3rd Grade - Gateway 3

The materials reviewed for Snappet Math Grade 3 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students to guide their mathematical development. The Documentation section of the materials provides comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• Snappet Teacher Manual, 3.1 Teacher Guide, “A Teacher Guide is available for every instructional lesson in Snappet, both digitally and on paper. The Teacher Guide contains the lesson overview, math content standards alignments, materials needed, vocabulary, EL/SEL strategies, common errors, and step-by-step support for teaching the lesson. Consistent design: The Teacher Guide, like the lesson itself, always has the same structure and is therefore, easy and clear to follow. From the Teacher Guide, the teacher has access to the learning path for every learning objective with constant visibility into the progress of the class.  Full support: The learning phases explained in the teacher manual are also visible while teaching the lesson in the digital environment. This gives the teacher the support they need not only while planning their lessons, but also while teaching their lessons. Easy to print: The teacher manual is easy to print by course or by lesson. Each downloadable and printable Teacher Guide is customized with the most up-to-date information about the progress and skill development for each student.”

• Instructional videos include 1-2 minute videos showing how to use the software, 5-minute videos of the classroom condensed to show each segment of the lesson, and full lesson videos. 

• Grade 3-Pacing Guide provides the number of weeks to spend on each Unit and a Materials list for each Unit.

Materials include sufficient and useful annotations and suggestions that are presented within the context of specific learning objectives. Preparation and lesson narratives within the Unit/Lesson Overviews and Teacher Tips provide useful annotations. Examples include:

• Grade 3-Unit Overviews, Unit 8 Overview: Area, Perimeter, and Geometry, Understanding the Math, “Geometry is essential for helping children understand spatial relationships. It teaches them to determine how large a room is, how far away a desk is, or which way to move. Geometry allows students to connect mapping objects in the classroom to real-world contexts regarding direction and place. Measurement helps describe our world using numbers. We use numbers to describe simple things like length, weight, and temperature, but also complex things such as pressure, speed, and brightness.”

• Unit 3: Division, Lesson 3.9, Instruction & guided practice, Exercise 1c, Teacher Tip, “(SEL) Give each student ten counters. Have students attempt to divide ten counters into ten equal groups. Ask them to write a division equation to show 10 ÷ 10  and its quotient. Have them try different dividends that have the same divisor.”

• Unit 7: Data, Lesson 7.2, Lesson Overview, Common Error (CE), “Look for the (CE) label for ideas of where to apply this suggestion. If students misread the graph by looking at the number below the top of the scale instead of right at the top, then tell them their answer is too small. If students still struggle, have them start at 0 and see that the value of the graph increases by one multiple of the scale as it reaches each gridline, so the value of the gridline at the top is the correct value.”

The materials reviewed for Snappet Math Grade 3 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject. 

Snappet Math provides explanations for current grade-level concepts within the Understanding the Math and Learning Progressions components of the Unit Overviews. Prior, current, and future standards are connected within the Lesson Overview of each lesson. Additionally, each Lesson Overview includes Deepening Content Knowledge Beyond Grade Level, which provides explanations and examples of more complex grade-level concepts and concepts beyond the current course. Examples include:

• Unit Overviews, Unit 2 Overview: Multiplication, Understanding the Math, “Understanding that multiplication is repeated addition of the same number is essential for success with division. Interpreting products of whole numbers into multiple groups of the same size of objects helps solidify the meaning and use of multiplication. Multiplication fluency allows students to make connections to real-world contexts involving money, cooking, gardening, sports, and other topics where making a number larger through multiplication has an impact on the situation. A solid foundation in multiplication facts for single-digit numbers allows for success in solving a wide variety of math problems.” 

• Unit Overviews, Unit 4 Overview: Solve Word Problems, Learning Progression, “In prior grade levels, students solved addition and subtraction word problems that had missing or extra information, writing equations to represent different situations (2.OA.A.1). They compared two-digit numbers using a number line, place value, and symbols (1.NBT.B.3). They solved word problems involving money (2.MD.C.8). In this grade level, students will continue to multiply and divide within 100 fluently using the relationship of multiplication and division. They will multiply and divide to solve one- and two-step word problems, using equal groups, arrays, bar diagrams, and equations. They will also use their knowledge of multiplication and division to understand and solve comparison word problems by pulling information directly from the word problem and/or from visual representations. They will identify information in a word problem as either given or missing, and then they will decide if an equation or visual is best to use for solving. In future grade levels, students will solve more complex multi-step word problems (4.OA.A.3). They will estimate to solve addition/subtraction word problems (4.OA.A.3). They will solve word problems involving money (4.MD.A.2, 5.NBT.B.7). They will use multiplication and division to solve word problems involving decimals (5.NBT.B.7) and fractions (5.NF.B.3).”

