The materials reviewed for Snappet Math Grade 1 meet expectations for developing a conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials develop conceptual understanding throughout the grade level. According to the Snappet Teacher Manual, 1. Deeper Learning with Snappet Math, conceptual understanding is a part of the design of the materials. Balancing Rigor states, “Each lesson embeds Conceptual Learning as the foundation and is designed to progress students along the learning path that begins with Student Discovery, transitions to Applying in Concrete pictorial representations, and then provides opportunities for Processing in Abstract representations.” According to the Grade 1 Teacher's Edition Volume 1, “Snappet’s Student Discovery Phase of the lesson design helps teachers present important math concepts using hands-on manipulatives, games, and classroom activities. Virtual manipulatives are also provided for guided practice and adaptive practice. The lesson design includes Concrete Pictorial Representations that utilize models and visuals during the lesson instruction. This approach helps teachers deliver high-quality instruction and builds a deeper understanding of math concepts for students.” Examples include:

• Unit 3: Addition within 20, Lesson 3.5, Instruction & Guided Practice, Exercise 1c, students develop conceptual understanding as they add within 20 using doubles. “Play Double It! In pairs, students use their fingers to show doubles within 20. One partner makes a number between 6 and 10. The other partner makes the same number. Together, they find the sum. Repeat until each partner has had a chance to make several numbers.” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; creating equivalent but easier or known sums.)

• Unit 4: Subtraction Within 20, Lesson 4.5, Instruction & Guided Practice, Exercise 1c, students develop conceptual understanding as they relate addition and subtraction using fact families. “Game: Add, Subtract, Repeat! ‘Rules of the Game’”, “The teacher says a number between 10 and 20. In pairs, students count out counters to represent the number. One student separates the counters into two groups, and the other student counts the groups. Together, students write a sum equation. Then a student takes one of the groups away. Together, students write a difference equation. Repeat using a variety of numbers between 10 and 20.” 1.OA.4 (Understand subtraction as an unknown-addend problem.)

• Unit 7: Addition and Subtraction Within 100, Lesson 7.8, Instruction & Guided Practice, Exercise 1c, students develop conceptual understanding as they use a number line to demonstrate adding a two-digit number and a one-digit number. “Partner Jumps: Addition, Try It: Pick a 2-digit number and a 1-digit number. Put the 2-digit number on the number line. Have your partner add on a part of the 1-digit number up to the next ten. Then you add the rest of the 1-digit number.” 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.)

According to Snappet, “Student Discovery, Lessons begin with hands-on learning. Research supports that new concepts are best learned using manipulatives in real, informal situations. This learning serves as the basis for conceptual understanding. Apply in Concrete Actual situations are presented as a concrete representation using models and visuals. Students learn to establish the relationship between the actual situation and the concrete representation.” Guidance is given for the teacher to use with struggling students to complete the Independent Practice items. In the Snappet Teacher Manual, Section 3.2, “When the teacher has completed the instruction for the day, students are given the opportunity to practice independently on their new skills. Each lesson includes approximately ten practice problems that are scaffolded for difficulty and are common for the whole class. Students are then presented with ten adaptive exercises that are customized to their skill levels. While students are working on their practice problems, the teacher can monitor the progress of their class in real-time. If the teacher notices a student or groups of students struggling with their exercises, they can intervene and provide support targeted to the needs of the students. At the same time, students that are “getting it” can move directly into adaptive practice and receive more challenging practice problems customized to their skill levels.” Examples include:

• Unit 2: Place Value, Lesson 2.9, Independent Practice, Example 2d, students compare two-digit numbers. “28__31” Students choose from “>,<,=.” The teacher can support struggling students with teacher direction: “Ask: Do you compare the tens or ones first? [Tens] What do you do if the tens are different? [Sample answer: The number with the greater tens digit is the greater number.]” 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.)

• Unit 5: Add and Subtract Fluently, Lesson 5.1, Independent Practice, Exercise 2f, students apply properties of operations as strategies to add and subtract. “$$5+5=$$__ . $5+8=$ ___.” The teacher can support struggling students with teacher direction: “Encourage students to look at how the second addends are different.” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; creating equivalent but easier or known sums); 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used...)

• Unit 7: Addition and Subtraction Within 100, Lesson 7.1, Independent Practice, Exercise 2d, students count backward by 10’s. “___, ___, ___, 41, 51. Think about a hundreds chart. What happens to the tens place?” The teacher can support struggling students with teacher direction: “Ask: Which blank should you fill in first and why? [The one on the right, because you can continue the pattern by counting back by 10s from 41.]” 1.NBT.5 (Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.)

