3rd Grade - Gateway 1

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum is divided into eight units and each unit contains a written End-of-Unit Assessment for individual student completion. The Unit 8 Assessment is an End-of-Course Assessment and it includes problems from across the grade. Examples from End-of-Unit Assessments include: 

• Unit 1, Introducing Multiplication, End-of-Unit Assessment, Problem 4, “Elena has 5 bags. Each bag has 8 rubber bands. How many rubber bands does Elena have? Explain or show your reasoning.” (3.OA.3)

• Unit 4, Relating Multiplication to Division, End-of-Unit Assessment, Problem 4, “Lin covers her desk with 77 sticky notes. The sticky notes are in 7 equal rows. How many sticky notes are in each row? a. Write a division equation to represent the situation. Use a symbol for the unknown quantity. b. Write a multiplication equation to represent the situation. Use a symbol for the unknown quantity. c. Solve the problem. Explain or show your reasoning.” (3.OA.3, 3.OA.4, 3.OA.6)

• Unit 5, Fractions as Numbers, End-of-Unit Assessment, Problem 5, “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. a. 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) 

• Unit 8, Putting It All Together, End-of-Course Assessment, Problem 4, “Seven bags of dog food weigh 63 kilograms. If all the bags have the same weight, how many kilograms does each bag of dog food weigh? a. Write an equation to represent the situation. Use a letter or symbol for the unknown. b. Solve the problem.” (3.MD.2, 3.OA.4)

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 3 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Grade 3 as students engage with all CCSSM standards within a consistent daily lesson structure, including a Warm Up, one to three Instructional Activities, a Lesson Synthesis, and a Cool-Down. Examples of extensive work include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Lesson 15 engages students with extensive work with grade-level problems for 3.NBT.1 (Use place value understanding to round whole numbers to the nearest 10 or 100). Lesson 15, Round to the Nearest Ten and Hundred, Activity 1, students round given numbers to the nearest ten and hundred and see that the result can be the same for some numbers. Student Facing, “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.” Activity 2, students practice rounding to the nearest ten and hundred in context. Student Facing, “The table shows the numbers of people in different parts of a school at noon during a school day. Andre and Lin are trying to estimate the number of people in the whole school. Andre plans to round the numbers to the nearest hundred. Lin plans to round them to the nearest ten. 1. Make a prediction: Whose estimate is going to be greater? Explain your reasoning. 2. Work with a partner to find Andre and Lin’s estimates. Record them in the table.” Table shows “playground 94, cafeteria 163, art room 36, library 13, classrooms 216, gymnasium 109, music room 52, total ___.” Cool-Down, Student Facing, “1. Round 237 to the nearest ten. Show or explain your reasoning. 2. Round 237 to the nearest hundred. Show or explain your reasoning.”

• Unit 5, Fraction as Numbers, Lessons 5, 6, and 7 engage students in extensive work with 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram). Lesson 5, To the Number Line, Activity 1, students further develop the idea that fractional amounts can be represented on a number line, “Groups of 2. Distribute one set of pre-cut cards to each group of students. ‘Work with your partner to sort some number lines into categories that you choose. Make sure you have a name for each category.’ 3-5 minutes: partner work time. Select groups to share their categories and how they sorted their cards. Choose as many different types of categories as time allows. Be sure to highlight categories created based on whether the tick marks represent whole numbers or fractions. If not mentioned by students, ask, ‘Can we sort the number lines based on what the tick marks represent? Let’s look at B and E. Both are partitioned into 4 parts. What do the unlabeled tick marks in E represent?’ (1, 2, 3) ‘What do you think those in B represent?’ (... or amounts less than 1). ‘Take a minute to sort your cards by number lines where the tick marks only represent whole numbers and number lines where the tick marks represent fractions.’ 1-2 minutes: partner work time.” Lesson 6, Locate Unit Fractions on the Number line, Warm-up: Which One Doesn’t Belong, students compare four images and talk about the characteristics of the items in comparison to one another, “Groups of 2. Display the image. ‘Pick one that doesn’t belong. Be ready to share why it doesn’t belong.’ 1 minute: quiet think time.” Lesson 7, Non-unit Fractions on the Number Line, Warm-up: Choral Count, students practice counting by \frac{1}{4} and notice patterns in the count. ‘Count by \frac{1}{4}, starting at \frac{1}{4}.’ Record as students count. Record 4 fractions in each row, then start a new row. There will be 4 rows. Stop counting and recording at \frac{16}{4}.”

