2nd Grade - Gateway 1

The materials reviewed for Snappet Math Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The curriculum is divided into nine units with one assessment per unit, except for Units 1, 3, 5, and 6. Unit 1 includes two Summative Assessments that assess Lessons 1.1 - 1.8 and Lessons 1.9 - 1.16. Unit 3 includes two Summative Assessments that assess Lessons 3.1 - 3.6 and Lessons 3.7 - 3.13. Unit 5 includes two Summative Assessments that assess Lessons 5.1 - 5.9 and Lessons 5.10 - 5.18. Unit 6 includes two Summative Assessments that assess Lessons 6.1 - 6.6 and Lessons 6.7 - 6.12. Assessments include Unit Summative Assessments and formative assessments. Examples include:

• Unit 3: Add and Subtract Within 100, Assessment: Lessons 3.1 - 3.6, Exercise 1c, students solve a subtraction problem. “Subtract. 63-6=?” Students choose from “57, 60, 63, 69.” (2.NBT.5)

• Unit 4: Solve Word Problems, Assessment: Lessons 4.1 - 4.9, Exercise 2b, students add and subtract to solve a two-step word problem. “Our school has 56 tablets and 37 laptops. Unfortunately, 18 devices are broken. How many devices are there left? Our school has ___ devices left.” (2.OA.1)

• Unit 6: Measurement, Assessment: 6.1 - 6.6, Exercise 5b, students use an interactive ruler to measure a rectangle. “Drag the inch ruler to the rectangle. How long is this rectangle? It is about ___ inches.” (2.MD.1)

• Unit 7: Time and Money, Assessment: 7.1 - 7.9, Exercise 6b, students find the total amount of coins. “Sandra has 41¢ in her wallet. She finds a quarter and a penny in her pocket. How much money does Sandra have now?” (2.MD.8)

• Unit 9: Geometry, Assessment: 9.1 - 9.8, Exercise 3a, students sort six shapes, by their given attributes, as quadrilaterals and not quadrilaterals. “Sort the polygons by dragging.” (2.G.1)

Materials include above-grade assessment items that could be removed or modified without impacting the structure of the materials. Examples include:

• Unit 6: Measurement, Assessment: 6.7 - 6.12, Exercise 2a, students estimate the height of a boy. “1 meter and 33 centimeters. This is the same as ___ centimeters.” This problem is aligned to 2.MD.2 in the materials (Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.) This problem better aligns to 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit....)

• Unit 6: Measurement, Assessment: 6.7 - 6.12, Exercise 2b, students estimate the length of a cart. “2 meters and 15 centimeters. This is the same as ____ centimeters.” This problem is aligned to 2.MD.2 in the materials (Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.) This problem better aligns to 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.)

The materials reviewed for Snappet Math Grade 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. 

The materials present opportunities for students to engage with the full intent of grade-level standards through a consistent lesson structure. According to the Snappet Teacher Manual, 3. Lesson Structure, “Snappet lessons are organized by learning objective and focus on one learning objective per lesson. Each lesson consists of three parts: Instruction and guided practice, Independent and adaptive practice, and Small group instruction.” Within Instruction and guided practice, “The teacher introduces the learning goal, activates prior knowledge, delivers the lesson, and monitors guided practice.” Within Independent and adaptive practice, students work independently “while receiving immediate feedback, and are continuously challenged at their own level while working in adaptive practice.” Within Small group instruction, “The teacher can help students who need additional support with these extension exercises.” Examples of full intent include:

• Unit 3: Add and Subtract Within 100, Lesson 3.4, Lesson 3.9, and Lesson 3.11 engage students in extensive work with 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) Lesson 3.4, Independent practice, Exercise 2b, students add using properties of operations. “Add 76 + 13 using number sentences.  76+___$$=$$___; ___$$+$$___$$=$$___; 76+13=___.” Lesson 3.9, Independent practice, Exercise 2c, students use place value to add two digit numbers. “You can make a quick drawing to solve. Regroup, if needed. 38+17.” Lesson 3.11, Exercise 2e, “Use the addition strategy to solve. Enter the numbers. 92-89=___.” 

