3rd Grade - Gateway 1

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 3 meet expectations for assessing grade-level content and if applicable, content from earlier grades. The materials for Grade 3 are divided into eight units, and each unit contains a written End-of-Unit Assessment. Additionally, the Unit 8 Assessment is an End-of-Course Assessment, and it includes problems from the entire grade level.  Examples of End-of-Unit Assessments include: 

• Unit 2, Area and Multiplication, End-of-Unit Assessment, Problem 3, “A rectangle has an area of 12 square inches. What could be the length and width of the rectangle? Select all that apply. A. 2 inches and 6 inches. B. 5 inches and 7 inches. C. 3 inches and 4 inches. D. 2 inches and 4 inches. E. 1 inch and 12 inches.” (3.MD.5, 3.MD.7b)

• Unit 4: Relating Multiplication and Division, End-of-Unit Assessment, Problem 2, students “Select all situations that match the equation 48\div6=?. A.There are 48 volleyball players on 6 equal teams. How many players are on each team? B.There are 48 basketball teams at the tournament. There are 6 players on each team. How many basketball players are at the tournament? C.There are 48 kids swimming in the pool. Then 6 kids leave the pool. How many kids are swimming in the pool now? D.There are 6 buses. Each bus has 48 students on it. How many students are there altogether? E.There are 48 oranges in the box. Jada puts 6 oranges in each bag. How many bags does Jada need for all the oranges?” (3.OA.2, 3.OA.6)

• Unit 5, Fractions as Numbers, End-of-Unit Assessment, Problem 5, students “Write two fractions that are equivalent to \frac{1}{2}.” (3.NF.3b)

• Unit 7, Two-dimensional Shapes and Perimeter, End-of-Unit Assessment, Problem 7, “Priya wants to make a rectangular playpen for her dog. She has 18 meters of fencing materials. Andre suggests that Priya make a playpen that is 10 meters long and 8 meters wide. Explain why Priya does not have enough fencing to make this playpen. b. What are 2 possible pairs of side lengths Priya could use for the playpen that would give different areas? Explain or show your reasoning. c. Which playpen do you think Priya should make? Explain or show your reasoning.” (3.MD.7, 3.MD.8)

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 3 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide extensive work with and opportunities for students to engage in the full intent of Grade 3 standards by including in every lesson a Warm Up, one to three instructional activities, and Lesson Synthesis. Within Grade 3, students engage with all CCSS standards.

Examples of extensive work include:

• Unit 1, Introducing Multiplication and Unit 4, Relating Multiplication to Division, engage students with extensive work with grade-level problems from 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations to represent the problem). Unit 1, Introducing Multiplication, Lesson 19, Solve Problems Involving Arrays, Activity 2: Tyler’s Trees, students write an equation with a symbol for the unknown to represent an array situation. “‘Now you are going to practice what we just learned about solving array situations and writing an equation with a symbol for the unknown.’ Problem 1, ‘A field of coconut trees in Mexico has 5 rows of trees. Each row has 9 trees. How many trees are there?’” Unit 4, Relating Multiplication and Division, Lesson 7, Relate Multiplication and Division, Activity 2 Sets of School Supplies, students represent and solve problems involving equal groups. “Read through each situation and write an equation with a symbol that represents the unknown quantity for each situation. Then, solve and determine the unknown number in each equation. You can solve the problem first or write an equation first depending on what order makes the most sense to you. Be prepared to explain your reasoning.” Problem 1, “Kiran had 32 paper clips. He gave each student 4 paper clips. How many students received paper clips? a. Equation: ___.”

• Unit 3, Wrapping Up Addition and Subtraction Within 1000, Lesson 15, Round to the Nearest Ten and Hundred, engages students with extensive work with grade-level problems for 3.NBT.1 (Use place value understanding and properties of operations to perform multi-digit arithmetic.) Activity 1: Can the Nearest Ten and Hundred be the Same? Student Task Statements, students round given numbers to the nearest ten and hundred and see that the result can be the same for some numbers. “1. Round each number to the nearest ten and the nearest hundred. Use number lines if you find them helpful. 18, 97, 312, 439, 601. 2. Kiran and Priya are rounding some numbers and are stuck when trying to round 415 and 750. Kiran said, ‘415 doesn’t have a nearest multiple of 10, so it can’t be rounded to the nearest ten.’ Priya said, ‘750 doesn’t have a nearest multiple of 100, so it can’t be rounded to the nearest hundred. Do you agree with Kiran and Priya? Explain your reasoning.’”

