5th Grade - Gateway 1

The materials reviewed for Snappet Math Grade 5 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, and 3. Unit 1 includes two Summative Assessments that assess Lessons 1.1 - 1.7 and Lessons 1.8 - 1.16. Unit 2 includes two Summative Assessments that assess Lessons 2.1 - 2.6 and Lessons 2.7 - 2.13. Unit 3 includes two Summative Assessments that assess Lessons 3.1 - 3.7 and Lessons 3.8 - 3.15. Assessments include Unit Summative Assessments and formative assessments. Examples include:

• Unit 3: Operations with Decimals, Assessment: Lessons 3.1 - 3.7, Exercise 2c, students subtract decimals to hundredths using money. “Enter the number. $$ 11.35 - 7.70 = $___.” (5.NBT.7)

• Unit 5: Fractions - Multiply and Divide, Assessment: Lessons 5.1 - 5.10, Exercise 7c, students multiply fractions to solve a word problem. “Brandon opened a bag of carrots. There was \frac{3}{4} of the bag left. Brandon ate \frac{3}{5} of the remaining carrots. How much of the carrots did Brandon eat? \frac{3}{4}\times\frac{3}{5}= —-.” (5.NF.6)

• Unit 6: Expressions and Patterns, Assessment: 6.1 - 6.7, Exercise 2a, students interpret a numerical expression. “Enter the number: [(54-6)\div16]+9=\box.(5.OA.1)

• Unit 7: Measurement and Geometry, Assessment: 7.1 - 7.10, Exercise 6c, students determine the volume of a pool. “A pool is in the shape of a rectangular prism. The base area of the pool is 40 m^2. The pool is 3m deep. How much water can the pool hold? ___$$m^3$$ of water.” (5.MD.4)

• Unit 7: Measurement and Geometry, Assessment: 7.1 - 7.10, Exercise 10c, students use knowledge of triangle properties to solve a problem. “Is the statement always true, sometimes true, or never true? An isosceles triangle is an equilateral triangle.” Students click to choose from the following, “always true”, “sometimes true”, and “never true”.” (5.G.3)

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 2.7 - 2.13, Exercise 7a, students solve a division problem, “$$11,446\div118$$. This problem is aligned to 5.NBT.6 (Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.) This problem better aligns to 6.NS.2 (Fluently divide multi-digit numbers using the standard algorithm.)

The materials reviewed for Snappet Math Grade 5 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: Numbers, Lessons 1.2, 1.3 and 1.16, engage students with the full intent of 5.NBT.2 (Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.Use whole-number exponents to denote powers of 10.) In Lesson 1.2, Instructional & guided practice, Exercise 1q, students focus on the pattern for the number of zeros in the product when multiplying by powers of 10. “Multiplying By large(r) numbers, We will multiply by 10, 100, and 1000. 4\times10=40, 4\times1=400, 4\times1,000=4,000. Multiplying by 10 inserts 1 zero. Multiplying by 100 inserts 2 zeros. Multiplying by 1,000 inserts 3 zeros.” In Lesson 1.3, Instructional & Guided Practice, Exercise 1j, students use a similar strategy when dividing by powers of zero. “$$620\div10=$$___, Teacher Tip: For struggling students, write a division problem such as 48\div10 on the board. Then take your hands and cover both zeros. Ask: How can you solve the division problem you see now? [A number by 1 is itself.] Tell them that 49\div1 is equivalent to 490\div10 because a zero has been removed from each number.” In Lesson 1.16, Instructional & guided practice, Exercise 1i, students drag ×10 over to an equation to show the multiplication equation for an exponent.  “How can you write ten to the fifth power as a multiplication of tens? 10⁵” 

• Unit 6: Expressions and Patterns, Lesson 6.2 and 6.3 engage students with the full intent of 5.OA.1 (Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.) Lesson 6.2, Independent practice, Exercise 2h, students simplify expressions. “$$3\times(63\div9)+5=$$___.” Lesson 6.2, Independent Practice, Exercise 2d, students solve a multi-step equation. “$$9+[3\div(7-4)]=$$___.” Lesson 6.3, Instruction & Guided Practice, Exercise 1j, students solve a multi-step equation. “$$16\times(\frac{1}{4}\times3)=$$ ___.”