• Unit 6: Measurement, Lesson 6.8, Exercise 1m and 2j, engage students in the full intent of 2.MD.2 (Measure the length of an object twice, using length units for the two measurements; describe how the two measurements relate to the size of the unit chosen.) Students measure using meters and centimeters, then convert to centimeters. In Exercise 1m, the students find the height of a door in the classroom in centimeters and then convert to meters and  centimeters. “Measure the door. The door is: ___ centimeters tall. That is the same as ___ meters and ___ centimeters.” Students then practice doing a similar problem type independently in 2j. The problem shows a pair of snow skis measuring 176 centimeters. “This is the same as ___meters and ___centimeters.”

• Unit 7: Time and Money, Lesson 7.2, Lesson 7.4, and Lesson 7.5 engage students in the full intent of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) Lesson 7.2, Instruction & guided practice, Exercise 1j, students tell and write time. “I eat my breakfast. What could be the time you eat breakfast? Choose the best option.” Students choose from “1:15 a.m., 1:15 p.m., 7:15 a.m., 7:15 p.m.” Lesson 7.4, Independent practice, Exercise 2h, students use an analog clock to tell time. An analog clock shows 6:10.“What time is it? It is ___.” Lesson 7.5, Instruction & guided practice, Exercise 1p, students tell time using a digital clock. “What time is it?” A digital clock shows 11:05 a.m.

• Unit 9: Geometry, Lesson 9.4 and Lesson 9.5 engage students in the full intent of 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.) Lesson 9.4, Instruction & guided practice, Exercise 1l, students draw shapes having specified attributes. “Draw a polygon with 6 sides and 6 angles. The polygon is a,” students select from, “quadrilateral, pentagon, hexagon.” Lesson 9.4, Independent practice, Exercise 2j, “Draw a polygon with 4 equal sides. The polygon has ___ angles. The polygon is a: quadrilateral, pentagon. hexagon.” Lesson 9.5, Independent practice, Exercise 2j, use dot paper to draw a cube. “Draw a cube.” 

The materials present opportunities for students to engage with extensive work with grade-level problems, with the exception of 2.MD.9. Examples of extensive work include:

• Unit 1: Numbers, Lesson 1.6, Lesson 1.10, and Lesson 1.11 engage students in extensive work in 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s.) Lesson 1.6, Instruction & guided practice, Exercise 1i, students count using place value and number patterns. “78, 79,” click on blurred numbers to reveal “80, 81, 82, 83.” Given “578,” click on blurred numbers to reveal “579, 560, 561, 562, 563.” “First count from 78. Can you continue counting from 578? Hint: which ten comes after 79?” Lesson 1.10, Independent practice, Exercise 2f, “Count by 10s.” Given, “672, 682, ___, ___, ___.” Lesson 1.11, Independent practice, Exercise 2b, “580, 590, 600.’ Teacher tip, “Ask: Does the pattern change when you start with different numbers that end in zero or five, like 260? [No.] How about if you start with a number that does not end in zero or five? [Yes, the pattern changes.] Do you get a new pattern? [Yes. But it depends on the starting number.]”

• Unit 4: Solve Word Problems, Lesson 4.2, Lesson 4.5, and Lesson 4.9 engage students in extensive work with 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.) Lesson 4.2, Instruction & guided practice, Exercise 1f, students solve problems using objects or drawings. “Steph counted 18 ladybugs and 23 beetles in her garden. How many bugs did Steph count in all? Steph counted ___ bugs.” Lesson 4.5, Independent practice, Exercise 2d, solve comparison problems using equations. “In Seaside Elementary School, 45 teachers drink coffee and 10 teachers drink tea. How many more teachers drink coffee than tea? Complete the equation to solve the problem. ___ -10= ___ and ___ more teachers drink coffee than tea.” Lesson 4.9, Instruction & guided practice, Exercise 1k, students solve one and two-step problems. “Polly gives away 24 gum balls. Then she gives away 13 more gum balls. There were 65 gum balls in the box before Polly gave any of them away. How many gum balls does Polly have left? Step 1: How many gum balls did Polly give away? Step 2: How many gum balls does Polly have left?”

• Unit 6: Measurement, Lesson 6.10 and 6.11 engage students in extensive work with 2.MD.5 (Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units). Lesson 6.10, Instruction & guided practice, Exercise 1k, students solve word problems using length. “Judy planted a flower seed in her garden. In June, her flower grew 15 centimeters. In July, her flower grew 26 centimeters. How many centimeters did Judy’s flower grow in all? ___ + ___$$=$$___ centimeters.” Lesson 6.10, Instruction & guided practice, Exercise 1m, “Jada used 46 inches of string to make necklaces for friends. Sam used 78 inches of string to make necklaces. How much more string did Sam use than Jada? ___$$-$$ ___$$=$$___ inches.” Lesson 6.11, Independent Practice, Exercise 2j, students find the difference in the lengths of two objects. “Chris wants to ride his scooter 100 meters. He rides 62 meters. How many more meters does he have to ride? Draw a number line on paper. ___ meters.”