• Unit 7: Data, Lesson 7.1, Lesson Overview, Deepening Content Knowledge Beyond Grade Level, “Statistics and Data Analysis: The skills learned in analyzing scaled picture graphs form the foundation for more advanced studies in statistics and data analysis. In higher grades, students will engage with more complex data sets, learning to create and interpret histograms, box plots, and scatter plots. They will also begin to understand concepts such as mean, median, mode, range, and standard deviation.”

• Unit 8: Area, Perimeter, and Geometry, Lesson 8.9, Lesson Overview, “In prior lessons, students have measured using an inch ruler (2.M.A.1); solved word problems involving length (2.MD.B.5). In this lesson, students will use a ruler, tape measure, and string to measure the outline of an object and make the connection that the outline of the object is the perimeter (3.MD.D.8); find the perimeter using unconventional forms of measurement (3.MD.D.8). In future lessons, students will choose an appropriate unit of measurement (4.MD.A.1); solve problems with perimeter and area of rectangles (4.MD.A.3).”

The materials reviewed for Snappet Math Grade 3 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series. 

Correlation information is present throughout the grade level and can be found in the Pacing Guide, Unit Overviews, and each Lesson Overview. Explanations of the role of the specific grade-level mathematics in the context of the series can be found in each Lesson Overview under The Specific Role of the Standard in the Overall Series. Examples include:

• The Pacing Guide provides a table separated by unit and includes columns identifying previous skills, grade-level skills, and future skills. The skills are grouped by standard and are linked to identify lesson(s) standard alignment.  

• Unit Overviews identify the standards addressed in each unit and a lesson standard alignment. The Unit Overviews also include a learning progression that links current standards to previous and future standards for each unit.

• Unit 6: Measurement, Lesson 6.4, Lesson Overview, The Specific Role of the Standard in the Overall Series, “Foundation for Time-Based Reasoning: The standard 3.MD.A.1 is crucial as it lays the foundational skills for time-based reasoning, an integral aspect of everyday life and scientific inquiry. By mastering elapsed time problems, students develop an essential skill set for understanding sequences of events, duration, and the concept of causality.”

• Unit 8: Area, Perimeter, and Geometry, Lesson 8.8, Lesson Overview, Mathematical Content Standards, “3.MD.D.8 Solve real world and mathematical problems related to finding the perimeter of a polygon, finding unknown lengths, and comparing figures with the same perimeter, and different areas, or same areas and different perimeters.”

The materials reviewed for Snappet Math Grade 3 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. Instructional approaches of the program are described within the Teaching using the Snappet Method document. The four lesson components—Instruction and Guided Practice, Extend Learning using Math Practices, Independent and Adaptive Practice, and Small Group Instruction are described. Examples include:

• Instruction and guided practice, “The lesson design for instruction follows the CRA approach to teaching: Concrete, Representational, Abstract. The exercises begin with Activate Prior Knowledge exercises which are designed to be used as real-time feedback opportunities during the introduction of the new lesson. This is followed by Student Discovery where manipulatives, games, or activities will be introduced to prepare students minds and bodies for new learning. These activities are followed by instruction slides that provide opportunities for students to think out loud, think pair share, co-craft questions, and talk about the new concept in a variety of ways. Instruction is followed by Guided Practice exercises where students can try it on their own while being supported by the teacher. The Guided Practice exercises also give the teacher the opportunity to identify if students are ready to begin practicing independently and to identify any common errors that might be occurring. Following Instruction and Guided Practice, teachers can go deeper into the mathematics by introducing the Math Practices exercises.”

• Extend lLearning using Math Practices, “Teachers will utilize the exercises available in Math Practices to go deeper in the complexity of student learning. These exercises are designed to be non-routine, open-ended, and an extension of the discussions that occurred during the lesson. Often, these exercises will extend beyond the Student Discovery activities. It is recommended to group students into groups of 2 (K-2) or 3 (3-5) to encourage students to discuss their thinking and give evidence for their reasoning.”

• Independent and Adaptive Practice “Students continue their learning of the concepts during independent practice. Independent Practice exercises are written at grade level and act as a “diagnostic assessment” to determine the appropriate level of Adaptive Practice. Adaptive practice offers 5 levels of difficulty that are defined by the quintile measures. Level 3 is considered grade-level proficient. Quality is the goal over quantity. It is recommended that only 1-3 sets (10-30 questions) of adaptive practice exercises be completed in any one practice session. Once students have reached their target goals and attained their desired level, they should either practice on a different concept or finish practice for the day.”

