4th Grade - Gateway 1

The materials reviewed for Snappet Math Grade 4 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The curriculum is divided into eight units with one assessment per unit, with the exception of Units 1, 2, 4, 5, and 6. Unit 1 includes two Summative Assessments that assess Lessons 1.1 - 1.7 and Lessons 1.8 - 1.15. Unit 2 includes two Summative Assessments that assess Lessons 2.1 - 2.10 and Lessons 2.11 - 2.20. Unit 4 includes two Summative Assessments that assess Lessons 4.1 - 4.8 and Lessons 4.9 - 4.16. Unit 5 includes two Summative Assessments that assess Lessons 5.1 - 5.5 and Lessons 5.6 - 5.12. Unit 6 includes two Summative Assessments that assess Lessons 6.1 - 6.7 and Lessons 6.8 - 6.14. Assessments include Unit Summative Assessments and formative assessments. Examples include:

• Unit 1: Numbers, Assessment: Lessons 1.8 - 1.15, Exercise 4a, students sort whole numbers as prime or composite. “Sort the numbers. 3, 4, 5, 12, 19.” (4.OA.4)

• Unit 2: Operations with Whole Numbers, Assessment: Lessons 2.1 - 2.10, Exercise 1c, students use the standard algorithm to add multi-digit whole numbers. “In Minnesota, 64,374 people had a leg injury. In Texas, 537,826 people had a leg injury. How many people had a leg injury in both states? ___ people.” (4.NBT.4)

• Unit 4: Operations with Fractions, Assessment: Lessons 4.1 - 4.8, Exercise 7c, students use properties of operations to add fractions. “Use the Commutative and Associative Properties to find the sum 9\frac{2}{8}+2\frac{5}{8}+1\frac{1}{8}. ” (4.NF.3)

• Unit 7: Geometry, Assessment: 7.1 - 7.7, Exercise 1a, students classify shapes by properties of their lines.“How many line segments are in this shape?” Students choose from, “3, 4, 5, 6.” (4.G.1)

• Unit 8: Geometric Measurement, Assessment: 8.1 - 8.6, Exercise 1a, students find the measure of an angle using a circle. “The angle measurement of the five colored parts in all is ___°.” (4.MD.5)

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

• Unit 2: Operations with Whole Numbers, Assessment: Lessons 2.1 - 2.10, Exercise 3b, students multiply to compare answers. “Which product is the greatest?” Students select from  the answer choices, “$$28\times422$$, 91\times97, 52\times293” This problem is aligned to 4.NBT.5(Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.) This problem better aligns to 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm.)

The materials reviewed for Snappet Math Grade 4 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 4: Operations with Fractions, Lessons 4.6 and 4.9, and Unit 5: Solve Word Problems, Lesson 5.10 engage students with the full intent of 4.NF.3c (Add and subtract mixed numbers with like denominators…) In Lesson 4.6, Instruction & guided practice, Exercise 2g, students add mixed numbers with common denominators. “$$3\frac{1}{5}+1\frac{2}{5}=$$___.” In Lesson 4.9, Independent practice, Exercise 2i, students subtract mixed numbers with common denominators. “$$4\frac{6}{10}=1\frac{7}{10}-$$___.” In Unit 5: Solve Word Problems, Lesson 5.10, Instruction & guided practice, Exercise 1i, students add two mixed numbers within a word problem context. “A bread recipe calls for 2\frac{1}{8} cups of white flour and 1\frac{3}{8} cups of whole wheat flour. How many cups of flour are needed altogether? If possible, simplify. 2\frac{1}{8}+1\frac{3}{8}=___.” 

• Unit 5: Solve word problems, Lesson 5.4, engages students in the full intent of 4.OA.3 (Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.)  In Exercise 1h, students use mental math to check the solution to a multistep problem, “Grace makes 5 pies. She divides the pies in 8 pieces. She gets 39 guests on her birthday. Grace thinks she has enough cake. Check with mental math of this can be correct.” In Exercise 2a, students independently use mental math to check the solution, “Maison buys 5 sweaters for 19 euros and 3 trousers for 45 euros. Maison has 200 euros.  He thinks he has enough money to buy everything. Check with mental math if Maison is correct. Maison is ___, because:___.”

