3rd-5th Grade - Gateway 1

The materials reviewed for Kiddom IM® v.360 Grade 3 through 5 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The materials for Grade 3 are divided into eight units, each containing an End-of-Unit Assessment. The Unit 8 Assessment is an End-of-Course Assessment, including questions from the entire grade level. An example of an End-of-Unit Assessment includes:

• Unit 4, Relating Multiplication and Division, End-of-Unit Assessment, Question 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)

The materials for Grade 4 are divided into nine units, each containing an End-of-Unit Assessment. The Unit 9 Assessment is an End-of-Course Assessment, including questions from the entire grade level. An example of an End-of-Unit Assessment includes:

• Unit 5, Multiplicative Comparison and Measurement, End-of-Unit Assessment, Question 1, “There are 93 students in the cafeteria. There are 3 times as many students in the cafeteria as there are students on the playground. Part A, Write a multiplication equation that represents the situation. Part B, How many students are on the playground?” (4.OA.1, 4.OA.2)

The materials for Grade 5 are divided into eight units, each containing an End-of-Unit Assessment. The Unit 8 Assessment is an End-of-Course Assessment, including questions from the entire grade level. An example of an End-of-Unit Assessment includes:

• Unit 3, Multiplying and Dividing Fractions, End of Unit Assessment, Question 6, “An apple weighs \frac{1}{2} pound. Diego cuts the apple into 4 equal pieces. How many pounds does each piece of the apple weigh? Explain your reasoning.” (5.NF.7)

The materials reviewed for Kiddom IM® v.360 Grades 3 through 5 meet expectations for having assessment information included in the materials to indicate which standards are assessed. 

Formal assessments in Grade 3, including End-of-Unit and End-of-Course Assessments, consistently align with grade-level content standards. For example: 

• Unit 6 End-of-Unit Assessment answer key specifies the standards addressed for each question, such as Question 6, which aligns with 3.MD.2: “A young humpback whale weighs 835 kg. A young killer whale weighs 143 kg. How much heavier is the humpback whale than the killer whale? Explain or show your reasoning.” The materials also provide guidance for assessing Mathematical Practices (MPs). 

Formal assessments in Grade 4, including End-of-Unit and End-of-Course Assessments, consistently align with grade-level content standards. For example: 

• Unit 6, Multiplying and Dividing Multi-digit Numbers, End-of-Unit Assessment answer key specifies the standards addressed for each question, such as Question 5, which aligns with 4.NBT.6: “Find the value of each quotient. Explain or show your reasoning. Part A. 714\div6. Part B. 3,626\div7.” The materials also provide guidance for assessing Mathematical Practices (MPs).

Formal assessments in Grade 5, including End-of-Unit and End-of-Course Assessments, consistently align with grade-level content standards. For example: 

• Unit 5, Place Value Patterns and Decimal Operations, End-of-Unit Assessment answer key specifies the standards addressed for each question, such as Question 3, which aligns with 5.NBT.4: “Answer the following questions about rounding 1.357. Part A. What is 1.357 rounded to the nearest hundredth? Part B. What is 1.357 rounded to the nearest tenth? Part C. What is 1.357 rounded to the nearest whole number?” The materials also provide guidance for assessing Mathematical Practices (MPs).

According to the Course Overview, Standards for Mathematical Practice, “The Standards for Mathematical Practice (MP) describe the types of thinking and behaviors in which students engage as they do mathematics. Throughout the curriculum, the Teacher Guide identifies lessons and activities in which to observe the different MPs. Some instructional routines are generally associated with certain MPs. For example, the Card Sort routine often asks students to reason abstractly and quantitatively (MP2), and to look for and make use of structure (MP7). The Estimation Exploration offers students opportunities to share a mathematical claim and the thinking behind it (MP3), and to make an estimate or a range of reasonable answers, with incomplete information, which is a part of modeling with mathematics (MP4). The unit-level Mathematical Practice Chart is meant to highlight a handful of lessons in each unit that showcase certain MPs.” An example includes:

•  “MP1: I Can Make Sense of Questions and Persevere in Solving Them. I can ask questions to make sure I understand the problem. I can say the problem in my own words. I can keep working when I’m having a hard time, and try again. I can show that I try to figure out or solve the problem at least once. I can check that my solution makes sense.” 