The materials reviewed for Snappet Math Grade 1 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 

According to the Snappet Teacher Manual, “In Snappet, students will build understanding by problem-solving using Models, Number Sentences, and Word Problems to develop mathematical fluency.” Process in Abstract: “Concrete situations are replaced with abstract mathematical symbols such as dashes, squares, or circles. Different schemas, models and step-by-step plans are often used for this. Learning takes place at a higher, more abstract level, preparing students for practicing procedural skills, developing fluency, and applying concepts flexibly to different situations.” The Instruction & Guided Practice problems provide ongoing practice of procedural skills within lessons. Examples A include: 

• Unit 1: Numbers, Lesson 1.4, Instruction & Guided Practice, Exercise 1m, students develop procedural skill and fluency as they complete a sequence of numbers by filling in missing numbers. “Fill in the missing numbers. 112, __, 114, __, 116, __. Write the numbers on your paper.” 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.)

• Unit 3: Addition within 20, Lesson 3.7, Instruction & guided practice, Exercise 1p, students develop procedural skill and fluency as they add within 20. “$$9+8=$$__”. Teacher tip, “Ask: What strategy would you use to find the sum? [Sample answer: I would use a make-a-ten strategy.] How would you use it? [Sample answer: I would break 8 into $1+7$. I would add 9 + $1=10$ and then add the 7.]” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction, and creating equivalent but easier or known sums.)

• Unit 5: Add and Subtract Fluently, Performance Task, Exercise 1d, Question 11, students develop procedural skills and fluency as they use strategies to find totals. “Is each total correct? Circle Yes or No. 8 red daisies and 6 yellow daisies. $8+6=14$ Yes; No. 10 pink daisies and 3 red daisies. $10+3=13$ Yes; No. 9 pink daisies and 9 orange daisies $9+9=17$ Yes; No.” Teacher tip, “Ask: What strategy did you use for each total? If you circled NO, what is the correct total?” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction, and creating equivalent but easier or known sums.)

In the Snappet Teacher Manual, Lesson Structure, “Automating and memorizing, Automating and memorizing is embedded in the learning goals of the Snappet program where this skill is important. The moment that Snappet recognizes the student has mastered the arithmetic knowledge and skill of the learning goal, the system automatically switches to tasks aimed at automation and memorization. This is accomplished by using exercises that students must completed in a given amount of time. Using this method, identifies whether a student knows the answer by automation or memorization or if they are still working out the calculations. If the student does not provide the correct answer in the given amount of time, then the program will allot more time for that exercise on the next attempt. The Snappet program will recognize when a student has sufficiently automated and memorized a goal and will adapt accordingly.” Students have opportunities to independently demonstrate procedural skills and fluency throughout the grade. Examples include:

• Unit 2: Place Value, Lesson 2.1, Independent Practice, Exercise 2h, students demonstrate procedural skill and fluency as they represent a two-digit number as amounts of tens and ones. “Now I have 2 tens and 9 ones. What number do I have?” “You can use the place-value chart.” Students type the number and complete a hundreds chart to represent tens and ones. 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones.)

• Unit 3: Addition within 20, Lesson 3.6, Independent Practice, Exercise 2i, students develop procedural skills and fluency as they practice adding within 20.  “$$7+7=$$___, $7+6=$___” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; creating equivalent but easier or known sums.)

• Unit 4: Subtraction Within 20, Lesson 4.9, Independent Practice, Exercise 2f, students demonstrate procedural skill and fluency as they complete an equation to subtract within 20. “$$12-8=$$___.” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction, and creating equivalent but easier or known sums.)

The materials reviewed for Snappet Math Grade 1 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. 

Students have opportunities to engage with multiple routine and non-routine application problems with teacher support and independently. Snappet Teacher Manual, Performance Tasks, “Each grade-level course includes Performance Task Lessons that are designed to be a cumulative lesson encompassing multiple mathematical concepts. These lessons are designed as group projects or whole class discussion opportunities.” 

Examples of teacher-supported routine and non-routine applications of mathematics include:

• Unit 3: Addition within 20, Lesson 3.8, Instruction & Guided Practice, Exercise 1h, students add three numbers in a word problem in a routine application. “You have six pencils. You take 3 more. Your friend gives you 4 more pencils. First, make a 10. Then, add the rest.” Teacher tip, “Ask: Why does the make-a-ten strategy work for this problem? [Sample answer: Two of the addends equal 10. Add the third addend to 10.]” 1.OA.2 (Solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the  unknown number to represent the problem.)

