3rd Grade - Gateway 1

The materials reviewed for Snappet Math Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. There are no grade-level assessment items for standard 3.G.2. 

The curriculum is divided into eight units with one assessment per unit, except for Units 2, 3, and 6. Unit 2 includes two Summative Assessments that assess Lessons 2.1 - 2.9 and Lessons 2.10 - 2.19. Unit 3 includes two Summative Assessments that assess Lessons 3.1 - 3.9 and Lessons 3.10 - 3.18. Unit 6 includes two Summative Assessments that assess Lessons 6.1 - 6.6 and Lessons 6.7 - 6.13. Assessments include Unit Summative Assessments and formative assessments. Examples include:

• Unit 1: Addition, Subtraction, and Patterns, Assessment: Lesson 1.1 - 1.8, Exercise 1a, students round numbers to the nearest hundred. “263 rounds to ____.” “Round to the nearest hundred.” (3.NBT.1)

• Unit 2: Multiplication, Assessment: Lessons 2.1 - 2.9, Exercise 3b, students complete a multiplication problem, using a picture of 3 groups of 3 buttons. “Complete the multiplication equation. 3 \times ___ = 9.” (3.OA.1)

• Unit 5: Fractions, Assessment: Lessons 5.1 - 5.9, Exercise 4a, students identify sixths on a number line. Students are given a number line from 0 to 1, partitioned into 6 equal parts and an arrow above the 5th line. “What fraction names the point where the arrow is located?” (3.NF.2)

• Unit 7: Data, Assessment: 7.1 - 7.7, Exercise 3a, students construct a scale bar graph. “Stan counted the balls in the gym. There are 3 beach balls, 9 tennis balls, 12 volleyballs, and 6 footballs. Use a scale of 3 to complete the graph.” (3.MD.3)

• Unit 8: Area, Perimeter, and Geometry, Assessment: 8.1 - 8.10, Exercise 1a, students sort shapes into different categories. “Sort the shapes.” (3.G.1)

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

• Unit 4: Solve Word Problems, Assessment: Lessons 4.1 - 4.8, Exercise 3a, students solve a comparison word problem. “There are 5 times as many chickens on the farm as roosters. There are 40 chickens. How many roosters are there? Complete the model and equation to solve. 5\times? = 40 ? = ___. So, there are ___ roosters on the farm.” This problem is aligned to 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.) This problem better aligns to 4.OA.1 (Interpret a multiplication equation as a comparison.)

• Unit 4: Solve Word Problems, Assessment: Lessons 4.1 - 4.8, Exercise 3b, solve a comparison word problem. “Ben has 10 pencils. Jenny has 5 times as many pencils as Ben. How many pencils does Jenny have? Enter the numbers. 5 times as many as 10 is ___ 5 \times10= ___ Jenny has ___ pencils.” This problem is aligned to 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.) This problem better aligns to 4.OA.1 (Interpret a multiplication equation as a comparison.)

• Unit 4: Solve Word Problems, Assessment: Lessons 4.1 - 4.8, Exercise 3c, students solve a word problem. “David bought 5 times as many stamps as Joe. Joe bought 8 stamps. How many stamps did David buy? David bought ___ stamps.” This problem aligns to 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.) This problem better aligns to 4.OA.1 (Interpret a multiplication equation as a comparison.)

• Unit 4: Solve Word Problems, Assessment: Lessons 4.1 - 4.8, Exercise 5c, students solve a comparison word problem. “Jimmy plays in a band that has 5 brass instruments. There are 3 times as many percussion instruments as brass instruments. Jimmy likes playing in the band. How many percussion instruments are there? Use the strip diagram to solve if needed. There are ___ percussion instruments.” This problem aligns to 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.) This problem better aligns to 4.OA.1 (Interpret a multiplication equation as a comparison.)

The materials reviewed for Snappet Math Grade 3 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 1: Addition, Subtraction, and Patterns, Lesson 1.6, Independent practice, Exercise 2h, engages students with the full intent of 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.) Students use strategies and the algorithm to solve a three-digit subtraction problem. “Line up the numbers by place value. Regroup to subtract. 803-523=___.”

