5th Grade - Gateway 1

The materials reviewed for Reveal Math Grade 5 meet expectations for assessing grade-level content, and if applicable, content from earlier grades. Each unit contains a Performance Task, two Summative Assessments, and editable auto-scored assessments in the digital library. The summative assessments, found in the Assessment Resource Book, include two forms (Form A and B) for each Unit Assessment. The Assessment Resource Book also includes three Benchmark Assessments and a Summative Assessment at the end of the book. There are a few instances of above grade level material in the assessments that can be modified or omitted without changing the structure of the materials. There is no Unit 1 Assessment or Performance Task.

Examples of grade-level assessment items include:

• Unit 2, Volume, Unit Assessment, Form A, Item 8, “Lydia’s school box is 10 inches long, 8 inches wide, and 4 inches high. What is the volume of the school box? A. 22 cubic inches, B. 24 cubic inches, C. 320 cubic inches, D 480 cubic inches.” (5.MD.5)

• Unit 3, Place Value and Number Relationships, Unit Assessment, Form A, Problem 2, students solve, “How can you write the number in standard form? In standard form, the number nine hundred two and fifty-one thousandths is written _______.” (5.NBT.2)

• Benchmark Assessment 1, Item 1, “Look at the expression 36.18 - 27.19  What is the value of the expression?” (5.NBT.7)

• Unit 6, Multiply Decimals, Unit Assessment, Form B, Problem 3, students solve, “Ben earns $2.75 for each crate of berries he picks. About how much would Ben earn if he picks 4 crates of berries?” (5.NBT.7) 

• Unit 11, Divide Fractions, Performance Task, Part B, and C, “For the second event, a team of students runs 2 times around the track. If each student runs 1/10 of the track, how many students do they need on each team? Use a representation to solve.” (5.NF.7b) “For the third event, student teams will bunny hop 14 of the way around the track. If there are 6 students on a team, how far will each person go? Show your work.” (5.NF.7a)

• Summative Assessment, Item 3, “What is the product? 56 x 604 = _____.” (5.NBT.5)

Examples of above grade level items that could be modified or omitted include:

• Unit 8, Divide Decimals, Performance Task, Parts B, C and D. “Part B: A 6th player had 36 hits resulting in a batting average of 0.178. Estimate the player’s number of at bats. Part C: Suppose Player 5 wants to increase their batting average to 0.275. If they get 35 more hits, how many times at bat will the player need to have? Part D: Suppose Player 3 makes 32 more hits and now has a batting average of 0.270. Calculate Player 3’s number of times at bat.” Division of decimals beyond  hundredths is a Grade 6 standard (6.NS.3) This performance task could be omitted because it goes to the hundredth place but could still be mathematically reasonable since it talks about batting averages which always go to the hundredths.

• Unit 13, Geometry, Performance Task, Item Part A, “Naji is trying to draw an isosceles triangle. He is given point A at (-4, -2) and point B at (2, -2). Plot these two points, then help Naji make the isosceles triangle ABC by plotting point C. Give your coordinates for point C. It must be on the grid provided.” In Grade 5, coordinate planes are limited to quadrant 1. Additionally, students are not introduced to negative numbers until Grade 6. (6.G.3)

• Summative Assessment, Item 32, “Carlos generates Patterns W and Z using these rules: Pattern W: Start with 0 and add 7. Pattern Z: Start with 0 and subtract 4. Which set of ordered pairs is generated from corresponding terms of Patterns W and Z? A) (0, 0), (-7, 4), (-14,8), (-21, 12); B) (0, 0), (7, - 4), (14, -8), (21, -12); C) (0, -4), (7, -8), 14, -12), (21, -16); D) (7, 0), (14,-4); 21, -8), (28, -12).” In Grade 5, coordinate planes are limited to quadrant 1. Additionally, students are not introduced to negative numbers until Grade 6. (6.G.3)

• Benchmark Assessment 3, Item 17, “Write the quotient for each division problem.” Option 3, 0.0020.1 = ?” Division of decimals beyond hundredths is a Grade 6 standard (6.NS.3)

The materials reviewed for Reveal Math Grade 5 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. Within the materials, all standards are represented, and all meet the full intent of the grade-level standard.