• Unit 4: Subtraction Within 20, Lesson 4.7, Instructional & guided practice, Exercise 1g, students solve word problems using subtraction in a routine application. “Nina is 17 years old. Anna is 9 years old. Anna is ___ years younger. 17-9= ___”1.OA.1 (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.)

• Unit 6: Add and Subtract to Solve Word Problems, Lesson 6.4, Instruction & Guided Practice, Example 1c, students solve word problems using addition in a non-routine application. “How Many Counters? Directions: Give each student pair 5 red and 5 yellow counters. Read the following problem: Amal has 5 counters. Some are red and some are yellow. How many of each color could Amal have? As students share their solutions, write equations on the board to match ($$3+2=5$$, $1+4=5$, etc). Are there other possible answers? How do you know?” Teacher tip, “Have students form pairs. Give each pair five red counters and five yellow counters. Read the following: Amal has five counters. Some are red, and some are yellow. How many of each color could Amal have? Write the solutions as students give them. If students leave possible answers unsaid (1R-4Y, 2R-3Y, 3R-2Y, 4R-1Y), ask if there are other answers.” 1.OA.1 (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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.)

• Unit 9: Data, Lesson 9.1, Instruction & Guided Practice, Exercise 1c, students collect and represent data on a tally chart in a non-routine application. “Which do you prefer? Give each student pair a blank tally chart and a clipboard. They fill the first column with two options that complete the question, “Do you prefer ___ or ___?” Model using the apples and oranges chart, as shown. Students spend 5 minutes surveying classmates and making tally marks in the chart to record their preferences. how many students prefer each option?” 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many are in each category, and how many more or less are in one category than in another.)

Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of mathematics throughout the grade level. Examples of independent demonstration of routine and non-routine applications of mathematics include:

• Unit 4: Subtraction Within 20, Lesson 4.1, Independent Practice, Exercise 2c, students subtract using objects or drawings in a routine application. “There are 6 muffins. Put 1 muffin on the plate. There are ___ muffins left.” 1.OA.1 (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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.)

• Unit 6: Add and Subtract to Solve Word Problems, Lesson 6.2, Independent Practice, Exercise 2f, students use addition to solve word problems in a routine application. “Adam sells 6 loaves of bread in the morning. He sells some more bread in the afternoon. Adam sold 16 loaves in all. How much bread did he sell in the afternoon? Draw to solve the problem. ___ loaves of bread.” 1.OA.2 (Solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the  unknown number to represent the problem.)

• Unit 8: Measurement, Lesson 8.1, Exercise 2n, students compare three objects and the lengths of each in a non-routine application. Students see pictures of a trash can, tree, and a house next to each other. “The house is… the trash can. shorter than, as tall as, taller than.” 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object.)

• Unit 9: Data, Lesson 9.6, Independent Practice, Exercise 2h, students use a bar graph to solve a word problem in a routine application. “Rita plays soccer. How many more goals did she score on Wednesday than on Friday?” 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many are in each category, and how many more or less are in one category than in another.)

• Unit 11: Equal Shares, Lesson 11.1, Exercise 2j, students partition a round pizza equally between four people in a non-routine application. Students see 4 people and a pizza.  “How can you share this pizza equally? Draw a circle and show the parts.” 1.G.3 (Partition circles and rectangles into two and four equal shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that composing into more equal shares creates smaller shares.)

The materials reviewed for Snappet Math Grade 1 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

The materials address the aspects of rigor, however, not all are addressed equally. Heavy emphasis is placed on conceptual understanding, procedural skills, and fluency. All three aspects of rigor are present independently throughout the materials. Examples include:

• Unit 3: Addition within 20, Lesson 3.8, Instruction & Guided Practice, Exercise 1i, students apply their understanding as they add three addends to solve a word problem. “You have seven pencils. You take seven more. Your friend gives you 1 more. Use your double facts, then add.” Teacher tip, “Ask: How does knowing doubles help you find this sum? [Sample answer: I can find the doubles fact and add 1 more.]” 1.OA.1 (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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.)

• Unit 5: Add and Subtract Fluently, Lesson 5.1, Instruction & Guided Practice, Exercise 1i, students develop procedural skill and fluency as they use strategies to add and subtract within 20. “Try to solve it in your head. $8+3=$___, $16-8=$___, $13-4=$___” Teacher tip,  “Have students solve the problems. When they have finished, have volunteers share their methods.” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction, and creating equivalent but easier or known sums.)