• Unit 6: Measurement and data, Lesson 6.14 engages students with the full intent of 4.MD.4 (Make a line plot to display a data set of measurements in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}$$). Solve problems involving addition and subtraction of fractions by using information presented in line plots.) In Exercise 1n, students use the data provided in the line plot to solve an addition of fractions problem.  “Andrew has different lengths of rope.  If he puts all the pieces of \frac{4}{5} in a row, what would the total length be?”  In Exercise 2i, students independently use the data from a line plot to solve a fraction problem.  “What is the total length of the two \frac{6}{8} pencils?”

• Unit 7: Geometry, Lesson 7.7 engage students with the full intent of 4.G.3 (Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.) Instruction & guided practice, Exercise 1g, students draw and determine the number of lines of symmetry in different figures. “Use a ruler to draw one or more lines of symmetry. The butterfly has ___ lines of symmetry.” Independent practice, Exercise 2a, students determine the correct line of symmetry. “Tap on the line of symmetry.” Independent practice, Exercise 2h, students determine the number of lines of symmetry. “A. This letter has ___ line(s) of symmetry.”

• Unit 8: Geometric Measurement, Lessons 8.2 and 8.3 engage students with the full intent of 4.MD.6 (Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.) In Lesson 8.2, Instruction & Guided Practice, Exercise 1i, students use a protractor to measure and draw angles. “What is the measure of the angle?” Independent practice, Exercise 2b, students use a protractor to measure an obtuse angle. “What is the measure of this angle? 40\degree, 50\degree, 130\degree, 140\degree” In Lesson 8.3, Instruction & guided practice, Exercise 1n, students draw an angle with an exact measurement with a protractor. “Draw a 165\degree angle with your protractor. Label the vertex with the letter D.”

The materials present all students opportunities with extensive work with grade-level problems within a consistent daily lesson structure, including Instruction & guided practice, and Independent practice. Examples of extensive work include:

• Unit 2: Operations with Whole Numbers, Lessons 2.16, 2.17, and 2.18 engage students in extensive work with 4.NBT.6 (Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.) In Lesson 2.16, Instruction & guided practice, Exercise 1m, students divide using the standard algorithm. “Use the diagram or paper and pencil. 822\div6=___.” In Lesson 2.17, Independent practice, Exercise 2i, “Use an area model or partial quotients to solve. 2,024\div8=___.” In Lesson 2.19, Independent practice, Exercise 2g, students solve “Seventeen darts sit on the table. They are divided into sets of 3. How many full sets are there? How many remain? ___ whole sets ___darts.”

• Unit 3: Fractions, Lesson 3.5 engages students in extensive work with 4.NF.3b (Decompose a fraction into a sum of fractions with the same denominator in multiple ways). Instruction & guided practice, Exercise 1d, students draw to show another decomposition of a sum of fractions. “Ethan is making pizza. On each piece, he uses tomato, cheese, and one extra topping: pepperoni, onions, or mushrooms. He can do it this way: \frac{2}{8} pepperoni + \frac{3}{8} onion + \frac{3}{8} mushroom. Think of another way. Draw to show.” Independent practice, Exercise 2c, “Show two ways you could find the sum. \frac{7}{10}=__$$\frac{}{}$$__$$+$$__$$\frac{}{}$$__$$+$$__$$\frac{}{}$$__ or \frac{7}{10}= $$\frac{}{}$$$$+$$__$$\frac{}{}$$__$$+$$__$$\frac{}{}$$__” Independent practice, Exercise 2h, “Tap on the two addition problems that have the same sum.” Students choose from “$$\frac{3}{5}+\frac{1}{5}+\frac{1}{5}$$, \frac{2}{5}+\frac{3}{5}, \frac{2}{5}+\frac{2}{5}+\frac{3}{5}, \frac{3}{5}+\frac{2}{5}+\frac{1}{5}”. 

