Kindergarten - Gateway 1

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for assessing grade-level content.

Assessments are located in the Assessment Guide book. Assessments consist of a Prerequisite Skills Inventory, Middle-of-Year Test, End-of-Year Test, 20 Module Tests, and 5 Unit Performance Tasks. Each Module Assessment consists of Form A and Form B.

The Middle of Year Test assesses the standards taught in approximately the first half of the year of Into Math Florida, and the End of Year Test assesses the full year of standards. Examples include:

• End of Year Test Problem 18 - “Ashley is making books. She needs 10 pieces of paper for her books. Ashley has only 5 pieces of paper. Which picture shows how many more pieces of paper Ashley needs so she has 10?” This problem aligns to K.MD.1.1.
• End-of-Year Test Problem 6 shows a group of 10 plus some more and students choose the equation that matches the picture. (K.NBT.1.1)

Module Tests are available digitally and in the Assessment Guide. Examples include:

• Module 4 Test, Problems 4-6 Forms A and B, students classify objects into given categories of big and small (K.MD.2.3). Students label groups with socks, airplanes, and teddy bears as “big” or “small”.
• Module 8 Test, Problems 5 and 6 Forms A and B, students represent a number of objects with a written numeral 0-20. (K.CC.1.3)
• Module 12 Test, Problems 1-3 Forms A and B, students are read a word problem and add and subtract within 10 by using objects to represent the problem. (K.OA.1.2) Example: Carl has 2 plants that are big. The rest are small. Which picture shows Carl’s plants?
• Module 12 Test, Problems 5 and 7 Forms A and B, students represent subtraction with objects, drawings, or equations (K.OA.1.1). The students use a given picture representation and write a corresponding subtraction equation to match.
• Module 16 Test Problems 1 and 3, Forms A and B, students identify shapes by selecting the matching shape. (K.G.1.2) Example: Which shape matches Jessa’s?
• Module 16 Test Problems 2, 5, and 7, Forms A and B, students analyze shapes to identify the correct number of sides or vertices and whether the shapes are 2 dimensional or 3 dimensional. (K.G.2.4)
• Module 20 Test, Problems 1-2 Form A, students identify objects that are heavier or lighter. Students find an object that is heavier than a piece of paper or identify the word which describes a tennis ball. (K.MD.1.2)

Performance Assessments with multiple tasks for each unit are provided in the Assessment Guide. Examples include:

• Unit 4, Problem 3,“Yoshi and Neela are picking flowers. They pick more than 10 flowers but no more than 19 flowers. Write a number that could be the number of flowers they pick.” (K.CC.2.3)

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of Modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 20, which is approximately 75 percent. 
• The approximate number of Lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 77 out of 99, which is approximately 78 percent.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 136 out of 169, which is approximately 80 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each module. As a result, approximately 78 percent of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Into Math Florida Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Throughout the instructional materials, major work of the grade is supported by non-major work.

Examples of how the materials connect supporting work to the major work of the grade include:

• In Module 4, students classify, count, and sort objects throughout the module (K.MD.2.3). In Lesson 1, students sort buttons, cubes, shirts, and various shapes. After sorting the objects, students count the number of objects in each group (K.CC.2.5).
• In Module 4, Lesson 1, Step It Out, students listen to a story and identify the color of each cube. Students classify the blocks in categories by color (K.MD.2.3) and count the number of colored objects in each category. Lastly, students compare the size of the groups within 5 (K.CC.3.6) and/or compare numbers within 5 (K.CC.3.7).
• In Module 14, Lesson 5, students answer, “Does the shape have any flat surfaces? If so, how many?”  “Does the shape have any curved surfaces?”, which connects K.G.2.4 with K.CC.2.5.
• In Module 19, students compare the lengths and heights (K.MD.1.2) of objects using the pictures, connecting cubes, and crayons. The questioning throughout the lesson makes connections to counting “how many” (K.CC.2.5) and comparing which one is greater than, less than, or equal to (K.CC.3.6).

The instructional materials for Into Math Florida Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 169 days. The suggested amount of time and expectations for teachers and students in the materials are viable for one school year as written and would not require significant modifications.