• Unit 6: Add and Subtract to Solve Word Problems, Lesson 6.6, Instruction & Guided Practice, Exercise 1c, students extend their conceptual understanding by using counters to demonstrate the relationship between addition and subtraction. “How Many More? Directions: Give each student pair 5 red and 5 yellow counters. Record the following word problem: “There are 4 red counters and 2 yellow counters. How many more red counters are there than yellow counters?” Students model the problem and share their answers. Write the equation “$$2+?=4$$” on the board. Repeat with similar problems within 10. Can you write an addition equation to show the problem? Could you use subtraction to solve?” Teacher tip, “Have students form pairs. Give each pair five red counters and five yellow counters. Read the following: There are four red counters and two yellow counters. How many more red counters are there than yellow counters? Students model the problem and share their answers. Write “$$2+?=4$$” on the board. Repeat with similar problems within 10. Ask: Can you write an addition equation to show the problem? Could you use subtraction to solve?” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; creating equivalent but easier or known sums.)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study. Heavy emphasis is placed on procedural skill and fluency and teacher-guided conceptual understanding. Examples include:

• Unit 3: Addition within 20, Lesson 3.6, Instruction & Guided Practice, Exercise 1f, students develop conceptual understanding alongside procedural skill and fluency as they add near doubles. “Count on to find the sum. $8+8=16$, $9+8=$___.” Teacher tip, “Ask: How can you use the doubles to find the second sum? [Sample answer: One of the addends is one greater, so I can add 1.]” 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; creating equivalent but easier or known sums.)

• Unit 4: Subtraction Within 20, Lesson 4.5, Independent Practice, Exercise 2h, students develop conceptual understanding alongside procedural skill and fluency as they relate addition and subtraction by using fact families. “$$9-4=?$$, $4+?=9$, $9-?=4$.” Students select from answers 2, 3, 4, and 5. 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; creating equivalent but easier or known sums.)

• Unit 8: Measurement, Lesson 8.1, Instruction & Guided Practice, Exercise 1c, students develop conceptual understanding alongside procedural skill and fluency as they order their classmates by length. “Game: Who is the tallest? Rules of the Game: Call 3 students to the front of the room. Ask the class: Who is the tallest? How can you tell that? Are any of the students the same height? Repeat the activity with several groups of 3 students.” 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object.)

The materials reviewed for Snappet Math Grade 1 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the Mathematical Practice standards. 

The Mathematical Practice Standards are identified in the Course Overview/Unit Pacing Guide, Teacher Guide, Unit Overviews, and Lesson Overviews. Each lesson has a Math Practices tab that provides 3-5 structured exercises supporting the intentional development of each Math Practice throughout the year. 

MP 1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with the teacher's support and independently throughout the units. Per Snappet Learning phases math, "MP1: Make sense of problems and persevere in solving them. Found in almost every math problem across the board. Students must understand the problem, figure out how to solve it, and work until it is finished. Standards encourage students to work with their current knowledge bank and apply the skills they already have while evaluating themselves in problem-solving. This standard is easily tested using problems with a tougher skill level than already mastered. While students work through more difficult problems, they focus on solving them instead of just getting to the correct answer." Examples include:

• Unit 3: Addition within 20, Lesson 3.7, Math practices, Exercise 4c, “The intent of Exercise 4 is to have students practice MP 1 (Make sense of problems and persevere in solving them) as they decide the strategy they think is best and implement it when adding within 20.”  “This problem challenges students to find the sum of 4 addends. The goal of this problem is for students to see how they can use the make-a-ten strategy to add $8+2=10$; and then they can use near doubles when they add $4+3$ as $3+3=6$, plus 1 more equals 7.” The exercise states, “Think about this addition problem 8+4+3+2 Decide how you will find the solution. Explain the strategies you used to find the sum. $8+4+3+2=$__”

• Unit 7: Addition and Subtraction Within 100, Lesson 7.3, Math practices, Exercise 4b, “The purpose of Exercise 4 is to focus on MP 1 (Make sense of problems and persevere in solving them) as students interpret addition expressions that involve a 2-digit number and a multiple of 10.” “This problem removes the scaffold of the number line with the individual jumps by 10; with the eventual goal of the students not needing to rely on the number line. Ask: What is the sum of this equation? [47] Call on a student to share one way to find the sum. [Sample answer: Count by 10s three times.] Call on another student to share a second way to find the sum. [Sample answer: Add 3 tens to 1 ten.]” The exercise shows a number line starting at 17 and one jump of +30 and states, “$$17+30=$$__ Explain how to find the sum.”

