zilongwang/ReadingBank huggingface dataset:
502 600 160 2 2.NBT.7 2.NBT.8 The student solves one to two out of six parts correctly by using the arrow way or solves all six parts correctly, but does not use the arrow way. The student solves three to four out of six parts correctly by using the arrow way or provides a correct answer for up to six parts, but only uses the arrow way for three parts. The student solves five out of six parts correctly by using the arrow way. The student correctly models the arrow way and solves to find: 442, +100 -100, -10 658, 758 749 791 470 3 2.NBT.7 2.NBT.9 The student solves one or two out of six parts correctly with or without a chip model and with or without providing a written explanation. The student attempts to use a chip model to answer Parts (a) and (b), but arrives at an incorrect answer, and the student shows no explanation for Parts (c), (d), (e), and (f), but correctly answers true or false. Or the student provides some explanation for Parts (c), (d), (e), and (f), but the explanation is incorrect. The student solves five out of six parts correctly by using a chip model for Parts (a) and (b) or explaining using pictures, words, or numbers for Parts (c), (d), (e), and (f). The student correctly: Models with place value chips and the vertical form to solve: 587 920 Explains using pictures, words, or numbers to solve: False True False False 4 2.NBT.7 2.NBT.8 2.NBT.9 The student solves one problem correctly with or without a written strategy. The student solves two problems correctly by using a strategy correctly, or the student solves two or more problems correctly without any strategies shown. The student solves all four problems correctly and shows six to seven correct strategies, or the student solves three out of the four problems correctly with six correct strategies. The student correctly uses two different strategies to solve: 735 860 390 140
lesson. Any combination of the questions below may be used to lead the discussion. What makes Problems 1(e) and (f) more challenging? In Problem 1(e), does 10 more mean we should add 10 to 319? Why not? In Problem 1(f), why did you add 100 to 499 when it says 100 less? What do you need to know to complete each pattern in Problem 2? In Problem 3(b), what total quantity did you subtract from 187? How can you write it as an equation? In Problem 4(b), what total quantity did you add to 323 to arrive at 400? How did you show the missing addend using the arrow way? How can we show it as an equation? Which simplifying strategy did we use today to record a sequence of numbers? How is it helpful? What important connection did we make today? What are we actually doing when we talk about 10 more, 10 less, 100 more, or 100 less than a number? Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with assessing students’ understanding of the concepts that were presented in today’s lesson and planning more effectively for future lessons. The questions may be read aloud to the students.
Name Date Redraw the objects below in an array. Circle one column. Then, circle one row. Write a repeated addition number sentence to match the columns of hearts. _______________________________________________________ Draw and label a tape diagram to match your addition sentence and array.
2 2.OA.4 The student solves zero out of three parts correctly. The student solves one out of three parts correctly. The student solves two out of three parts correctly. The student correctly: Circles both 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3. Writes 5 + 5 + 5 + 5 = 20 or 4 + 4 + 4 + 4 + 4 = 20. Draws an array showing 4 columns of 5. 3 2.OA.4 The student solves zero out of two parts correctly. The student solves one out of two parts correctly. The student correctly shows an array and writes a matching equation for a sum other than 15. The student correctly: Draws an array showing 3 rows of 5. Answers 5 + 5 + 5 = 15. 4 2.OA.4 The student solves zero out of two parts correctly. The student only answers Part (a) or Part (b) correctly. The student answers Parts (a) and (b) correctly but fails to provide a clear explanation. The student correctly: Draws an array to show 3 rows of 3, and draws an array to show either 2 rows of 5 or 5 rows of 2. Clearly explains that Sarah would make more money with Choice 2.
A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. In this chart, this progress is presented from left (Step 1) to right (Step 4). The learning goal for students is to achieve Step 4 mastery. These steps are meant to help teachers and students identify and celebrate what the students CAN do now and what they need to work on next. A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 2.MD.2 2.MD.3 2.MD.4 The student answers fewer than four out of eight parts correctly. The student answers four or five out of eight parts correctly. The student answers six or seven out of eight parts correctly. The student correctly: Estimates the length of each item. Measures to the nearest whole unit to answer: Envelope is about 4 in and 10 cm. Pencil is about 6 in and 15 cm. Crayon is about 3 in and 8 cm. Scissors are about 5 in and 13 cm. Answers that the envelope is 2 cm longer than the crayon. Answers centimeters. Explains that centimeters have a smaller length unit than inches, so there are more
______________ ______________ 10. ______________ 11. ______________ 12. ______________ 13. ______________ 14. ______________ 15. ______________
Name Date Count or add to find the total value of each group of coins. Write the value using the ¢ or $ symbol. ______________ 2. _______________ 3. ______________ 4. _______________
______________ ______________ 10. ______________ 11. ______________ 12. ______________ 13. ______________ 14. ______________ 15. ______________
2 2.G.1 The student answers one out of four parts correctly. The student answers two out of four parts correctly. The student answers three out of four parts correctly. The student draws appropriate shapes and correctly answers: Triangle. Quadrilateral. 3 2.G.1 The student answers one out of four parts correctly. The student answers two out of four parts correctly. The student answers three out of four parts correctly. The student correctly: Draws a square. Answers 6. Answers 8. Answers 12. 4 2.G.3 The student is unable to answer any of the questions. The student answers one out of three parts correctly. The student answers two out of three parts correctly. The student correctly circles: 1 fourth. 1 half. 1 whole.