Examples where the materials engage all students in extensive work with grade-level problems to meet the full intent of the standard include:

• In Lesson 2-3, Use Formulas to Determine Volume, Differentiation, Reinforce Understanding, Independent Work, Differentiation Resource Book, p. 5, students move from counting all packed unit cubes to finding the number of unit cubes in the base and multiplying the number layers to using the base x height and length x width x height to find the volume of a right rectangular prism.” There are two formulas you can use to find the volume of a prism. (Multiply the number of cubes in one layer by the number of layers.) One Formula:  Volume = base x height.  Another formula:  Volume = length x width x height.”  This exercise engages students with the full intent of 5.MD.5, relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

• In Lesson 5-7, Multiply Multi-Digit Factors Fluently, On My Own, Exercise 6, “378 x 29 = ?” This lesson meets the full intent of 5.NBT.5 (fluently multiply multi-digit whole numbers using the standard algorithm) as students are given multiple opportunities to practice multiplying whole numbers using the standard algorithm. 

• In Lesson 11-4, Divide Whole Numbers by Unit Fractions, Additional Practice, Exercise 8, “A watermelon weighs 7 pounds. Slices are cut so that each piece weighs \frac{1}{4} pound. How many slices are cut from the watermelon?” This exercise meets the full intent of 5.NF.7 (apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions) by giving students opportunities to divide whole numbers by a unit fraction.  

• In Lesson 13-6, Classify Quadrilaterals by Properties, Exercises 1 - 8, students classify 8 figures into several subcategories. Students, “Use the figures for Exercises 1-8. Identify the figures that could be classified into each subcategory. 1. quadrilaterals, 2. trapezoids, 3. parallelograms, 4. rectangles, 5. rhombuses, 6. squares.” These exercises engage students in the full intent of standard 5.G.3, understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category.

• In Lesson 14-1, Digital Interactive Student Edition, On My Own: Write Numerical Expressions, Work Together, students solve, “Show the answer. What numerical expressions represent the description? Add 35 and 2. Then multiply by 12.” This exercise engages students with the full intent of standard 5.OA.2, write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

The materials reviewed for Reveal Math Grade 5 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

Within the materials, at least 65% of instructional materials address the major work of the grade, or supporting work is connected to the major work of the grade. For example: 

• There are 14 Units, of which 10.5 address major work, or supporting work connected to major work of the grade, approximately 75%.

• There are 92 lessons, of which 73 address major work, or supporting work connected to major work, approximately 79%.

• There are 156 days of instruction,123 of which address major work, or supporting work connected to major work, approximately 79%.

The materials contained discrepancies with the number of days per unit, and guidance was not given as to how those days were accounted for; therefore, a lesson level analysis is most representative of the materials. As a result, approximately 79% of the instructional materials focus on major work of the grade.

The materials reviewed for Reveal Math Grade 5 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Examples of supporting work engaging simultaneously with major work of the grade when appropriate include:

• In Lesson 2-4, Determine the Volume of Composite Figures, Exit Ticket, Exercise 3, connects the supporting work 5.OA.1, use parentheses in numerical expressions, and evaluate expressions with these symbols to the major work of 5.MD.5c, find volumes of solid figures composed of two non-overlapping right rectangular prisms. “Which expression shows how to find the volume of the composite figure? A. (12 x 4 x 4) + (20 x 4 x 4) + (12 x 4 x 4), B. (8 x 4 x 4) + (16 x 4 x 4) + (8 x 4 x4), C. (8 x 4 x 4) + (12 x 4 x 4) + (20 x 4 x 4), D. (12 x 4 x 4) + (16 x 4 x 4) + (8 x 4 x 4).” A composite figure is provided.

• In Lesson 12-2, Convert Metric Units, Practice & Reflect, On My Own, Exercise 14, connects the supporting work of 5.MD.1, convert among different-sized measurement units within a given measurement system to the major work of 5.NBT.7, add subtract, multiply, and divide decimals to hundredths... “Ada’s backpack has a mass of 9,080 grams. What is the mass in kilograms?” 