• Unit 8: Measurement, Lesson 8.6, Math practices, Exercise 4a, “Exercise 4 is designed to provide students with practice applying MP 1 (Make sense of problems and persevere in solving them) as they apply what was learned in previous lessons and continue to practice and explore the concept of measurement. Ask: What is the nonstandard unit of measure used in this problem? [paper clips] Ask: Which object was 2 clips tall? [burger] Call on a student to share their answer to the question with their peers. [Sample answer: I could tell just by looking at the objects, but I dragged the paperclips just to be sure.]” The exercise shows a burger, ice cream cone, and jar of honey. Paperclip images can be dragged to measure. “Tap on the object that is 2 paper clips tall. How could you tell before dragging the paper clips?”

MP 2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with the teacher's support and independently throughout the units. Per Snappet Learning phases math, “MP2: Reason abstractly and quantitatively. When trying to problem solve, it is important that students understand there are multiple ways to break apart the problem in order to find the solution. Using symbols, pictures or other representations to describe the different sections of the problem will allow students to use context skills rather than standard algorithms.” Examples include:

• Unit 2: Place Value, Lesson 2.8, Math practices, Exercise 4c, “Exercise 4 allows students to practice MP 2 (Reason abstractly and quantitatively) as they deepen their understanding of using place value to compare two-digit numbers.” “This extended problem allows students to think about how they apply the ideas about comparing two-digit numbers. Have students work in pairs to respond to this problem. Ask students to share their explanations. [The greatest number has the most tens. The least number has the fewest tens.]” The exercise states, “Think about these numbers. 51 38 79 40 80 How could you find the greatest number? How could you find the least number?”

• Unit 4: Subtraction Within 20, Lesson 4.8, Math practices, Exercise 4b, “Exercise 4 provides students with the opportunity to apply MP 2 (Reason abstractly and quantitatively) as they attend to the meaning of quantities, not just how to compute them when using doubles to subtract.” “This problem is a continuation of the previous one. Now that the beads have been presented, students will be expected to proceed with the subtraction equation. Call on a student to answer the question. [To subtract 8, I just move all the beads (either on top or bottom) from left to right. Then what remains on the left side is the difference.)” The exercise shows two rows of beads with each row having 8 beads on the left and 2 beads on the right. “Since $8+8=16$, $16-8=$__. How can the beads help you find the difference?”

• Unit 8: Measurement, Lesson 8.10, Math practices, Exercise 4a, “The purpose of Exercise 4 is to provide students practice applying MP 2 (Reason abstractly and quantitatively) as they demonstrate their ability to decontextualize a picture and context clues, which represent time on a clock ot the half hour. Ask: What time did you enter? [6:30 PM] Call on a student to explain how the picture provided the information needed to tell the time. [Sample answer: The waitress states the time to the half hour and says it is evening. The view outside the window also tells us it is the evening, so it is PM.]” The exercise states, “It is six thirty in the evening. The digital time is : __. How did the picture tell you the time?”

The materials reviewed for Snappet Math Grade 1 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the Mathematical Practice standards.

The Mathematical Practice Standards are identified in the Course Overview/Unit Pacing Guide, Teacher Guide, Unit Overviews, and Lesson Overviews. Each lesson has a Math Practices tab that provides 3-5 structured exercises supporting the intentional development of each Math Practice throughout the year. 

MP 3 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students construct viable arguments and critique the reasoning of others as they work with the support of the teacher and independently throughout the units. Per Snappet Learning phases math, “MP3: Construct viable arguments and critique the reasoning of others. This standard is aimed at creating a common mathematical language that can be used to discuss and explain math as well as support or object to others’ work. Math vocabulary is easily integrated into daily lesson plans in order for students to be able to communicate effectively. “Talk moves” are important in developing and building communication skills and can include such simple tasks as restating a fellow classmate’s reasoning or even supporting their own reason for agreeing or disagreeing. Prompting students to participate further in class mathematical discussions will help build student communication skills. Examples include:

• Unit 2: Place Value, Lesson 2.10, Math practices, Exercise 4a, “Exercise 4 provides students the ability to apply MP 3 (Construct viable arguments and critique the reasoning of others) as they develop explanations for how they ordered the five two-digits numbers from least to greatest. Have students collaborate with a partner to write an explanation they agree upon. [Students should recognize they need to compare the tens digits.]” The exercise states, “Drag the numbers from least to greatest. 81, 25, 54, 60, 39 Explain how to order these numbers.”