• Small Group Instruction, “Every lesson includes a Small Group Instruction intervention lesson for students that are struggling with the concept. This becomes evident when students are not able to progress during adaptive practice. Student initials will appear in yellow and will be identified as being “stuck” on their progress towards their target goals. It is recommended to provide reteaching to these students in a small group setting using the exercises in the small group instruction section. These exercises are scaffolded to provide support for struggling students. Once you have completed this lesson with students and they have demonstrated understanding using the guided practice exercises in the small group lesson, you can continue to monitor the students progress by having them continue to practice adaptively on the lesson.”

Research-based strategies within the program are cited and described in the Snappet Teacher Manual within Research-based Strategies in Snappet Math. Snappet Math states, “The Snappet Math curriculum integrates a series of rigorously research-based instructional approaches and strategies explicitly designed to facilitate effective K-5 mathematics education. Informed by eminent educational researchers and institutions, including the National Council of Teachers of Mathematics (NCTM) and the Institute of Education Sciences (IES), the key strategies are as follows:...” Examples include: 

• Concrete-Pictorial-Abstract (CPA) Approach, “This method involves the sequential use of concrete materials, pictorial representations, and abstract symbols to ensure thorough understanding (Bruner, 1966). Snappet's curriculum employs and explicitly references the CPA approach in the lesson phases ‘Apply in a concrete pictorial representation’ and ‘Apply in an abstract representation.’”

• Problem-Solving Instruction, “Snappet encourages students to engage with real-world problems, enhancing the relevance and application of mathematical concepts and procedures (Jonassen, 2000). Guidance is provided on various problem-solving strategies (Polya, 1945) in both instruction & guided practice and during independent practice.”

• Formative Assessment, Feedback, and Error Correction, “Regular assessments help to understand a student's learning progress, provide opportunities to give feedback, and adjust instruction (Black & Wiliam, 1998). Feedback is one of the most powerful influences on learning and achievement (Hattie, 2003), and correcting common errors has been identified as a factor that positively influences student achievement (Smith & Geller, 2004). Due to Snappet’s elaborate and immediate feedback system, every activity serves as a formative assessment. During instruction and guided practice, student responses appear on the Interactive Whiteboard in real-time for all students and the most common errors made by the students are summarized and highlighted. This feedback allows teachers to identify and correct common errors quickly, promoting student understanding and success. For every lesson and standard, both the teacher and students get continuous feedback on the current performance and progress. The immediate and actionable feedback, along with prompt error correction, is integral to promoting student achievement and progress in the Snappet Math curriculum.”

• Direct Instruction, “Direct instruction is a major factor in contributing to student achievement (Rosenshine, 2012). This involves clear, concise teaching where the teacher models what is to be learned and provides guided practice with immediate feedback. The Snappet Math curriculum incorporates this approach, with teachers provided with detailed lesson plans, strategies for explicitly teaching concepts, and resources for modeling mathematical thinking. The interactive nature of Snappet also allows for real-time guided practice and these exercises are explicitly referenced in every lesson with the guided practice icon ( ), aligning with the principles of direct instruction.”

The materials reviewed for Snappet Math Grade 3 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The program provides a Material List, and specific lessons include a Materials heading needed to support instructional activities within the Lesson Overview. Examples include:

• Grade 3-Material List, “The list below includes materials used in the 3rd Grade Snappet Math course, excluding printed materials and templates. The quantities reflect the approximate amount of each material that is needed for one class. More detailed information about the materials needed for each lesson can be found in the Lesson Overview.” A table lists the Materials, Unit(s), and Approximate Quantity Needed, “Paper cups; 3, 6; 13 cups per pair of students.” 

• Unit 2: Multiplication, Lesson 2.5, Lesson Overview, Materials, “Per pair: 24 counters.”

• Unit 6: Measurement, Lesson 6.5, Lesson Overview, Materials, “Per group: a drinking glass, a small bottle, a milk container, a larger bottle, a measuring cup, empty cups, a mug, water.”

The materials reviewed for Snappet Math Grade 3 meet expectations for having assessment information included to indicate which standards are assessed.

Snappet Math identifies two types of assessments with the program. Within each Unit Overview, Assessments provide detailed information about both types. Formative Assessments, “Every lesson embeds “Check for Understanding” assessment items that are graded and recorded in real-time.” Formative assessments are identified within the lessons' Instruction & Guided Practice portion. Standards and practices are not directly identified for the formative assessments but are named within the Lesson Overviews. Summative Assessments, “Summative assessments are available in each unit and are graded automatically. Each assessment item includes the standard objective, lesson, and math practice standard (if applicable).” Summative assessments within or at the end of units have standards and practices identified within the Teacher Tips. Examples include but are not limited to: 

• Unit 2: Multiplication, Assessment 2.10-2.19, Exercise 1a, Teacher Tip, “3.OA.C.7, MP 7.” Students drag, “the double of 3 x 7; 1 x more than 6 x 7; or, 1 x less than 10 x 7.” “Fill in the blanks. 7 x 7 is: ___; 6 x 7 is: ___; 9 x 7 is: __.”