• Unit 9: Geometry, Lesson 9.1 and 9.2 engage students in extensive work with 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.) In Lesson 9.1, Instruction & Guided Practice, Exercise 1k, students identify the number of angles associated with a hexagon. Students see a hexagon. “You can describe a polygon by its number of corners, or angles. This shape has ___ angles.” In Lesson 9.2, Independent Practice, Exercise 2a, students identify the number of sides and angles a triangle has. “A triangle has ___ angles and ___ sides.”  

Materials do not give students opportunities to engage in extensive work of 2.MD.9. For example:

• Students have limited opportunities to engage in extensive work with 2.MD.9 (Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.) In Unit 8: Data, Lesson 8.5, students have opportunities to use measurements to create a line plot, but students do not have any opportunities to generate measurement data by measuring the length of several objects. All measurements are given in the problems. Unit 8: Data, Lesson 8.5, is the only lesson identified in the program to cover 2.MD.9.  Four problems are cited as examples for 2.MD.9, Exercise 1c, 1r, 1u, and 2j.

The materials reviewed for Snappet Math Grade 2 meet expectations that, when implemented as designed, most of the materials address the major clusters of each grade. The materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to the major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 9, approximately 67%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 88 out of 115, approximately 77%. 

• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 24 out of 35, approximately 69%.

A lesson-level analysis is most representative of the materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 77% of the materials focus on major work of the grade.

The materials reviewed for Snappet Math Grade 2 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed to connect supporting standards/clusters to the grade's major standards/ clusters. These connections are listed for teachers in the Course Overview/Pacing Guide and Teacher Guides within each unit. Examples of connections include:

• Unit 7: Time and Money, Lesson 7.4, Instruction & Guided Practice, Exercise 1g, students determine the time on an analog clock and use skip counting by 5’s to determine the time. Students see an analog clock set to 11:10, “What time is it?  It is ____.” This connects the supporting work of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) to the major work of 2.NBT.2 (Count within 1000; skip- count by 5s, 10s, and 100s.) 

• Unit 7: Time and Money, Lesson 7.7, Independent Practice, Exercise 2l, students calculate change when paying with coins. “The toy costs 85¢. You pay $1. Which is the correct change? Tap it.” Students chose images showing three-quarters, three nickels, or three dimes. This connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions).

• Unit 8: Data, Lesson 8.4, Instruction & Guided Practice, Exercise 1c, students use information from bar graphs to solve addition and subtraction problems. “Have students work in groups of two to create a graph on their desktops. Say: Take turns between who rolls the dot cube and who adds the counters. Ask the students to explain their reasoning as they answer each question. Student answers should show an understanding of how to read a bar graph and interpret the results. Ask one student to write a problem and have the other students answer it. Switch roles.” An additional teacher tip includes, “Ask all pairs the following questions: 1. Look at column B and column D. How many counters do you have all together? Which column has the greatest number of counter? 3. How much would you have if you added 2 to column A?” This connects the supporting work of 2.MD.10 (Draw a picture graph and a bar graph [with single-unit scale] to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph)to the major work of 2.OA.2 (Fluently add and subtract within 20 using mental strategies).

The materials reviewed for Snappet Math Grade 2 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. These connections are listed for teachers in the Course Overview/Pacing Guide and Teacher Guides within each unit. Examples include:

• Unit 2: Addition and Subtraction, Lesson 2.5, Instruction & Guided Practice, Exercise 1d, students add and subtract within 20 using tools based on place value. “These are ___ beads. How many beads do you take away to equal 10? ___. Start with 15 again. How many beads do you take away to have 4 beads left? ___. How is the place value chart represented in the abacus? [Sample answer: The top row is the tens place and the bottom row is the ones place.]” This activity connects the major work of 2.OA.B (Add and subtract within 20) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract),

• Unit 4: Solve Word Problems, Lesson 4.7, Independent Practice, Exercise 2e, students solve two-step word problems by adding and/or subtracting within 100. “Tina and Drew are playing with blocks. They have a total of 45 blocks. Tina has 25 blocks, and Drew has the rest of the blocks. Tina gives 6 of her blocks to Drew. How many blocks does Drew have now? You can act it out, if needed. ___ blocks.” This activity connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract).