• Unit 5, Fractions as Numbers, Lesson 16, Compare Fractions with the Same Numerator, engages students with extensive work with 3.NF.3d (Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model). In Warm-up: True or False: Unit Fractions, Student Task Statements, students compare and order common fractions. “Decide whether each statement is true or false. Be prepared to explain your reasoning.$$\frac{1}{2}>\frac{1}{4}$$, \frac{1}{4}>\frac{1}{3}, \frac{1}{6}>\frac{1}{8}.” Activity 1: Five Parts of Something, Student Task Statements, Problem 3, “Locate and label each fraction on a number line: \frac{5}{2}, \frac{5}{3}, \frac{5}{4}, \frac{5}{6}, \frac{5}{8}.”

Examples of full intent include:

• Unit 1, Introducing Multiplication, Lesson 5, Represent Data in Scaled Bar Graphs, Lesson 6, Choose a Scale, and Lesson 7, Answer Questions about Scaled Bar Graphs, engage students in the full intent of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.) In Lesson 5, Represent Data in Scaled Bar Graphs, Activity 2, Create a Scaled Bar Graph, Student Task Statements, students create a scaled bar graph to represent data. “Represent the data we collected earlier in a scaled bar graph. Use the graph with a scale of 2 or the graph with a scale of 5. If you have time, you can make 2 graphs. Be sure to label your title and categories.“ In Lesson 6, Choose a Scale, Cool-down, Reflection on Bar Graphs and Scale, “1. How did you decide on the scale for your graph in the last activity? 2. What was the most important thing you learned today that will help when you make your next scaled bar graph?” In Lesson 7, Answer Questions about Scaled Bar Graphs, Activity 1, Questions about Favorite Time of the Year, students use data presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems. Student Task Statements, “Use your Favorite Time of the Year graph to answer the questions. Show your thinking using expressions or equations. 1. How many students are represented in the graph? 2. How many students chose spring or fall as their favorite season? 3. How many more students chose summer than winter? 4.How many fewer students chose spring than fall?”

• Unit 2, Area and Multiplication, Lesson 3, Tile Rectangles, meet the full intent of 3.MD.6 (Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Students measure area by counting tiles in Lesson 3, Tile Rectangles, Activity 1, “Describe or show how to use the square tiles to measure the area of each rectangle. You can place square tiles on the handout where squares are already shown. You can also move the tiles, if needed.” Students use square units to count area in Lesson 4, Area of Rectangles, Activity 2, “Find the area of each rectangle and include the units. Explain or show your reasoning.” Problems 1-4 each show different rectangles, Problem 1 has an area of 18; Problem 2 has an area of 30; Problem 3 has an area of 60; and Problem 4 has an area of 45. Students use inches and centimeters to measure area in Lesson 6, Different Square Units (Part 1). In Activity 2, students estimate how many square centimeter and square inch tiles would be needed to cover a square, and then measure the square. “Estimate how many square centimeters and inches it will take to tile this square. square inches (estimate) ___, square centimeters (estimate) ___, 1. Use the inch grid and centimeter grid to find the area of the square, square inches ___, square centimeters ___.” There is a picture of a square shown in the materials. In Lesson 7, Different Square Units (Part 2), students learn what square feet and square meters look like from 2 images of a student holding a square, one that measures 1 square meter, the second that measures 1 square foot during Activity 1. Then, in Activity 2, students select which unit makes sense to measure the area of various objects, “For each area tell if you would use square centimeters, square inches, square feet, or square meters to measure it and why you chose that unit. a. The area of a baseball field, b. The area of a cover of a book you’re reading, c. The area of our classroom, d. The area of a piece of paper, e. The area of the top of a table, f. The area of the screen on a phone.”

• Unit 5, Fractions as Numbers, Lesson 1, Name the Parts, meets the full intent of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.), students divide shapes into equal areas. Activity 2, “Fold each rectangle your teacher gives you into 3, 6, 4, or 8 equal parts. Draw lines where you folded to partition the rectangles. Be prepared to share how you folded your shapes.” During the Activity 2 Synthesis, the teacher is instructed to lead a discussion naming the parts as unit fractions, “‘When we partition a shape into 6 equal parts, each part is called a ‘sixth.’ When we partition a shape into 8 equal parts, each part is called an ‘eighth,’ before instructing students to label each of their folded rectangles with unit fractions, ‘Let’s label the parts in each of your rectangles with fractions.’” In The Cool Down, students show eighths, “Partition the rectangle into eighths.” In Lesson 2, Non-unit Fractions, students have another opportunity to partition shapes and label unit fractions in the Cool Down, “1. Label each part with the correct fraction. 2. Partition and shade the rectangle to show \frac{1}{4}.” Problem 1 is accompanied by a rectangle split into 2 rows of 4 to show eighths, and Problem 2 has an empty rectangle for students to partition and shade.

