3rd-5th Grade - Gateway 1

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The assessments are aligned to grade-level standards and do not include content from future grades. Each unit includes Sub-Unit Quizzes and an End-of-Unit Assessment, both available in Forms A and B, and offered in print and digital formats.

Examples include:

• Grade 3, Unit 1: Introducing Multiplication, End-of-Unit Assessment: Form A, students solve multiplication problems. Problem 5 states,  “Jada has 5 bags. Each bag has 8 rubber bands. How many rubber bands does Jada have? Show or explain your thinking.” (3.OA.3)

• Grade 4, Unit 4: From Hundredths to Hundred Thousands, End-of-Unit Assessment: Form A, Problems 2 and 3, students compare multidigit numbers. Problems 2 and 3 state, “For Problems 2 and 3, complete the comparison using <, >, or =. Problem 2. 587,207 ___ 591,025. Problem 3. 386,981 ___ 386,898.” (4.NBT.2)

• Grade 5, Unit 5: Place Value Patterns and Decimal Operations, End-Of-Unit Assessment: Form B, Problem 9, students divide decimals. Problem 9 states, “Han has a collection of pennies worth $2.50. How many pennies does he have? Show or explain your thinking.” (5.NBT.7)

The materials reviewed Amplify Desmos Math Grades 3 through Grade 5 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Formal assessments, including Sub-Unit Quizzes and End-of-Unit Assessments, are consistently aligned to grade-level content standards and Mathematical Practice Standards. This alignment is clearly identified in the program’s Assess and Respond section.

Examples include:

• Grade 3, Unit 2: Area and Multiplication, Sub-Unit 1 Quiz, Problem 2 states, “Diego places these squares on the rectangle and says the area of the rectangle is 10 square units. Do you agree with Diego? Explain your thinking.” The Assess and Respond Item Analysis denotes the standards assessed as 3.MD.5 and MP3.

• Grade 4, Unit 3: Extending Operations to Fractions, Sub-Unit 2 Quiz, Problem 1 states, “Determine which expressions are equivalent to 8558​. Select all that apply. A. 5×185×81​  B. 8×158×51​   C. 2×452×54​   D. 4×254×52​  E. 2×652×56​ ” The Assess and Respond Item Analysis denotes the standards assessed as 4.NF.4 and MP7.

• Grade 5, Unit 7: Geometry and Patterns, End-of-Unit Assessment: Form B, Problem 2 states, “Plot the point (7, 3) on the coordinate grid and label it D.” The Assess and Respond Item Analysis denotes the standards assessed as 5.G.1 and MP7.

The materials reviewed for Amplify Desmos Math Grades 3 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Summative assessments include Sub-Unit Quizzes and End-of-Unit Assessments. Each unit provides Assess and Respond guidance for both assessment types. Each lesson also ends with Show What You Know tasks. The assessments address grade-level content and practice standards using a range of item types, including multiple choice, multiple response, short answer, and extended response.

Examples include:

• Grade 3, Unit 1: Introduction to Multiplication, 3.1 Sub-Unit 2 Quiz, Problem 2 states, “There are 3 rows of chairs in the room. Each row has 7 chairs. How many chairs are there? Use this information for Problems 2–4. Create an array to represent the total number of chairs.” Problem 3 states, “Write 2 equations to represent the total number of chairs. Use a ? for the unknown.” Problem 4 states, “Determine the number of chairs. Show or explain your thinking.” Unit 2: Area and Multiplication, End-of-Unit Assessment, Form A, Problem 3 states, “A rectangle has an area of 12 square inches. What could be the length and width of the rectangle?” Answer choices include, “2 inches and 24 inches, 3 inches and 4 inches, 5 inches and 7 inches, 2 inches and 12 inches.” Unit 4: Relating Multiplication to Division, End-of-Unit Assessment, Form A, Problem 2 states, “A school art hallway displays 78 student paintings arranged in equal rows. There are 26 paintings in each row. How many rows of paintings are there?” Problem 4 states, “Priya covers her desk with 77 sticky notes. The sticky notes are in 7 equal rows. How many sticky notes are in each row? Write a division equation to represent the story problem. Use a symbol for the unknown value.” Unit 6: Measuring Length, Time, Liquid Volume, and Weight, End-of-Unit Assessment, Form A, Problem 8 states, “Use the information for Problems 8 and 9. A softball team is preparing water for a softball tournament. There are 24 players on the team. Each player needs 2 liters of water. How many liters of water do all the players need? Show or explain your thinking.” Problem 9 states, “Each water jug holds 6 liters of water. How many water jugs does the softball team need? Explain your thinking.” The materials assess the full intent of 3.OA.3 as students solve multiplication and division word problems within 100, represent situations with arrays and equations, and determine unknown values in a variety of real-world contexts.

