4th Grade - Gateway 1

The materials reviewed for Reveal Math Grade 4 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 is no Unit 1 Assessment or Performance Task.

Examples of grade-level assessment items include:

• Unit 3, Addition and Subtraction Strategies and Algorithms, Unit Assessment, Form B, Item 1, “What is the sum? 5,917 + 9,352  A. 15,269; B. 15,169; C. 14,279; D. 14,269.” (4.NBT.4)

• Benchmark Assessment 1, Item 10, “How many times larger is 700 than 70? A. 10, B. 100, C. 1,000, D. 10,000? (4.NBT.1)

• Unit 9, Addition and Subtraction Meanings and Strategies with Fractions, Performance Task, Part A, “Fido eats \frac{2}{8} of a pound of food in the morning and \frac{2}{8} of a pound of food in the afternoon. How much food does Fido eat in 1 day? Use an addition equation and an area model to solve. Show your work.” (4.NF.3a, 4.NF.3d)

• Benchmark Assessment 3, Item 10, “What is the difference of 9,304 - 3,135?” (4.NBT.4)

• Unit 11, Multiply Fractions by Whole Numbers, Performance Task, Part B, “Karli practices the flute for \frac{3}{5} of an hour 5 days a week. How many hours does Karli practice each week? Use an equation and number line to show your work.” (4.NF.4)

• Unit 13, Unit Assessment, Form B, Item 4, “Sean makes a fruit basket for his teacher. After he puts fruit in it, it weighs 8 pounds. How many ounces does it weigh?” (4.MD.1, 4.MD.2)

• Summative Assessment, Item 16, “How can you compare the decimals? Write <, >, =. 432.53____432.63.” (4.NF.7)

Reveal Math assesses students with fractions that have denominators other than the grade level expectation of 2, 3, 4, 5, 6, 8, 10, 12, and 100. These items could be modified or omitted without changing the structure of the materials. Additionally, some assessment items include 3 digit by 2 digit multiplication which is above grade level for Grade 4. These items could be modified or omitted without changing the structure of the materials. Examples include:

• Unit 6, Multiplication Strategies with Multi-Digit Numbers, Unit Assessment, Form A, Item 14, “How can you use an area model to multiply 273 x 43? Use drawings and words to explain your work” Multiplication of 3 digit by 2 digit numbers is a Grade 5 standard. (5.NBT.6)

• Unit 6, Unit Assessment, Form B, Item 14, “How can you use an area model to multiply 172 x 94? Use drawings and words to explain your work” Multiplication of 3 digit by 2 digit numbers is a Grade 5 standard. (5.NBT.6)

• Benchmark Assessment 2, Item 12, “Which is a reasonable estimate of the product of 723 and 58? A. 5,000 B. 13,000 C. 42,000 D. 350,000” Multiplication of 3 digit by 2 digit numbers is a Grade 5 standard. (5.NBT.6)

• Unit 11, Unit Assessment, Form A, Item 7, “Which of these are equivalent to 5 x \frac{2}{7}? Choose all that apply.” Multiplying a whole number by a fraction is part of the Grade 4 standard; however, \frac{2}{7} has a denominator of 7 which is beyond a Grade 4 expectation (5.NF.4). Grade 4 fractions are limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. 

• Unit 12, Unit Assessment, Form A, Item 7, “Matt has 12.00 to buy a new pair of goalie gloves for soccer. A pair of gloves cost 8.20. How much money does he have after buying the gloves? A. 3.00, B. 3.80, C. 20.20, D. 8.20” Students solve problems using operations with decimals which is a 5th grade standard, (5.NBT.7).

The materials reviewed for Reveal Math Grade 4 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 2-4, Generalize Place-Value Structure, Reinforce Understanding, Exercises 1-3, directions state, “Use a number line to help you round each number.” Exercise 1, “Round 40,189 to the nearest hundred.” Exercise 2, “Round 64,688 to the nearest thousand.” Exercise 3, “Round 80,791 to the nearest ten.” These exercises engage students with the full intent of 4.NBT.3, use place value understanding to round multi-digit whole numbers to any place.

