4th Grade - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics, Grade 4 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The i-Ready Classroom Mathematics assessments are found in the Teacher Toolbox and include Mid-Unit and Unit Assessments. The Grade 4 materials contain five units, with each unit providing numerous opportunities for both formative and summative assessments. Summative assessment items include:

• Unit 1, Assess, Unit Assessment, Form A, Item 11, “What number has 62 ones, 20 ten thousands, and 300 tens? Show your work.” (4.NBT.2)

• Unit 2, Assess, Mid-Unit Assessment, Form A, Item 8, “Last year 63 inches of rain fell in Oaktown. In Pine City, 7 inches of rain fell last year. Write and solve an equation to find out how many times as much rain fell in Oaktown last year as fell in Pine City.” (4.OA.2)

• Unit 3, Assess, Unit Assessment, Form A, Item 7, “The community center has a rectangular back deck with a length of 16 feet and a width of 14 feet. Workers install a rectangular side deck that is half of the length and half of the width of the back deck. What is the area of the side deck in square feet? Record your answer on the grid. Then fill in the bubbles.” (4.MD.3)

• Unit 4, Assess, Mid-Unit Assessment, Form A, Item 1, “In art class, Luke spends \frac{2}{6} of the time drawing and \frac{3}{6} of the time painting. He spends the rest of the time working with clay. What fraction of art class time does Luke spend working with clay? Choices include \frac{1}{6}, \frac{5}{12}, \frac{5}{6}, \frac{7}{12}.” (4.NF.3)

• Unit 5, Assess, Unit Assessment, Form B, Item 4, “Draw all the lines of symmetry on the square below. How many lines of symmetry does the square have? ___ lines of symmetry.” A picture of a square is shown. (4.G.3)

The materials reviewed for i-Ready Classroom Mathematics, Grade 4 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards

According to the Program Overview, Program Organization document, “The lessons in i-Ready Classroom Mathematics span multiple days and integrate several standards to help students make connections and develop a deep understanding.” There are three types of lessons: 1. Strategy Lessons, which comprise the majority of lessons in the program and “help students make important connections and deepen their understanding while acquiring and developing mathematical skills and strategies,” 2. Understand Lessons, which “begin with the word “Understand” focus primarily on conceptual understanding and occur at key points in the instructional sequence,” and 3. Math in Action Lessons, which occur at the end of each unit and “review and apply unit content and teach students how to develop complete responses to a performance task.” 

The i-Ready Classroom Mathematics materials provide a consistent structure within each lesson, which is a session or “day”, and each “plays a different role in supporting student understanding.” “Each session takes 45-60 minutes to complete and includes time for instruction, practice, and differentiation.” Day 1 consists of an Explore session which “connects prior knowledge and introduces new content.” Days 2-4 consist of Develop sessions which “build multi-dimensional understanding using rich tasks, problem solving, discourse and multiple representations.” Day 5 consists of a Refine session which “strengthen skills and understanding with in-class practice time” and “reteach, reinforce, and extend learning.” The materials present all students with opportunities to meet the full intent and engage in extensive work with each grade-level standard. Examples include:

• Unit 2, Lessons 7 and 10, engage students with the full intent and extensive work with 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.) Unit 2, Lesson 7, Multiplication and Division in Word Problems, Session 2, Additional Practice, Practice Multiplication in Word Problems, Problem 5, “Which problem can be solved using the equation 8\times2=m?  Choose all that apply.” Answer choices: “Abeni reads 8 books in June. She reads half as many books in July. How many books does Aneni read in July?; Pedro is twice as old as his sister. His sister is 8 years old. How old is Pedro?; A pen costs $8. Kele buys 8 pens. How much does Kele spend on pens?; Alita has 8 apples and 2 oranges. How many pieces of fruit does she have altogether?”; and Fadil makes 8 paper airplanes. He gives 2 paper airplanes to a friend. How many paper airplanes does Fadil have now?” Session 3, Additional Practice, Practice Division in Word Problems, Problem 3, “A school for guide dogs has 42 black dogs. That is 6 times as many as the number of yellow dogs at the school. Write and solve an equation to find the number of yellow dogs. Show your work.” Lesson 10, Model and Solve Multi-Step Problems, Session 2, Develop, Apply It, Problem 8, “Miguel has 28 markers. His sister has 33 markers. They buy 3 more boxes of markers. Each box has 8 markers. Write an equation to represent the total number of markers Miguel and his sister have. Show your work.” Session 2, Additional Practice, Practice Modeling Multi-Step Problems, Problem 3, “Josh goes to the book fair and buys 3 comic books for $5 each, 2 chapter books for $9 each, 4 posters for $2 each, and 1 picture book for $7. Write an equation that can be used to find out how much Josh spends at the book fair. Show your work.” Session 3, Develop, Apply It, Problem 8, “ Aun will host a dinner to celebrate Tet, the Vietnamese Lunar New Year. She has $200 to buy groceries. She needs $95 for a pork and egg dish, $54 for sticky rice cakes, and $38 for soup. Write and solve an equation to find out if she has enough money for the food. Estimate to check that your answer is reasonable. Show your work.” Problem 9, “Look at your answer to problem 8. Does Aun get any change back from her $200? Explain how you know.” 

• Unit 3, Lessons 11 and 12, engage students with the full intent and extensive work with 4.NBT.5 (Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models). Students multiply a whole number of up to four digits by a one and two-digit numbers. Lesson 11, Multiply by One-Digit Numbers, Session 1, Explore, Additional Practice, Prepare for Multiplying by One-Digit Numbers, Problem 2, “Fill in the blanks below to show how to find 2\times48. 2\times48=(2\times__)+(2\times__); =___$$+$$___ ; =___.” Session 2, Explore, Apply It, Problem 9, “Find the product of 5 and 738. Estimate to check that your answer is reasonable. Show your work.” Session 3, Additional Practice, Practice Multiplying a Four-Digit Number by a One-Digit Number, Problem 2, “Show how to use partial products to find 5\times1,643. Session 4, Refine, Apply It, Problem 5, “Robyn and her foster mom volunteer at a food bank. They help fill 273 food boxes. Robyn puts 3 cans of soup in each food box. How many cans of soup does Robyn put in the food boxes in all?” Answers include: 276, 546, 619, and 819. Lesson 12, Multiply by Two-Digit Numbers, Session 1, Additional Practice, Prepare for Multiplying by Two-Digit Numbers, Problem 2, “Complete the area model. Then add the four partial products to find 18\times24. ___$$+$$___$$+$$___$$+$$___$$=$$___. ” There is an image of a partially completed area model with the following equations: 10\times20=___, 10\times4=___, 8\times20=___, and 8\times4=___ . Session 2, Develop, Apply It, Problem 7, “Complete the area model below. Then add the partial products to find the product of 27 and 21. Show your work.” There is an image of a partially completed area model with the following equations: 20\times20=___, 20\times7=___, 1\times20=___, and 1\times7=___.” Session 3, Refine, Apply It, Problem 1, “A farmer replaces all the sprinklers in one of their fields. The field has 15 rows of sprinklers. Each row has 24 sprinklers. How many sprinklers does the farmer replace? Show your work.” 

• Unit 4, Lesson 17,Understand Equivalent Fractions, Sessions 1-3, engage students with the full intent and extensive work with 4.NF.1 (Explain why a fraction \frac{1}{b} is equivalent to a fraction \frac{(n\timesa)}{(n\timesb)} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions). Students develop an understanding of equivalent fractions. Session 1, Explore, Model It, Problem 3, “Shade each model to represent the fraction shown. a. Is the area you shaded in each model the same? b. How do you know that \frac{1}{3}, \frac{2}{6}, and \frac{4}{12} are equivalent fractions? c. Compare the models. How many times as many equal parts and shaded parts does each model have than the model above it?”  Pictures of equal sized rectangles partitioned into thirds, sixths, and twelfths with \frac{1}{3}, \frac{2}{6}, and \frac{4}{12} labeled above each rectangle are provided. Session 2, Develop, Model It, Problem 3, “Write the missing numbers to find a fraction equivalent to \frac{5}{6} using multiplication. \frac{5\times2}{6x}=\frac{10}{}” Session 3, Refine, Apply It, Problem 3, “Use different methods to find two fractions that are equivalent to \frac{3}{3}.”