• Unit 3: Addition within 20, Lesson 3.10, Math practices, Exercise 4c, “Exercise 4 provides students the ability to apply MP 3 (Construct viable arguments and critique the reasoning of others) as they analyze the addition strategies used by others to solve a problem.” “This problem gives students the chance to apply more than one strategy to find the sum of 4 addends. Have students work in pairs to decide what strategies to employ. After a few minutes, call on a student-pair to share their answer and strategies. Allow others to ask questions or critique their presentation, as needed. Remind students there can be more than one correct way to solve a problem.” The exercise states, “Find the sum using addition strategies. $4+5+6+5$ ___ Explain the strategies you used to find the sum.”

• Unit 10: Geometry, Lesson 10.7, Math practices, Exercise 4b, “Exercise 4 gives students practice with MP 3 (Construct viable arguments and critique the reasoning of others). Students analyze figures using definitions to determine the attributes of a solid figure and to classify a solid figure based on defining attributes.” “Now, students analyze another pair of figures to determine an attribute they share. Call on a student to name an attribute. [Sample answer: can roll] To enhance learning, Ask: What is different about the shapes? [Sample answer: One shape has 2 faces that are circles and the other shape has no faces.]” The exercise shows a cylinder and sphere. “Name an attribute the shapes share.”

The materials reviewed for Snappet Math Grade 1 meet expectations for supporting the intentional development of MP6: Attend to precision and to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the Mathematical Practice Standards.

The Mathematical Practice Standards are identified in the Course Overview/Unit Pacing Guide, Teacher Guide, Unit Overviews, and Lesson Overviews. Each lesson has a Math Practices tab that provides 3-5 structured exercises supporting the intentional development of each Math Practice throughout the year. 

MP 6 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students attend to precision and the specialized language of mathematics as they work with the teacher's support and independently throughout the units. Per Snappet Learning phases math, “MP6: Attend to precision. Math, like other subjects, involves precision and exact answers. When speaking and problem-solving in math, exactness and attention to detail is important because a misstep or inaccurate answer in math can be translated to affect greater problem-solving in the real world.” Examples include:

• Unit 3: Addition within 20, Lesson 3.9, Math practices, Exercise 4b, students “practice MP 6 (Attend to precision) as they apply what they have learned about the strategies of adding to calculate sums with efficiency and accuracy.” “This problem gives students 4 addends and offers them some guidance for finding their sum with accuracy. Ask: What strategy did you use to add the numbers in green? [Students may use a variety of strategies such as make-a-ten or counting on.] Ask: What strategy did you use to add the numbers in blue? [Students may use a variety of stratgies such as near doubles or counting on.] Have students share their responses to the question. [Check my work by using a different strategy than I used the first time.]” The exercise states, “Find the sum. $9+3+1+4=$; $$+$$ $$=$$__ What can help so you do not make a mistake?”

• Unit 7: Addition and Subtraction within 100, Lesson 7.8, Math practices, Exercise 4a, students “practice MP 6 (Attend to precision) as they understand that breaking apart an addition or subtraction problem into two or more steps does not change the value of the final answer.” “Add to the next ten. Then add the rest. Show your work in two steps.  36+7=____Step 1: , Step 2: , Explain what “Then add the rest.” means.”

• Unit 10: Geometry, Lesson 10.1, Math practices, Exercise 4a, students practice with MP 6 (Attend to precision), as they “use clear mathematical language to determine the attributes of a plane figure.” “Ask a student to share their thoughts about all rectangles. [No. Sample answer: All of these rectangles are red, but a rectangle can be a different color.] Ask: What is true about all rectangles? [4 sides, 4 corners]” The exercise states, “Fred says all rectangles are red. Is this true? Explain.” Three red rectangles are shown.

• Unit 11: Equal Shares, Lesson 11.1, Math practices, Exercise 4b, students “practice MP 6 (Attend to precision). Students name equal shares by using the correct language.” “Allow time for students to look at the figure. Students will use correct language to give an answer. Have a volunteer share their answer. Encourage them to use clear language. [Yes. Sample answer: The parts are the same size.]” The exercise states, “Are equal shares shown? Why or why not?”

The materials reviewed for Snappet Math Kindergarten meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the Mathematical Practice Standards. 

The Mathematical Practice Standards are identified in the Course Overview/Unit Pacing Guide, Teacher Guide, Unit Overviews, and Lesson Overviews. Each lesson has a Math Practices tab that provides 3-5 structured exercises supporting the intentional development of each Math Practice throughout the year. 