• Unit 5: Solve Word Problems, Lesson 5.1 engages students in extensive work with 4.OA.1 (Interpret a multiplication equation as a comparison, e.g., interpret 35=5\times7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.) Instruction & guided practice, Exercise 1f, “$$4\times8=12$$, Write a comparison sentence that represents the equation. 4 times as ____ as ____ is 32.” Independent practice, Exercise 2j, “Farmer Harry has 4 times as many pigs as chickens. He has 9 chickens on the farm. How many pigs does he have? Farmer Harry has ___ pigs.” Independent practice, Exercise 2g, “42 is 6 times as many as 7, Write an equation that represents the comparison sentence.  ____$$=6\times$$ ____.” 

• Unit 7: Geometry, Lesson 7.1 and Lesson 7.4, engages students in extensive work with 4.G.1 (Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.) in Lesson 7.1, Independent practice, Exercise 2i, students identify the number of lines, lines segments and points associated with a shape. “This shape has ___ line segment(s), ___ lines, and ___ points where lines meet.” In Lesson 7.4, Independent practice, Exercise 2f, students identify a pair of parallel lines.  Students see 5 lines intersecting each other.  “Which line is parallel to line b?”

The materials reviewed for Snappet Math Grade 4 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 8, approximately 75%.

• 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 111, approximately 77%. 

• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 26 out of 35, approximately 74%.

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 4 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 6: Measurement and Data, Lesson 6.9, Independent Practice, Exercise 2j, students solve a multi-step word problem involving measurement. “An 8 foot shelf is full of boxes. If each box is 8 in. long, how many boxes fill the shelf? ___ boxes.” This connects the supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit) to the major work of 4.OA.3 (Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted).

• Unit 6: Measurement and Data, Lesson 6.10, Independent Practice, Exercise 2j, students solve a multi-step word problem involving time. “It takes 1 hour and 5 minutes to get ready. It takes 18 minutes to walk to the bus stop. What is the latest I can wake up? I should wake up by ___ AM. Draw your jumps on paper, if needed.” An image of a clock shows 8:25 AM and arrival time 9:05 AM. This connects the supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit) to the major work of 4.OA.3 (Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations…).

• Unit 8: Geometric Measurement, Lesson 8.6, Instruction & Guided Practice, Exercise 1f, students solve a multi-stop work problem using their knowledge of shapes. Students see a pizza with two portions of the pizza eaten. “There are ___° in a whole pizza. What is the angle measure of the share that was eaten? ___° + ___°=___° of the pizza was eaten.” This connects the supporting work of 4.MD.7 (Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.) to the major work of 4.OA.3 (Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding.)  

Connections between supporting work and major work of the grade that are entirely absent from materials:

• No connections are made between the supporting work of 4.MD.4 (Make a line plot to display a data set of measurements in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots) to the major work of 4.NF.3 (Understand a fraction \frac{a}{b} with a>1 as a sum of fractions \frac{1}{b}.) In the lesson related to line plots, students do not have the opportunity to “solve problems involving addition and subtraction of fractions by using information presented in line plots.”

The materials reviewed for Snappet Math Grade 4 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: Operations with Whole Numbers, Lesson 2.3, Independent Practice, Exercise 2a, students apply place value understanding to estimate products of multi-digit whole numbers, “$$8\times192=$$, 800, 1,000, 1,600, 1,800.” This activity connects the major work of 4.NBT.A (Generalize place value understanding for multi-digit whole numbers) with the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic).

• Unit 2: Operations with Whole Numbers, Lesson 2.7, Independent Practice, Exercise 2j, students solve word problems involving multi-digit multiplication. “Jep’s sister is renting a room for 7 months. The rent is $376 per month. How much is the rent in total? Multiply numerically $$7\times376=$$ $___.” This activity connects the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit multiplication) to the major work of 4.OA.A (Use the four operations with whole numbers to solve problems).