• Unit 5, Lesson 31, Angles, Sessions 2-4, engage students with the full intent and extensive work with 4.MD.6 (Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure). Students measure angles in whole-number degrees using a protractor, and sketch angles of specified measure. Session 2, Additional Practice, Practice Using a Protractor, Problem 1, “Read the number of degrees on the protractor to find the measure of the angle. The angle measures ___ degrees.” An image of an angle drawn over a picture of a protractor is shown. Session 3, Additional Practice, Practice Drawing Angles, Problem 3, “Draw a 160° angle.” Session 4,  Refine, Apply It, Problem 8, “Explain how you can use a protractor to measure the angle shown.” 

• Unit 5, Lesson 30, Points, Lines, Rays, and Angles, Sessions 1-5, engage students with the full intent and extensive work with 4.G.1 (Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines, identify these in two-dimensional figures). Session 1, Additional Practice, Prepare for Points, Lines, Rays, and Angles, Problem 1, “Think about what you know about geometric figures. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.” A chart with the headings Word, In My Own Words and Example is shown. Words in the chart include: point, line segment, line, ray, and angle.  Session 2, Develop, Apply It, Problem 6, “Samir cuts this shape from old clothes to make a patchwork quilt. How many lines are in this shape? How many rays? Explain How you know.” An image of a pentagon with angles labeled A-E is shown. Session 3, Additional Practice, Practice Identifying Angles, Problem 1, “How many right angles are in this shape?” Problem 2, “How many acute angles are in this shape?” Problem 3, “How many obtuse angles are in this shape?” Session 4, Develop, Apply It, Problem 7, “Damari copies the shape below from his brother’s kente stole. How many pairs of parallel sides does the shape below have? Explain how you know.” An image of a trapezoid is shown. Session 5, Refine, Apply It, Problem 2, “A crosswalk is marked with a pair of parallel line segments that extend from one side of the street to the other. The distance between the two line segments from point A to point B is 6 feet. What is the distance from Point C to Point D?” An image of a crosswalk with labeled line segments is shown.

The materials reviewed for i-Ready Classroom Mathematics, Grade 4 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the grade. 

• The approximate number of Units devoted to major work of the grade, including supporting work connected to major work is 4 of 5 units, approximately 80%.

• The number of Lessons (Strategy and Math in Action) devoted to major work of the grade, including supporting work connected to major work is 31 of 39, approximately 79%. 

• The number of instructional days (including Strategy and Math in Action Lessons, Mid-Unit Assessments, and Unit assessments) devoted to major work of the grade, including supporting work connected to major work is 116 of 149, approximately 78%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of Strategy Lessons, Math in Action Lessons, and Unit Assessments. As a result, approximately 78% of the instructional materials focus on the major work of the grade.

The materials reviewed for i-Ready Classroom Mathematics, Grade 4 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

The materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Within Program Implementation, Correlations, Content Focus in the Common Core State Standards (CCSS), teachers are encouraged to "Use the tables to help inform i-Ready Classroom Mathematics instructional pacing so that students spend the majority of their time on the work of the major clusters, with time spent on supporting and additional clusters used to enhance that work." Examples of connections include:

• Unit 2, Lesson 8, Multiples and Factors, Session 3, Develop, connects supporting work of 4.OA.4 (Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite) to the major work of 4.OA.3 (Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding), as students use factors to solve a multiplication word problem. Apply It, Problem 6, “Alberto is helping his mom make siopao buns. He needs to arrange 18 siopao buns in equal-size rows on a tray. What are all the different ways Alberto can arrange the siopao buns? Show your work.” Additional Practice, Practice Factors and Factor Pairs, Problem 5, “Carlos and Zene have the same number of building blocks. Carlos arranges his building blocks into 2 rows of 12 blocks. Zene arranges her building blocks into 6 rows of 4 blocks. What are two other ways they can arrange their blocks? Show your work.”

