5th Grade - Gateway 3

The materials reviewed for Snappet Math Grade 5 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 5-Pacing Guide provides the number of weeks to spend on each Unit as well as 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 5-Unit Overviews, Unit 8 Overview: Line Plots and the Coordinate System, Understanding the Math, “Line plots are necessary to organize and provide a visual display of data, so that its distribution is obvious. Data is most useful when it is in a form where it can easily be interpreted, such as a line plot display. Students can identify general trends in data just by looking at a line plot. They can tell the least and greatest values, for example, and can use this information to solve problems. The coordinate system is a way for students to identify and communicate the exact location of objects and places. This type of grid system is the basis of maps used for locations all around the world.”

• Unit 1: Numbers, Lesson 1.13, Independent Practice, Exercise 2d, Teacher Tip, “Encourage students to recall the place-value charts from lesson 5. How many 10ths does 0.58 have? [5.] How many 100ths? [8.] How does this compare to 0.5, which has five 10ths? [It is eight 100ths larger.]”

• Unit 5: Fractions - Multiply and Divide, Lesson 5.1, Exercise 1c, Teacher Tip, “(SEL) After students complete the activity, ask: What does the fact that both factors are greater than three-eighths tell you about fraction multiplication? [Multiplying by fractions makes things smaller.]”

The materials reviewed for Snappet Math Grade 5 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 Levels, which provide explanations and examples of more complex grade-level concepts and concepts beyond the current course. Examples include:

• Unit Overviews, Unit 1 Overview: Numbers, Learning Progression, “In this grade level, students will extend their understanding of numbers and place value to decimal numbers up to the thousandth place. Students will read, write, compose, and decompose decimal numbers to understand the relationships among the digits in the numbers. They will use patterns to multiply multi-digit whole numbers, multiply decimal numbers, and divide decimal numbers by 10, 100, and 1,000. Using their prior understanding of rounding whole numbers, they will now round decimal numbers to the nearest whole number, tenth, and hundredth. Students will also understand the value of decimal numbers by placing them on number lines and by using symbols to compare and order them.”

• Unit 2: Operations with Whole Numbers, Lesson 2.2, Lesson Overview, Deepening Content Knowledge Beyond Grade Level, “Integration with Algebraic Thinking: This lesson’s focus on the standard algorithm for multiplication provides an important foundation for algebraic thinking. Students can use these skills to understand and simplify algebraic expressions, especially when dealing with multiplication of polynomials or variables. By mastering the standard algorithm, students gain an intuitive understanding of distributive properties and the structure of mathematical expressions, paving the way for more advanced algebraic concepts.”

• Unit Overviews, Unit 6 Overview: Expressions and Patterns, Understanding the Math, “Expressions and patterns show relationships among numbers or objects. Expressions and patterns can be used to describe how something grows. For example, as a tree grows over time, it can show a pattern, and that pattern may be written as a mathematical expression. Numerical expressions can be translated into verbal phrases, and likewise, verbal phrases can be translated into numerical expressions. Some key words help us with this task, like if the cost of an item is $1 more than you have, you can use the key words ‘more than’ as a clue to use addition. Some numerical expressions even form a pattern that can be extended. If the cost of an item is $2, a pattern results from adding one more item each time and relating the items to the cost. That is because there is a rule relating the number of items and the cost.”

• Unit 7: Measurement and Geometry, Lesson 7.8, Lesson Overview, “In prior lessons, students have found the volume of a rectangular prism by using a formula. (5.MD.C.5.B) found the volume of a composite figure composed of rectangular prisms. (5.MD.C.5.C), In this lesson, students will classify polygons according to their number of sides. (5.MD.G.3) determine whether a polygon is also a regular polygon. (5.MD.G.3), In future lessons, students will classify polygons and quadrilaterals. (5.G.B.3) classify two-dimensional figures in a hierarchy. (5.G.B.4)”

The materials reviewed for Snappet Math Grade 5 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 5: Fractions - Multiply and Divide, Lesson 5.5, Lesson Overview, The Specific Role of the Standard in the Overall Series, “Developing Fraction Fluency: 5.NF.B.4.B plays a critical role in building students’ fraction fluency. By learning to multiply fractions through both conceptual models (like area models) and procedural approaches (multiplying numerators and denominators), students gain a dual perspective. This comprehensive understanding is vital for future learning, as fraction fluency is a cornerstone of many higher mathematical concepts, including algebra and geometry.”