• Unit 2: Multiplication, Lessons 2.1 and Lesson 2.4 engage students with the full intent of 3.OA.1 (Interpret products of whole numbers, e.g., interpret 5\times7 as the total number of objects in 5 groups of 7 objects each.) In Lesson 2.1, Independent Practice, Exercise 2b, “Where do you see 4 times 3?” In Lesson 2.4, Instruction & guided practice, Exercise 1b, “Drag and show 3 times 5.” Students select the image that shows the total number of objects. In Lesson 2.1, Instruction & Guided Practice, Exercise 1n, students interpret products of the same whole. A picture of five groups of three balloons is shown. “How can you represent the balloons?” ___ times a group of ___ = 15.” 

• Unit 5: Fractions, Lesson 5.5 engages students with the full intent of 3.NF.3a (Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.) Instruction & guided practice, Exercise 1i, students determine if two fractions are equivalent using number lines. “Tap on the number lines that show equivalent fractions.” Independent practice, Exercise 2a, “Tap on the shapes that show equivalent fractions. Is the same amount of circle shaded in all circles? How can you tell which circles show equivalent fractions?” Independent practice, Exercise 2e, “Do the points show equivalent fractions? Yes. They are equivalent; No. The points are at different distances; No. Fourths and sixths cannot be equivalent.” Two number lines are provided for students. One number line counts by \frac{1}{4}’s and the other number line counts by \frac{1}{6}’s. 

• Unit 7: Data, Lesson 7.3, Lesson 7.5, and Lesson 7.6 engage students with the full intent of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.) In Lesson 7.3, Instruction & Guided Practice, Exercise 1i, students draw picture graphs. “There are 3 circles, 12 squares, 6 triangles, and 9 crosses in the game. Drag shapes to complete the graph. Use a scale of 3. How many squares did you use? ___ squares.” In Lesson 7.5, Independent Practice, Exercise 2k, students use data from scaled bar graphs to answer one-step problems. “Make a bar graph. Use it to answer the question. How many more visitors were at the museum on Friday than on Wednesday?” Students choose from “20, 60, 80,” In Lesson 7.6, Instruction & guided practice, Exercise 1l, students use data from scaled bar graphs to answer two-step problems. “How many more hours of practice were done on Wednesday and Thursday compared to Tuesday?” Students choose from “40, 60, 120,160.”

• Unit 8: Area, perimeter, and geometry, Lesson 8.1, Exercise 1o and Exercise 2l, engage students with the full intent of 3.G.1 (Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.) In Exercise 1o, students draw a quadrilateral that follows the given guidelines. “Draw a shape with four straight sides.  That is not a rhombus. Did you draw a square, rectangle, or other quadrilateral?” In 2l, students identify which shapes are quadrilaterals. A variety of shapes are shown. “Tap all the quadrilaterals. Ask: What do all quadrilaterals have? [4 sides.]”

The materials present opportunities for students to engage with extensive work with grade-level problems, except for 3.G.1 and 3.G.2. Examples of extensive work include:

• Unit 3: Division, Lessons 3.6 and 3.8 engage students in extensive work with 3.OA.4 (Determine the unknown whole number in a multiplication or division equation relating three whole numbers.) In Lesson 3.6, Independent Practice, Exercise 2c, students relate division to multiplication. “25 flowers divided among 5 vases. How many flowers are in each vase? 25\div5=___ because 5\times___ flowers is 25 flowers.” In Lesson 3.8, Instruction & Guided Practice, Exercise 1n, students find the unknown in a multiplication problem. “What is the missing value? 7\times ___$$=56$$”. Lesson 3.8, Independent practice, Exercise 2n, “___ \times8=48.” 

• Unit 5: Fractions, Lessons 5.1 and Lesson 5.2 engage students in extensive work with 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size \frac{1}{b}.) Lesson 5.1, Independent & guided practice, Exercise 1p, students understand the concept of a unit fraction as they begin to write unit fractions through one eighth. A pie circle partitioned into 4 equal parts is shown. “There are ___ equal parts. Each part is \frac{}{}.” In Lesson 5.1, Independent practice, Exercise 2i, “Represent the fraction$$\frac{1}{8}$$.” In Lesson 5.2, Instruction & guided practice, Exercise 1a, “Divide 1 pizza into 3 equal parts. Each part is \frac{1}{}.”