• “MP4: I Can Model with Mathematics. I can wonder about the mathematics involved in a situation. I can think of mathematical questions to ask about a situation. I can identify the questions to answer in order to solve a problem. I can identify the information I need to know, and don’t need to know, to answer a question. I can collect data or explain how to collect it. I can model a situation, using a representation such as a drawing, an equation, a line plot, a picture graph, a bar graph, or a building made of blocks. I can think about the real-world implications of my model.”

• “MP6: I Can Attend to Precision. I can use units or labels appropriately. I can communicate my reasoning, using mathematical vocabulary and symbols. I can explain carefully so that others understand my thinking. I can decide if an answer makes sense for a problem.”

The materials reviewed for Kiddom IM® v.360 Grades 3 through 5 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative assessment opportunities include instructional tasks, practice problems, and checkpoints in each section of each unit. Summative assessments include End-of-Unit Assessments and the End-of-Course Assessment. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, short answer, restricted constructed response, and extended response. 

An example of a summative assessment item in 3rd Grade includes:

• Unit 8, Putting It All Together, End-of-Course Assessment develops the full intent of MP3, construct viable arguments, and critique the reasoning of others, as students choose plants for a garden. Question 15, “Lin's class is designing a garden at school. Their garden is a rectangle that is 8 feet by 12 feet. The table shows how far some different plants need on all sides to grow well. Part A. Which plant takes up the most amount of space? Which plant takes up the least amount of space? Part B. Andre wants to plant pumpkins. Lin says that there is not enough room. Do you agree with Lin? Explain or show your reasoning. Part C. How many lettuce plants can the class fit in the garden? Explain or show your reasoning.”  

An example of a summative assessment item in 4th Grade includes:

• Unit 4, From Hundredths to Hundred-Thousands, End-of-Unit Assessment develops the full intent of 4.NBT.4, fluently add and subtract multi-digit whole numbers using the standard algorithm. Question 5, “Find the sum or difference. (Both problems are written vertically.) Part A. 324,567+34,762; Part B. 827,419-80,125.”

An example of a summative assessment item in 5th Grade includes:

• Unit 1, Finding Volume, End-of-Unit Assessment develops the full intent of MP4, model with mathematics, as students design a composite prism to meet certain criteria. Question 7, “Mai's class is designing a garden box that is made of two rectangular prisms. Part A. The garden needs to have a total of at least 200 square feet for the plants. What are some possibilities for the length and the width of the base of each prism? Part B. The soil volume of the garden box needs to be less than 500 cubic feet. What are some possibilities for the height of each rectangular prism?”

The materials reviewed for Kiddom IM® v.360 Grades 3 through 5 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 in Grades 3 through 5 by including in every lesson a Warm-Up, one to three instructional Activities, and Lesson Synthesis. Within Grades 3 through 5, students engage with all CCSS standards. 

An example of extensive work in Grade 3 includes:

• Unit 5, Fractions as Numbers, Lesson 16, 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, Student Task Statement, students compare and order common fractions. “Decide whether each statement is true or false. Be prepared to explain your reasoning. 1. \frac{1}{2}>\frac{1}{4} 2. \frac{1}{4}>\frac{1}{3} 3. \frac{1}{6}>\frac{1}{8}.” Activity 1, Question 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}.”

An example of extensive work in Grade 4 includes:

• Unit 6, Multiplying and Dividing Multi-digit Numbers, Lesson 20, Interpret Remainders in Division Situations, engages students with extensive work with grade-level problems with 4.OA.3 (Use the four operations with whole numbers to solve problems). Activity 2: Students solve word problems with remainders. “1. A school needs $1,270 to build a garden. After saving the same amount each month for 8 months, the school is still needs $6. How much did they save each month? Explain or show your reasoning using one of the tools below. 2. Choose one of the following division expressions. 711\div3, 3128\div8. Part A. Write a situation to represent the expression. Part B. Find the value of the quotient. Explain or show your reasoning. Part C. What does the value of the quotient represent in your situation?”