composite shape (e.g., a hexagon) and relate the different parts, or shares, to halves, thirds, and fourths. They make connections between fraction concepts and telling time, explaining the connection between their work with halves and quarters to the analog clock. MP.6 Attend to precision. Students describe and analyze various two-dimensional shapes by attending to their specific attributes. Students accurately draw shapes using their knowledge of attributes and rulers. Then, while working with a partner, students name and analyze their partner’s shape drawings by counting the number of sides or angles. Students also appropriately name parts of a whole using terms such as halves, thirds, and fourths or quarters. MP.7 Look for and make use of structure. Students identify attributes, such as the number of sides and angles, in order to classify shapes such as triangles and quadrilaterals. They make use of the part–whole structure to understand that a whole unit can be partitioned into equal shares, or smaller units (e.g., each of 4 equal shares = a fourth of the whole). Students use their understanding of the partitioning of a circle to tell time to the quarter and half hour. Through previous fluency practice, students use the pattern of skip-counting by fives to tell time on an analog clock. Overview of Module Topics and Lesson Objectives Standards Topics and Objectives Days 2.G.1 2.MD.1 A Attributes of Geometric Shapes Lesson 1: Describe two-dimensional shapes based on attributes. Lesson 2: Build, identify, and analyze two-dimensional shapes with specified attributes. Lesson 3: Use attributes to draw different polygons including triangles, quadrilaterals, pentagons, and hexagons. Lesson 4: Use attributes to identify and draw different quadrilaterals including rectangles, rhombuses, parallelograms, and trapezoids. Lesson 5: Relate the square to the cube, and describe the cube based on attributes. 5 2.G.3 2.G.1 B Composite Shapes and Fraction Concepts Lesson 6: Combine shapes to create a composite shape; create a new shape from composite shapes. Lessons 7–8: Interpret equal shares in composite shapes as halves, thirds, and fourths. 3
A Progression Toward Mastery Assessment Task Item and Standards Addressed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.OA.2 3.OA.3 3.OA.4 3.OA.7 Student is unable to answer any question correctly. The attempt shows the student may not understand the meaning of the questions. Student answers at least one question correctly. Mistakes may include those listed in the box to the right, and/or Writes the incorrect factor in the multiplication equation. Does not show understanding of the meaning of the unknown factor. Writes an incorrect division sentence. Student answers at least two questions correctly. Mistakes may include the following: Incorrectly writes in the missing factor but understands that it represents the number of biscuits in each row. Places the numbers incorrectly in the division sentence. Student correctly: Draws an array. Fills in the missing factor (6) and understands what it represents. Writes a related division sentence (18 ÷ 3 = 6). 2 3.OA.2 3.OA.3 3.OA.5 Student attempts to draw the picture. The attempt, however, shows the student may not understand the meaning of the questions. Student answers at least one question correctly. Mistakes may include those listed in the box to the right, and/or: Draws incorrect pictures of the number of bags. Attempts to draw the two arrays but inaccurately explains the relationship between them. Student answers at least two questions correctly. Mistakes may include the following: Incorrectly calculates the number of bags either in Part (a) or Part (b). Draws the arrays correctly but explanation includes some inaccuracies. Student answers every question correctly: Finds the number of bags Melanie packs for biscuits and rolls. Draws two arrays to represent the biscuits and rolls. Provides an accurate explanation of the commutative property in Part (c).
T: What does 4 represent? S: The size of each group. T: Write a number sentence to represent Diana’s stickers where the answer represents the size of the group. S: (Write 12 ÷ 3 = 4.) T: (Write 12 ÷ 3 = 4 and 12 ÷ 4 = 3 on the board, even if students have written the correct number sentence.) What is the difference between these division sentences? S: In the first one, the answer represents the size of each group. In the second one, the answer represents the number of groups. T: If we’re writing a division sentence where the answer represents the size of the group, then which number sentence should we use? S: 12 ÷ 3 = 4. Abstract to pictorial: Analyze equations for the meaning of the solution and represent the equation with a drawing. Write 8 ÷ 4 = ___. T: If 8 is the total and 4 is the number of groups, then what does the unknown factor represent? S: The size of the groups! T: Draw a picture on your personal white board to go with my division equation. Use your picture to help you find the unknown factor, then write the complete equation. S: (Draw various pictures that show 8 ÷ 4, then write 8 ÷ 4 = 2.) Repeat the process with 10 ÷ 2. As you design examples, keep in mind that Lesson 5 introduces students to division where the unknown factor represents the number of groups. Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students should solve these problems using the RDW approach used for Application Problems. Student Debrief (10 minutes) Lesson Objective: Understand the meaning of the unknown as the size of the group in division. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson.