MP 7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and use structure as they work with the teacher's support and independently throughout the units. Per Snappet Learning phases math, “MP7: Look for and use structure. When students can identify different strategies for problem-solving, they can use many different skills to determine the answer. Identifying similar patterns in mathematics can be used to solve problems that are out of their learning comfort zone. Repeated reasoning helps bring structure to more complex problems that might be able to be solved using multiple tools when the problem is broken apart into separate parts.” Examples include:

• Unit 2: Place Value, Lesson 2.6, Math practices, Exercise 4a, “The intent of Exercise 4 is to allow students to practice MP 7 (Look for and make use of structure) as they compose tens and ones into two-digit numbers and decompose two-digit numbers into tens and ones. Have students discuss with a partner how they will answer the question. [I can skip-count by 10s for each ten-dollar bill. Then I can count on by 1 for each one-dollar bill.] Call on a student to share their response:” The exercise shows four ten-dollar bills and two one-dollar bills. “Look for tens and ones. How much money is here? $__ How did you use tens and ones to count the money?”

• Unit 4: Subtraction Within 20, Lesson 4.2, Math practices, Exercise 4c, “Exercise 4 gives students the opportunity to use MP 7 (Look for and make use of structure) as they look for patterns in the process of counting back to subtract.” “This problem encourages the students to use the count back strategy to subtract 4 from 20. Ask: How could you find the difference if you are not sure about counting back? [Sample answer: Draw a picture of 20 objects, cross out 4 of them, and count how many are left] Call on a student to share their answer to the question. [Sample answer: You do not start with the starting number, just like you do not count the starting point on the number line.]” The exercise shows a student counting backwards, “19, 18, …”. “Count back to subtract. $20-4=$__ Why does the student begin with 19?”

• Unit 7: Addition and Subtraction Within 100, Lesson 7.4, Math practices, Exercise 4d, “Exercise 4 gives students practice with MP 7 (Look for and make use of structure), where the goal is for them to use the place value structure of a two-digit number to add to or subtract from the number of tens.” “This problem also does not suggest any method for subtracting the multiples of 10. It requires students to explain the pattern they see when subtracting multiples of 10, which should encourage them to think about the structure of place value. Call on a student to share their explanation. [Sample answer: Subtract the digits in the tens place. The ones digit is always 0.]” The exercise states, “$$70-30=$$__ Explain the pattern you see when you subtract multiples of 10.”

MP 8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with the teacher's support and independently throughout the units. Per Snappet Learning phases math, “MP8: Look for and express regularity in repeated reasoning. In mathematics, it is easy to forget the big picture while working on the details of the problem. In order for students to understand how a problem can be applied to other problems, they should work on applying their mathematical reasoning to various situations and problems. If a student can solve one problem the way it was taught, it is important that they also can relay that problem-solving technique to other problems.” Examples include:

• Unit 2: Place Value, Lesson 2.2, Math practices, Exercise 4c, “The purpose of Exercise 4 is to provide students with an opportunity to practice MP 8 (Look for and express regularity in repeated reasoning) as they use skip counting to count two-digit numbers.” “This problem enables students to further think about how using groups can help them count two-digit numbers of objects more efficiently. Have students work in pairs to answer the question. [I could group the popsicles in either 5s or 10s and then skip-count. Then I can count on the popsicles not grouped.] Call on a student-pair to explain their response.” The exercise shows 26 popsicles in a random configuration. “Explain how using groups could help you find how many popsicles there are.”

• Unit 7: Addition and Subtraction Within 100, Lesson 7.2, Math practices, Exercise 4a, “Exercise 4 represents students the chance to apply MP 8 (Look for an express regularity in repeated reasoning) as they make jumps on a number line of the same length to create a number pattern and to count on and count back by multiples of 10. Ask: How can you tell the first arrow begins at 16? [Sample answer: The bold tick marks that are halfway between the multiples of ten are multiples of 5. Halfway between 10 and 20 is 15. The first arrow is one tick mark past 15, so it is 16.] Call on a student to share their answer and explanation. [Sample answer: I looked at where each of the arrows ended until I got to the last one.]” The exercise shows a number line from 10 to 50. Three jumps of +10 are shown starting at 16. “Start at 16. Then make 3 jumps of 10. You will get to __ on the number line. Explain how you counted on by multiples of 10.”

• Unit 10: Geometry, Lesson 10.8, Math practices, Exercise 4b, “Students practice MP 8 (Look for an express regularity in repeated reasoning) in Exercise 4. Students see similar structure in three-dimensional objects to identify and classify shapes based on attributes.” “Now, students recognize and verbalize the similar structure they see in cones. Have partners discuss the question. [Sample answer: Cones have a face that is a circle, and the opposite end is a point. It has a curved surface and can roll.] Make sure student-pairs tap all the cones.” The exercise shows six objects and states, “How do you know which are cones? Tap the cones.”