An example of extensive work in Grade 5 includes:

• Unit 1, Finding Volume, Lessons 4 and 10; Unit 2, Fractions as Quotients and Fraction Multiplication, Lesson 8, Divide to Multiply Non-Unit Fractions; Unit 4, Wrapping Up Multiplication and Division with Multi-Digit Numbers, Lesson 3; Unit 5, Place Value Patterns and Decimal Operations, Lessons 17 and 23; and Unit 7, Shapes on the Coordinate Grid, Lesson 12 provide students with extensive work with 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them). In Lesson 4, Activity 2, students interpret multiplication expressions that represent the volume of an illustrated rectangular prism with dimensions 4, 5, 6, Question 1, “How does the expression 5\times24 represent the volume of this rectangular prism? Question 2. How does the expression 6\times20 represent the volume of this rectangular prism? Question 3. Find a different way to calculate the volume of this rectangular prism. Write an expression to represent the way you calculated the volume.” In Lesson 10, Activity 1, students write expressions to represent the volume of an illustrated prism that has an L-shaped base, “Question 1. Write an expression to represent the volume of the figure in unit cubes.” In Unit 2, Fractions as Quotients and Fraction Multiplication, Lesson 8, students determine if expressions are equivalent during the Warm-up, “Decide if each statement is true or false. Be prepared to explain your reasoning. Part A. 2 \times \left( \frac{1}{3} \times 6 \right) = \frac{2}{3} \times 6, Part B. 2\times(\frac{1}{3}\times6)=2\times (6\div 3), Part C. 2\times6=2\times(\frac{1}{4}\times6).” In Unit 4, Wrapping Up Multiplication and Division with Multi-Digit Numbers, Lesson 3, Activity 1, students use different illustrated area models to represent multi-digit multiplication with different expressions, “1. Take turns. Choose a set of expressions that when added together have the same value as 245\times35 . Use the diagrams if they are helpful., 2. Explain how you know the sum of your expressions has the same value as 245\times35. 3. What is the value of 245\times35?” In Unit 5, Place Value Patterns and Decimal Operations, Lesson 17, Activity 1, students create visual models of different expressions using 100s grids, “Student Task Statement, Find the value of each expression in a way that makes sense to you. Explain or show your reasoning. Use the diagrams if they are helpful. 1. 2/times0.7 , 2. 2\times0.08, 3. 2\times0.78. In Lesson 23, Activity 2, students relate a multiplication and division expression to a single diagram. The provided diagram is a 100s grid with 2 columns colored blue, followed by 2 columns colored orange, repeated for 10 columns. “2. Tyler uses this diagram and explanation Tyler to justify why 12\div0.2=60. ‘12\div0.2=60 There are 5 groups of 0.2 in 1 and there are 12 so that is 12 groups of 5.’ Explain how the expression 12\times(0.1\div0.2) relates to Tyler’s reasoning.” In Unit 7, Shapes on the Coordinate Grid, Lesson 12, students decide if expressions are equivalent during the Warm up, “‘Give me a signal when you know whether the statement is true and can explain how you know.”, 1. (2\times10)+(3\times5)=(3\times10)+(1\times5), 2. (3\times25)+(5\times5)=8\times25, 3. (4\times25)+(10\times5)=(2\times25)+(10\times10).”

The materials provide opportunities for students to engage in the full intent of the standards in Grade 3 through 5 by including in every lesson a Warm-Up, one to three instructional Activities, and Lesson Synthesis. Within Grades 3 through 5, students engage with all CCSS standards. 