• Unit 5: Add and Subtract Within 1,000, Lesson 5.16, Instruction & Guided Practice, Exercise 1i, students understand and use place value while adding and subtracting with properties of operations. “What is important to remember when adding all the numbers in the 100s place column? [It is important to remember to add the 1 from the 10s column if you are regrouping.] Add 342+267.”This activity connects the major work of 2.NBT.A (Understand place value) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract).

• Unit 9: Geometry, Performance task, Exercise 1c, students work with equal groups as they reason with shapes. “Design another quilt. 5. Draw lines to divide the quilt into 3 equal rows. What are 3 equal shares called? 6. Draw lines to divide the quilt into equal columns so that the rows and columns are same-size squares. How many squares are there? Show how you can use equal groups to find the total.” This activity connects the supporting work of 2.G.A (Reason with shapes and their attributes) to the supporting work 2.OA.C (Work with equal groups of objects to gain foundations for multiplication).

The materials reviewed for Snappet Math Grade 2 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Prior and Future connections are identified within the Pacing Guide and every Lesson Overview. Connections are further described within each Unit Overview embedded in the Learning Progression. 

Examples of connections to future grades include:

• Unit 4: Solve Word Problems, Lesson 4.9, Lesson Overview, “In this lesson, students will write a number sentence to model a one- or two- step word problem (2.NBT.B.5), solve a one- or two- step word problem (2.NBT.B.5). In future lessons, students will estimate to solve addition/subtraction word problems (4.OA.A.3) and solve word problems with fraction addition/subtraction (4.NF.B.3.D).”

• Unit 7 Overview: Time and Money, Learning Progression, “In this grade level, students will tell time to the nearest quarter hour and 5 minutes using digital and analog clocks. They will find the value of a collection of coins, calculate the change when paying with coins, find values greater than $1, and solve word problems involving money. In future grade levels, students will tell time to the nearest minute, convert between analog and digital time, and solve problems involving time (3.MD.A.1).” 

• Unit 9 Overview: Geometry, Learning Progression, “In this grade level, students will name, classify, and draw two-dimensional shapes. They will describe and draw cubes. They will determine the area of a shape using square units. They will divide a circle or strip into equal pieces and name each piece as a fraction. They will divide pizzas equally and write fractions to demonstrate the parts of a whole. In future grade levels, students will describe and classify quadrilaterals (3.G.A.1, 3.MD.C.5). They will find the area of rectangles and solve problems involving area (3.MD.C.7, 3.OA.A.3, 3.OA.B.5). They will use the area of rectangles to demonstrate the Distributive Property (3.MD.C.7.D). They will find the area of composite figures (3.MD.D.8). They will solve problems involving perimeter (3.G.A.1, 3.MD.D.8).” 

Examples of connections to prior knowledge include:

• Unit 2: Addition and Subtraction, Lesson 2.3 Lesson Overview, “In prior lessons, students have counted on to add and subtract numbers within 20 (1.OA.A.1); completed addition and subtraction fact families. (2.OA.B.2) In this lesson, students will use models and mental math to add doubles (2.OA.B.2).”

• Unit 7: Time and Money, Lesson 7.6, Lesson Overview, “In prior lessons, students have jumped by 10s forward and backward (1.NBT.C.5), skip counted by 5s. (2.NBT.A.2)  In this lesson, students will understand how to use the cents symbol (2.MD.C.8) find the value of several coins by identifying coins and their values (2.MD.C.8).” 

• Unit 9 Overview: Geometry, Learning Progression, “In prior grade levels, students determined the attributes of and named two-dimensional shapes including circles, triangles, and rectangles and three-dimensional shapes including pyramids, cones, and cubes (1.G.A.1). They composed and decomposed two- and three- dimensional shapes and made tessellations of two-dimensional shapes (1.G.A.2). They divided shapes into equal pieces, and partitioned shapes into halves and fourths (1.G.A.3). In this grade level, students will name, classify, and draw two-dimensional shapes. They will describe and draw cubes. They will determine the area of a shape using square units. They will divide a circle or strip into equal pieces and name each piece as a fraction. They will divide pizzas equally and write fractions to demonstrate the parts of a whole.”