5th Grade - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 5 materials contain five units, with each unit providing numerous opportunities for both formative and summative assessments. Summative assessment items include:

• Unit 2, Assess, Mid-Unit Assessment, Form A, Item 7, “A golf ball has a mass of 0.04 kilogram and a football has a mass of 0.4 kilogram. How is the mass of the football-related to the mass of the golf ball? Write a sentence or equation to show your answer.” (5.NBT.1)

• Unit 3, Assess, Unit Assessment, Form A, Item 11, “A rectangular cork board is \frac{2}{3} yard wide and \frac{10}{9} yards long. Complete the equation to find the area of the cork board in square yards. Write your answer in the blanks. ___$$\times$$___$$=$$ ___ square yards.” (5.NF.4)

• Unit 4, Assess, Mid-Unit Assessment, Form A, Item 5, “How many centimeters are in 15 meters?” Answer choices include 0.15 centimeter, 1.5 centimeters, 150 centimeters, and 1,500 centimeters. (5.MD.1)

• Unit 4, Assess, Unit Assessment, Form A, Item 2, “Name one attribute that rhombuses and squares always share. Name an attribute they only sometimes share.” (5.G.3)

• Unit 5, Assess, Unit Assessment, Form B, Item 9, “Chelsea makes number patterns. Pattern A starts at 0 and has the rule ‘add 16’. Pattern B starts at 0 and has the rule ‘add 4’. Write the first five terms of each pattern. How are the corresponding terms related? Show your work. Solution_____.” (5.OA.3)

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 1, Lesson 1, Understand Volume, Sessions 1-3 engage students with the full intent and extensive work with 5.MD.3 (Recognize volume as an attribute of solid figures and understand concepts of volume measurement). Students explore the idea that the amount of space inside a solid figure can be measured. Session 1, Additional Practice, Prepare for Volume, Problem 3, ”Mei uses unit cubes to measure the volume of the box shown. She thinks the volume of the box is 8 cubic units. Do you agree? Explain.” Session 3, Refine, Apply It, Problem 1, “Felipe is stacking unit cubes in a box. He partially fills the box, pauses, and says “The volume of this box is 18 cubic units.” Explain how Felipe might have found the volume of the box.” Problem 2, “Zene says that a box that is 1 unit wide, 2 units long, and 3 units tall has a greater volume than a box that is 2 units wide, 3 units long, and 1 unit tall.  Is she correct? Explain your answer.” 

• Unit 2, Lessons 10, 11, 14 and Unit 3, Lessons 15, 16, and 17, engage students with the full intent and extensive work with 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). Unit 2, Lesson 10, Add Decimals, Session 1, Explore, Try It, “Shanika and Jana run in a relay race. Shanika runs 100 meters in 13.6 seconds. Jana runs the same distance in 12.2 seconds. What is their total time?” Session 2, Develop, Apply It, Problem 7, “Nuka makes trail mix with 6.25 ounces of dried fruit and 1.8 ounces of sunflower seeds. How many ounces of trail mix does Nuka make? Show your work.” Problem 8, “What is the value of the expression 2.25+63.05+0.6? First, estimate the sum. Then find an exact answer. Show your work.” Lesson 11, Subtract Decimals, Session 1, Explore, Try It, “The mass of a white throated hummingbird is 4.5 grams. The mass of a red throated hummingbird is 3.2 grams.  What is the difference between the masses of the two hummingbirds?” Session 3, Develop, Apply It, Problem 6, “At a swim meet, Fiona swims 50 meters in 39.3 seconds. Her sister, Dagny, swims the same distance in 38.85 seconds. How much faster does Dagny swim 50 meters than Fiona? Show your work.” Problem 7, “Isaiah has two guinea pigs for pets. Spot weighs 39.73 ounces and Fluffy weighs 42.25 ounces. How much more does Fluffy weigh than Spot. Show how to solve the problem by adding on.” Lesson 14, Add and Subtract Decimals in Word Problems, Session 3, Develop, Try It, “Bobby is conducting a science experiment. He has 3.74 liters of Liquid A and 3.65 liters of Liquid B. He pours both liquids into a container. How much liquid is in the container? Estimate and solve. Tell if your answer is reasonable.” Session 3, Additional Practice, Practice Using Estimation with Decimals, Problems 3, “Diego and Efia are looking at cell phone plans. They could share a group plan that costs $119.95 per month, or they could each pay for an individual plan that costs $62.77 per month. Estimate which choice would cost less for Diego and Efia. Explain why. How much money could they save per month by paying for the choice that costs less instead of the plan that costs more. Show your work. Diego and Efia can save ______ by choosing a(n) ______ plan.” Unit 3, Lesson 15, Multiply a Decimal by a Whole Number, Session 3, Refine, Apply It, Problem 1, “Walela and her dad collect 16 bags of saskatoon berries to sell at the farmers market. Each bag weighs 1.8 pounds. How many pounds of saskatoon berries do they collect in all? Show your work.” Lesson 16, Multiply Decimals, Session 2, Develop, Apply It, Problem 8, “What is the value of the expression 0.6\times0.8 Show your work using an area model on the hundredths grid below.”  Session 3, Develop, Apply It, Problem 9, “Heidi’s stepfather fills their gas tank with 9.8 gallons of gas. Each gallon costs $3.85. How much does Heidi’s stepfather spend on gas? Show your Work.” Lesson 17, Divide Decimals, Session 4, Develop, Try It, “Jacy has $1.20 to buy ribbon. Each foot of ribbon costs $0.08. How much ribbon can Jacy buy?” Session 5, Refine, Apply It, Problem 1, “What number multiplied by 8 gives a product of 9.6? Write an equation and solve. Show your work.” Problem 2, “Darius uses a card to pay to ride the city bus. His card has a value of $18 left on it. How many times can Darius ride the bus with the value left on the card? Show your work.”