Write a division sentence where the answer represents the number of Daniel’s bags. Draw a number bond to represent the problem. Jacob draws cats. He draws 4 legs on each cat for a total of 24 legs. Use a count-by to find the number of cats Jacob draws. Make a drawing to match your counting. Write a division sentence to represent the problem.
Nolan draws the array below to find the answer to the multiplication expression 10 × 4. He says, "10 × 4 is just double 5 × 4!” Explain Nolan’s strategy. Name Date Destiny says, “I can use 5 × 4 to find the answer to 7 × 4.” Use the array below to explain Destiny’s strategy using words and numbers.
Assessment Task Item STEP 1 Little evidence of reasoning without a correct answer. (1 STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.NBT.1 3.MD.2 Student is unable to answer the question correctly. The attempt shows the student may not understand the meaning of the question. Student attempts to answer the question. Mistakes may include those listed in the box to the right, and/or misreading the scale, but correctly rounding based on error. Same criteria as for a 4, but may omit the unit (kg) in one or more parts of the answer. Student answers the question correctly: Accurately reads the scale as 127 kg. Rounds on a number line to estimate 100 kg. 2 3.NBT.2 Student is unable to answer the question correctly. The attempt shows the student may not understand the meaning of the question. Student attempts to answer the question. Mistakes may include those listed in the box to the right, and/or decomposing the numbers incorrectly. Student may or may not answer question correctly. Mistakes may include decomposing the numbers correctly but making a calculation when subtracting. Student correctly writes and solves 205 g – 186 g = 19 g. 3 3.NBT.1 3.NBT.2 3.MD.1 Student is unable to answer questions correctly. The attempt the student may not understand the meaning of the questions. Student attempts to answer the questions. Mistakes may include those listed in the box to the right, and/or inaccurately reading one or both of the clocks. Student answers at least one question correctly. Mistakes may include a rounding error in either Part (a) or (b) affecting Part (c), but solves correctly based on wrong answer. Student answers every question correctly: a. Rounds 10:19 to 10:20. b. Rounds 10:53 to 10:50. c. Estimates 30 minutes before the plane leaves.
5 3.NBT.2 3.MD.1 3.MD.2 Student gives an incorrect answer. Attempt shows the student may not understand the meaning of the questions. Student gives an incorrect answer with a reasonable attempt. Student misreads scale but calculates other parts of the problem correctly based on mistake. Student gives a partially correct answer. All parts are correct besides Part (c), which may not be correctly calculated. Student correctly answers each part of the question: Accurately reads scale at 3 kg. Estimates 21 kg. Estimates 12 kg. Calculates 46 minutes.
Types of Horses Weight in kg Shetland pony kg American Saddlebred 478 kg Clydesdale horse _____ kg Miniature horse 56 kg A miniature horse weighs 268 fewer kilograms than a Shetland pony. Use the table to find the weight of a Shetland pony. A Clydesdale weighs as much as a Shetland pony and an American Saddlebred horse combined. How much does a Clydesdale horse weigh?
Name Date Solve the subtraction problems below. 280 g − 90 g 450 g − 284 g 423 cm − 136 cm 567 cm − 246 cm 900 g − 58 g 900 g − 358 g 4 L 710 mL − 2 L 690 mL 8 L 830 mL − 4 L 378 mL
A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.OA.3 3.OA.4 Student is unable to write an equation for the problem. The attempt shows the student may not understand the meaning of the question. The student mixes up the order of numbers in the division equation (e.g., 21 ÷ 3 = ?). The student writes the correct equation, but divides incorrectly (e.g., 21 ÷ 7 = wrong answer). The student correctly: Writes 21 ÷ 7 = 3. Identifies that the answer represents the number of weeks. 2 3.OA.3 3.OA.4 Student is unable to write both equations and does not correctly solve the problem. The attempt shows the student may not understand the meaning of the questions. The student gives an incorrect answer with reasonable attempt that includes: Attempt to represent the problem with multiplication and division equations. Use of a letter to represent the unknown. Student provides a partially correct answer. The student correctly: Writes n × 8 = 48. Writes 48 ÷ 8 = n. The student correctly: Writes n × 8 = 48. Writes 48 ÷ 8 = n. Solves to find 6 containers. 3 3.OA.5 Student is unable to explain and label how the array represents both expressions. Student attempts to explain and label how the array represents one of the expressions. Student accurately labels how the array represents both expressions, but the explanation lacks clarity. Student accurately explains and labels how the array represents both expressions, showing understanding of the associative property of multiplication.