• In Lesson 3-8, Represent and Solve Multi-Step Problems, On My Own, Exercise 3, “Use diagrams and equations with variables to solve each problem. An art teacher had 140 jars of paint. In the first half of the year, her students used 95 jars of paint. The teacher bought 35 more jars of paint. At the end of the year, she had 15 unused jars of paint. How many jars of paint did her students use in the second half of the year?” This exercise engages students with the full intent 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.

• In Lesson 8-5, Other Ways to Compare Fractions, On My Own, Exercise 11, “Janet’s family eats \frac{4}{8} of a large pizza. Julie’s family eats \frac{3}{6} of a small pizza. Julie says her family ate the same amount as Janet’s family because \frac{4}{8}=\frac{3}{6}. Is Julie correct?” This exercise engages students with the full intent of 4.NF.2, compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as \frac{1}{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

• In Lesson 13-6, Solve More Problems That Involve Units of Measure, Additional Practice, Exercise 6, “A tomato plant grows \frac{3}{4} of a foot each month. How many inches does it grow in 4 months?” This exercise engages students with the full intent 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. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

• In Lesson 14-7, Classify Polygons, On My Own, Exercises 1 through 6, engage students with the full intent of 4.G.2, classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Students are presented with 6 shapes and asked, “How can you classify the polygons? Write parallel lines only, perpendicular lines only, both, or neither.”

The materials reviewed for Reveal Math Grade 4 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 93 lessons, of which 68 address major work, or supporting work connected to major work, approximately 73%.

• There are 157 days of instruction,120 of which address major work, or supporting work connected to major work, approximately 76%.

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 73% of the instructional materials focus on major work of the grade.

The materials reviewed for Reveal Math Grade 4 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Some supporting standards are taught in isolation, but the separation is mathematically reasonable.

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

• In Lesson 8-2, Generate Equivalent Fractions Using Models, Learn, Work Together, connects the supporting work of 4.OA.5, generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern…, is connected to the major work of 4.NF.1, explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fractions models.... “What fraction is missing from the pattern? Explain how you can find the equivalent fraction. \frac{3}{4}= \frac{6}{8}= \frac{?}{?}= \frac{12}{16}.”

• In Lesson 13-1, Relate Metric Units, Explore & Develop, Learn, Work Together, connects the supporting work of 4.MD.1, know relative sizes of measurement units within one system of units…, is connected to the major work of 4.OA.2, multiply or divide to solve word problems involving multiplicative comparison... “Mr. Decker needs 7 liters of paint for his classroom art project. How many milliliters of paint does he need?”

• In Lesson 13-3, Relate Customary Units of Capacity, Exit Ticket, Item 6, connects the supporting work of 4.MD.1, know relative sizes of measurement units within one system of units… is connected to major work of 4.NF.4c, solve word problems involving multiplication of a fraction by a whole number. “Jazmine buys 1\frac{1}{2} gallons of milk. How many quarts of milk does she buy?”

• In the Interactive Student Edition, Lesson 13-6, On My Own: Solve More Problems That Involve Units of Measure, Exercise 2, connects the supporting work of 4.MD.2, use the four operations to solve word problems involving masses of objects is connected to the major work of 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. “Show or explain the answer. Fasil makes 3 gallons of soup. He puts the soap in 1-quart containers. How many containers can he fill?” 

• In Lesson 13-7, Solving Problems Using a Perimeter Formula, On My Own, Exercise 11, connects the supporting work of 4.MD.3, apply the area and perimeter formulas for rectangles in the real world and mathematical problems, to the major work of 4.NF.4c, solve word problems involving multiplication of a fraction by a whole number. “A rectangular tablecloth has a width of 60 inches. If the length is 1\frac{1}{2} times the width, what is the perimeter? Explain how you found the solution.”