• Unit 4, Relating Multiplication to Division, Lessons 11 and 20; Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 8; and Unit 8, Putting It All Together, Lesson 9 engage students in the extensive work with 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division). Unit 4, Lesson 11, Multiplication Strategies on Ungridded Rectangles, Cool-Down, “1. Mark or shade this rectangle to show a strategy for finding its area. 2. Write one or more expressions that represent how you find the area.” An image of a rectangle with sides labeled 6 and 9 is provided. Unit 4, Lesson 20, Strategies for Dividing, Activity 2, students practice finding the value of division expressions using any strategy that makes sense to them. Student Facing, “Find the value of each quotient. Explain or show your reasoning. Organize it so it can be followed by others. 1. 80\div5 2. 68\div4 3. 91\div7 If you have time: Eighty-four students on a field trip are put into groups. Each group has 14 students. How many groups are there?” Unit 6, Lesson 8, Estimate and Measure Liquid Volume, Warm-up, students use strategies for dividing within 100, “Display one expression. ‘Give me a signal when you have an answer and can explain how you got it.’” Student Facing, “Find the value of each expression mentally. 30\div3, 60\div3, 63\div3, 54\div3.” Unit 8, Lesson 9, Multiplication Game Day, Activity 2, students practice multiplying within 100 by playing a game of their choice. Student Facing, “Choose a center to practice multiplying within 100. Compare, Multiply within 100: Decide which expression has the greatest value. How Close? Multiply to 100: Choose 2–3 numbers to multiply to get a product closest to 100. Rectangle Rumble, Factors 1–10: Multiply numbers to create rectangular areas to fill a grid with the most squares.”

The materials provide opportunities for all students to engage with the full intent of Grade 3 standards through a consistent lesson structure. According to the IM Teacher Guide, A Typical IM Lesson, “Every warm-up is an instructional routine. The warm-up invites all students to engage in the mathematics of the lesson. After the warm-up, lessons consist of a sequence of one to three instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class. After the activities for the day, students should take time to synthesize what they have learned. This portion of class should take 5-10 minutes. The cool-down task is to be given to students at the end of the lesson and students are meant to work on the cool-down for about 5 minutes independently.” Examples of meeting the full intent include:

• Unit 2, Area and Multiplication, Lessons 2, 3, 4, and 6 engage students in full intent of 3.MD.6 (Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Lesson 2, How Do We Measure Area?, Activity 2, students use square tiles to measure area. Student facing, “Your teacher will give you handouts with some figures on them. Use square tiles to find the area of each figure. Record your answers here. Be prepared to explain your reasoning.” Figures have areas of 9, 18, 13, 30, 36, and 21 square units. Lesson 3, Tile Rectangles, Activity 1, students practice tiling with no gaps or overlaps. Student facing, “Your teacher will give you square tiles and a handout showing 4 rectangles and squares. 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. 2. Describe how to use square tiles to find the area of any rectangle.” Lesson 4, Area of Rectangles, Activity 2, students use squared units to find the area of 4 different rectangles, “Find the area of each rectangle and include the units. Explain or show your reasoning.” Lesson 6, Different Square Units (Part 1), Activity 2, students estimate and then find the area of squares using square inches and centimeters. Student Facing, “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 ___ 2. Write a multiplication expression that describes the rows and columns in the square and can tell us the area in each unit. square inches ___ square centimeters ___.”