An example in Grade 3 includes:

• Unit 2, Area and Multiplication, Lesson 3, Tile Rectangles, meets 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, 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, Activity 2, “Find the area of each rectangle and include the units. Explain or show your reasoning.” Questions 1-4 each show different rectangles, Question 1 has an area of 18; Question 2 has an area of 30; Question 3 has an area of 60; and Question 4 has an area of 45. Students use inches and centimeters to measure area in Lesson 6. 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. About ____square inches, about ____square centimeters, 1. Use the inch grid and centimeter grid to find the area of the square. Part A ____ square inches, Part B____square centimeters.” There is a picture of a square shown in the materials. In Lesson 7, 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. Part A. a baseball field, Part B. a book cover, Part C. our classroom floor, Part D. a piece of paper, Part E. the top of a table, Part F. the screen on a phone.”

An example in Grade 4 includes:

• Unit 3, Extending Operations to Fractions, Lessons 8 and 9, engage students with the full intent of 4.NF.3a (Understand addition and subtraction of fractions as joining and separating parts referring to the same whole). In Lesson 8, Activity 2, students use number lines to represent the addition of two fractions and to find the value of the sum. “1. Use a number line to represent each addition expression and to find its value. Part A. 

\frac{5}{8}+\frac{2}{8} Part B. \frac{1}{8}+\frac{9}{8} Part C. \frac{11}{8}+\frac{9}{8} Part D. 2\frac{1}{8}+\frac{4}{8}.” In Lesson 9, Cool-down, students use number lines to represent subtraction of a fraction by another fraction with the same denominator, including a mixed number and by a whole number. “Use a number line to represent each difference and to find its value. 1. \frac{12}{5}-\frac{4}{5}. 2. 2\frac{1}{5}-\frac{7}{5}.”

An example in Grade 5 includes:

• Unit 5, Place Value Patterns and Decimal Operations, Lessons 7 and 8, provides the opportunity for students to engage with the full intent of standard 5.NBT.4 (Use place value understanding to round decimals to any place). Lesson 7, Activity 1, students round to the nearest tenth and hundredth. “Display the image. “This is a doubloon. What do you notice? What do you wonder?” Question 4, “Show each doubloon weight on the number line. Which hundredth of a gram is each weight closer to?” Lesson 8, Activity 2, students round a decimal number to the nearest whole number, tenth, and hundredth. Question 2, “Round 4.158 to the nearest whole number, tenth, and hundredth.”

The materials reviewed for Kiddom IM® v.360 Grade 3 through 5 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

The instructional materials in Grade 3 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 related supporting work) is 6 out of 8, approximately 75%.

• The number of lessons devoted to major work of the grade (including assessments and related supporting work) is 109 out of 143, approximately 76%. 

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 121 out of 159, approximately 76%.

• The number of days devoted to major work of the grade (including assessments and supporting work, excluding optional lessons) is 114 out of 152, approximately 75%.

The instructional materials in Grade 4 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 related supporting work) is 8 out of 9, approximately 89%.

• The number of lessons devoted to major work of the grade (including assessments and related supporting work) is 132 out of 151, approximately 87%.

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 148 out of 168, approximately 88%.

• The number of days devoted to major work of the grade (including assessments and supporting work, excluding optional lessons) is 139 out of 155, approximately 90%.

The instructional materials in Grade 5 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 related supporting work) is 7 out of 8, approximately 88%.

• The number of lessons devoted to major work of the grade (including assessments and related supporting work) is 132 out of 147, approximately 90%. 

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 146 out of 163, approximately 90%.

• The number of days devoted to major work of the grade (including assessments and supporting work, excluding optional lessons) is 135 out of 150, approximately 90%.

An instructional day 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 76% in Grade 3, 88% in Grade 4, and 90% in Grade 5 of the instructional materials focus on the major work of the grade.

The materials reviewed for Kiddom IM® v.360 Grades 3 through 5 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Pacing Guides and Dependency Diagrams document. 

An example of a connection in Grade 3 includes:

• 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.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram). 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 Task Statement, “1. Kiran and Jada measure 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 each worm.” Images of four worms of various lengths are shown.