• Unit 3, Lessons 19 and 20, engage students with the full intent and extensive work with 5.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction). Students apply and extend their understanding of multiplication to multiply fractions and whole numbers to help find areas. Lesson 19, Understand Multiplication by a Fraction, Session 1, Explore, Model It, Problem 3, “Shade and label the ruler to find the length of \frac{1}{4} of \frac{1}{2} inch. Complete the sentence and the multiplication equation that represents the total length you shaded. \frac{1}{4} of \frac{1}{2} is ___of an inch. \frac{1}{4}\times\frac{1}{2}=___.” An image of a 4-inch ruler with eighth inch markings is provided. Session 2, Develop, Model It, Problem 3, “The shading overlaps here to make the darker purple rectangle. Explain why the rectangle represents \frac{1}{2} of \frac{1}{3}. Then complete the product.” An image of a square divided in halves horizontally with \frac{1}{2}  shaded and thirds vertically with \frac{1}{3} shaded is shown. Session 3, Apply It, Problem 2, “Marcus says that \frac{2}{3}\times\frac{1}{6}=\frac{5}{6}. Tell how Marcus might have found his product and then explain how to find the correct product.” Lesson 20, Multiply Fractions to Find Area, Session 1, Additional Practice, Prepare for Multiplying Fractions to Find Area, Problem 3, “Solve the problem. Show your work. Mrs. Patel designs a square park with a side length of 1 mile. She makes a square with \frac{6}{10}-mile sides in her park for sports fields. How many square miles of the park does she use for sports fields?” Session 2, Develop, Apply It, Problem 9, “An artist designs rectangular refrigerator magnets. The magnets need to be the same size. Each magnet needs to cover \frac{1}{12} square foot. Draw lines in the model below to show one way to tile a 1-foot square with magnets with the correct area. What are the length and width of each magnet?” Session 3, Additional Practice, Practice Tiling a Rectangle to Find Area, Problem 4, “Tamasha and her dad make a set of wooden dominoes. Each domino is shaped like a rectangle with a length of \frac{5}{2} inches and a width of \frac{5}{4} inches. Use a visual model to find how many square inches of wood Tamasha needs for each domino. Then write an equation to describe your model. Show your work.” Session 4, Refine, Apply It, Problem 2, “Susan La Flesche Picotte was the first Native American to graduate from medical school. Nahele makes a poster about Dr. Picotte for a class project. The rectangular poster is \frac{3}{4}yard long and \frac{1}{3}yard wide. What is the area of the poster? Show your work.” 

• Unit 4, Lesson 29, Classify Two-Dimensional Figures, Sessions 1-4, engage students with the full intent and extensive work with 5.G.4 (Classify two-dimensional figures in a hierarchy based on properties). Students classify two-dimensional figures. Session 1, Explore, Try It, “Kenji is decorating place mats with sashiko stitching. His sashiko patterns include the quadrilaterals shown below. Arrange the quadrilaterals into a Venn diagram that shows a hierarchy of categories from most general to most specific. Label the categories represented by these shapes in your Venn diagram.” Session 2, Develop, Connect It, Problem 2, “Explain how the Venn diagram supports this statement: All parallelograms are quadrilaterals, but not all quadrilaterals are parallelograms.” Additional Practice, Practice Classifying Two- Dimensional Figures, Problem 4, “Draw a Venn diagram in the space below to show the relationships among the categories of isosceles, scalene, and equilateral triangles within the broader category, Triangles.” Session 3, Develop, Connect It, Problem 5, “Explain the relationship between the properties of categories when you move left or right (or up or down) in a tree diagram.” Session 4, Refine, Apply It, Problem 6, “Could you add the two shapes below to your tree diagram for polygons in problem 4? If so, where would you put them? Name each shape as you explain your thinking.”