Overview of Module Topics and Lesson Objectives Standards Topics and Objectives Days 3.OA.4 3.OA.5 3.OA.7 3.OA.9 3.OA.1 3.OA.2 3.OA.3 3.OA.6 A The Properties of Multiplication and Division Lesson 1: Study commutativity to find known facts of 6, 7, 8, and 9. Lesson 2: Apply the distributive and commutative properties to relate multiplication facts 5 × n + n to 6 × n and n × 6 where n is the size of the unit. Lesson 3: Multiply and divide with familiar facts using a letter to represent the unknown. 3 3.OA.3 3.OA.4 3.OA.5 3.OA.7 3.OA.1 3.OA.2 3.OA.6 B Multiplication and Division Using Units of 6 and 7 Lesson 4: Count by units of 6 to multiply and divide using number bonds to decompose. Lesson 5: Count by units of 7 to multiply and divide using number bonds to decompose. Lesson 6: Use the distributive property as a strategy to multiply and divide using units of 6 and 7. Lesson 7: Interpret the unknown in multiplication and division to model and solve problems using units of 6 and 7. 4 3.OA.3 3.OA.4 3.OA.5 3.OA.7 3.OA.1 3.OA.2 3.OA.6 3.OA.8 C Multiplication and Division Using Units up to 8 Lesson 8: Understand the function of parentheses and apply to solving problems. Lesson 9: Model the associative property as a strategy to multiply. Lesson 10: Use the distributive property as a strategy to multiply and divide. Lesson 11: Interpret the unknown in multiplication and division to model and solve problems. 4 Mid-Module Assessment: Topics A–C (assessment ½ day, return ½ day, remediation or further applications 1 day) 2
1 × 1 2 × 2 3 × 3 4 × 4 5 × 5 × 6 In the table, only the products on the diagonal are shown. Label each product on the diagonal. Draw an array to match each expression in the table below. Then, label the number of squares you added to make each new array. The first two arrays have been done for you. 1 × 1 2 × 2 3 × 3 4 × 4 5 × 5 6 × 6
A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer or with a partially correct answer in a multi-step question. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.MD.7c 3.MD.7d Response demonstrates little or no evidence of reasoning without a correct answer. Student identifies that Sarah is correct, demonstrating evidence of limited reasoning to support the answer. Student identifies that Sarah is correct. Response shows evidence of accurate reasoning to support the answer using at least one representation. Student identifies that Sarah is correct. Explanation shows evidence of solid reasoning using multiple representations. 2 3.MD.5b 3.MD.6 3.MD.7a 3.MD.7b Student attempts but is unable to draw any correct arrays with labels. Multiplication sentences are not shown. Student correctly draws and labels one array. Side lengths are labeled without units. A multiplication sentence is shown. Student correctly draws and labels two different arrays. Side lengths are labeled in inches. Multiplication sentences are shown for those two arrays. Student correctly draws and labels three different arrays. Side lengths are labeled in inches. Possible arrays are as follows: 1 × 36 2 × 18 3 × 12 4 × 9 6 × 6 Correct multiplication sentences are shown for each array drawn. 3 3.MD.7d 3.MD.7b Response demonstrates little or no evidence of reasoning without a correct answer. Student miscalculates one area. Student may identify that House A has the greater area with limited reasoning. Response demonstrates correct calculations and area. Student identifies that House A has the greater area. Student demonstrates correct area calculations with answers: House A = 102 sq meters House B = 84 sq meters Explanation identifies that House A has the greater area. Response provides evidence of solid reasoning.
A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.MD.5 3.MD.6 Response demonstrates little evidence of reasoning without a correct answer. Response shows limited reasoning with at least one correct answer. Response includes evidence of some reasoning with three correct answers, or evidence of solid reasoning with an incorrect answer. Student correctly answers: Jasmine’s array, giving strong evidence of understanding that tiling must have no gaps or overlaps. The area is 24 tiles. Provides appropriate explanation of the calculation including counting or strategies. Yes, there are 4 rows of 6 squares, so it is possible to skip-count by six. 2 3.MD.7b Response demonstrates little evidence of reasoning without a correct answer. Response shows limited reasoning with at least one correct answer. Student identifies at least two of three rectangles correctly. Response includes evidence of accurate reasoning with pictures, numbers, or words. Student correctly identifies three rectangles: 1 × 12 or 12 × 1 2 × 6 or 6 × 2 3 × 4 or 4 × 3 Response shows evidence of solid reasoning using pictures, numbers, and words.