• Grade 4, Unit 5: Multiplicative Comparison and Measurement, 4.5 Sub-Unit 1 Quiz, Problem 3 states, “Jada has 18 pennies in her piggy bank. Diego has 4 times as many pennies as Jada. How many pennies do Jada and Diego have altogether? Show or explain your thinking.” 4.5 Sub-Unit 2 Quiz, Problem 1 states, “Priya ran 312321​ kilometers. How many meters did Priya run? Show or explain your thinking.” Problem 2 states, “A rectangle has a length of 8 inches. The perimeter of the rectangle is 2 feet. What is the width of the rectangle? Show or explain your thinking.” The materials assess the full intent of MP1 as students interpret multi-step word problems, select appropriate strategies, and explain their reasoning to solve multiplicative comparison and measurement situations.

• Grade 5, Unit 6: More Decimal and Fraction Operations, 5.6 Sub-Unit 2 Quiz, Problem 1 states, students convert measurements between inches, feet, and yards using a table. In Problem 2, students solve a multi-step word problem that requires converting meters to kilometers. “The distance around a track is 325 meters. Jada ran around the track 12 times. How many kilometers did Jada run?” End-of-Unit Assessment, Form A, Problems 7–9 require students to convert millimeters, centimeters, and kilometers to meters. “For Problems 7–9, determine how many meters are equivalent to the given length. 350 millimeters, 1.2 centimeters, 0.19 kilometers.” Problem 10 states, “Clare drinks 9 glasses of water throughout the day. Each glass is 250 milliliters. How many liters of water does Clare drink throughout the day?” The materials assess the full intent of 5.MD.1 as students convert among standard measurement units within both the customary and metric systems and apply these conversions to solve multi-step real-world problems.

The materials reviewed for Amplify Desmos Math Grades 3 through 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 provide students with consistent opportunities to engage in the full intent of Grade 3–5 standards. Each lesson includes a Warm-Up, one or more Activities, Lesson Practice, a Lesson Synthesis, and a Show What You Know task. Units also include Pre-Unit Checks to identify students’ prior knowledge and readiness for the unit content.

Examples include:

• Grade 3, Unit 6: Measuring Length, Time, Liquid Volume, and Weight, Lessons 11, 12, 13, 14, and 17 engage students with the full intent of 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes). Students use what they know about telling time to solve problems about elapsed time. In Lesson 11, Activity 2, Problem 6, students are prompted to “Write the time shown on each clock” and are provided with three clocks showing different times. In Lesson 12, Activity 1, Problem 1, students solve, “Sasha got to Evelyn’s coop at 7:27 a.m. It took her 24 minutes to clean the coop. What time did she finish cleaning the coop? Show or explain your thinking,” and are provided with a clock showing 7:27. In the Lesson Practice and Lesson Summary, students are shown how to use a number line to find elapsed time. In Lesson 13, Lesson Practice, Problem 1, students answer, “How long was Priya’s haircut? Use the clocks if it is helpful. Show or explain your thinking,” and are provided with two clocks showing the start and end times. In Lesson 14, Activity 1, Problem 3, students solve, “Han started a puzzle at 3:33 p.m., and he took 45 minutes to complete it. At what time did Han put in the last piece of the puzzle?” In Lesson 17, Lesson Practice, Problem 4, students answer, “Clare got in line for the Ferris wheel at 5:53 p.m. She got off the ride at 6:18 p.m. How long was Clare at the Ferris wheel?” and select from the provided answer choices: 25 minutes, 24 minutes, 35 minutes, or 36 minutes.