• Unit 5, Lesson 33, Analyze Patterns and Relationships, Sessions 1-4, engage students with the full intent and extensive work with 5.OA.3 (Generate two numerical patterns using two given rules...) Students will understand that there can be a relationship between corresponding terms of two different number patterns. Session 1, Additional Practice, Prepare for Analyzing Patterns and Relationships, Problem 3, “DeAndre works at a gift shop. Each T-shirt costs $15 and each snow globe costs $5. DeAndre makes a list of the costs for buying 0, 1, 2, 3, 4, 5, or 6 T-shirts. He also makes a list of the costs for the same number of snow globes. Show how DeAndre may have made his list of the costs. Write a sentence describing the rules for each list.” Session 2, Develop, Apply It, Problem 6, “Maps of Hollywood tourist attractions costs $4, and bus tickets cost $24. Write a pattern for the costs of 0 - 5 maps and a second pattern for the costs of 0 - 5 tickets. How do the corresponding terms of the two patterns compare?” Session 3, Develop,  Apply It, Problem 7, “Consider the two patterns below. Start each pattern with 0. Pattern A: add 1. Patterns B: add 3. Write five ordered pairs made up of corresponding terms from the two patterns. Plot the points in the coordinate plane to the right. Describe the relationship between the two patterns.” Session 4, Refine, Apply It, Problem 1, “One pattern starts at 0 and has the rule add 8. Another pattern starts at 0 and has the rule add 4. Write six terms for each pattern of numbers. How do the corresponding terms in the patterns compare?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 30 of 38, 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 114 of 140, approximately 81%.

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 81% of the instructional materials focus on the major work of the grade.

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 4, Lesson 25, Convert Measurement Units, Sessions 2 and 4, connects the supporting work of 5.MD.1 (Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems) to the major work of 5.NBT.2 (Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10), as students multiply and divide decimals in order to convert measurements. Session 2, Develop, Apply It, Problem 9, “How many millimeters are in 9.25 centimeters? Show your work. (1 centimeter = 10 millimeters)” Session 4, Refine, Apply It, Problem 2, “How many kilograms are equivalent to 450 grams? Show your work.”

• Unit 4, Lesson 27, Make Line Plots and Interpret Data, Session 3, Develop, Apply It, Problem 7, connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions (\frac{1}{2}, \frac{1}{4}, \frac{1}{8})) to the major work of 5.NF.1 (Add and subtract fractions with unlike denominators (including mixed numbers] by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators), as students add fractions to solve word problems involving line plot data. Apply it, Problem 7, “What is the difference between the weights of the lightest piece and the heaviest piece of driftwood Soo collects? Show your work. Solution___.” A line plot  from 9 to 12 is shown titled, “Driftwood Weight.” It is divided into eighths with fourths, halves, and whole numbers labeled.

• Unit 5, Lesson 30, Evaluate, Write, and Interpret Expressions, Session 4, Refine, Apply It, Problem 1, connects the supporting work of 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expression without evaluating them) to the major work of 5.NBT.5 (Fluently multiply multi-digit whole numbers using the standard algorithm), as students write simple expressions in order to fluently multiply whole numbers. “Soledad makes bracelets and necklaces made from recycled plastic. Each item sells for $8. Write a word phrase that describes the calculations you would do to find out how much money Soledad makes by selling 23 bracelets and 17 necklaces. Then write and evaluate an expression to find how much money she makes. Show your work.”

The materials reviewed for i-Ready Classroom Mathematics, 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 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, Multiply Multi-Digit Numbers, Session 3, Apply It, Problem 8, 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.MD.C (Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.) “The tank for a pet lizard is shaped like a rectangular prism. The base of the tank has an area of 603 square inches. The height of the tank is 18 inches. What is the volume of the tank? Estimate to check for reasonableness. Show your work.”

• Unit 2, Lesson 10, Add Decimals, Session 1, Explore, Connect It, Problem 2, connects the major work of 5.NBT.A (Understand the place value system) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths), as students use expanded form to add decimals. “You can add decimals in different ways, just as you can add whole numbers in different ways. Think about the problem 32.14+17.5. Use expanded form to break apart each addend by place. Break apart 32.14: ___ Break apart 17.5: _____ Find the sum 34.14+17.5 by adding the parts in any order.”