• Unit 8: Area, Perimeter, and Geometry, Lesson 8.5 engage students in extensive work with 3.MD.7b (Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.) Lesson 8.5, Instruction & guided practice, Exercise 1k, students solve problems that involve finding the area of rectangles.“Bo’s room is in the shape of a rectangle. The length of the room is 10m, and the width of the room is 9m. What is the area of the room? Step 1: Draw a rectangle to model the problem. Step 2: Multiply to find the area. 10\times ___$$=$$___ The room is ___ square ___.”  Lesson 8.5, Independent practice, Exercise 2g, “Nancy has a frame in the shape of a rectangle. The frame is 6 in. long and 8 in. wide. What is the area of the frame? The area of the frame is ___ square in.” Lesson 8.5, Independent practice 2i, “Marcus painted a rectangle with an area of 36 square ft. The width of the rectangle is 6 ft. How long is the rectangle? The rectangle is ___ ___ long.”

Materials do not present all students with extensive work of 3.G.1 and 3.G.2. Examples include:

• Students do not have the opportunity to engage in extensive work of 3.G.1 (Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides) and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.) Unit 8: Area, Perimeter, and Geometry, Lesson 8.1, Independent practice, Exercise 2j, students draw and identify quadrilaterals. “Draw a shape with two longer sides and two shorter sides. What shape did you draw?” Lesson 8.1 is the only lesson the program identifies as addressing 3.G.1.

• Students have limited opportunities to engage in extensive work with 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.) Unit 5: Fractions, Lesson 5.1, Instruction & guided practice, Exercise 1i, students partition a circle. “How do you share this pizza equally? Draw a circle and a way to divide it.” Lesson 8.2 is the only lesson the program identifies as addressing 3.G.2.

The materials reviewed for Snappet Math Grade 3 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 6.5 out of 8, approximately 81%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 86 out of 106, approximately 81%. 

• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 28 out of 35, approximately 80%.

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 81% of the materials focus on major work of the grade.

The materials reviewed for Snappet Math Grade 3 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 5: Fractions, Lesson 5.1, Independent Practice, Exercise 2k, students understand fractions as they partition a circle into equal parts. “Represent the fraction \frac{1}{6}.” This connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole) to the major work of 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction \frac{a}{b} as the quantity formed by a parts of size \frac{1}{b}.)

• Unit 7: Data, Lesson 7.6, Instruction & Guided Practice, Exercise 1l, students solve a two-step word problem using information presented from a scaled bar graph. “How many more hours of practice were done on Wednesday and Thursday compared to Tuesday?” Answer choices include, “40, 60, 120, 160.” This connects the supporting work of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs) to the major work of 3.OA.8 (Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding).

• Unit 7: Data, Lesson 7.7, Independent Practice, Exercise 2d, students represent data on a line plot. “Use the data to create a line plot. 4\frac{1}{2}, 5\frac{1}{2}, 6\frac{1}{2}, 6, 4, 4, 6\frac{1}{2}, 4\frac{1}{2}, 4, 4\frac{1}{2}”. This connects the supporting work of 3.MD.4 (Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters) to the major work of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram).

The materials reviewed for Snappet Math Grade 3 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 3: Division, Lesson 3.8, Instruction & Guided Practice, Exercise 1b, students solve a division problem by modeling and solving it as a multiplication problem. “Do you remember? 32\div4=…$$4\times$$___$$=32$$ 32\div4=___.” This activity connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division).

• Unit 4: Solve Word Problems, Lesson 4.2, Independent Practice, Exercise 2n, students solve a one-step word problem within 100 using multiplication. “Jolene handed out pencils to 7 children. Each child received 4 pencils. How many pencils did Jolene hand out? Jolene handed out ___ pencils.” This activity connects the major work of 3.OA.C (Multiply and divide within 100) to the major work of 3.OA.A (Represent and solve problems involving multiplication and division).