• Unit 4: Operations with Fractions, Lesson 4.3, Instruction & Guided Practice, Exercise 1f, students solve a fraction addition problem and use their understanding of fraction equivalence to simplify the answer. “ \frac{2}{6}+\frac{1}{6}=___$$=$$___.” This activity connects the major work of 4.NF.A (Extend understanding of fraction equivalence and ordering) to the major work of 4.NF.B (Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers).

• Unit 8: Geometric Measurement, Lesson 8.1, Instruction & Guided Practice, Exercise 1c, students use geometric measurement to work with the concept of angles in circles. “How many angles are in each circle? In pairs, students use fraction circles to explore how angles are formed by two rays intersecting at the center of a circle. Find one third. Trace the angle with our finger. How can you describe the angle? (Obtuse.) How many fraction pieces make a whole circle? How many angles is that? Repeat with fourths and eighths. What happens to the size of each angle as you break the circle into more equal pieces?” This activity connects the supporting work of 4.MD.C (Geometric measurement: understand concepts of angle and measure angles) to the supporting work of 4.G.A (Draw and identify lines and angles, and classify shapes by properties of their lines and angles).

The materials reviewed for Snappet Math Grade 4 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 5: Solve Word Problems, Lesson 5.11, Lesson Overview, “In this lesson, students will solve word problems by multiplying a fraction by a whole number. (4.NF.B.4.C) In future lessons, students will multiply a whole number by a fraction. (5.NF.B.4.A) use the area model for fraction multiplication (5.NF.B.4.B).”

• Unit 6 Overview: Measurement and Data, Learning Progression, “In this grade level, students will choose an appropriate unit of measurement and convert between units of length, weight, time, and capacity. They will compare and order weights. They will also solve problems involving the perimeter and area of rectangles. They will solve problems involving time, liquid, volume, mass, distance, and money. They will also make and solve problems using the information in line plots. In future grade levels, students will continue to work with measurement, converting metric units of length, weight, and capacity (5.MD.A.1). They will measure volume by counting cubic units (5.MD.C.4). They will calculate the volume of right rectangular prisms and of composite figures (5.MD.C.5).” 

• Unit 7 Overview: Geometry, Learning Progression, “In this grade level, students will learn about the similarities and differences between points, lines, line segments, and rays. They will determine if lines are perpendicular, parallel, or neither and then use this information to classify figures. They will also learn to recognize the different types of angles - acute, right, and obtuse, and then classify figures based on the types of angles it possesses. They will identify if a figure has one or more line(s) of symmetry (reflection), and then draw a reflected figure. In future grade levels, students will understand the coordinate system and plot ordered pairs (5.G.1). They will represent and solve problems by plotting points (5.G.2). They will also graph ordered pairs from patterns (5.OA.3).” 

Examples of connections to prior knowledge include:

• Unit 1: Numbers, Lesson 1.15, Lesson Overview, “In prior lessons, students have recognized and determined patterns. (3.OA.D.8) In this lesson, students will analyze number patterns (4.OA.C.5).”

• Unit 3 Overview: Fractions, Learning Progression, “In prior grade levels, students learned about unit fractions (3.NF.A.1). They represented fractions on a number line (3.NF.A.2). They also worked with equivalent fractions, renaming them and comparing them using models or symbols (3.NF.A.3). In this grade level, students will recognize and generate equivalent fractions. They will compare fractions using benchmarks, including those with different denominators. They will also decompose fractions into the sum of multiple fractions.” 

• Unit 8: Geometric Measurement, Lesson 8.6, Lesson Overview, “In prior lessons, students have solved one-step measurement problems. (3.MD.A.2), draw a diagram to solve problems. (3.MD.A.2) In this lesson, students will recognize angle measures as additive and apply this knowledge to solve problems. (4.MD.C.7) compose and decompose angles to find unknown angles using the known angle measurements of 90, 180, and 360 degrees (4.MD.C.7).”