• Grade 4, Unit 4: From Hundredths to Hundred Thousands, Lessons 9, 10, 12, and 13 engage students with the full intent of 4.NBT.2 (Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons). Students read and write numbers in standard, word, and expanded form, and compare multi-digit whole numbers. In Lesson 9, Warm-Up, students analyze and compare representations of the number 245, including base-ten blocks, standard form, expanded form, and word form. In Activity 2, Problem 10, students represent numbers in expanded and standard form with examples such as 117,903; 1,000+80,000+70+51,000+80,000+70+5; 50,031; 1,000+301,000+30; 99,098; and 200,000+900+10+60,000+5,000+1200,000+900+10+60,000+5,000+1. In Lesson 10, Activity 2, Problem 7, students write numbers in standard form, expanded form, and in words, filling in missing forms on a chart with examples such as 784,003; 50,000+9,000+300+60+150,000+9,000+300+60+1; eight hundred three thousand, ninety-nine; 310,060; and nine hundred thirty-four thousand, nine hundred. In Lesson 12, Show What You Know, Problems 1–3, students compare pairs of multi-digit numbers and record the comparisons using the < and > symbols, such as 63,951 ___ 65,003; 91,568 ___ 123,068; and 245,100 ___ 245,090. In Lesson 13, Activity 1, students analyze a data table showing the number of nests counted for different types of sea turtles over a five-year period, identify the least and greatest numbers for each type, and discuss strategies for determining these values. In Problem 4, students answer, “What strategies did you use to determine the least and greatest numbers? How does place value help you when determining the least and greatest numbers?” In Activity 2, students play a game using number cards to make six-digit numbers, aiming to create a greater number than their partner and recording their comparisons using the <, >, and = symbols, then share the strategies they used during the game.

• Grade 5, Unit 5: Place Value Patterns and Decimal Operations, Lessons 9, 12, 15, and 20 engage students with the full intent 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). Students apply a variety of strategies to perform decimal operations and explain their reasoning. In Lesson 9, Warm-Up, students are presented with several fraction addition and subtraction problems and consider how similar strategies can be applied to decimals. In Activity 1, students estimate sums and differences for problems 1–4 with a partner, then join another group to solve problem 5 before engaging in a whole-class discussion. In Lesson 12, Lesson Practice, Problem 2, students drag values to set up the standard algorithm for 0.5+9.880.5+9.88, determine the sum, and show their thinking. In Problem 6, students solve, “Diego has 5 yards of rope. It takes 1331​ yards to make a boat knot. How many boat knots can Diego make with the rope? Show or explain your thinking.” In Lesson 15, Activity 1, students investigate decimal multiplication by determining the total area each local business owner bought, working with a partner and then sharing responses as a class. In Lesson 20, Lesson Practice, Problems 2–3, students find quotients for 0.9÷60.9÷6. Problem 3. 0.16÷20.16÷2, applying strategies based on place value and properties of operations to justify their answers.

The materials provide opportunities for students to meet the full intent of all Grade 3 through Grade 5 standards; however, they do not provide extensive work for all standards, with a missed opportunity for extensive work with one standard in Grade 3.

Example includes:

• Grade 3, Units 3: Wrapping Up Addition and Subtraction Within 1,000 and Unit 4: Relating Multiplication to Division do not engage students in extensive work with 3.OA.9 (Identify arithmetic patterns, and explain them using properties of operations). There are two lessons that address 3.OA.9, one focused on addition patterns and the other on multiplication patterns. In Unit 3, Lesson 2, Activity 1, students use addition patterns to see how adding 9 or 11 is related to adding 10. In Problem 3, students continue a pattern by adding 11, starting at 46 and repeating the process four times to help a panda reach an island. In Problem 4, students discuss patterns they notice when adding 11. In Problem 6, students compare patterns when adding 11 and 9. In Activity 2, students continue addition patterns to see how adding 101 or 99 is related to adding 100. In Problem 8, students continue a pattern beginning with 207 by adding 101. In Problem 9, they discuss patterns noticed when adding 101, and in Problem 11, compare patterns when adding 101 and 99. In the Synthesis, students are shown an addition table with three-digit numbers at the top of each column and at the start of each row; this is their only opportunity in the lesson to identify patterns using an addition table. In Unit 4, Lesson 8, Activity 1, students fill in a multiplication table to identify patterns that can be used to determine products. In the Teacher Edition Activity 1, students determine products for shaded boxes in the table without filling in unshaded boxes. Students are asked, “How are the products with factors of 5 related to the products with factors of 10? How can you use 4×104×10 to help you determine 4×54×5?” and “How are the products with factors of 9 related to the products with factors of 10? How can you use 8×108×10 to help you determine 8×98×9?” In Activity 2, students identify even products to describe and explain patterns. In Problems 3 and 4, students use the multiplication table to color all the even products and discuss patterns they notice and why they occur. Lesson Practice includes three problems related to multiplication patterns on a multiplication table. For example, in Problem 1, students determine whether an unknown number represented by “?” is odd or even based on a pattern in the table and explain their reasoning.

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade:

In Grade 3:

• The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 5 out of 7 which is approximately 71%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 77 out of 120, which is approximately 64%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 109 out of 152, which is approximately 72%.