An example of a connection in Grade 4 includes:

• Unit 3, Extending Operations to Fractions, Lesson 13, Activity 2 connects the supporting work of 4.MD.4 (Make a line plot to display a data set of measurements in fractions of a unit [\frac{1}{2} , \frac{1}{4} , \frac{1}{8} ]. Solve problems involving addition and subtraction of fractions by using information presented in line plots) to the major work of 4.NF.3d (Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators). Students create a line plot using measurements to the nearest \frac{1}{4} and \frac{1}{8}inch and use their understanding of fraction equivalence to plot and partition the horizontal axis. Student Task Statement, “1. Andre’s class measured the length of some colored pencils to the nearest \frac{1}{4} inch. Here is the class data: 1\frac{3}{4}, 2\frac{1}{4},5\frac{1}{4},5\frac{1}{4},4\frac{2}{4},4\frac{2}{4},6\frac{1}{4},6\frac{3}{4},6\frac{3}{4},6\frac{3}{4} a. Plot the colored- pencil data on the line plot. b. Which colored-pencil length is the most common in the data set? c. Write 2 new questions that could be answered using the line plot data. 2. Next, Andre’s class measured their colored pencils to the nearest \frac{1}{8} inch. Here is the class data: 1\frac{6}{8},2\frac{2}{8},5\frac{2}{8},5\frac{3}{8},4\frac{4}{8},4\frac{4}{8},6\frac{3}{8},6\frac{6}{8},6\frac{6}{8},6\frac{6}{8} a. Plot the colored-pencil data on the line plot. b. Which colored-pencil length is the most common in the line plot? c. Why did some colored-pencil lengths change on this line plot? d. What is the difference between the lengths of the longest colored pencil and the shortest colored pencil? Show your reasoning.”

An example of a connection in Grade 5 includes:

Unit 6, More Decimal and Fraction Operations, Lesson 14, Activity 1 connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit [½, ¼, ⅛], Use operations on fractions for this grade to solve problems involving information presented in line plots) to the major work of 5.NF.2 (Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers). Students make a line plot and then analyze the data to solve problems using operations with fractions. A spinner with the fractions ½, ¼, ⅛, ⅝ is provided. Student Task Statement: “1. Play Sums of Fractions with your partner. Spin the spinner twice. Add the two fractions. Record the sum on the line plot. Take turns until you and your partner together have 12 data points. 2. How did you know where to plot the sums of eighths? 3. What is the difference between your greatest and least numbers? 4. What do you notice about the data you collected?”

The instructional materials for Kiddom IM® v.360 Grades 3 through 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. 

Connections between major works are present throughout the grade-level materials where appropriate. These connections are listed for teachers in the Course Overview in the Dependency Diagram, and may appear in one or more phases of a typical lesson: warm-up, instructional activities, lesson synthesis, or cool-down. 

An example of a connection in Grade 3 includes:

• 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 Task Statement: “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.

An example of a connection in Grade 4 includes:

• Unit 3, Extending Operations to Fractions, Lesson 15, Activity 1 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). Students reason about problems that involve combining or removing fractional amounts with different denominators in the context of stacking playing bricks. Student Task Statement, “Priya, Kiran, and Lin are using large playing bricks to make towers. Here are the heights of their towers: Priya: 21\frac{1}{4} inches, Kiran: 32\frac{3}{8} inches, Lin: 55\frac{1}{2} inches. Show your reasoning for each question. 1. How much taller is Lin’s tower compared to: Part A. Priya’s tower? Part B. Kiran’s tower? 2. They are playing in a room that is 109 inches tall. Priya says that if they combine their towers to make a super tall tower, it would be too tall for the room. She says they must remove 1 brick. Do you agree with Priya? Explain your reasoning.”