• Unit 5: Solve Word Problems, Lesson 5.9, Lesson Overview, “Mathematical Content Standards: 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding. Mathematical Practice Standards: MP 3 Attend to precision.”  Instruction & Guided Practice , Exercise 1i, “A supermarket orders 4 boxes of pumpkin soup. Each box contains 24 cans of pumpkin soup. They can fit 7 cans in each row. How many rows can they fill? They can fill ___ rows and will have ___ cans left for restocking later.”

• Unit 8: Area, Perimeter, and Geometry, Assessment 8.1 - 8.10, Exercise 5c, Teacher Tip, “3.MD.C.7 MP 1.” “Marcus painted a rectangle with an area of 36 ft.² The width of the rectangle is 6 ft. How long is the rectangle? The rectangle is ____ ____ long.” 

Some assessment exercises have misaligned standards. Examples include but are not limited to: 

• Unit 1: Addition, Subtraction, and Patterns, Assessment: Lessons 1.1-1.8, Exercises 2a - 2d, Exercise 2a, “Round to the nearest ten. Estimate the sum. 248 \approx 250, 521 \approx ___, 248 + 521 \approx ___.” Exercise 2b, “Round to the nearest ten. Estimate the difference. 573 \approx 570, 218 \approx ____, 573 - 218 \approx ____.”  Exercise 2c, “Estimate the sum. 314 + 227 " Exercise 2d, “Estimate the difference. 639 - 312 .” Teacher Tip aligns these problems to “3.OA.D.8 (Solve two-step word problems using the four operations…). These problems better align to 3.NBT.1 (Use place value understanding to round whole numbers to the nearest 10 or 100.), and 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.)

The materials reviewed for Snappet Math Grade 3 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

There are no tools for scoring as all assessments are online and scored by the computer system. Information about the assessment system and interpreting student performance can be found in the Quick Start User’s Guide, Teacher Manual, Lesson Overview, and Lessons. Examples include:

• Documentation, Quick Start User’s Guide, 5. Progress Monitoring, “The Progress Monitoring page can be accessed by clicking on the Monitor menu located on the left of the screen. The monitoring page provides the “real-time” responses by your students on every item in the lesson including the adaptive practice. The colored dots represent the same information throughout the program: A green dot represents a correct response, a red dot an incorrect response, and a green/red dot an incorrect response that has been corrected. However, from anywhere else in the program, other than the Instruct page, clicking on a response dot will open the item details. All the relevant information from the student’s response is visible, including the number of times the exercise was attempted and a timestamp for when each attempt occurred.” 

• Documentation, Quick Start User’s Guide, 6. Student and Class Reports, Summative Assessment, “To view Summative Assessments within a unit, navigate to the Assessment and click on it. This will open the Assessment preparation page where you will be able to view the Assessment items and the Standards that are addressed within each item.”

• Documentation, Teacher Manual, 5.4 Tests and reports, Summative tests, “Summative tests are also available in Snappet. Summative tests function differently than other exercises.  When a student enters an answer in a summative test, the results are only visible to the teacher. Once the class has completed the assessment, the teacher can close the test and open the results to the students. The students are then allowed to go back and correct any problems they got wrong. Teachers can use the results from the assessment to provide additional instruction or support to students that are still struggling.”

• Unit 3: Division, Lesson 3.11, Small group instruction, Exercise 3a, Teacher Tip, “Remind the students that dividing by two means to cut a group in half, creating two equal groups. You can also use repeated subtraction, but counting backwards from 2 is a little harder than counting forward by 2.  Ask: What are the methods you can use to divide by 2? [I can make two equal groups.].”

• Unit 6: Measurement, Lesson 6.7, Lesson Overview, Common Error (CE), “If students have difficulty dragging the arrow to 600 mL, remind students that the numbers are on each line. If they still struggle, point out that 600 milliliters is less than 1 liter.”