• The provided scope and sequence found in the Planning and Pacing Guide includes materials for 121 instructional days.
• There are 3 days per year for the Growth Assessments
• There are 5 units. One day per Unit for the Performance Task and Unit Opener review activities, 5 days. 
• There are 20 modules, and there are 2 days per module for the Module Are You Ready?, Module Review, and Module Test, 40 days.

The suggested pacing from the publisher is one day per lesson for most lessons. However, some lessons are listed for two days. There are no lessons that require more than two instructional days to complete.

The instructional materials for Into Math Florida Kindergarten meet expectations for being consistent with the progressions in the Standards, providing all students with extensive work of the grade, and explicitly identifying prior knowledge needed for grade level work.

In the Planning and Pacing Guide, a Correlations Chart is included containing all grade-level standards. Tasks are aligned to grade-level work and are connected to prior knowledge. A typical lesson has Are You Ready? to assess student readiness for the upcoming module, Warm-Up Options, and Spark Your Learning activities intended to assist with activating prior knowledge. Build Understanding/Step It Out, On My Own, and More Practice/Homework, which includes a spiral review, are available in most lessons. Additionally, every lesson provides Small Group Options or Math Center Options that can be used to plan for differentiated instruction.

The instructional materials clearly identify content from future grade levels and use it to support the progression of the grade-level standards. Each Module and Lesson begin with Teaching for Success identifying the standards for “Prior Learning”, “Current Development”, and “Future Connections” respectively. Units begin with lessons connected to the standards from prior grades that are relevant to the current topic. Examples include:

• In Module 1, Lesson 4, Prior Learning is identified as “Children used counting and numbers to determine quantities up to 5.” Current Development for the lesson states, “Children understand that the last number said tells the name of objects counted. Children understand that each successive number refers to a quantity that is one larger. Children count to answer 'how many?' questions about as many as 1 and 2 things. K.CC.2.4a, K.CC.2.4b, K.CC.2.4c, K.CC.2.5." Future Connections for the lesson state, “Children will count to 120, starting at any number less than 120. Children will read and write numerals and represent a number of objects with a numeral. (1.NBT.1.1) Grade 1 Lessons 6.1, 6.9-6.10, 10.2, 10.5-10.60."
• In Module 3, Teaching for Success, Mathematical Progressions Across the Grades, prior Grade K Lessons 1.1-1.6 (counting and ordering numbers to five), addressing standards K.CC.2.4 and K.CC.2.5, are identified as prior learning. This learning is used to connect with the current development lessons which address K.CC.3.6 and K.CC.3.7. In these lessons, students begin to compare numbers by matching groups of objects and practicing representing and describing one-to-one comparisons. From these lessons, future connections will be made with 1.NBT.2.3, found in lessons 11.1-11.4 where students will compare two-digit numbers based on the meanings of tens and ones digits and compare with <, >, and =. 
• In Module 5, Lesson 3 identifies Prior Learning as K.CC.A.3 (Grade K Lessons 1.1, 1.4) which is addressed in the Warm Up options, Activate Prior Knowledge. The Current Development, K.OA.A.2, K.OA.A.1, and K.OA.5, are addressed in the lesson activities. In the lesson, students solve addition word problems by drawing to represent the problem (K.OA.A.2) and acting out situations (K.OA.A.1). Students also work on addition fluency (K.OA.A.5) with the Sharpen Skills activity at the beginning of the lesson. The lesson also identifies Future Connections for students in the Grade 1 lessons for 1.OA.A.1 to add and subtract within 20. 
• In Module 9, Lesson 1, Prior Learning is identified as "Children understand how to count numbers 1-10. Identified and arranged numbers 1-10. Standards K.CC.2.4a,c, and K.CC.2.5. These standards were taught initially in Lesson 7.5." Current Development for the lesson addresses "Count to 100 by ones. Understand how to find a number that comes after another number. Standard K.CC.1.1." Future Connections for the lesson state, "Will understand how to count to 120. Will count to 120 by starting at any number that is not one. 1. NBT.1.1 This standard correlates to Grade 1 Lessons 6.1, 6.9-6.10, 10.2, 10.5-10.6.” 
• In Module 11, Lesson 5, Prior Learning is identified as, “Children wrote subtraction equations within 5. K.OA.2. Grade K Lessons 11.1-2." Current Development for the lesson states, “Children represent addition problems with objects, drawings, and equations. Children use reasoning to give verbal explanations of addition problems (KOA.2.)." Future Connections for the lesson state, “Children will use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. 1.OA.1.1 Grade 1 Lessons 1.1, 1.7, 2.1, 2.6, 5.1-5.4, 6.1-6.7, 7.1-7.7."
• In Module 7, Lesson 4, Mathematical Progressions identify prior learning from Grade K Lessons 1.2 and 1.3 (K.CC.1.1- counting and representing numbers to 10). This learning connects to the current development lessons which target K.OA.1.4 and K.CC.2.4b. In these lessons, students make ten and understand the last number said is the number of objects counted. From these lessons, future connections will be made with 1.OA.3.5, found in lessons 1.2, 2.2, 2.3, 3.2, and 4.1 where students relate counting to addition and subtraction.
• In Module 15, Lesson 2, Mathematical Progressions identify prior learning from Grade K Lessons 14.1-14.1 (K.G.1.2- describing 3D shapes and using positional words like above or below). This learning connects to the current development lessons which target K.G.1.1. In these lessons, students begin to use the positional words next and beside. From these lessons, future connections will be made with 1.G.1.1, found in lessons 2.6, 5.2, 15.1-15.3, 16.1-16.5, and 17.1-17.4, where students distinguish between defining attributes and build and draw shapes to possess defining attributes.

