, Bounce Back, students discuss that other perspectives are valuable and not everyone sees things in the same way.

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The materials provide teachers with Sample Guided Discussions, Turn and Talks, and Leveled Questions to assist teachers in engaging students in discourse. There is also some teacher guidance on how to lead discussions beyond the provided questions. Examples include:

• In Lesson 3.5, Step It Out, the Turn and Talk states, “Have students share their drawings and strategies and speak sentences about Problems 4 and 5 using the words less than, fewer than, greater than and more.”
• In Lesson 4.1, Build Understanding, Connect Math Ideas, Reasoning, and Language, Compare and Connect states, “Before beginning the task, have children describe and give examples in their own words of the meaning of the words color, classify, and category. Have students discuss their examples. Prompt discussion by asking: Do you agree or disagree? Why?”.
• In Optimize Output of Lesson 5.6, Stronger and Clearer, the teacher directs students to share their Turn and Talk responses with a partner, encouraging them to describe mathematical ideas clearly. Students are asked to discuss other possible solution strategies and refine their answers if necessary throughout the conversation.
• In Lesson 7.2, the Turn and Talk states, “Have children explain to partners how they chose what counters to use. Did they use all red or all yellow? Did they use one color for each number? Why?”.
• In Lesson 16.4, the Learn Together, Connect Math Ideas, Reasoning, and Language, Compare and Connect states, “Help children identify the relationship between a square and a rectangle. Ask children to discuss whether all squares are rectangles and whether all rectangles are squares.”
• In Lesson 19.3, the Turn and Talk states, “Have children talk about what would happen if the birdbath on the right were placed in a hole instead of on the same surface as the one on the left. What would be different about how they could or could not compare the heights?”.
• In Lesson 20.3, Optimize Output, the materials assist teachers by having them ask students to identify the error, correct the placement of the label, and explain their reasoning.

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for attending to the specialized language of mathematics. The materials provide explicit instruction on communicating mathematical thinking with words, diagrams, and symbols. The materials use precise, accurate terminology and definitions when describing mathematics and support students in using them. Examples are found throughout the materials.

The Planning and Pacing Guide has a section for Language Development that states Into Math Florida is built upon four design principles to promote the use and development of language:

• Principal 1: Support Sense-Making;
• Principal 2: Optimize Output to help students describe their mathematical reasoning and understanding;
• Principal 3: Cultivate Conversations to facilitate mathematical conversations among students; and
• Principal 4: Maximize Linguistic and Cognitive Meta-Awareness to help students evaluate their use of language and see how mathematical ideas, reasoning and language are connected.

Language Routines and new/review vocabulary are summarized on the Language Development page for each module, and this also includes Key Academic Vocabulary for Prior Learning - Review Vocabulary and Current Development - New Vocabulary with definitions. Also in Language Development, Linguistic Notes provide teachers help with possible misconceptions relating to academic language. For example:

• Module 3 identifies and defines review vocabulary, larger, and Current Development, greater than, count, less than, equal to, compare, and match.
• In Module 5, the Linguistic Note states, “Listen for children who mix up the language between addition and subtraction. For example, children should say that when two groups are joined together, the result is the number “in all.” When a group is taken apart, children should say the number that is “left.” Help children use the correct terms throughout each lesson.”
• Module 6 includes Key Academic Vocabulary such as: put together and take apart.
• In Module 8, the Linguistic Note states, “Point out the difference between an amount of something and a number of objects. Discuss this idea in terms of ‘how much’ versus ‘how many.’ To help children understand the difference, provide examples from a variety of contexts. For example, ‘how much’ can be used to describe a value of a coin or an amount of liquid in a jar. On the other hand, ‘how many’ could be used to describe the number of coins or the number of ice cubes in a jar.”

The Guided Student Discussion often provides prompts related to understanding vocabulary such as: Lesson 14.4, Task 1 states, “What does a cone look like? What do curved surfaces look like? What do flat surfaces look like? Which objects have all the qualities of a cone?”

Student pages include vocabulary boxes defining content vocabulary. Vocabulary is highlighted and italicized within each lesson in the materials. The vocabulary review at the end of each Module requires students to match new vocabulary terms with their meaning and/or examples provided, fill-in-the-blank with definitions or examples, or create a graphic organizer to help make sense of terms. Some lessons include Vocabulary Review. Connect Math Ideas, Reasoning, and Language Compare and Connect encourage students to use vocabulary terms to discuss mathematics with correct terminology. For example:

• In Lesson 3.2, Connect Math Ideas, Reasoning, and Language Compare and Connect states, “Remind children that they have learned the vocabulary term greater than. Have children compare the meanings of the terms greater than and less than. As children discuss, ask questions to help them clarify their reasoning.”
• In Lesson 4.2, Build Understanding, Connect Math Ideas, Reasoning, and Language Compare and Connect states, “Before beginning the task, have children describe and give examples in their own words of the meaning of the word shape. Have children discuss their examples. Prompt discussion by asking: Do you agree or disagree? Why?”.
• In Lesson 5.7, students use visual models and equations to help review the module’s vocabulary for addition and subtraction.
• In Lesson 16.1, students use graphic organizers with the terms, circle, square, rectangle, and triangle. Students draw a picture to illustrate each term and give an example of a real world object of that shape.