• Unit 7: Measurement and Geometry, Lesson 7.8 engages students with the full intent of 5.G.3  (Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles). Independent practice, Exercise 2g, students complete a hierarchy diagram for polygons using their understanding of the rules for polygons. Students see a diagram with three blanks. At the bottom, students see the three terms missing from the diagram: Quadrilaterals, Parallelograms, and Squares. “Drag the names to the diagram to show how a square can be classified.”

• Unit 8: Line Plots and the Coordinate System, Lesson 8.1 and Lesson 8.2 engage students with the full intent of 5.MD.2 (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}). Use operations on fractions for this grade to solve problems involving information presented in line plots.) Lesson 8.1, Instruction and guided practice, Exercise 1n, students create a line plot with the following numbers: “$$5$$, 5, 5, 5\frac{1}{2}, 5\frac{1}{2}, 5\frac{1}{2}, 5\frac{1}{2}, 5\frac{1}{2}, 6, 6, 6\frac{1}{2}, 6\frac{1}{2}, 6\frac{1}{2}, 7, 7. Make a line plot of the data using the X.” Lesson 8.2, Independent practice, Exercise 2g, students use a line plot to solve a word problem. “The line plot shows Cam’s measuring cups. Cam needs three times the amount of flour that the largest cup holds. How much flour does Cam need?” Students select from the choices “$$\frac{9}{4}$$,$$\frac{6}{4}$$, \frac{3}{2}.” Lesson 8.2, Independent practice, Exercise 2j, students use the information from a line plot to find the length of a yarn. “The \frac{1}{2} yard pieces are joined and then cut into 8 equal pieces. What is the length of each piece?” Students select from the choices “$$\frac{1}{8}$$, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}”.

The materials present opportunities for students to engage with extensive work with grade-level problems. Examples of extensive work include:

• Unit 2: Operations with Whole Numbers, Lessons 2.4 and 2.5 engage students in extensive work with 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm.) Unit 2: Operations with Whole Numbers, Lesson 2.4, Instruction & guided practice, Exercise 1h, students solve 542\times12 using the standard algorithm. “$$12\times542=$$___.” Lesson 2.4, Independent practice, Exercise 2h, “$$65\times517$$”. Lesson 2.5, Instruction & guided practice, Exercise 1h, students estimate a product. “Step 1: Round to the nearest leftmost place value. 315≈___ 67≈___ Step 2: Estimate the product. So 315\times67≈___  .” 

• Unit 5: Fractions: Multiply and Divide, Lessons 5.6 and 5.7 engages students in extensive work with 5.NF.6 (Solve real-world problems involving multiplication of fractions and mixed numbers.) Lesson 5.6, Independent practice, Exercise 2h, “$$2\frac{1}{3}\times4\frac{1}{3}=$$___.” Teacher tip, “Have students write a word problem that involves the product of the mixed numbers given in the multiplication problem. Students can then share their problem with a partner, who should answer it using a complete sentence.” Lesson 5.7, Instruction & guided practice, Exercise 1j, students solve a word problem involving fractions. “Liam has \fracc{4}{5} of a fruit tart. He eats \frac{1}{4} part of that. How much does he eat? \frac{1}{4}\times\frac{4}{5}=___.” Lesson 5.7, Independent practice, Exercise 2g, students solve a word problem with fractions. “Sofia opened a pizza box. Inside, there was \frac{1}{4} of a pizza. Sofia ate \frac{3}{5} of the remaining pizza. How much of the pizza did Sofia eat? ___ \times ___$$=$$___” Lesson 5.7, Independent practice, Exercise 2i, students solve a word problem. “Faleesa opened a bag of carrots. There was \frac{3}{8} of the bag left. Faleesa ate \fracc{2}{4} of the remaining carrots. How much carrots did Faleesa eat? \frac{3}{8}\times\frac{2}{4}=___.” 

• Unit 6: Expressions and Patterns, Lesson 6.2, engages students in extensive work with 5.OA.1 (Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.) In Instruction & guided practice, Exercise 1m, students order of operation rules to solve a multi-step problem.  “(7+5)÷6+9=___” In Independent practice, Exercise 2j, students use order of operation rules to determine if both sides of an equation are equal.  “Simplify each side to determine if the equation is true.  (10÷ 5+8)× 6 = (10 ÷ 5) + 8 × 6.  The equation is ___ true.”