3 3.MD.7b Response demonstrates little evidence of reasoning without a correct answer. Response shows limited reasoning without a correct answer. Student finds the missing side length of 8 units but may not show enough work to clearly justify the answer. Student correctly finds the missing side length of 8 units. Response shows evidence of solid reasoning using pictures, numbers, and words. 4 3.MD.5 3.MD.6 3.MD.7a Response demonstrates little evidence of reasoning without a correct answer. Response shows evidence of some reasoning in attempt to write equations and complete the array, but work may not include a correct answer. Student accurately completes the array and finds the area of 48 sq cm, but may not accurately provide both addition and multiplication equations. Student correctly: Completes the array with 8 columns and 6 rows. Writes an addition equation (repeated addition of 8 sixes or 6 eights); writes a multiplication equation (6 × 8 or 8 × 6); and gives an area of 48 sq cm. 5 3.MD.5a 3.MD.5b 3.MD.7a 3.MD.7d Response demonstrates little evidence of reasoning without a correct answer to either part. Response shows limited reasoning with a correct answer in one part. Student slightly miscalculates the number of tiles needed to fill the remaining area, but the explanation shows evidence of solid reasoning. Part (b) is correct based on the student’s slight miscalculation but not the correct answer of 32 units. Student correctly: Identifies that 16 tiles are needed to fill the remaining area. Says the area of the large rectangle is 32 square units. Explanation gives evidence of solid reasoning to support answer.
BIG IDEA (Understand…) What do we want students to DO? (Activities, lessons…) Content (& Elaborations) (Know) The likelihood of possible outcomes (Data and Probability: Analyzing data and chance enables us to compare and interpret) can be examined, compared, and interpreted. Questions to support inquiry with students: How is the probability of an event determined and described? What events in our lives are left to chance? What are the possible outcomes of these events? One-to-one correspondence (collecting data, creating a graph, and describing, comparing, and discussing the results; choosing a suitable representation) with bar graphs, pictographs, charts, and tables Likelihood of simulated events (using comparative language (e.g., certain, uncertain; more, less, or equally likely); developing an understanding of chance (e.g., tossing a coin creates a 50-50 chance of landing a head or tail; drawing from a bag, using spinners, rolling dice all simulate probability events). Story: The Snowsnake Game using comparative language Evidence of Experience (Show)
Lesson 16 Objective: Apply knowledge of area to determine areas of rooms in a given floor plan. Suggested Lesson Structure Practice (15 minutes) Development (35 minutes) Student Debrief (10 minutes) Total Time (60 minutes) Fluency Practice (15 minutes) Group Counting 3.OA.1 (3 minutes) Multiply by 9 3.OA.7 (7 minutes) Find the Area 3.MD.7 (5 minutes) Group Counting (3 minutes) Note: Group counting reviews interpreting multiplication as repeated addition. Instruct students to count forward and backward, occasionally changing the direction of the count. Sixes to 60 Sevens to 70 Eights to 80 Multiply by 9 (7 minutes) Materials: (S) Multiply by 9 (6–10) Pattern Sheet Note: This activity builds fluency with multiplication facts using units of 9. It works toward students knowing all products of two one-digit numbers from memory. See Lesson 2 for the directions for administration of a Multiply-By Pattern Sheet. T: (Write 6 × 9 = .) Let’s skip-count up by nine to solve. (Count with fingers to 6 as students count.) S: 9, 18, 27, 36, 45, 54. T: Let’s skip-count down to find the answer, too. Start at 90. (Count down with fingers as students count.) S: 90, 81, 72, 63, 54.
______________________________________________________________________________ What ordered pair of numbers is the solution of the system? *Make sure your equations are in slope-intercept form before you graph them! Try on your own! (Use the same graph.) Example 2: Use the data below to find the year when men and women will have the same Dash time. Year 1968 1972 1976 1980 1984 1988 1992 1996 2000 Men 43.86 44.66 44.26 44.60 44.27 43.87 43.50 43.49 43.84 Women 52.03 51.08 49.29 48.88 48.83 48.65 48.83 48.25 49.11 Answer in a complete sentence: __________________________________________________ Example 3: Solving Systems of Linear Equations by Substitution Step 1: Solve for one of the variables.
3 3.NF.3d 3.NF.1 The student does not demonstrate understanding of the meaning of the question and does not produce meaningful work. The student may say that the son has eaten more, but does show some understanding. This is possibly evidenced by two fraction strips correctly partitioned, but perhaps not the same size. The student shows that Jerry has eaten more and compares to correctly; the explanation includes some reasoning. The student clearly explains: Jerry has eaten more of his granola bar. > . is greater than because the units are larger. 4 3.NF.2a, b 3.NF.3a, b, c, d 3.NF.1 The student does not demonstrate understanding of the meaning of the question and does not produce meaningful work. The student completes part of the problem correctly, but may fail to draw accurate models or explain reasoning. The student completes Parts (a), (b), and (c) correctly; the explanation includes some reasoning. The student correctly: Shows all of the fractions from up to numerically, including renaming the wholes. Explains or of the whole roll was eaten with an accurate model in Part (b). Uses words, pictures, and numbers to explain that is equal to in Part (c).