• Unit 5, Fractions as Numbers, Lessons 10, 11, and 12 engage students in the full intent of 3.NF.3b (Recognize and generate simple equivalent fractions, e.g., \frac{1}{2}=\frac{2}{4}, \frac{4}{6}=\frac{2}{3}. Explain why the fractions are equivalent, e.g., by using a visual fraction model). Lesson 10, Equivalent Fractions, Activity 2, students use fraction strips to identify equivalent fractions and explain why they are equivalent. Student Facing, “Use your fraction strips from an earlier lesson to find as many equivalent fractions as you can that are equivalent to: 1. \frac{1}{2} 2. \frac{2}{3} 3. \frac{6}{6} 4. \frac{3}{4}.” Lesson 11, Generate Equivalent Fractions, Cool-down, students generate equivalent fractions, including for fractions greater than 1, given partially shaded diagrams. Student Facing, “1. Write two fractions that the shaded part of this diagram represents. (Bar diagram shows 3/6 shaded.) 2. Show that the shaded part of this diagram represents both \frac{5}{4} and \frac{10}{8}.” Lesson 12, Equivalent Fractions on a Number Line, Activity 3, students practice generating equivalent fractions. Student Facing, “1. Roll 6 number cubes. If you roll any fives, they count as a wild card and can be any number you’d like. 2. Can you put the numbers you rolled in the boxes to make a statement that shows equivalent fractions? Work with your partner to find out. 3. If you cannot, re-roll as many number cubes as you’d like. You can re-roll your number cubes twice. 4. If you can make equivalent fractions, record your statement and show or explain how you know the fractions are equivalent. You get 1 point for each pair of equivalent fractions you write.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lessons 9, 10, 11, and 14 engage students in the full intent of 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram). Lesson 9, Time to the Nearest Minute, Activity 2, students tell and write time to the nearest minute. Student Facing, “1. Show the time given on each clock. (Four clock images are provided. A. 2:36 PM ,B. 3:18 PM, C. 12:17 PM, D. 9:02 PM) 2. Draw a time on this clock. Trade with a partner and tell the time on their clock.” Lesson 10, Solve Problems Involving Time (Part 1), Activity 1, students solve problems involving elapsed time in a way that makes sense to them. Student Facing, “1. Kiran arrived at the bus stop at 3:27 p.m., as shown on this clock. He waited 24 minutes for his bus to arrive. What time did his bus arrive? Show your thinking. Organize it so it can be followed by others. 2. Elena arrived at the bus stop at 3:45 p.m. She also waited 24 minutes for her bus to arrive. What time did the bus arrive? Show your thinking. Organize it so it can be followed by others.” Two clock images are provided. Lesson 11, Solve Problems Involving Time (Part 2), Activity 1, students solve problems involving addition and subtraction of time intervals when given times on a clock. Student Facing, “1. For how many minutes was Han on the bus? Explain or show your reasoning. (The times when Han got on the bus and off the bus are shown with two analog clock images displaying 5:43 and 6:36.) 2. Draw the minute hand to show that Elena waited for the bus for 32 minutes.“ 2 additional analog clocks are pictured. Lesson 14, What Makes Sense in the Problem? Cool-down, students solve problems with time intervals. Student Facing, “1. A show at the carnival starts at 2:45 p.m. and lasts 47 minutes. What time does the show end? Explain or show your reasoning. 2. Another show that is 24 minutes long ends at 5:10 p.m. Kiran says that the show starts before 4:40 p.m. Do you agree? Explain or show your reasoning.”

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each 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 major work of the grade (including assessments and supporting work connected to the 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 the major work) is 109 out of 151, approximately 72%. The total number of lessons devoted to major work of the grade includes 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 the major work) is 115 out of 159, approximately 72%.

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

The materials reviewed for Kendall Hunt's 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 so supporting standards/clusters are 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 within the Course Guide tab for each unit. Examples of connections include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Lesson 2, Cool-down connects supporting work of 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) to the major work of 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 Facing states, “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 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 3, Activity 1 connects the supporting work of 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 major work of 3.NF.3 (Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size). Students measure lengths using a ruler that is marked with half inches and quarter inches, students recognize that lengths that line up with a half-inch mark can be read as one-half of an inch or two-fourths of an inch. Student Facing states, “1. Kiran and Jada are discussing the length of a worm, Kiran says that the worm is 4\frac{2}{4} inches long, Jada says that the worm is 4\frac{1}{2} inches long. Use the ruler to explain how both of their measurements are correct. 2. Measure the length of the following worms.” Images of four worms of various lengths are shown.

• Unit 7, Two-Dimensional Shapes and Perimeter, Lesson 8, Activity 1 connects the supporting work of 3.MD.8 (Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters) to the major work of 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). Students practice finding the perimeter of shapes that have labeled side lengths. Some of the figures are not regular shapes and will require multiple steps using addition to solve. Student Facing states, “What do you notice? What do you wonder? Find the perimeter of each shape. Explain or show your reasoning.” Students find the perimeter of seven different shapes, both regular and composite shapes.

The materials for Kendall Hunt's 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. These connections can be listed for teachers in one or more of the four phases of a typical lesson: warm-up, instructional activities, lesson synthesis, or cool-down. Examples of connections include:

• Unit 2, Area and Multiplication, Lesson 8, Activity 1 connects the major work of 3.MD.C. (Geometric measurement: understand concepts of area and relate area to multiplication and to addition) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division). Students solve an area problem with a partially tiled rectangle while using multiplication knowledge. This encourages students to multiply to solve problems involving area, but still provides some visual support to see the arrangement of the rows and columns. Student facing (students are provided two rectangles), “What do you notice? What do you wonder?, After learning about azulejos in Portugal, Elena is making her own tile artwork. This rectangle shows the project Elena is tiling. Each tile has a side length of 1 inch. How many tiles are needed to tile the whole rectangle? Explain or show your reasoning.” Activity Synthesis states, “‘How did you know how many tiles would be in each row or column?’ (The first row had 10 tiles, so I know every other row has 10 tiles because I could put more tiles to fill in the rows. It’s like an array. Each column has to have the same number of tiles, so there is 9 in each column.) ‘How did you find the total number of tiles needed?’ (I counted by ten 9 times. I multiplied 9 times 10.)”