The materials reviewed for Snappet Math Grade 1 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 lesson segment, and full lesson videos. 

• Grade 1-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 1-Unit Overviews, Unit 3 Overview: Addition Within 20, Understanding the Math, “Addition within 20 is one of the prerequisites for performing addition of all types of numbers. Students need to be able to use mental math strategies to compute numbers quickly and accurately. They learn strategies such as adding double numbers like 4 + 4, and then realize that adding 4 + 5 is like adding one more to 4 + 4. Since our number system is a base-10 system, the number 10 is important to us. Students build on numeracy skills learning different strategies to use 10 when adding. If they are adding 9 and 6 for example, they can add 9 + 1 and then 5 more.”

• Unit 2: Place Value, Lesson 2.4, Small group instruction, Exercise 3a, Teacher Tip, “(SEL) Encourage students to use the cartons to help them solve the problem. Ask: How many eggs can fit in each carton? [10] How many eggs can fit in each row? [5]”

• Unit 6: Add and Subtract to Solve Word Problems, Lesson 6.4, Independent practice, Exercise 2b, Teacher Tip, “Inform students that the pencils are draggable.”

The materials reviewed for Snappet Math Grade 1 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 Expanding Content Knowledge and Application Beyond Kindergarten, which provides explanations and examples of more complex grade-level concepts and concepts beyond the current course. Examples include:

• Unit Overviews, Unit 2: Place Value, Learning Progression, “In prior grade levels, students composed and decomposed teen numbers (K.NBT.A.1), compared groups of objects to understand terms like more and less (K.CC.C.6) and compared numbers to 10 (K.CC.C.7). In this grade level, students will represent and understand the composition of two-digit numbers as tens and ones, and compare and order two-digit numbers, including using relationship symbols. In future grade levels, students will extend their understanding of place value to three-digit numbers (2.NBT.A.1.a, 2.NBT.A.1.b, 2.NBT.A.1.c), and compare three-digit numbers (2.NBT.A.4).”

• Unit 3: Addition within 20, Lesson 3.5, Lesson Overview, Deepening Content Knowledge Beyond Grade Level, “Introduction to Exponential Growth: The concept of doubling also introduces students to basic exponential growth, a crucial component in understanding more complex mathematical concepts and real-world phenomena like population growth, compound interest, and computer science (e.g., binary numbers and data storage).”

• Unit 8: Measurement, Lesson 8.6, Lesson Overview, “In prior lessons, students have compared the lengths of objects; measured an object using hands and feet. In this lesson, students will measure lengths indirectly using nonstandard units of measure; understand the relationship between the length measurement of an object and the same-size length units that are being used to measure the object. In future lessons, students will choose a measure for length; measure using a centimeter and inch ruler.”

• Unit Overviews, Unit 11: Equal Shares, Understanding the Math, “Equal shares provide a foundation for fractions starting with the understanding of a whole and introducing fractional amounts. When a whole pizza is partitioned into four equal shares, students know that each part is a fourth. Partitioning into equal shares helps children understand the meaning of fractions and relative sizes of fractional amounts. Children will build on their conceptual understanding of fractions and continue to use it through high school and beyond.”

The materials reviewed for Snappet Math Grade 1 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:

• Pacing Guide, provides a table separated by unit and includes columns that identify 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, as well as 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: Add and Subtract to Solve Word Problems, Lesson 6.1, The Specific Role of the Standard in the Overall Series, “Building Blocks for Mathematical Proficiency: Standards 1.OA.A.1 and 1.OA.A.2 are not isolated goals but integral parts of a comprehensive mathematics curriculum designed to build proficiency. These standards emphasize the practical application of plus and minus signs, fostering a deeper understanding of their functions beyond mere symbols on a page. This knowledge is not an end in itself but serves as a stepping stone for students to advance to higher-order mathematical skills, ensuring a smooth transition as they move up in grade levels and complexity.”

• Unit 9: Data, Lesson 9.2, Lesson Overview, Mathematical Content Standards, “1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.”

The materials reviewed for Snappet Math Grade 1 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 1 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 1-Material List, “The list below includes materials used in the 1st 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, “Counters (Red/Yellow or 2 different colors); 1, 2, 3, 4, 6; 50 per student of each color.”

• Unit 2: Place Value, Lesson 2.3, Lesson Overview, Materials, “Per team: A mystery bag of items, Per pair: 60 counters.”

• Unit 9: Data, Lesson 9.4, Lesson Overview, Materials, “Per student: 1 sticky note (1 in one of 5 different colors).”