• Unit 3, Lesson 22, Multiply Fractions in Word Problems, Session 2, Develop, Apply It, Problems 7-9, 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), as students solve real-world problems involving multiplication of fractions and mixed numbers. Problem 7, “Luis walks \frac{8}{10} of a mile. Tiana walks \frac{3}{4} of the way with Luis. How many miles does Tiana walk with Luis? Show your work.” Problem 8, “Bridget has \frac{15}{16} pound of tiles in different colors. She uses \frac{2}{3} of the tiles to decorate a picture frame. How many pounds of tiles does Bridget use for the picture frame? Show your work.” Problem 9, “Cristobal works \frac{5}{6} hour filing papers for his mother. He listens to music for \frac{4}{5} of the time he spends filing.How much time does Cristobal spend listening to music? Show your work.”

• Unit 5, Lesson 32, Represent Problems in the Coordinate Plane, Session 2, Additional Practice, Practice Graphing Points and Finding Distances, Problem 4a, connects the supporting work of 5.G.A (Graph points on the coordinate plane to solve real world and mathematical problems) to the supporting work of 5.G.B (Classify two dimensional figures into categories based on their properties), as students explore the idea that geometric figures can be graphed in the coordinate plane. “Plot and label the points K(2, 2), G(6, 2), and S(6, 5). Connect the points to form a triangle.” A picture of a coordinate grid is shown. Problem 4b states, “Which two sides of the triangle form a right angle?”

• Unit 5, Lesson 33, Analyze Patterns and Relationships, Session 3, Develop, Apply It, Problem 7, connects supporting work of 5.OA.B (Analyze patterns and relationships.) to the supporting work of 5.G.A (Graph points on the coordinate plane to solve real-world and mathematical problems.) “Consider the two patterns below. Start each pattern with 0. Pattern A: add 1, Pattern B: add 3, Write 5 ordered pairs made up of corresponding terms from the two patterns. Plot the points in the coordinate plane to the right. Describe the relationship between the two patterns.” A coordinate plane is provided.

The materials reviewed for i-Ready Classroom Mathematics, 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.

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 1: Whole Number Operations and Applications: Volume, Multiplication, and Division, Lesson 3: Overview, Find Volume Using Formulas, Learning Progression, “In this lesson students explain how volume formulas are related to finding volume as (number of cubes per layer) x (number of layers). Students recognize volume as additive, understanding that the volume of a solid figure is the combined volume of the rectangular prisms that compose the solid figure. In Grade 6 students will continue using these techniques to find volumes of solid figures with fractional side lengths.”

• Unit 4: Measurement, Data, and Geometry: Converting Units, Using Data, and Classifying Figures, Lesson 25: Overview, Convert Measurement Units, Learning Progression, “In this lesson students gain a conceptual understanding of the relative sizes of measurements units within a measurement system and reason about converting from one unit of measurement to another…In the next lesson students will solve word problems involving conversions of measurement units. In Grade 6 students will work with measurement units when they learn about ratios and unit rates.”

• Unit 5: Algebraic Thinking and the Coordinate Plane: Expressions, Graphing Points, Patterns and Relationships, Lesson 33: Overview, Analyze Patterns and Relationships, Learning Progression, “In this lesson students continue their work with number patterns as they begin to look at the relationships between patterns. In Grade 6 students will build on their understanding of the relationship between corresponding terms of two related patterns when they work with tables and graphs of equivalent ratios and begin to reason about relationships between an independent variable and a dependent variable.”

Examples of connections made to prior grades include:

• Unit 2: Decimals and Fractions: Place Value, Addition and Subtraction, Lesson 10: Overview, Add Decimals, Learning Progression, “In this lesson students add decimals to hundredths…In Grade 4 students achieved proficiency with adding multi-digit whole numbers. Building on place-value strategies from earlier grades, students gained an understanding of the standard algorithm for addition. They used place value charts as a guide to lining up digits in the correct place before computing. Previously in Grade 5 students wrote decimals to the thousandths in expanded form and learned to compare and round decimals.”

• Unit 4: Measurement, Data, and Geometry: Converting Units, Using Data, and Classifying Figures, Lesson 29: Overview, Classify Two-Dimensional Figures, Learning Progression, “IN this lesson students use their understanding of shape properties, categories, and subcategories to classify shapes into Venn diagrams and tree diagrams…In Grade 4 students classified two-dimensional figures based on their attributes, such as having parallel or perpendicular sides and having right, acute, or obtuse angles.”

• Unit 5: Algebraic Thinking and the Coordinate Plane: Expressions, Graphing Points, Patterns and Relationships, Lesson 31: Overview, Understand the Coordinate Plane, Learning Progression, “In previous grades students graphed points on a number line and identified perpendicular lines. In this lesson students are introduced to the coordinate plane in the first quadrant. Students learn that a coordinate plane is determined by a pair of perpendicular lines called axes…”