1 3.NF.1 The student has one answer correct. The student has two answers correct. The student answers Parts (b) through (d) correctly, but answers Part (a) with a fractional answer, or has answered one of the four questions incorrectly or incompletely. The student correctly: Identifies how many parts the whole is divided into—8. Labels each unit fraction as . Identifies the fraction shaded. Identifies the fraction unshaded. 2 3.NF.3c 3.G.2 The student is unable to answer either question correctly. The student is unable to shade a fraction greater than 1, but answers Part (b) correctly. The student answers Part (a) correctly, but does not seem to understand Part (b). The student correctly: Shows two rectangles divided into thirds with a fraction greater than shaded. Writes a number bond with the whole as 1 or , and , , and as the parts. 3 3.NF.3d 3.G.2 The student’s work shows no evidence of being able to partition the cakes into fractional units to make sense of the problem. The student has poorly represented the cakes, making it difficult to compare the fractions. The student incorrectly states that Mrs. Ramirez bought the larger piece. The student draws two equivalent cakes and realizes Mr. Chu has the larger piece, but the explanation is not clear, perhaps poorly labeled, lacking a statement of the solution. The student clearly: Explains that Mr. Chu bought the larger piece of cake using words, pictures, and numbers. 4 3.NF.1 3.NF.3d 3.G.2 The student is unable to recognize or show that he or she recognizes either fraction in the model. The student recognizes 3 fourths, but is unable to recognize 3 halves within the picture, or vice versa. The student is able to recognize 3 fourths and 3 halves within the same picture, which is clear perhaps by markings on the strip, but the explanation lacks clarity. The student clearly: Uses words, pictures, and numbers to explain how the picture can be interpreted either as 4 halves with shaded, the whole being defined by the middle line of the strip or as 4 fourths with shaded, with the whole being
Name Date The shape represents 1 whole. Write a fraction to describe the shaded part. The shaded part represents 1 whole. Divide 1 whole to show the same unit fraction you wrote in Part (a). a. b. a. b. a. b. a. b.
End-of-Module Assessment Task Topics A–B Standards Addressed Represent and interpret data. 3MD.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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 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. Evaluating Student Learning Outcomes A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. In this chart, this progress is presented from left (Step 1) to right (Step 4). The learning goal for each student is to achieve Step 4 mastery. These steps are meant to help teachers and students identify and celebrate what the students CAN do now and what they need to work on next. A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.MD.3 Student is unable to answer either question correctly. Student attempts to draw and label the bar graph but does not use an appropriate scale. Student may or may not find the correct answer in Part (b). Student creates an accurate bar graph with labels and an appropriate scale but does not answer Part (b) correctly. OR Student creates a Student: Creates an accurate, labeled bar graph with a scale of 4. Finds that there are 4 more maple and oak trees than birch trees.
The final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter. Topic A begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations (3.OA.8). The lessons emphasize modeling and reasoning to develop solution paths. They incorporate teacher facilitated problem solving, opportunities for students to independently make sense of problems and persevere in solving them, and time for students to share solutions and critique peer strategies. Topic B introduces an exploration of geometry. Students build on Grade 2 ideas about polygons and their properties, specifically developing and expanding their knowledge of quadrilaterals. They explore the attributes of quadrilaterals and classify examples into various categories, including recognizing the characteristics of polygons (3.G.1). Students draw polygons based on their attributes, producing sketches from descriptions like, “This shape has two long sides that are parallel, two short sides, and no right angles.” Students next use tangrams and tetrominoes (see examples to the right) to compose and decompose shapes. They reason about the relationships between shapes and between attributes. For example, students understand that quadrilaterals can be decomposed into triangles, and recognize that the two smallest triangles in a tangram puzzle can be put together to form a parallelogram, a square, and a medium triangle. Students tessellate to bridge geometry experience with the study of perimeter in Topic C. They first decompose a quadrilateral and then rearrange the parts. They use the new shape to tile. Students then define perimeter in two distinct ways: (1) as the boundary of a planar region and (2) as the length of the boundary curve. Students see varied examples from the tiles used to tessellate.