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade:

• The approximate number of units devoted to the major work of the grade (including assessments and supporting work connected to major work) is 6 out of 8, approximately 75%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to major work) is 109 lessons out of 151 lessons, approximately 72%. The total number of lessons include 101 lessons plus 8 assessments for a total of 109 lessons. 

• The number of days devoted to major work of the grade (including assessments and supporting work connected to major work) is 115 days out of 159 days, approximately 72%.

The lesson-level analysis is the most representative of the instructional materials, as the lessons include major work, supporting work connected to major work, and assessments in each unit.  As a result, approximately 72% of the instructional materials focus on major work of the grade.

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed with supporting standards/clusters connected to the major standards/clusters of the grade. These connections are listed for teachers on a document titled, “Pacing Guide and Dependency Diagram” found on the Course Guide tab for each Unit. Teacher Notes also provide the explicit standards listed within the lessons. Examples of connections include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Lesson 2, Addition and Subtraction Situations, Cool-down: How Much Taller?, connects supporting work 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) and major work 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic). Students solve multi-digit, multi-step word problems. Student Task Statements, “The Statue of Liberty is 305 feet tall. The Brooklyn Bridge is 133 feet tall. How much taller is the Statue of Liberty than the Brooklyn Bridge? Explain or show your reasoning.”

• Unit 4, Relating Multiplication to Division, Lesson 17, Use the Four Operations to Solve Problems, Warm Up, connects the supporting work of 3.NBT.3 (Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.) to the major work of 3.OA.5 (Apply properties of operations as strategies to multiply and divide.) Students determine if multiplication equations involving ten and multiples of ten are true or false. In the Student Task Statement, “Decide if each statement is true or false. Be prepared to explain your reasoning. 2\times40=2\times4\times1, 2\times40=8\times10, 3\times50=15\times10, 3\times40=7\times10, 2\times40=2\times4\times10.”  

• Unit 5, Fractions as Numbers, Lesson 2, Name Parts as Fractions, Cool-down: Label the Parts, connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas) to the major work of 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts.) Students partition shapes into parts and determine the fraction. Student Task Statements, “1. Label each part with the correct fraction. 2. Partition and shade the rectangle to show \frac{1}{4}.”

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 3 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. 

Materials are coherent and consistent with the Standards. Examples of connections between major work to major work and/or supporting work to supporting work throughout the materials, when appropriate, include:

• Unit 4, Relating Multiplication to Division, Lesson 22, School Community Garden, Activity 2: Plan the Garden, connects the major work 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.MD.C (Geometric measurement: Understand concepts of area and relate area to multiplication and to addition). Students use multiplication and division within 100 to plan a school garden. Student Task Statements, “1. Read the information about some plants you could grow in a garden. Then, circle 2 plants to grow in your part of the school garden. a. strawberries. b. cantaloupe. c. zucchini. d. tomatoes. e. pinto beans. f. potatoes. 2. Plan your garden. Both of your plants should harvest between 50–100 fruits or vegetables. a. How many of each plant will you grow? b. Predict how many fruits or vegetables you will harvest. Show or explain your reasoning. 3. Make a diagram that shows how the plants are arranged and how much space is needed.” 

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 8, Estimate and Measure Liquid Volume, Cool Down, connects the major work of 3.MD.A (Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects) to the major work of 3.NF.A (Develop understanding of fractions as numbers). Students use fractions to measure volume in images of liquid in containers. “What is the volume of the liquid shown in each image?” The first image shows a beaker with 3 liters of water inside a container that shows large tick marks to count by 2s and small tick marks to count by 1s. The second image shows a beaker with 1\frac{1}{2} liters of water inside a container that shows large tick marks to count by 1s and small tick marks to count by halves. 

• Unit 7, Two-Dimensional Shapes and Perimeter, Lesson 14, Wax Prints connects the supporting work of 3.G.A (Reason with shapes and their attributes) to the supporting work of 3.MD.D (Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measurement). In Activity 1, Create A Wax Print Pattern, students apply what they’ve learned about quadrilaterals to geometric measurement. Problem 1, “Use the dot paper to design your own wax print pattern. Your pattern should: a. use a rhombus, rectangle, or square. b. use a quadrilateral that is not a rhombus, rectangle, or square. c. have each shape repeat at least 5 times.”