• In Lesson 13-11, Solve Problems Involving Data on a Line Plot, Assess, Exit Ticket, Item 2, connects the supporting work of 4.MD.4, make a line plot to display a data 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 is connected to the major work of 4.NF.3d, solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. “What is the difference, in pounds, between the weight of the heaviest apple and the weight of the lightest apple?”  \frac{5}{8}- \frac{2}{8}=?

Examples of supporting standards taught in isolation, but the separation is mathematically reasonable:

• In Lesson 5-1, Understand Factors of a Number, Interactive Student Edition, Exercise 6, “What are all the factor pairs for 100?” This exercise allows students to practice 4.OA.4, find all factor pairs for a whole number in the range of 1-100.

The materials reviewed for Reveal 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. 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 Interactive Student Edition, Unit 2, Fluency Practice: Decompose by Place Value to Subtract (within 1000), Exercise 1 connects the major work of 4.NBT.A, generalize place value understanding for multi-digit whole numbers to the major work of 4.NBT.B, use place value understanding and properties of operations to perform multi-digit arithmetic, as place value to decompose numbers and subtract. Students solve, “Fill in the blanks. How can you decompose by place value to find the difference? 697 - 324 = ?”

• In Lesson 3-9, Solve Multi-Step Problems Involving Addition and Subtraction, Own My Own, Exercise 2 connects the major work of 4.NBT.B, use place value understanding and properties of operations to perform multi-digit arithmetic to the major work of 4.OA.A, use the four operations with whole numbers to solve word problems, as students add four values. “A school is collecting cans for the local food pantry. The first week they collected 1,415 cans. The second week they collected 973 cans. The third week they collected 200 cans more than they collected in the second week. After the fourth week, they had a total of 4,542 cans. How many cans did they collect the fourth week?”

• In Lesson 6-5, Multiply Multi-Digit by 1-Digit Factors, Assess, Exit Ticket, Exercise 1 connects the major work of 4.NBT.B, use place value understanding and properties of operations to perform multi-digit arithmetic to the major work of 4.NBT.A, generalize place value understanding for multi-digit whole numbers, as students multiply a whole number of up to four digits by a one-digit whole number by using equations (and expanded form). “How can you find the product? Use partial products to solve. 3 x 642, 3 x 642 = (3 x ___) + (3 x ___) + (3 x ___), 3 x 642 = ____ + ____ + ____, 3 x 642 = ____.”

• In Lesson 11-2, Understand Multiplying a Fraction by a Whole Number, Assess, Exit Ticket, Exercise 1 connects the major work of 4.NF.B, build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers to the major work of 4.OA.A, use the four operations with whole numbers to solve problems, as students solve multiplicative comparison word problems. “Yao is making dinner. The recipe calls for \frac{2}{5} cup of shredded cheese. Yao wants to make 4 times as much food as the recipe is for. Draw how many sets of the fraction tiles shown represent the cuts of cheese Yao needs.”

Connections between supporting clusters or domains include:

• In Lesson 5-6, Analyze Features of a Pattern, On My Own, Exercise 8 connects the supporting work of 4.OA.C, generate and analyze patterns to the supporting work of 4.MD.A, solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit, as students use patterns and multiplication to find area. “Stacy creates a square with side length 2 inches. She increases the length of the sides of the square by 1 in as she makes each new square. If she continues this pattern, what would be the area of the 9th square? Explain.”

• In Lesson 14-2, Classify Angles, Differentiate, Extend Thinking, Differentiation Resource Book, Exercise 5 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 angels, and classify shapes by properties of their lines and angles as students recognize angles as geometric shapes that are formed when two rays share a common endpoint and draw (acute, obtuse, and right) angles in two dimensional figures as students draw shapes. “What two-dimensional shape includes the type(s) or angles specified? Draw the shape. right, acute and obtuse angles.”