has at least 1 angle greater than a right angle is a quadrilateral has all equal sides (label side lengths) has at least 1 angle less than a right angle is a trapezoid has at least 2 equal sides (label side lengths) has at least 1 right angle is a hexagon has at least 1 set of parallel sides has more than 4 angles is a parallelogram has no parallel sides
Name Date Solve the addition problems below using the standard algorithm. a. 7,909 + 1,044 b. 27,909 + 9,740 c. 827,909 + 42,989 f. 258,983 + 121,897 e. 547,982 + 114,849 d. 289,205 + 11,845
S: 22,397 minus 3,745 equals 18,652. T: Check your answer using addition. S: Our answer is correct because 18,652 plus 3,745 equals 22,397. T: What is the value of A in the tape diagram? S: A equals 18,652. Problem 2: Subtract, decomposing three times. Write 210,290 – 45,720 vertically on the board. T: With your partner, draw a tape diagram to represent the whole, the known part, and the unknown part. T: Record the subtraction problem on your board. T: Look across the digits. Are we ready to subtract? S: No! T: Look across the top number’s digits to see if we have enough units in each column. Are there enough ones in the top number to subtract the ones in the bottom number? (Point to the zeros in the ones column.) S: Yes, 0 equals 0. T: We are ready to subtract in the ones column. Are there enough tens in the top number to subtract the tens in the bottom number? S: Yes, 9 is greater than 2. T: We are ready to subtract in the tens column. Are there enough hundreds in the top number to subtract the hundreds in the bottom number? S: No, 2 hundreds is less than 7 hundreds. T: There are no thousands to unbundle, so we look to the ten thousands. We can unbundle 1 ten thousand to 10 thousands. Unbundle 10 thousands to make 9 thousands and 12 hundreds. Now we can subtract the hundreds column. Repeat questioning for the thousands, ten thousands, and hundred thousands place, recording the renaming of units in the problem. T: Are we ready to subtract? S: Yes, we’re ready to subtract! T: 0 ones minus 0 ones? S: 0 ones. T: 9 tens minus 2 tens? S: 7 tens. Have partners continue using the algorithm, reminding them to work right to left, always naming the units. T: Read the equation to your partner and complete your tape diagram by labeling the variable. S: 210,290 minus 45,720 is 164,570. (A = 164,570.) Problem 3: Use the subtraction algorithm to solve a word problem, modeled with a tape diagram,
Name Date Mass 3 kg g 20 kg 300 g g 1 kg 74 g g 403 kg 4 g g Length 3 km m 9 km m 6 km 435 m m 12 km 12 m m Complete the conversion charts. Capacity 4 L mL 48 L 808 mL mL 2 L 20 mL mL 639 L 6 mL mL A student completed the problem below. Check his work. Explain how you know if each solution is correct or incorrect. Find the sum or difference. 493 km 43 m + 17 km 57 m 25 kg 32 g – 23 kg 83 g 100 L 99 mL + 2,999 mL Billy is training for a half marathon. For the problems below, use tape diagrams, numbers, and words to explain each answer. Each day, Billy runs on the treadmill for 5 kilometers and runs on the outdoor track for 6,000 meters. In all, how many meters does Billy run each day?
4 4.MD.1 4.MD.2 The student correctly answers fewer than two of the three parts. The student correctly answers two of the three parts, but shows little evidence of reasoning in Part (c). The student answers three parts correctly, but does not show solid reasoning of understanding metric conversions in Part (c). The student correctly answers all three parts: 11,000 meters 1,500 milliliters 68,000 grams; Explains or shows computation of all measurements and the conversion to grams.
3 4.OA.3 4.NBT.5 4.NBT.6 The student incorrectly answers both parts and shows no reasoning. The student correctly answers one part and shows little reasoning. The student answers one part correctly but shows solid reasoning in both problems, or the student shows some reasoning with correct answers for both parts. The student correctly answers using any place value strategy: 400 Each teacher received 72 pencils. 4 4.NBT.6 The student incorrectly represents division using place value disks and incorrectly solves numerically. The student incorrectly solves the numeric equation but shows some understanding of the place value chart and use of the algorithm. The student decomposes incorrectly in one place value or does not include the remainder. The student correctly decomposes and divides using the place value disks and provides a numerical answer of 142 with a remainder of 1. 5 4.NBT.6 The student answers fewer than two parts correctly, showing little to no evidence of place value strategies. The student correctly solves two parts, showing little evidence of place value strategies. The student correctly solves three parts with understanding of place value strategies, or the student correctly solves all four parts but does not show solid evidence of place value understanding. The student solves all parts correctly using any place value strategy: 1,772 761 with a remainder of 4 1,624 731 6 4.MD.3 4.OA.1 4.OA.2 4.OA.3 4.NBT.5 4.NBT.6 The student incorrectly answers two or more of the four parts, showing little to no reasoning. The student correctly answers two of four parts, showing some reasoning. The student answers all four parts correctly but shows little reasoning in Part (a), or the student answers three of four parts correctly showing solid reasoning and understanding mathematically. The student correctly answers all four parts showing solid evidence of place value understanding: 1,638 square meters of flooring (estimate 40 × 40 = 1,600 square m). It is a reasonable because the answer and estimate have a difference of only 38 square meters. 528 more small posters than large posters.
Draw and label a diagram of Nathan’s bedroom rug. What is its perimeter? Draw and label a diagram of Nathan’s living room rug. What is its perimeter? What is the relationship between the two perimeters? Find the area of the living room rug using the formula A = l × w. The living room rug has an area that is how many times that of the bedroom rug?