An example of a connection in Grade 5 includes:

• Unit 4, Wrapping Up Multiplication and Division with Multi-Digit Numbers, Lesson 15, Activity 2 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). Students estimate and solve multi-digit division with mixed-number quotients. “1. Han said that each person was served about 25\frac{1}{4} feet of noodle. Do you agree with Han? Explain or show your reasoning. A. Yes, I agree with Han. B. No, I do not agree with Han.” The problem context states that 400 people equally shared a 10,119 foot noodle. Activity Synthesis states, “Display: 25\frac{119}{400}. ‘What does 25\frac{119}{400} mean in this situation?’ (Each person gets 25 feet of the noodle and then the 119 feet leftover would be divided into 400 equal pieces.) Display:$$25\frac{1}{4}$$25 ’Why is Han's estimate reasonable?’ (Because is \frac{119}{400} really close to \frac{100}{400} and \frac{100}{400}=\frac{1}{4}) ‘Do you think they actually measured and cut the noodle into equal pieces when they served it?’ (No, because it would take too long and be too difficult. Yes, because they probably want to serve the noodle soup with sections that are one piece of the original noodle.’”

The instructional materials reviewed for Kiddom IM® v.360 Grade 3 through 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. 

The Course Overview contains a Scope and Sequence explaining content standard connections. Prior and Future connections are identified within materials in the Course Overview, Course Guide, Section Dependency Diagram which states, “an arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.” Some Unit Overviews, Lesson Narratives, and Activity Syntheses describe the progression of standards for the concept being taught. Each Lesson contains Preparation identifying learning standards (Building on, Addressing, or Building toward). 

An example of a connection to future grades in Grade 3 includes:

• Course Guide, Scope and Sequence, Unit 8, Putting It All Together 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. “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.”

An example of a connection to prior knowledge in Grade 3 includes:

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 4, 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, “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.”

An example of a connection to future grades in Grade 4 includes:

• Unit 8, Properties of Two-dimensional Shapes, Lesson 3, Activity 2 connects 4.G.2 (Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.) to work with classifying two-dimensional figures in 5.G.B. Narrative, “Students are not expected to recognize that the attributes of one shape may make it a subset of another shape (for example, that squares are rectangles, or that rectangles are parallelograms). They may begin to question these ideas, but the work to understand the hierarchy of shapes will take place formally in IM Grade 5. During the Activity Synthesis, highlight how sides and angles can help us define and distinguish various two-dimensional shapes.”

An example of a connection to prior knowledge in Grade 4 includes:

• Course Overview, Scope and Sequence, Unit 2, Fraction Equivalence and Comparison, Unit Learning Goals connects 4.NF.A (Extend understanding of fraction equivalence and ordering) to work with unit fractions from Grade 3. “In grade 3, students partitioned shapes into parts with equal area and expressed the area of each part as a unit fraction. They learned that any unit fraction \frac{1}{b} results from a whole partitioned into b equal parts. Students used unit fractions to build non-unit fractions, including fractions greater than 1, and represented them on fraction strips and tape diagrams. The denominators of these fractions were limited to 2, 3, 4, 6, and 8. Students also worked with fractions on a number line, establishing the idea of fractions as numbers and equivalent fractions as the same point on the number line.”

An example of a connection to future grades in Grade 5 includes:

• Course Overview, Scope and Sequence, Unit 5, Place Value Patterns and Decimal Operations connect the work of 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) to work with operations with decimals in Grade 6. “Students then apply their understanding of decimals and of whole-number operations to add, subtract, multiply, and divide decimal numbers to the hundredths, using strategies based on place value and the properties of operations. Students see that the reasoning strategies and algorithms they used to operate on whole numbers are also applicable to decimals. For example, addition and subtraction can be done by attending to the place value of the digits in the numbers, and multiplication and division can still be understood in terms of equal-size groups. In IM Grade 6, students will build on the work to reach the expectation to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.”

An example of a connection to prior knowledge in Grade 5 includes:

• Unit 7, Shapes on the Coordinate Plane, Lesson 4, Warm-up connects 5.G.3 (Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category) to work with classifying two-dimensional shapes from Grade 4. Narrative, “The purpose of this What Do You Know about ___? is for students to share what they know about quadrilaterals and how they can represent them. In previous courses, students have drawn and described squares, rectangles, and rhombuses. They will revisit and classify all of these shapes over the next several lessons.”