• Unit 8, Putting It All Together, Lesson 8, Estimate and Measure Liquid Volume, Cool-down: Measure in Liters connects the major work of 3.MD.A (Solve problems involving Measurement and estimation of intervals of time, liquid volumes, and masses of objects) to the major work of 3.NF.A (Develop understanding of fractions as numbers) as students find the volume of liquid shown. Student Task Statements, “What is the volume of the liquid shown in each image?”

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 3 meet expectations that content from future grades is identified and related to grade-level work and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

The Section Dependency Chart explores the Unit sections relating to future grades. The Section Dependency Chart states, “arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.” 

Examples of connections to future grades include:

• Unit Overview, Full Unit Narrative, Unit 3: Wrapping Up Addition and Subtraction Within 1,000, Unit Learning Goals, “Students explore various algorithms but are not required to use a specific one. They should, however, move from strategy-based work of grade 2 to algorithm-based work to set the stage for using the standard algorithm in grade 4. If students begin the unit with knowledge of the standard algorithm, it is still important for them to make sense of the place-value basis of the algorithm.”

• Unit 3, Wrapping Up Addition and Subtraction within 1,000, Full Unit Narrative, connects 3.NBT.1 (Use place value understanding to round whole numbers to the nearest 10 or 100.), 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.), 3.OA.5 (Apply properties of operations as strategies to multiply and divide), 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division…), 3.OA.8 (Solve two-step word problems using the four operations. 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), 3.OA.9 (Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations) to work in grade 4. “Students explore various algorithms but are not required to use a specific one. They should, however, move from strategy-based work of grade 2 to algorithm-based work to set the stage for using the standard algorithm in grade 4. If students begin the unit with knowledge of the standard algorithm, it is still important for them to make sense of the place- value basis of the algorithm. Understanding of place value also comes into play as students round numbers to the nearest multiple of 10 and 100. Students do not need to know a formal definition of “multiples” until grade 4. At this point, it is enough to recognize that a multiple of 10 is a number called out when counting by 10, or the total in a whole-number of tens (such as 8 tens). Likewise, a multiple of 100 is a number called out when counting by 100, or the total in a whole-number of hundreds (such as 6 hundreds). Students use rounding to estimate answers to two-step problems and determine if answers are reasonable.”

• Unit 8, Unit Overview, Full Unit Narrative, Putting It All Together, Unit Learning Goals, “In section A, students reinforce what they learned about fractions, their size, and their location on the number line. In section B, students deepen their understanding of perimeter, area, and scaled graphs by solving problems about measurement and data. Section C enables students to work toward multiplication and division fluency goals through games. The concepts and skills strengthened in this unit prepare students for major work in grade 4: comparing, adding, and subtracting fractions, multiplying and dividing within 1,000, and using the standard algorithm to add and subtract multi-digit numbers within 1 million.”

Examples of connections to prior knowledge include:

• Unit 1, Introducing Multiplication, Lesson 1, Make Sense of Data, Activity 1: Picture Time connects 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.) to the work in grade 2 (2.MD.10), “In grade 2, students learned how to draw and label single-unit scale bar graphs and picture graphs and used categorical data presented in graphs to solve simple problems. In this lesson, students revisit the structure of picture graphs and bar graphs, the features of graphs that help communicate information clearly, and the information they can learn by analyzing a graph. Students learn that a key is the part of a picture graph that tells what each picture represents. Students contextualize and make sense of the data based on the title, the given values, and their own experiences.”

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000 (version 1), Lesson 4, Introduction to Addition Algorithms, About this lesson, connects 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to the work in grade 2. “An algorithm is different from a strategy because it is a set of steps that works every time as long as the steps are carried out correctly. The algorithms introduced in this lesson draw on the grade 2 work within 1,000 in that they show the addition of ones to ones, tens to tens, and hundreds to hundreds. Students should have access to base-ten blocks if they choose to use them.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 4, Interpret Measurement Data on Line Plots, Warm-up: Notice and Wonder: A List and a Line Plot connects 3.MD.4 (Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units–-whole numbers, halves, or quarters.) to the work in grade 2. “In grade 2, students made line plots to show measurements to the nearest whole unit. In previous lessons, they measured objects with rulers marked with halves and fourths of an inch. In this lesson, students interpret line plots that show lengths in half inches and quarter inches and ask and answer questions about the data (2.MD.9).”