In Grade 4:

• The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 5 out of 7 which is approximately 71%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 79 out of 120, which is approximately 66%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 107 out of 148, which is approximately 72%.

In Grade 5:

• The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 6 out of 7 which is approximately 86%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 94 out of 117, which is approximately 80%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 122 out of 145, which is approximately 84%.

An instructional day analysis across Grade 3 through Grade 5 is most representative of the instructional materials as the days include major work, supporting work connected to major work, and the assessments embedded within each unit. Any day marked optional was excluded. As a result, approximately 72% of the materials in Grade 3, 72% of the materials in Grade 4, and 84% of the materials in Grade 5 focus on major work of the grade.

The materials reviewed for Amplify Desmos Math Grades 3 through 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 so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher Edition.

Examples include:

• Grade 3, Unit 6: Measuring Length, Time, Liquid Volume, and Weight, Lesson 6, Lesson Practice 6.06, 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). Problem 3, states “Create a line plot that matches the statements. The line plot shows the lengths of 10 rectangles. The shortest rectangle has a length of 514541​ inches. The longest rectangle has a length of 9 inches. 6 of the rectangles are longer than 724742​ inches. 812821​ inches is the most common rectangle length.”

• Grade 4, Unit 3: Extending Operations to Fractions, Lesson 15, Activity 2, connects the supporting work of 4.MD.4 (Make a line plot to display a data set of measurements in fractions of a unit [1221​, 1441​, 1881​]. Solve problems involving addition and subtraction of fractions by using information presented in line plots) to the major work of 4.NF.3d (Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction). Activity 2 states, “At the library, Henry researched the heights of different kinds of plants and plotted the data on the line plot shown. Problem 5. Represent the data on the line plot. 1010, 918981​, 834843​, 768786​, 912921​, 818881​, 768786​, 948984​, 818881​, 924942​. Problem 9. What is the difference between the tallest plant height and the shortest plant height? Show or explain your thinking.” 

• Grade 5, Unit 6: More Decimal and Fraction Operations, Lesson 18, Lesson Practice 6.18, connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit [1221​, 1441​, 1881​], Use operations on fractions for this grade to solve problems involving information presented in line plots) to 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, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers). The materials state, “Several students were surveyed about how many hours they read in a week. The results are shown in the table. Use the information for Problem 1. 314341​, 234243​, 324342​, 212221​, 33, 228282​, 348384​, 212221​, 22, 228282​, 334343​, 212221​, 248284​, 214241​, 114141​, 234243​, 33, 248284​, 312321​, 314341​, 114141​. Problem 1. Use the data points in the table to create a line plot to represent the number of hours read in a week. Be sure to include a title and label. Problem 2. How many students completed the survey? Problem 3. What fraction of the students read less than 214241​ hours? Problem 4. What fraction of the students read at least 212221​ hours? Problem 5. What is the difference between the greatest number of hours read and the least number of hours read? Show or explain your thinking?”

The materials reviewed for Amplify Desmos Math Grades 3 through 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.

Connections among the major work of the grade are present throughout the materials where appropriate. These connections are listed for teachers in the Teacher Edition within each Unit Overview and may appear in one or more phases of a typical lesson: Warm-Up, Activity, Synthesis, Centers or Show What You Know. 

Examples include:

• Grade 3, Unit 3: Wrapping Up Addition and Subtraction Within 1,000, Lesson 20, Lesson Practice 3.20 connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic). Problem 2 states, “Match each diagram with the equation it represents.” There are four diagrams labeled A, B, C, and D. Diagram A shows the numbers 168, 7, 7, and ? Diagram B shows 80, ?, ?, ?, and 200. Diagram C shows ?, 7, 7, and 168. Diagram D shows ?, 8, 8, 8, and 200. These diagrams are meant to match the following equations: ?+(2×7)=168?+(2×7)=168, ?+(3×8)=200?+(3×8)=200, 168+(2×7)=?168+(2×7)=?, 80+(3×?)=20080+(3×?)=200.

• Grade 4, Unit 3: Extending Operations to Fractions, Lesson 13, Lesson Practice 3.13 connects the major work of 4.NF.A (Extend understanding of fraction equivalence and ordering) to the major work of 4.NF.C (Understand decimal notation for fractions, and compare decimal fractions). Problem 1 states, “Complete the table with equivalent fractions in tenths or hundredths. Tenths: 810108​ Hundredths: ?, Tenths: ? Hundredths: 3010010030​, Tenths: 40101040​ Hundredths: ?, Tenths: ? Hundredths: 160100100160​.”