Overall, the materials provide opportunities for students to engage in extensive grade-level work. For example:

• Unit 1 introduces the counting sequence and numbers to 5. In Modules 1 through 4, students identify, compare, classify, sort, add, and subtract within 5. Modules 5-6 introduce word problems involving addition and subtraction. 
• Unit 2 introduces the counting sequence and numbers to 10. In Modules 7 through 13, students identify, compare, classify, sort, add, and subtract within 10.

Are You Ready? and Activate Prior Knowledge are included in lessons frequently for students to work with prior-grade standards in ways that support learning of grade-level problems. Examples include:

• In Module 6, Lesson 1, Are You Ready? includes writing numbers to make 5 (K.OA.1.5) that builds to students representing addition with objects, fingers, images, or equations (K.OA.1.1). 
• In Module 12, Lesson 4, Activate Prior Knowledge is used to assess and activate prior knowledge as needed through the Problem of the Day which reviews prior learning of subtraction problems within 10 (K.OA.1.2). Based on the Problem of the Day, students participate in Interactive Reteach, Grade K, Lesson 2.2 or complete a prerequisite skills activity.
• In Module 20, Lesson 3, Spiral Review includes reviewing questions that will help determine if students have retained information taught in the past. This spiral review assesses whether children will identify a hexagon from a group of shapes (K.G.1.2). These spiral reviews are located in the More Practice/Homework section of the student materials.

The instructional materials for Into Math Florida Kindergarten meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by MAFS cluster headings, including:

• In Lesson 12.4, the learning objective, "Use objects, drawings, and equations to solve take apart problems within 10", is shaped by K.OA.1, Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
• In Lesson 17.3, the learning objective, "Use objects to decompose the numbers 16 to 19 into ten ones and some more ones", is shaped by K.NBT.1, Work with numbers 11–19 to gain foundations for place value.
• In Lesson 19.2, the learning objective, "Explain how you compare the lengths of two objects", is shaped by K.MD.1, Describe and compare measurable attributes.

The materials include problems and activities connecting two or more clusters in a domain or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

• In Module 1, Lesson 6, students count how many counters are in each group (counters increase in succession). Students point to the counter as they count, trace, and write the corresponding numbers. Questions in the lesson connect K.CC.2 and K.CC.3, “How many counters will you need to show for the number that comes after 3?” Students then put four counters on the page and count aloud as they place each one. 
• In Module 11, Lesson 6, On My Own connects K.CC.1 and K.OA.1 as students count groups of children and represent each number counted to create and solve subtraction equations.
• In Module 17, Lesson 2, Task 1 connects K.NBT.1 and K.CC.3 as students build the numbers 14 and 15. Students describe both of the numbers using tens and ones and “tell how both representations are similar and different”.