103 230–31 207–8 rename 1 dollar as 10 dimes subtract a 3-digit money problem with renaming multi-step money word problems distance between 2 objects addition facts 104 232–33 209–10 subtract 3-digit numbers with and without renaming money word problems multiplication equations 5c Evangelism and missions 7a Grace 7b Exaltation of Christ 105 234–35 211–12 Chapter 12 Review count by 10s to 150 addition facts 106 TP 236 213 Cumulative Review Test Day Fahrenheit thermometer 10° less Chapter 13: Multiplication Facts 107 240–41 214–16 multiplication equation for equal sets of pictures multiplication word problems draw a picture for a multiplication pictograph addition facts 2e Work 108 PA 242–43 217–18 factors and product Order Principle of Multiplication multiplication facts with 2 as a factor multiplication word problems count by 2s to 30 greatest or least possible number from 3 given digits 109 PA 244–45 219–20 multiplication facts with 5 as a factor number line multiplication word problems write a multiplication word problem count by 5s to 50 expanded form of 3-digit numbers 110 246–47 221–22 multiplication facts with 10 as a factor Order Principle of Multiplication multiplication word problems write a word problem for a multiplication equation count by 10s to 150 word problems 111 PA 248–49 223–24 multiplication facts with 1 or 0 as a factor Identity Principle of Multiplication Zero Principle of Multiplication ordinal positions: first–twentieth addition facts H. God as Father 112 250–51 225–26 multiplication facts with 3 as a factor number line multiplication word problems color an array count by 3s to 30 even/odd numbers 1b Repentance and faith 5c Evangelism and missions 113 252–53 227–28 multiplication facts with 4 as a factor number line multiplication word problems color an array write a word problem for a multiplication equation count by 4s to 20 count back by 2s from 20 1b Repentance and faith 114 254–55 229–30 multiplication facts with 0–5 or 10 as a factor multiplication word problems count by 4s to 40 word problems 6a Bible study 115 256–57 231–32 Chapter 13 Review subtraction facts
Name Date Partial Products Standard Algorithm b. 3 1 5 × 4 3 1 5 × 4 Solve using each method. Partial Products Standard Algorithm a. 4 6 _× 2_ 4 6 × 2 Solve using the standard algorithm. a. 2 3 2 × 4 b. 1 4 2 × 6 c. 3 1 4 × 7 d. 4 4 0 × 3 e. 5 0 7 × 8 f. 3 8 4 × 9
T: What product is represented in both arrays? S: 18. T: Record the multiplication sentences for each array. S: 1 × 18 = 18 and 2 × 9 = 18. T: Circle the factors. Write the factors of 18 that are represented in order from least to greatest. S: (Write 1, 2, 9, 18.) T: With your partner, draw an array to represent another pair of factors with the product of 18. T: (Pause while students work.) What new factors of 18 did you find? S: 3 and 6. T: Revise your list of factors of 18. S: 1, 2, 3, 6, 9, and 18. T: How can we make sure we found all of the factors of 18? S: I can use my multiplication chart. I can think through my multiplication facts. But what if the number is really big, like 92? I don’t know all the factors of 92. I could draw arrays to find all the factors, making rows of 3, then 4, then 5, and all the way to 92. That will take a long time. T: Look at the list of factors for 18. Draw an arrow from 1 to 18. These are factor pairs because 1 × 18 = 18. With your partner, draw the rest of the arrows to connect the factor pairs. S: (Draw as pictured to the right above.) T: Notice that 3 and 6 are the middle pairs. We’ve checked everything up to 3, and the counting numbers between 3 and 6 are not factors of 18, so we found all the pairs. Try that with the factors of 8. Problem 2: Identify factors to define prime and composite numbers. Display the number sentence 2 × 8 = 16. T: What are the factors? S: 2 and 8. T: What other multiplication sentences can you write using different factors that will give us the same product? S: 1 × 16 = 16. 4 × 4 = 16. T: So, what are all of the factors of 16? S: 1, 2, 4, 8, and 16. T: How do you know those are all of the factors of 16? S: I listed them in order. When I got to 8, I noticed
Solve 57 15 using 2 partial products. Match each partial product to its rectangle on the area model. Solve the following using 2 partial products. Visualize the area model to help you. 1 8 6 2 _____ × _____ _____ × _____ 2 5 4 6 _____ × _____ _____ × _____ 3 9 4 6 7 8 2 3
Name Date Solve 26 34 using 4 partial products and 2 partial products. Remember to think in terms of units as you solve. Write an expression to find the area of each smaller rectangle in the area model. 3 4 2 6 6 ones 4 ones 6 ones 3 tens 2 tens 4 ones 2 tens 3 tens 3 4 2 6 6 ones × 34 ones 2 tens 34 ones 4 1 8 2 2 ones × 41 ones 8 tens 41 ones Solve using 4 partial products and 2 partial products. Remember to think in terms of units as you solve. Write an expression to find the area of each smaller rectangle in the area model. 4 1 8 2 2 ones 1 one 2 ones 4 tens 8 tens 1 one 8 tens 4 tens