Vocabulary cards can be used with vocabulary games. The eGlossary includes vocabulary terms and definitions translated into ten different languages. The Interactive Glossary provides the definition and a visual (diagrams, symbols, etc.) is provided for each vocabulary word.The Interactive Glossary also provides space for students to make graphic organizers or drawings for each new vocabulary term. In the student materials, the instructions state, “As you learn about each new term, add notes, drawings, or sentences in the space next to the definition. Doing so will help you remember what each term means.”

The instructional materials for Into Math Florida Kindergarten meet the expectations that there is a clear distinction between problems and exercises in the materials.

Each Module presents lessons with a consistent structure. During the instructional sections, which include Build Conceptual Understanding and Connect Concepts and Skills, students have opportunities to learn new content through examples and problems for guided instruction, step-by step procedures, and problem solving.

At the end of the lesson, Apply and Practice provides a variety of exercises which allow students to independently show their understanding of the material. Exercises are designed for students to demonstrate understandings and skills in application and non-application settings. Test Prep and Spiral Review also include exercises. 

The materials distinguish between problems and exercises within each lesson. Lessons include Spark Your Learning or Step it Out, Turn and Talk, Build Understanding, Check Understanding, and On My Own sections. Spark Your Learning Problems activate prior knowledge and introduce new mathematics to students. Build Understanding includes problems that help students build conceptual understanding of the mathematics topic being taught.

Check Understanding and On My Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional practice and homework is available in separate student edition, providing more exercises for students to solve.

The instructional materials for Into Math Florida Kindergarten meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop their understanding of mathematical concepts and skills. The structure of a lesson provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that utilize concrete and abstract representations and increase in complexity.

Exercises are given in intentional sequences. In general, lessons are designed to begin with activating prior knowledge and build toward conceptual development and procedural skill. In Spark Your Learning, students use manipulatives and/or visual models to experiment with the mathematics. Thus developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner allowing students to process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in Build Understanding and Step It Out, where the abstract concept is broken down into smaller steps with additional Turn and Talks, and students complete independent exercises to build understanding and mastery. Check Understanding provides a mid-lesson check in and can be used to indicate the need to differentiate learning for students. Students practice the abstract concept in On My Own.

The instructional materials for Into Math Florida Kindergarten meet the expectations for having a variety in what students are asked to produce.

In Spark Your Learning, Build Understanding, and Step It Out, students use visuals to show their thinking. In Turn and Talks, students frequently construct arguments and give explanations. There are opportunities for students to produce answers and solutions in On My Own, while also providing opportunities for students to provide written explanations. Throughout the materials, students represent mathematics using equations.

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials identify the manipulatives needed at the beginning of each lesson, and on the student pages, there is a picture of the manipulative they will use. Examples of manipulatives for Kindergarten include: connecting cubes, fraction circles, pattern blocks, and counters. 

The instructional materials for Into Math Florida Kindergarten meet the expectations for providing quality questions to help guide students’ mathematical development. 

Throughout the Teacher Edition, questions are posted to help support teachers with questions to guide students’ mathematical development. Activate Prior Knowledge, Spark Your Learning, Build Understanding, Learn Together, and Turn & Talk consistently provide questions to drive student discussion.

The instructional materials for Into Math Florida Kindergarten meet the expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

In the Module planning pages, there is a variety of information that can help teachers understand the materials in order to present the content. Each lesson identifies the relevant content standards and Mathematical Practices, an Essential Question, Learning Objective, Language Objective, materials needed, and Mathematical Progressions Across Grades that contain prior learning, current development, and future connections. Unpacking the Standards provides further explanations of the standards’ connections. This section gives an explanation of the content standard contained in the lesson and Professional Learning, which sometimes contains information about the practice standard contained in that lesson. Teaching for Depth provides teachers with information regarding the content and how this relates to student learning. There are additional suggestions about activating prior knowledge or identifying skills in Warm-up Options, activities to Sharpen Skills, Small-Group Options, and Math Centers for differentiation.

There are two prompts in each module related to Online Ed: “Assign the auto-scored Are You Ready for immediate access to data and grouping recommendations.” Also, “Assign the auto-scored Module Test for immediate access to data.” Within lessons, there are multiple prompts: Warm-Up Options and Step It Out both have an icon, “Printable & projectable.”; “More print and digital resources for differentiation are available in the Math Activities Center.”; and “Assign the auto-scored Check Understanding for immediate access to the data and recommendations for differentiation.”

The instructional materials for Into Math Florida Kindergarten meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

Each module in the Teacher Edition includes Mathematical Progressions Across the Grades which lists prior learning, current development, and future connections. Similarly, the beginning of each lesson in the Teacher Edition includes Mathematical Progressions that show connections to prior and future grades’ standards, as well as other lessons within the program.