• Unit 6: Expressions and Patterns, Lesson 6.5, Lesson Overview, Mathematical Content Standards, “5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ‘add 8 and 7, then multiply by 2’ as 2\times(8+7). Recognize that 3\times(18,932+921) is three times as large as 18,932+921, without having to calculate the indicated sum or product.”

The materials reviewed for Snappet Math Grade 5 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 Learning 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. 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 5 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 5-Material List, “The list below includes materials used in the 5th 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, “Play money; 2, 3; one $10 dollar bill, one $5 dollar bill, and ten $1 dollar bills per student.”

• Unit 5: Fractions - Multiply and Divide, Lesson 5.8, Lesson Overview, Materials, “Per student: paper, scissors.”

• Unit 8: Line Plots and the Coordinate System, Lesson 8.3, Lesson Overview, Materials, “Per pair: grid paper, two game pieces, two number cubes.”

The materials reviewed for Snappet Math Grade 5 meet expectations for having assessment information included in the materials 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  Instruction & Guided Practice  portion of the lessons. 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 located within or at the end of units have standards and practices identified within the Teacher Tips. Examples include but are not limited to: 

• Unit 3: Operations with Decimals, Assessment: Lessons 3.8-3.15, Exercise 6a, Teacher Tip, “5.NBT.B.7, MP 2.” Students are shown a jar of applesauce labeled “$0.99.” “How much do 5 jars of applesauce cost? 5 x $0.99 = $___. 5 x $1.00 = $___.” 

• Unit 6: Expressions and Patterns, Assessment 6.1 - 6.7, Exercise 4a, Teacher Tip, “5.OA.A.2, MP 4.” “Write an expression for the statement. “Triple the quotient of 16 and 12” 3 __ (__$$\div$$__).”

• Unit 7: Measurement and Geometry, Lesson 7.4, Lesson Overview, “Mathematical Content Standards: 5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft, and improvised units. 5.MD.C.3 Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. Mathematical Practice Standards: MP.8 Look for and express regularity in repeated reasoning.”  Instruction & Guided Practice , Exercise 1p, “Each cube is 1 in.$$^{3}$$. What is the volume of the figure? ___in.$$^{3}$$”

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

• Unit 1: Numbers, Assessment: Lessons 1.1 - 1.7, Exercise 1a, given a place value chart from one to the ten thousands place, “50,000 + 7,000 + 300 + 2 = ____.” Teacher Tip, “5.NBT.A.1, MP 5” This problem does not align to 5.NBT.1 (Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and \frac{1}{10} of what it represents in the place to its left.). It aligns with 4.NBT.2 (Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.)

• Unit 1: Numbers, Assessment: Lessons 1.1 - 1.7, Exercise 1c, given a place value chart from one to the ten thousands place, “You can use this chart. 91,423 = ____ + ____ + ____ + ____ + ____.” Teacher Tip, “5.NBT.A.1.” This problem does not align to 5.NBT.1 (Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and \frac{1}{10} of what it represents in the place to its left.). It aligns with 4.NBT.2 (Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.)

• Unit 1: Numbers, Assessment: Lessons 1.8 - 1.16, Exercise 1b, “9.868 = ____ + ____ + ____ + ____.” Teacher Tip, “5.NBT.A.1.” This problem does not align to 5.NBT.1 (Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and \frac{1}{10} of what it represents in the place to its left.). It aligns more with 5.NBT.3a (Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × \frac{1}{10} + 9 × \frac{1}{100} + 2 × \frac{1}{1000}.)