The materials reviewed for Reveal 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. 

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

• Lesson 2-4, Round Multi-Digit Numbers, Coherence, Now includes 4.NBT.3, use place value understanding to round multi-digit whole numbers to any place. “Students expand their understanding of place value and rounding to greater numbers. Students justify decisions about to which place to round a given number.” In Next, “Students round decimals to any identified place value (Grade 5).” 5.NBT.4, use place value understanding to round decimals to any place.

• In Unit 4, Multiplication as Comparison, Unit Overview, Coherence, What Students Are Learning includes 4.OA.1, interpret a multiplication equation as a comparison and 4.OA.2, multiply or divide to solve world problems involving multiplicative comparison. “Students interpret a multiplication equation as a comparison and represent verbal statements of comparison as multiplication equations. Students distinguish between additive and multiplicative comparisons. Students write multiplication and division equations with an unknown to represent and solve multiplicative problems.” In Coherence, “Students interpret multiplication as scaling by explaining the size of a product in comparison to the size of factors. (Grade 5) Students fluently multiply multi-grade whole numbers using the standard algorithm. (Grade 5) Students interpret a fraction as division of the numerator by the denominator. (Grade 5).” 5.NF.5, interpret multiplication as scaling (resizing), by…, 5.NBT.5, fluently multiply multi-digit whole numbers using the standard algorithm, 5.NF.3, interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

• Lesson 6-6, Multiply Two Multiples of 10, Coherence, Now includes 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.... “Students extend their understanding of place value and properties of operations to find products of two multiples of 10.” In Next, “Students fluently multiply multi-digit numbers using the standard algorithm (Grade 5).” 5.NBT.5, fluently multiply multi-digit whole numbers using the standard algorithm.

• Lesson 13-1, Relate Metric Units, Teacher Edition, Coherence, Now, 4.MD.1, know relative sizes of measurement units within one system of units... “Students use multiplication to convert larger metric units to smaller units and students use the base-10 structure to understand the metric system.” In Next, “Students convert smaller to larger units to solve multi-step real-world problems (Grade 5).” 5.MD.1, convert among different-sized standard measurement units within a given measurement system, and use these conversations in solving multi-step, real world problems.

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

• Lesson 2-4, Round Multi-Digit Numbers, Coherence, Now includes 4.NBT.3, use place value understanding to round multi-digit whole numbers. “Students expand their understanding of place value and rounding to greater numbers. Students justify decisions about to which place to round a given number.” In Previous, “Students rounded whole numbers to the nearest ten and hundred (Grade 3). Students generalized the structure of place values to one million (Unit 2).” 3.NBT.1, use place value understanding to round whole numbers to the nearest 10 or 100.

• Lesson 4-1, Understand Comparing with Multiplication, Coherence, Now includes 4.OA.1, interpret a multiplication equation as a comparison. “Students use multiplication to compare quantities. Students use multiplication to represent multiplicative comparison statements.”  In Previous, “Students developed understanding of multiplication through problems involving equal groups and arrays (Grade 3).” (3.OA.3)

• Lesson 9-5, Subtract Fractions with Like Denominators, Teacher Edition, Coherence, Now, 4.NF.3, understand a fraction a/b with a >1 as a sum of fractions 1/b. “Students use fraction models to find a difference between fractions with like denominators.” In Previous, “Students represented fractions on a number line (Grade 3).” 3.NF.2, understand a fraction as a number on the number line; represent fractions on a number line diagram.

• Lesson 12-2, Understand Decimal Notation, Teacher Edition, Previous, Now, includes 4.NF.C, understand decimal notation for fractions, and compare decimal fractions. “Students represent tenths and hundredths as fractions and decimals” and “Students identify the place value of tenths and hundredths.” In Previous, “Students represented fractions as part of the whole (Grade 3).” 3.NF.1, understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal groups...