• Unit 7: Measurement and Geometry, Lesson 7.4, engages students in extensive work with 5.MD.4 (Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.) In Instruction & guided practice, Exercise 1i, students determine the volume of a rectangular prism.  Students see a prism with unit cubes with dimensions 1 by 5 by 3.  “Each cube is 1cm³. What is the volume of the box? Imagine packing the rest of the box with cubes. Use your own cubes to help you. The volume of the box is ___ cm³.”  In Independent Practice, Exercise 2h, students determine the volume of a rectangular prism with dimensions 2 by 2 by 6.  “Each cube is 1 in.³. What is the volume of the figure? ___ in.³”

• Unit 8: Line Plots and the Coordinate System, Lesson 8.4 and 8.5 engage students in extensive work with 5.G.2 (Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.) Lesson 8.4, Instruction & guided practice, Exercise 1j, students solve a real-world problem by plotting points in the first quadrant of a coordinate plane. “These are the locations of places in the community. School (2,2), Park (8, 2), Library (8,5), Gym (2,7) How many blocks does Ana walk from school to the playground and then to the library? The school to the park is ___ blocks. The park to the library is ___ blocks. Ana walks ___$$+3=$$___ blocks.” Lesson 8.5, Independent practice, Exercise 2h, “Pencils are sold in packages of ten. Complete the ordered pairs that can be graphed to show the relationship between the number of packages and the number of pencils. (0, ), (, 10), (2, ), (3, ).” Lesson 8.5, Independent practice, Exercise 2c, “Plot the relationship 3 for $1.” Students drag the dot onto the coordinate plane.

The materials reviewed for Snappet Math Grade 5 meet expectations that, when implemented as designed, most of the materials address the significant clusters of each grade. The materials devote at least 65 percent of instructional time to the significant 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 5.5 out of 8, approximately 69%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 76 out of 97, approximately 78%. 

• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 25.5 out of 35, approximately 73%.

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 78% of the materials focus on major work of the grade.

The materials reviewed for Snappet Math Grade 5 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: Expressions and Patterns, Lesson 6.3, Independent Practice, Exercise 2c, students multiply a whole number and a fraction as they solve problems with grouping symbols. “$$16\times(\frac{1}{4}+3)=$$___.” This connects the supporting work of 5.OA.1 (Use parenthesis, brackets, or braces in numerical expressions, and evaluate expressions with these symbols) to the major work of 5.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction).

• Unit 7: Measurement and Geometry, Lesson 7.6, Instruction & Guided Practice, Exercise 1k, students find the volume of rectangular prisms by evaluating expressions. “What is the volume of the suitcase? Volume = length \times width \times height. Volume = ___ \times8\times20. The volume of the suitcase is ___ in^3.” An image shows a suitcase with the length as 10 in., width as 8 in., and height as 20 in. This connects the supporting work of 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them) to the major work of 5.MD.5c (Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems).

• Unit 8: Line Plots and the Coordinate System, Lesson 8.2, Independent Practice, Exercise 2a, students use information from a line plot to solve a word problem involving fractions. “The line plot shows the lengths of yarn Cam has. What is the difference between the longest and shortest pieces? The longest piece is \frac{?}{4}yd. The shortest is \frac{?}{?} yd. The difference is: \frac{?}{?}- \frac{?}{?} = \frac{?}{?} yd.” This connects the supporting work of 5.MD.2 (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}). Use operations on fractions for this grade to solve problems involving information presented in line plots), with the major work of 5.NF.2 (Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators).

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

• No connections are made between the supporting work of 5.MD.1 (Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems) and the major work of 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, 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.) There are no problems in the lessons on converting measurement units that involve addition, subtraction, multiplication, or division of decimals.

The materials reviewed for Snappet Math Grade 5 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: Operations with Decimals, Lesson 3.6, Independent Practice, Exercise 2f, students round decimal monetary amounts prior to multiplying by a whole number. “$$6\times$$ $1.49 = ___. 6\times$1.50.” This activity connects the major work of 5.NBT.A (Understand the place value system) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths).