• In Lesson 12-3, Solve Multi-Step Problems Involving Measurement Units, On My Own, Exercise 1, connects the supporting work of 5.MD.1, convert among different-sized measurement units within a given measurement system to the major work of 5.NF.7, apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. “Adrian has a roll of wrapping paper that is 3 yards long. He uses \frac{1}{3} of the wrapping paper to wrap a present. What is the length, in feet, of the paper left on the roll? A. 1ft, B. 3ft, C. 6ft”

• In Lesson 12-5, Solve Problems Involving Measurement Data on Line Plots, Additional Practice, Exercise 4, connects the supporting work of 5.MD.2, make a line plot to display a data set of measurements in fractions of a unit to the major work 5.NF.1, add and subtract fractions with unlike denominators... Students use a line plot to practice subtracting fractions with unlike denominators, “What is the difference between the greatest amount of the time Sem spent practicing and the last amount of time Sem spent practicing?”

• In Lesson 14-2, Interpret Numerical Expressions, Own My Own, Exercise 6, connects the supporting work of 5.OA.1, use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, to the major work of 5.NBT.3 read, write, and compare decimals to thousandths and to the  major work of 5.NBT.7, add, subtract, multiply, and divide decimals to hundredths. “Compare the expression using <, > or =. Explain your reasoning. 50.5 x 7.2 ◯ (50.5 - 4.8) x 7.2”

• In Interactive Student Edition, Lesson 14-3, On My Own: Evaluate Numerical Expressions, Exercise 9, connects the supporting work of 5.OA.1, use parentheses, 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. “Fill in the blank. What is the solution? 2\frac{3}{8} + 1\frac{1}{4} x 6\frac{3}{4} - \frac{1}{2} = ____.” 

Some supporting standards are not connected to major standards or are taught in isolation, but the separation is mathematically reasonable. Examples include:

• 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 

• 5.G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond,

• 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.

The materials reviewed for Reveal 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. The materials contain connections from supporting work to supporting work, and connections from major work to major work throughout the grade-level materials, when appropriate.

Connections between major clusters or domains include:

• In Lesson 2-3, Use Formulas to Determine Volume, Differentiate, Extend Thinking, Exercise 3 connects major work of 5.MD.C, geometric measurement: understand concepts of volume and relate volume to multiplication and to addition to major work of 5.NBT.B, perform operations with multi-digit whole numbers and with decimals to hundredths as students use multiplication to calculate volume. “Each item is placed in the smallest possible box. Use the dimensions of the box to label the measurements of the objects. Then determine the volume of the box. Dimensions: 28cm x 22cm x 22cm.”

• In Lesson 6-5, Generalizations about Multiplying Decimals, Additional Practice, Exercise 9 connects major work 5.NBT.B, perform operations with multi-digit whole numbers and with decimals to hundredths to major work 5.NBT.A, understand the place value system as students use multiplication to calculate area. “A class makes a mural on a wall that is 35 feet long and 12 feet tall. A copy of the mural is made on a smaller surface 3.5 feet long and 1.2 feet tall. Find the area of each mural. How does the area of the smaller mural compare to the area of the larger mural?"

• In Lesson 10-1, Represent Multiplication of a Whole Number by a Fraction, Differentiate, Extend Thinking connects major work of 5.NF.A, use equivalent fractions as a strategy to add and subtract fractions to the major work of 5.NF.B, apply and extend previous understandings of multiplication and division as students multiply fractions by whole numbers to solve various problems. “What is the sum of the answers you found for 1-6? Write your answer as a mixed number.”

• In Interactive Student Edition, Lesson 10-9 , On My Own: Solve Problems Involving Fractions, Exercise 3 connects the major work of 5.NF.B, apply and extend previous understandings of multiplication and division to the major work of 5.NBT.A, understand the place value system as students multiply to solve word problems containing fractions. “Show the answer. The first chapter of a book has 40 pages. Connor read \frac{7}{8} of the pages in the first chapter. Simon read \frac{1}{5} of the pages that Connor read. How many pages have Connor and Simon each read?” 