• Unit 3, Lesson 13, Use Multiplication to Convert Measurements, Session 1, Additional Practice, Problem 3, connects supporting work of 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit…) to the major work of 4.NBT.5 (Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models), as students use relative sizes of measurement units within one system of units in order to multiply a whole number of up to four digits. Additional Practice, Prepare for Using Multiplication to Convert Measurement, Problem 3, “Lucia’s exercise class starts in 195 minutes. It takes Lucia 3 hours to do errands. Does Lucia have enough time to do errands before the class starts?”

• Unit 4, Lesson 28, Problems about Time and Money, Session 4, Refine, Apply It, Problem 2,  connects supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale) to the major work of 4.OA.2 (Multiply or divide to solve word problems involving multiplicative comparison), as students solve problems involving time and money using whole numbers. Apply It, Problem 2, “Kanatase sweeps the kitchen floor after he washes the dishes. Then he takes out the trash. He spends 18 minutes washing the dishes. This is 3 times as long as it takes him to sweep the floor. It takes him 3 minutes to take out the trash. How long does it take Kanatase to complete his chores? Show your work.”

The materials reviewed for i-Ready Classroom Mathematics, 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 are designed so major standards/clusters are connected to the major standards/ clusters of the grade as well as supporting standards/clusters being connected to supporting standards/clusters. Within Program Implementation, Correlations, Content Focus in the Common Core State Standards (CCSS), teachers are encouraged to "Use the tables to help inform i-Ready Classroom Mathematics instructional pacing so that students spend the majority of their time on the work of the major clusters, with time spent on supporting and additional clusters used to enhance that work.” Examples of connections include:

• Unit 1, Lesson 4, Add Whole Numbers, Session 2, Develop, Apply It, Problem 6, connects the major work of 4.OA.A (Use the four operations with whole numbers to solve problems) to the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic), as students use the standard algorithm to solve problems. “Bridget likes to check out mystery books and adventure books from the library. The library has 2,386 mystery books and 4,332 adventure books. How many mystery books and adventure books does the library have in all? Show your work.”

• Unit 2, Lesson 9, Number and Shape Patterns, Session 2, Develop, Apply It, Problem 9, connects the supporting work of 4.OA.B (Gain familiarity with factors and multiples) to the supporting work of 4.OA.C (Generate and analyze patterns), as students describe, analyze, and extend patterns in number and shapes. “Start with the number 16. Use the rule divide by 2. Write the next three numbers in the pattern. Show your work.”

• Unit 4, Lesson 25, Session 1, Additional Practice, Prepare for Fractions as Tenths and Hundredths, Problem 3, connects the major work of 4.NF.A (Extend understanding of fractions equivalence and ordering) to the major work of 4.NF.C (Understand decimal notation for fractions and compare decimals fractions), as students explain the relationship between tenths and hundredths. “Caroline jogs to the park. She has six tenths of a mile left to jog. Write an equivalent fraction to show how far Caroline has left to jog in hundredths of a mile.” 

• Unit 4, Math in Action, Use Fractions and Decimals, Persevere on Your Own, Picture Frame Problem, connects the major work of  4.NF.A (Extend understanding of fraction equivalence and ordering.) to the major work of 4.NF.B (Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.), as students solve problems using fractions. “Luna is using craft sticks to make a background for a photo. The background will look like a picture frame when Luna glues the photo on top of it. Below are her instructions. Paint 6 craft sticks. Each stick is \frac{3}{4} of an inch wide and 5\frac{3}{4} inches long. Line up the craft sticks horizontally with their edges touching and glue them on a piece of cardboard. Glue a photograph 2\frac{1}{4} inches wide and 2\frac{1}{4} inches tall on the craft sticks. Leave a space at least 2\frac{2}{4} inches wide to the right of the photo. You can put your decorations here. There needs to be at least \frac{2}{4} of an inch of space above and below the photo. Explain if Luna’s plan works.”