• Grade 5, Unit 4: Multiplication and Division With Multi-Digit Whole Numbers, Lesson 14, Lesson Practice 4.14 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). Problem 1 states, “A farmer picks 485 quarts of blueberries and distributes them equally into 15 bushels. How many quarts of blueberries are in each bushel? Show your thinking.”

The instructional materials reviewed for Amplify Desmos Math Grades 3 through 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. 

The Teacher Edition includes Unit and Lesson Overviews that identify content standard connections. Each Unit features a "Math of the Unit" section and a "Connections to Future Learning" component, both of which illustrate how current concepts relate to prior and future standards within the course and across grade levels. At the lesson level, materials specify the standards addressed and indicate how each lesson builds on prior learning, addresses current content, and/or prepares for future learning, categorized as Building On, Addressing, or Building Toward.

An example of a connection to future grades in Grade 3 includes:

• Unit 5: Fractions as Numbers, Connections to Future Learning connects 3.NF.1 (Understand a fraction 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 1/b.) to the work related to adding, subtracting, multiplying fractions (4.NF.3 and 4.NF.4). Connections to Future Learning states, “In this unit, students iterate unit fractions to name, label, and generate non-unit fractions. In Grade 4, Unit 3, students will add and subtract fractions with the same denominator and multiply fractions by whole numbers, extending their understanding to name a fraction abba​ as a multiple of 1bb1​. Example: Petra had 5885​ of her pizza left. She ate 2882​ of the remaining pizza for lunch. What fraction of the pizza did Petra have left after lunch?” 

An example of a connection to prior knowledge in Grade 3 includes:

• Unit 1: Introducing Multiplication, Lesson 8, Overview connects 3.OA.1 (Interpret products of whole numbers, e.g., interpret 5×75×7 as the total number of objects in 5 groups of 7 objects each) to the work related to adding equal groups in arrays (2.OA.4). Prior Learning states, “In Grade 2, students learned that a rectangular array contains objects arranged into rows and columns, with the same number of objects in each row and the same number of objects in each column.”

An example of a connection to future grades in Grade 4 includes:

• Unit 7: Angles and Properties of Shapes, Connections to Future Learning connects 4.G.1 (Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures) and 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) to the work related to recognizing attributes in categories (5.G.3). Connections to Future Learning states, “In this unit, students explore angle measurements, parallel and perpendicular lines, and symmetry as attributes of shapes. In Grade 5, Unit 7, they will identify and name quadrilaterals within hierarchies based on defining attributes that include angle measurements and side lengths. Example: A rectangle is always a parallelogram because every rectangle always has 2 sets of parallel sides. A rectangle is sometimes a square. A rectangle is a square if all 4 sides are equal. A rectangle is never a triangle because a triangle must have 3 sides and a rectangle has 4 sides.”

An example of a connection to prior knowledge in Grade 4 includes:

• Unit 5: Multiplicative Comparison and Measurement, Lesson 2, Overview connects 4.OA.2 (Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison) to the work related to representing additive comparison situations using tape diagrams and equations with unknowns (3.OA.8) and interpreting multiplication as equal groups (3.OA.1). Prior Learning states, “In Grade 3, students represented additive comparison situations using tape diagrams, and addition and subtraction equations using symbols to represent an unknown value. They also used multiplication as a way to represent equal groups.”

An example of a connection to future grades in Grade 5 includes:

• Unit 1: Volume, Connections to Future Learning connects 5.MD.5 (Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume) to the work related to finding volume with fractional edges (6.G.2). Connections to Future Learning states, “In this unit, students use the volume formulas to determine volumes of rectangular prisms with whole-number side lengths. In Grade 6, students will apply the volume formulas to determine the volumes of rectangular prisms with fractional edge lengths by packing them with unit cubes of the appropriate unit-fraction edge lengths. They see the volume is the same as would be found by multiplying the edge lengths of the prism. Example: The volume of the 3 stacked storage boxes is 11141141​ cubic feet. What is the height, in feet, of the storage box?”

An example of a connection to prior knowledge in Grade 5 includes:

• Unit 5: Place Value Patterns and Decimal Operations, Lesson 2, Overview connects 5.NBT.3 (Read, write, and compare decimals to thousandths) to the work related to representing tenths and hundredths (4.NBT.1 and 4.NF.6). Prior Learning states, “In Grade 4, students used place value understanding to consider fractions with denominators of 10 and 100. They represented tenths and hundredths with grids, number lines, and decimal notation.”