The materials reviewed for Snappet Math Grade 5 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 4: Fractions - Add and Subtract, Lesson 4.6, Small group instruction, Exercise 3e, Teacher Tip, “Ask: Is \frac{3}{3} equal to \frac{6}{6}? [Yes, they are whole pancakes, anything divided by itself is one.] Why are they named differently? [They are cut into different sized pieces.].

• Unit 5: Fractions - Multiply and Divide, Lesson 5.6, Lesson Overview, Common Error (CE), “If students try to multiply mixed numbers without converting them to improper fractions, tell students that the product will be too small if they use that method. If students still struggle, demonstrate to them that the product using improper fractions is different than the result of multiplying the whole number parts and adding them to the product of the fractional parts.”

The materials reviewed for Snappet Math Grade 5 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 3: Operations with Decimals, Lesson 3.7, Lesson Overview, English Learner (EL), “Entering/Emerging Reading: Display a rounding problem with an illustration. Have students read the text chorally. If needed, remind students that ÷ and = should be read as divided by and equals. Developing/Expanding Writing: Display a rounding problem with an illustration. Ask: How much less does [item] cost than [rounded price]? Have students write their answers using the sentence frame: [Item] costs ___ cents less than [rounded price]. Bridging/Reaching Reading/Speaking: Have partners view the illustrated slides together and take turns reading the text aloud. Then have them collaborate in English to find the answer.”

• Unit 4: Fractions-Add and Subtract, Lesson 4.8, Lesson Overview, Social-Emotional Learning (SEL), Developing positive relationships is a key element of learning math. Use these questions during teacher instruction, independent practice, or anytime during small-group instruction to promote relationship skills in your classroom. When working with a partner, how can you speak in a respectful manner? How can you show cooperation? What is the best way to handle a disagreement with your partner?”

• Unit 5: Fractions-Multiply and Divide, Lesson 5.8, Lesson Overview, Common Error, (CE), “If students place the numbers on the wrong side of the fraction bar, tell students that the fraction is not defined by the order the numbers are given. If students still struggle, discuss the context of the problem with them to determine how a fraction can appropriately represent the situation.”

The materials reviewed for Snappet Math Grade 5 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 5 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: Operations with Whole Numbers, Lesson 2.13, Lesson Overview, English Learners (EL), “Developing/Expanding Speaking/Listening: Display a word problem or problems requiring additional knowledge on the student’s part to solve. Have pairs collaborate to provide the information and solve the problem.”

• Unit 3: Operations with Decimals, Lesson 3.15, Lesson Overview, English Learners (EL), “Entering/Emerging Writing: Have students answer the text questions by writing the price per unit using the sentence frame: The price is ___ per ___. “

• Unit 5: Fractions - Multiply and Divide, Lesson 5.8, Lesson Overview, English Learners (EL), “Developing/Expanding Writing: Review the words share and divide with students. Note the silent e in each word. Have students write each word three times.”

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 3: Operations with Decimals (4 - 5 weeks); Materials: 0.08 L container, 2.4 L container, Money cards (cards with various dollar amounts printed on them), Play money, Play money coins.”

• Documentation, Material List, provides a table listing the materials, units, and approximate quantity needed. “Material: Geometric shapes (triangles and quadrilaterals); Unit(s): 7; Approximate Quantity needed: 1 set per group of students (2-4).”

• Unit 1: Numbers, Lesson 1.4, Lesson Overview, Materials, “Per pair: Tape Measure (cm, m).”

• Unit 5: Fractions: Multiply and Divide, Lesson 5.3, Instruction & guided practice, Exercise 1d, students use fraction models to help solve a fraction multiplication problem.  Students see a fraction model of two sections with one shaded in and another fraction model of two sections with one shaded in but shaded the opposite way.  They can virtually stack the two models on top of one another to see the product of the problem as one of the four resulting sections will be darkly shaded. “To find a fraction of a fraction, multiply. Stack area models to find the product. \frac{1}{2} $$\times$$ \frac{1}{2}”.