• Unit 5, Lesson 30, Points, Lines, Rays, and Angles, Session 5, Refine, Apply It, Problem 6, connects the supporting work of 4.MD.C (Geometric measurement: understand concepts of angle and measure angles.) to the supporting work of 4.G.A (Draw and identify lines and angles, and classify shapes by properties of their lines and angles.), as students use understanding of angle concepts to identify and classify shapes. “The side view of a wheelchair ramp is shown below. Which term describes the shape? Choose all that apply.” Answers include: parallel line segments, perpendicular line segments, right angle, acute angle, obtuse angle. A picture of a right triangle is shown.

The materials reviewed for i-Ready Classroom Mathematics, 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.

Each Unit contains a Beginning of Unit section that provides numerous resources including a Lesson Progression and Math Background document for the teacher. The Lesson Progression identifies: “Which lessons are students building upon?”, “Which lessons are students preparing for?”, along with connections to prior and future work. The Math Background identifies “Information to unpack the learning progressions and make connections between key concepts.”

Examples of connections made to future grades include:

• Unit 2: Operations: Multiplication, Division, and Algebraic Thinking, Lesson 7: Overview, Multiplication and Division in Word Problems, Learning Progression, “In this lesson students solve multiplication and division word problems. Students model problems involving times as many situations, write an equation using symbols, and solve to find the unknown.” “Developing student understanding and application of multiplicative comparisons forms the basis for students’ understanding of multiplication as scaling in Grade 5.”

• Unit 3: Multi-Digit Operations and Measurement: Multiplication, Division, Perimeter and Area, Lesson 15: Overview, Divide Four-Digit Numbers, Learning Progression, “In this lesson students will apply their knowledge of dividing, along with their understanding of place value and properties of operations to divide up to four-digit numbers by one-digit numbers…In Grade 5 students will find quotients of dividends with up to four digits and divisors with up to two digits.”

• Unit 4: Fractions, Decimals, and Measurement: Addition, Subtraction, and Multiplication, Lesson 18: Overview, Compare Fractions, Learning Progression, “In Grade 4 students extend their understanding of fractions to compare two fractions with different numerators and different denominators. In Grade 5 students will apply their understanding of fraction comparison when they learn to compare decimals.”

Examples of connections made to prior grades include:

• Unit 1: Whole Numbers: Place Value, Comparison, Addition, and Subtraction, Lesson 5: Overview, Subtract Whole Numbers, Learning Progression, “In this lesson students use strategies based on place value to build an understanding of the standard algorithm for subtraction...In Grade 3, students used a variety of strategies based on place-value understanding - including breaking apart numbers and regrouping as needed and adding on - to subtract two- and three-digit numbers. They used tools such as base-ten blocks, number lines…”

• Unit 2: Operations: Multiplication, Division, and Algebraic Thinking, Lesson 10: Overview, Model and Solve Multi-Step Problems, Learning Progression, “In this lesson students write and solve equations for multi-step problems using letters to represent unknown quantities and check answers for reasonableness.” “In Grade 3 students learned to write equations for two-step problems using whole numbers and the four operations.”

• Unit 4: Fractions, Decimals, and Measurement: Addition, Subtraction, and Multiplication, Lesson 28: Overview, Problems About Time and Money, Learning Progression, “In Grade 3 students solved word problems involving time intervals and elapsed time. In the lesson students apply their knowledge of time and money to solve word problems that involve all four operations. They solve problems that involve converting larger units of measurement to smaller units. They solve problems with more than one step.”