• Unit 4, Relating Multiplication to Division, Lesson 7, Activity 1 connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division). Students reason abstractly and quantitatively as they relate drawings, situations, and equations. The Launch states, “In the first box on your sheet, create a drawing that shows equal groups of objects. This drawing will be used by other students in your group to fill in the other boxes.” Student Facing states, “Your teacher will give you a sheet of paper with 4 boxes on it and instruct you to draw or write something in each box. After working on each box, pause and wait for your teacher's instructions for the next box. 1. Draw equal groups in Box 1 on your recording sheet. 2. In Box 2, write a description of a division situation that matches the drawing you just received. 3. In Box 3, write a multiplication equation that matches the drawing and division situation you just received. Use a symbol for the unknown quantity. 4. In Box 4, write a division equation that matches the drawing, division situation, and multiplication equation you just received. Use a symbol for the unknown quantity.“

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 8, 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 liters to estimate and measure liquid volumes, including fractional quantities. Student Facing states, “What is the volume of the liquid shown in each image?” An image shows two containers, containing 3 liters and 1\frac{1}{2} liters, respectively.

• Unit 7, Two-dimensional Shapes and Perimeter, Lesson 14, Cool-Down connects the supporting work of 3.MD.D (Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures) to the supporting work of 3.G.A (Reason with shapes and their attributes). Students analyze an image in order to reason with shapes and their attributes. Student Facing states, “1. Describe the quadrilaterals that were used in this pattern. 2. If the image of the pattern is a rectangle with side lengths of 9 inches by 6 inches, what is the perimeter? Explain your reasoning.” Student Response states, “1. Sample responses: There are quadrilaterals in white and gray that don’t have any right angles. The black quadrilaterals are rhombuses. The grey shapes and the white shapes are quadrilaterals that have 2 equal sides. They are not rectangles, rhombuses, or squares. It looks like there are tall skinny rectangles that are shaded white and gray behind the black rhombuses. 2. 30 inches. I added 9 plus 6 to get 15, then multiplied by 2 since there would be another set of sides that were 9 inches and 6 inches.”

The materials reviewed for Kendall Hunt's 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. 

Prior and Future connections are identified within materials in the Course Guide, Section Dependency Diagrams which state, “an arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.” While future connections are all embedded within the Scope and Sequence, descriptions of prior connections are also found within the Preparation tab for specific lessons, and within the notes for specific parts of lessons. 

Examples of connections to future grades include:

• Course Guide, Scope and Sequence, Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Unit Learning Goals connect 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 addition and subtraction of multi-digit numbers using the standard algorithm in 4.NBT.4. Lesson Narrative states, “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.”

• Course Guide, Scope and Sequence, Unit 7, Two-dimensional Shapes and Perimeter, Unit Learning Goals connect 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories) to work with identifying angles in Grade 4. Lesson Narrative states, “In this section, students describe, compare, and sort a variety of shapes. They have previously used terms such as square, rectangle, triangle, quadrilateral, pentagon, and hexagon to name shapes. Here, students think about ways to further categorize triangles and quadrilaterals. They see that triangles and quadrilaterals can be classified based on their sides (whether some are of equal length) and their angles (whether one or more right angles are present). Although students will not learn the formal definition of an angle until grade 4, they are introduced to the terms ‘angle in a shape’ and ‘right angle in a shape’ to describe the corners of shapes. This allows students to distinguish right triangles and to describe defining attributes of squares and rectangles.”

• Course Guide, Scope and Sequence, Unit 8, Putting It All Together, Unit Learning Goals connect 3.NF.A (Develop understanding of fractions as numbers), 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations), and 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 major work in Grade 4, including operations with fractions and operations with multi-digit numbers. Lesson Narrative states, “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, Preparation 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 creating and analyzing graphs from 2.MD.10. Lesson Narrative states, “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 (MP2).”

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Lesson 3, Warm Up connects the work of 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 work with adding and subtracting within 1000 from 2.NBT.7. Narrative states, “The purpose of this Number Talk is to elicit strategies and understandings students have for adding three-digit numbers. These understandings help students develop fluency and will be helpful later in this lesson when students are to use strategies based on place value and properties of operations to add within 1,000.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 4, Preparation connects work with 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 work generating measurement data from 2.MD.9. Lesson Narrative states, “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.”