• Unit 5: Fractions - Multiply and Divide, Lesson 5.4, Instruction & Guided Practice, Exercise 1h, students use the area model to multiply a fraction by a fraction. “$$\frac{1}{3}\times\frac{1}{3}=$$ ___. Show students how to divide the whole into equal thirds lengthwise by selecting and moving the dashed line twice. Then tell students that you need to find one-third of the original one-third and express that as part of the original whole.” This activity connects the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths) to the major work of 5.NF.B (Apply and extend previous understandings of multiplication and division to multiply and divide fractions).

• Unit 7: Measurement and Geometry, Lesson 7.6, Independent Practice, Exercise 2j, students use multiplication to calculate volume with multi-digit whole numbers. “A gift bag in the shape of a rectangular prism is 12 in. long, 4 in. wide, and 12 in. high. What is the volume of the bag? ___$$in^3$$.” This activity connects the major work of 5.MD.C (Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers).

• Unit 8: Line Plots and the Coordinate System, Lesson 8.5, Instruction & Guided Practice, Exercise 1n, students analyze patterns and graph points on a coordinate plane. “Pattern A: Add 2. Pattern B: Add 1.” A table chart with Pattern A, Pattern B, and Ordered Pairs is provided. Exercise 1o, “Plot the relationship between the patterns for (Pattern A, Pattern B).” This activity connects the supporting work of 5.OA.B (Analyze patterns and relationships) to the supporting work of 5.G.A (Graph points on the coordinate plane to solve real-world and mathematical problems).

The materials reviewed for Snappet Math Grade 5 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 2 Overview: Operations with Whole Numbers, Learning Progression, “In this grade level, students will develop an understanding of procedures to multiply including the use of the standard algorithm to find products of multi-digit whole numbers as they strive to develop fluency. They will also find quotients of multi-digit whole numbers up to four-digit dividends and two-digit divisors using properties of operations and place value and can articulate why these procedures work. In future grade levels, students will use the standard algorithm to divide multi-digit whole numbers (6.NS.B.3).” 

• Unit 6 Overview: Expressions and Patterns, Lesson Progression, “In this grade level, students will evaluate expressions involving whole numbers, with and without parentheses, using the order of operations. They will convert from a verbal description of a mathematical expression to a numerical and symbolic expression and interpret numerical expressions without calculating. They will also generate numerical patterns from rules. In future grade levels, students will extend their understanding of numerical expressions by writing and evaluating numerical expressions containing exponents (6.EE.A.1), and by writing expressions with variables (6.EE.A.2). They will reason about pairs of values by making tables relating quantities, finding missing values in tables, and plotting pairs of values on the coordinate plane (6.RP.A.3).” 

• Unit 8: Line Plots and the Coordinate System, Lesson 8.5, Lesson Overview, “In this lesson, students will identify patterns in ordered pairs. (5.OA.B.3) graph ordered pairs from patterns. (5.OA.B.3) In future lessons, students will write, read, and evaluate expressions in which letters stand for numbers. (6.EE.A.2) use variables for two quantities and their relationship to solve problems. (6.EE.9) understand the concept of a ratio (6.RP.A.1).”

Examples of connections to prior knowledge include:

• Unit 3: Operations with Decimals, Lesson 3.13, Lesson Overview, “In prior lessons, students have used place value to divide tens, hundreds, and thousands. (4.NBT.B.6) solved division problems, such as 250 divided by 5. (5.NBT.B.6) In this lesson, students will divide a whole number by decimal (5.NBT.B.7).”

• Unit 5 Overview: Fractions: Multiply and Divide, Learning Progression, “In prior grade levels, students multiplied a fraction by a whole number and solved word problems involving multiplication of a fraction and a whole number (4.NF.B.4). In this grade level, students will multiply and divide fractions and mixed numbers. They will multiply fractions by whole numbers and fractions by other fractions using models and other strategies, including area models. They will also multiply mixed numbers by mixed numbers. Students will divide fractions by whole numbers and divide whole numbers by unit fractions. They will use these skills to represent word problems with fraction models and equations, and solve the problems.” 

• Unit 7: Measurement and Geometry, Lesson 7.9, Lesson Overview, “In prior lessons, students have understood angle measurement (degrees). (4.MD.C.5) classified polygons. (5.G.B.3) In this lesson, students will classify quadrilaterals. (5.G.B.3) recall names of various quadrilaterals (5.G.B.3).”