• Unit 8: Area, Perimeter, and Geometry, Lesson 8.2, Instruction & Guided Practice, Exercise 1a, students find geometric measurements by reasoning with shapes and their attributes. “Provide students with enough paper squares to cover the top of their desks. Demonstrate how to cover a region with paper squares without gaps or overlaps. How many paper squares or sheets of printer paper do you need to cover your desk? Try it out.” This activity connects the supporting work of 3.MD.D (Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures) to the supporting work of 3.G.A (Reason with shapes and their attributes).

• Unit 8: Area, Perimeter, and Geometry, Lesson 8.5, Independent Practice, Exercise 2j, students solve missing side area problems. “The top of a box in the shape of a rectangle has an area of 80 square cm. The box is 8 cm long. How wide is the box? The box is ___ ___ wide.” This activity connects the major work of 3.MD.C (Geometric measurement: understand concepts of area and relate area to multiplication and to addition) and the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division). 

Connections entirely absent from the materials:

• No connections are made between the major work of 3.NF.A (Develop an understanding of fractions as numbers) and the major work of 3.MD.A (Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects) as students have no opportunities to use fractions as they solve measurement problems.

The materials reviewed for Snappet Math Grade 3 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 4.6, Lesson Overview, “In this lesson, students will solve a problem in two steps by acting it out. (3.OA.D.8), explain their process and reasoning as they act out the word problems. (3.OA.D.8) students will solve more complex multi-step word problems in future lessons. (4.OA.A.3) solve word problems involving money (4.MD.A.2).”

• Unit 5 Overview: Fractions, Learning Progression, “In this grade level, students will recognize unit fractions and other fractions as one part of a whole, partitioned into equal parts. They will express the area of each part of a whole as a unit fraction or other fraction. They will represent unit fractions and other fractions on a number line. They will also generate equivalent fractions and use them to compare fractions with models and symbols, determining which is least and which is greatest. They will write mixed numbers as whole numbers combined with fractions, recognizing how many equivalent parts are needed for 1 whole. In future grade levels, students add and subtract fractions with like and different denominators (4.NF.B, 4.NF.C, 5.NF.A). They will multiply and divide fractions (5.NF.B). They will make line plots with fractional units (5.MD.B.2).” 

• Unit 8 Overview, Learning Progression, “In this grade level, students will describe and classify quadrilaterals. They will recognize area and perimeter as attributes of plane figures and understand concepts of these measurements. They will measure areas by counting unit squares and relate area to the operations of multiplication and addition. They will use the Distributive Property to find the area of composite figures. They will also solve problems involving perimeters, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. In future grade levels, students will apply the area and perimeter formulas for rectangles in real-world and mathematical problems (4.MD.A.3). They will represent and use the associative property of multiplication and apply the formulas V=l\timesw\timesh and V=b\timesh for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems (5.MD.C.5).” 

Examples of connections to prior knowledge include:

• Unit 1 Overview: Addition and Subtraction, Learning Progression, “​​In prior grade levels, students modeled and wrote two- and three-digit numbers in expanded form (2.NBT.A.3). They also used the number line, a column format, and regrouping to add and subtract numbers within 1,000 (2.NBT.B.7, 2.NBT.B.5, 2.OA.B.2). In this grade level, students will read and write three-digit numbers using the place value of each digit. They will use pictorial representations, the hundreds, tens, ones chart, and expanded form to calculate the sum or difference of three-digit numbers and to solve addition and subtraction problems. Estimation and place value work together along with regrouping to recognize and determine patterns. Later in this grade, these patterns will help with multiplication and division fluency.” 

• Unit 2: Multiplication, Lesson 2.11, Lesson Overview, “In prior lessons, students have learned skip counting. (K.CC.A.2) learned to use strategies such as making ten, counting on, and making equivalent but easier known sums. (1.OA.C.6) In this lesson, students will learn strategies to multiply by 3. (3.OA.C.7) interpret products of whole numbers (3.OA.A.1).”

• Unit 8: Area, Perimeter, and Geometry, Lesson 8.10, Lesson Overview, “In prior lessons, students have solved two-step problems by using a model or diagram (2.OA.A.1) solved word problems involving length. (2.MD.B.5) In this lesson, students will find unknown side lengths (3.MD.D.8), find the perimeter of composite figures and 2-dimensional figures, including triangles (3.MD.D.8).”