Connections between supporting clusters or domains include:

• In Lesson 13-5, Properties of Quadrilaterals, Differentiate, Extend Thinking, Exercises 1-4, connects supporting work 5.G.A, graph points on the coordinate plane to solve real-world and mathematical problems to the supporting work 5.G.B, classify two dimensional figures into categories based on their properties as students draw a quadrilateral on the coordinate plane. “Draw the shape on the coordinate plane using the points given. What are the coordinates of the missing point(s) of the quadrilateral described?”

• In Lesson 14-6, Graphs of Numerical Patterns, Additional Practice, Exercises 5 and 6 connect supporting cluster 5.G.A, graph points on the coordinate plane to solve real-world and mathematical problems, to supporting work of 5.OA.B, analyze patterns and relationships, as students complete a graph and a table to determine the rule for the pattern. Exercise 5, “Fran earns $8.00 per hour at her job. Complete the table showing the number of hours Fran works and the amount of money she earns. Then graph the ordered pairs…” Exercise 6, “What is the rule for the pattern in the Number of Hours column in the table?”

The materials reviewed for Reveal 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. 

Content from future grades is identified within the chapters, units, and lessons; and is connected to grade-level work. Examples include:

• Lesson 2-5, Solve Problems Involving Volume, Coherence, Now, 5.MD.5b, apply the formulas V = l x w x h and V = b x h 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. “Students apply the formulas V = l x w x h and V = b x h for rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.” In Next, “Students find the volume of a right rectangular prism with fractional prism with fractional edge lengths (Grade 6).” 6.G.2, find the volume of a right rectangular prism with fractional edge lengths...

• Lesson 6-1, Patterns When Multiplying Decimals by Powers of 10, Coherence, Now, 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... “Students use their knowledge to create strategies based on place value to multiply decimals by powers of 10. In Next, “Students will write and evaluate numerical expressions involving whole-number exponents (Grade 6).” 6.EE.1, write and evaluate numerical expressions involving whole-  number exponents.

• Lesson 10-9, Solve Problems Involving Fractions, Teacher Edition, Previous, Now, 5.NF.B, apply and extend previous understandings of multiplication and division. “Students choose and use known methods to solve problems involving fractions.” In Next, “Students solve word problems involving division of fractions by fractions (Grade 6).” 6.NS.1, interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. 

• Lesson 12-4, Represent Measurement Data on a Line Plot, Teacher Edition, Previous, Now, 5.MD.2, make a line plot to display a data set of measurements in fractions of a unit... “Students represent and interpret measurement data to eighths of a unit on a line plot.” In Next, “Students develop understanding of statistical variability and summarize and describe distributions (Grade 6).” 6.SP.2, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Examples where the instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades include: 

• Lesson 8-4, Divide Decimals by Whole Numbers, Teacher Edition, Now, includes 5.NBT.6, find whole-number quotients with up to four-digit dividends and two-digit divisors... “Students use place-value understanding and equivalent representations to divide decimals by whole numbers.” In Previous, “Students found whole-number quotients and remainders (Grade 4).” 4.NBT.6, find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors... 

• Unit 9, Teacher Edition, Unit Overview, Coherence, 5.NF.1, add and subtract fractions with unlike denominators by replacing given fractions with... “What Students are Learning: Students will add and subtract fractions with unlike denominators.” In Previous, “What Students have Learned: students compared fractions by creating common denominators or numerators. (Grade 4).” 4.NF.2, compare two fractions with different numerators and different denominators…

• Lesson 10-8, Multiplication as Scaling, Teacher Edition, Now, includes 5.NF.5, interpret multiplication as scaling (resizing)... “Students interpret multiplication as scaling.” In Previous, “Students interpreted multiplication as a comparison(Grade 4).” 4.OA.1, interpret a multiplication equation as a comparison. 

• Lesson 11-7, Solve Problems Involving Fractions, Teacher Edition, Coherence, Now, 5.NF.7, apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. “Students choose and use strategies to solve division word problems that involve fractions and whole numbers.” In Previous, “Students applied previous understandings of multiplication to multiply a fraction by a whole number (Grade 4).” 4.NF.4, apply and extend previous understandings of multiplication to multiply a fraction of a whole number.