The materials reviewed for Snappet Math Grade 3 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in grade-level mathematics. Accommodations include the teacher’s ability to turn on/off the read aloud option in the settings tab on the teacher facing side of the materials. The speed of the read aloud can also be adjusted. On the student facing side of the program, students can click a button that will read aloud the introduction to the lesson. Directions for using the read aloud option is found under Documentation, instruction-videos, How to Read Out Loud Setting. The video guides the teacher on how to add the feature to selected students. The program is available in Spanish for students to use. Lessons and assessments are both available in Spanish, and no other language at this time is available. 

Most lessons provide adaptive exercises teachers can use to help reach all students at different levels of understanding. Snappet Teacher Manual, 6.2 Differentiation during the week, Flexible application, “While adaptively progressing through the Assignments, students practice the learning objectives interchangeably (when they are ready). After obtaining their own goals, students can choose additional learning objectives to practice, via the shuffle button. Through this format, exercises from achieved goals are presented, and thus students learn to recognize the appropriate math concept and the underlying skill is further anchored.”

Each lesson overview also provides opportunities to support ELL students, SEL (Social Emotional Learning), and advice on common errors (CE) in the lesson.  While the headings indicate strategies could be used in ELL, or SEL situations, the strategies could be used with other student groups to help better understand the content at that grade level.  Examples include:

• Unit 1: Addition, Subtraction, and Patterns, Lesson 1.6, Lesson Overview, English Learner (EL), “Entering/Emerging Listening: Review the meaning of the phrase What if with students. Ask them some What if questions, such as: What if we are outside and hear thunder? What if we spill water on the floor? Guide students in forming answers using: If we ___, then ___. Developing/Expanding Speaking: Review the meaning of the phrase What if with students. Working in pairs, have students ask each other silly What if questions, such as: What if we could fly? What if we saw a mermaid? Remind students to answer using: If we___, then ___. Bridging/Reaching Writing: Review the meaning of the phrase What if with students. Have them work with a partner to write two questions beginning with What if. 

• Unit 2: Multiplication, Lesson 2.8, Lesson Overview, Social-Emotional Learning (SEL), “Communicating effectively is a key element of learning math. Use these questions during the Student Discovery, independent practice, or anytime during small-group instruction to promote relationship skills in your classroom. How clearly do you understand explanations of new math ideas? When you don’t understand something, what can you do to get help? How can you explain your ideas to other students?”

• Unit 3: Division, Lesson 3.16, Lesson Overview, Common Error (CE), “If students struggle to understand the structure of a bar model, then show them how the bar model represents the division equation. If they still struggle, have them draw the bar model and use tally marks to count up to 63 as they create seven equal groups.”

The materials reviewed for Snappet Math Grade 3 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. Snappet Math Grade 3 materials are also available in Spanish, which provide teacher directions in English and student pages in Spanish. Within each Lesson Overview, a section titled “English Learners (EL)” provides teachers with strategies and supports for ELL students. While these strategies and supports are present in the Unit Overview, there is a lack of clarity in how they are applied to particular exercises. Examples include:

• Unit 2: Multiplication, Lesson 2.13, Lesson Overview, English Learners (EL), “Entering /Emerging Listening: Define multiple: The result of multiplying a number by a whole number. Have students repeat the definition after you.”

• Unit 5: Fractions, Lesson 5.7, Lesson Overview, English Learners (EL), “Bridging/Reaching Speaking: Have students choose a practice exercise and explain to the group how to rename the fraction.”

• Unit 7: Data, Lesson 7.2, Lesson Overview, English Learners (EL), “Developing/Expanding Listening/Speaking: Ask: What kinds of things does this graph show? What are some examples? Have students name the category and individual items. Sample response: fruits; orange, apple, banana.”

The materials reviewed for Snappet Math Kindergarten meet expectations for providing manipulatives, both physical and virtual, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The Snappet Math materials encourage students to use both physical and virtual manipulatives during lessons, as needed. Physical manipulative material lists are found in the Pacing Guides, Materials Lists, and Lesson Overviews. Virtual manipulatives can be found in a variety of lessons and accurately represent the math object. Examples include: 

• Documentation, Pacing Guide, provides a table that includes a column identifying the materials to be used in the unit. “Unit 2: Multiplication (4 - 5 weeks); Materials: Counters in 2 colors, Cubes.”

• Documentation, Material List, provides a table listing the materials, units, and approximate quantity needed. “Material: Counters in 2 colors; Unit(s): 1, 2, 3, 4, 7; Approximate Quantity needed: 25 of each color per student.”

• Unit 1: Addition, Subtraction, and Patterns, Lesson Overview, Materials, “Per small group: Set of counters.”

• Unit 3: Division, Lesson 3.1, Instruction & guided practice, Exercise 1j, “How can you equally divide 14 shoes? ___ equal groups of ___.” Students drag 14 virtual shoe counters to make groups representing division.