In the Planning and Pacing Guide, Progressions and Algebra Readiness notes, “Algebra as a course of study today is integrated around four progressions of elementary and middle school content leading to the Algebra course: Number and Operations, Operations and Algebraic Thinking, Statistics and Probability, and Functions” and includes a table that shows how the domains in Grades K-5, 6-7, and Grade 8 / Algebra fit into these progressions.

The instructional materials for Into Math Florida Kindergarten meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• At the beginning of each module, Teaching for Depth provides information on strategies to use when teaching the concept, including Represent and Explain, which focuses on ways for students to describe and picture a concept, or Make Connections, which helps students understand a new idea by connecting it to previous knowledge.
• At the beginning of each module, Mathematical Progression Across the Grades makes connections to both prior and future skills and standards to scaffold instruction.
• At the beginning of each module, Diagnostic Assessment, Are You Ready?, allow teachers to “diagnose prerequisite mastery, identify intervention needs, and modify or set up leveled groups.”
• Each lesson provides Warm-up Options to activate prior knowledge such as: Problem of the Day, Quick Check for Homework, and Make Connections.
• Throughout the lessons, there are notes, strategies, sample guided discussion questions, and possible misconceptions that provide teachers structure in making content accessible to all learners.
• Student practice starts with up to four Check Understanding exercises to complete with guidance before moving to independent work in On My Own.

The instructional materials for Into Math Florida Kindergarten meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• There are Reteach and Challenge activities for each lesson.
• Each module includes Plan for Differentiated Instruction that provides teachers with teacher-guided, Small-Group Options and self-directed Math Center Options based on student need: “On Track/Mixed Ability, Almost There (RtI), and Ready for More.”
• Each lesson provides Leveled Questions in the Teacher’s Edition identified as DOK 1, 2, and 3 with an explanation of the knowledge those questions uncover about student understanding.
• In the Teacher’s Guide, Spark Your Learning provides On Track, Almost There, and Common Error to support a range of learners. Each section describes student actions and has teachers either describe and practice or reminds them of important strategies to support learning and how to intervene.

There are three “Language Routines to Develop Understanding” used throughout the materials: 1) “Three Reads: Students read a problem three times with a specific focus each time.” 2) “Stronger and Clearer Each Time: Students write their reasoning to a problem, share, explain their reasoning, listen to and respond to feedback, and then write again to refine their reasoning.” Also, 3) “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.”

The instructional materials for Into Math Florida Kindergarten meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

STEM Tasks are provided at the beginning of every instructional unit and include cross-curricular tasks which allows multiple entry-points and various solution strategies or representations, for example:

• In Unit 4, STEM Task: “Have children work in partners. Children should work together to pick a teen totals card and make the groups both in the loop and outside the loop. Children should explain how they knew how many to put outside the loop and how the numbers in their teen totals card show the groups they made.”

Turn and Talks throughout each lesson provide opportunities for students to share a variety of ways to solve the problem, for example:

• In Lesson 6.1, Turn and Talk: “Encourage children to discuss different ways they could have solved the problem, using numbers in a different order or using objects to make visual models. Listen to children as they Turn and Talk to ensure they understand how to correctly solve addition problems.”

In the Planning and Pacing Guide, Spark Your Learning tasks are “designed as ‘low-floor/high ceiling’ tasks that all students can access but that can also be extended to provide challenge.” Teachers are provided guidance on how to assist various levels of learners, depending on how they respond to the problem.

The instructional materials for Into Math Florida Kindergarten meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

In addition to the strategies for meeting the needs of a range of learners described in Indicator 3s, there is further support in place for English Language Learners (ELLs) and other special populations.

There is Language Development to support English Learners in each module which includes linguistic notes that provide strategies intended to help students struggling with key academic vocabulary such as: “Speak with students about words that can have multiple meanings….”, and “Visual cues help students…”. Language Development also includes information about the Language Routines embedded in the instructional materials: Three Reads; Stronger and Clearer Each Time; Compare and Contrast; Critique, Correct, and Clarify. These are identified by a pink box throughout lessons with speech bubble that identifies the Language Routine to be used. In addition, there are supports for special populations including:

• Language Objectives are included in every lesson.
• Reteach and RtI worksheets can be assigned online or printed.
• Turn and Talk prompts designed to support students, for example, “go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”.
• A multi-lingual glossary is available online.

The instructional materials for Into Math Florida Kindergarten meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

In addition to the strategies for meeting the needs of a range of learners described in Indicator 3s, there is further support in place for advanced students:

• Optional lessons are provided online that teachers may choose to utilize with advanced students. 
• Each lesson has a corresponding Challenge page, provided in print or online, addressing the same concepts and standards where students further extend their understanding and often use more complex values in their calculations. 
• On the module opener page, Extend the Task in the margin of the Teacher’s Edition provides ideas for extending the task.

The instructional materials for Into Math Florida Kindergarten meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

Pictures of adults and children in the materials show a variety of demographics and personal characteristics. There are a variety of names used in word problems throughout the materials. The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. There is a balanced approach to the use of gender identification. Examples include:

• The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
• The materials include a set number of names used throughout the problems and examples (e.g., Janette, Anton, Zed, Ari, Tai, Nick, Sam). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity.