zilongwang/ReadingBank huggingface dataset:
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 4.NF.3ab 4.NF.4a The student correctly answers fewer than four of the eight parts. The student correctly answers four or five of the eight parts. The student correctly answers six or seven of the eight parts. The student correctly does the following: Draws and shades to represent the three given fractions and represents each as a sum of unit fractions: Records the decomposition using two addends. (Answers may vary.) Rewrites equations as multiplication of a whole number: 2 4.NF.1 The student is unable to correctly complete a majority of the problem. The student is able to correctly identify the fractions naming the three given models but is unable to complete the next model in the The student is able to correctly identify the fractions naming the three given models and is able to create the next model, as well as The student correctly does the following: Identifies the shaded fractions as and creates a
4.NF.3c 4.MD.2 F Addition and Subtraction of Fractions by Decomposition Lesson 29: Estimate sums and differences using benchmark numbers. Lesson 30: Add a mixed number and a fraction. Lesson 31: Add mixed numbers. Lesson 32: Subtract a fraction from a mixed number. Lesson 33: Subtract a mixed number from a mixed number. Lesson 34: Subtract mixed numbers. 6 4.NF.4 4.OA.2 4.MD.2 4.MD.4 G Repeated Addition of Fractions as Multiplication Lessons 35–36: Represent the multiplication of n times a/b as (n × a)/b using the associative property and visual models. Lessons 37–38: Find the product of a whole number and a mixed number using the distributive property. Lesson 39: Solve multiplicative comparison word problems involving fractions. Lesson 40: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots. 6 4.OA.5 H Exploring a Fraction Pattern Lesson 41: Find and use a pattern to calculate the sum of all fractional parts between 0 and 1. Share and critique peer strategies. 1 End-of-Module Assessment: Topics A–H (assessment ½ day, return ½ day, remediation or further applications 1 day) 2 Total Number of Instructional Days 45 Terminology New or Recently Introduced Terms Benchmark (standard or reference point by which something is measured)
Use area models to prove that , and What conclusion can you make about and Explain. Note: This Application Problem builds from Lesson 5, where students decomposed unit fractions using area models to show equivalence. Consider leading a discussion with a question, such as, “Why can you show = = on one model, = = on another, and = on another?” Or perhaps lead with a question, such as, “Why can’t you show = = on the same area model?” Concept Development (30 minutes) Materials: (S) Personal white board Problem 1: Use an area model to show that . T: Draw an area model representing 1, and then shade . T: Discuss with a partner how you can use this model to show the decomposition of 3 fourths into eighths. S: We could draw a line so that each of the fourths is split into 2 equal parts. That would give us eighths. Drawing a line will make each unit into 2 smaller units, which would be eighths. T: How many eighths are shaded? S: 6 eighths. T: Work with a partner to write an addition and a multiplication sentence to describe the decomposition. S: is equal to T: What do these addition and multiplication sentences tell you? S: The shaded area didn’t change. It’s still the same amount. The number of pieces increased, but the size of the pieces got smaller. Adding together all of the smaller units equals the total of the larger units shaded. Multiplying also equals the total of the larger units shaded and is easier to write out! Problem 2: Draw an area model to represent the equivalence of two fractions, and express the equivalence as the sum and product of unit fractions.
Name Date The rectangle below represents 1. Draw horizontal lines to decompose the rectangle into eighths. Use the model to give the shaded area as a sum and as a product of unit fractions. Use parentheses to show the relationship between the number sentences. Draw an area model to show the decomposition represented by the number sentence below.
Assessment Task Item and Standards Assessed 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 4.NF.5 4.NF.6 The student answers fewer than two parts correctly. The student answers two parts correctly. The student correctly answers three of the four parts of the question, showing solid reasoning. OR The student answers all parts correctly without correctly modeling on the place value charts. The student correctly uses the area models to represent: = ; 0.8 = 0.80 = ; 1.8 = 1.80 = ; 0.2 = 0.20 d. = ; 0.5 = 0.50 2 4.NF.6 The student correctly answers two or fewer parts of the question. The student correctly answers three parts of the question. The student correctly answers four or five parts of the question. The student correctly answers: 0.4 1.1 1.8 d. 3.67 3.78 3.82 3 4.NF.6 4.NF.7 The student answers four or parts of the question correctly with little to no reasoning. The student correctly answers four or five parts of the question, providing evidence of some reasoning. The student correctly answers six or seven parts of the question, with solid reasoning for each part correct. OR The student correctly The student correctly answers and reasons correctly using pictures, numbers, or words for each part: < =
solves all parts but does not provide solid reasoning for one or two parts. = < < = > > 4 4.NF.5 The student correctly answers one or no parts. The student correctly answers two parts of the question but does not include the units or provide ample evidence of reasoning. The student correctly answers two of the three parts of the question, providing solid evidence or reasoning. OR The student solves all three parts correctly, providing only some or partially correct reasoning. The student correctly answers: meters liters dollars 5 4.NF.5 The student correctly answers two or fewer parts of the question. The student correctly answers three or four of the six parts of the question. The student correctly answers five of the six parts of the question. The student correctly answers: or 1 or 1 or 1 or 1
6 4.NF.5 4.NF.6 4.NF.7 4.MD.2 The student correctly answers fewer than three problems, providing little to no reasoning. The student correctly answers three or four of the six problems, providing some reasoning. The student correctly answers five of the six problems with solid reasoning. OR The student answers all six parts correctly but provides less than solid evidence in no more than two parts. The student correctly: Answers 20.12 seconds. Plots the times on the number line and records each time as a decimal and fraction. Answers m < m; or 32.04 m < 35.84 m. Shades each area model representing each item. + = ; $1.39 Reasons that Brian’s container of juice is larger, and, therefore, each tenth unit will fill more juice than Sonya’s container. Comparing is only valid when the unit whole is the same. The containers’ unit wholes were of different sizes.
2 4.NF.5 4.NF.6 The student is unable to correctly answer any of the parts. The student answers one part correctly. The student correctly represents the decomposition or correctly writes an equivalent equation in one of the questions. OR The student correctly writes equivalent statements for all parts but incorrectly decomposes in just one part. The student correctly: Decomposes the models into hundredths, shading the correct amount. Expresses the equivalence using fractions and decimals: = and 0.3 = 0.30. = and 1.7 = 1.70. 3 4.NF.6 The student is unable to correctly compose or decompose. The student answers one part correctly. The student decomposes 3.24 into just two bonds (3, 0.24) and answers Part (b) correctly. The student correctly: Decomposes 3.24 into number bonds: 3, 0.2, 0.04. Composes 2.53. 4 4.NF.5 The student shows little understanding of the number disks and equivalence. The student models equivalence but does not use number disks. The student shows some understanding of the number disks and supplements with a written explanation. The student correctly uses number disks to show the equivalence of 20 hundredths and 2 tenths in the place value chart. 5 4.NF.5 4.NF.6 The student correctly answers fewer than 10 of the expressions in the chart. The student correctly answers 10 to 14 of the expressions in the chart. The student correctly answers 15 to 19 of the expressions in the chart. The student correctly answers each expression. (Note: Unit form may have more than one correct answer.) 1 tenth 6 hundredths; ; ) + (6 × ; (1 × 0.1) + (6 × 0.01); 0.16. 2 ones 7 tenths; 2 ; (2 × 1) + (7 × ; (2 × 1) + (7 × 0.1); 2.7. 6 ones 3 tenths 4 hundredths; 6 ; (6 × 1) + (3 × + (4 × ; (6 × 1) + (3 × 0.1) +
Overview of Module Topics and Lesson Objectives Standards Topics and Objectives 4.NF.6 4.NBT.1 4.MD.1 A Exploration of Tenths Lesson 1: Use metric measurement to model the decomposition of one whole into tenths. Lesson 2: Use metric measurement and area models to represent tenths as fractions greater than 1 and decimal numbers. Lesson 3: Represent mixed numbers with units of tens, ones, and tenths with number disks, on the number line, and in expanded form. 3 4.NF.5 4.NF.6 4.NBT.1 4.NF.1 4.NF.7 4.MD.1 B Tenths and Hundredths Lesson 4: Use meters to model the decomposition of one whole into hundredths. Represent and count hundredths. Lesson 5: Model the equivalence of tenths and hundredths using the area model and number disks. Lesson 6: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms. Lesson 7: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart. Lesson 8: Use understanding of fraction equivalence to investigate decimal numbers on the place value chart expressed in different units. 5 Mid-Module Assessment: Topics A–B (assessment 1 day, return ½ day, remediation or further applications ½ day) 2 4.NF.7 4.MD.1 C Decimal Comparison Lesson 9: Use the value chart and metric measurement to compare 3
4 4.MD.1 The student answers fewer than two parts correctly. The student correctly answers two or three of the parts. The student correctly answers four of the five parts. Or, the student answers all parts correctly but without labeling the units. The student correctly answers: 9,000 meters. 3,240 milliliters. 41 inches. 135 minutes 390 ounces. 5 4.MD.1 4.MD.2 The student answers fewer than two parts correctly. The student correctly answers two of the four parts. The student correctly answers three of the four parts. Or, the student answers all parts correctly but does not show work. The student correctly answers: 10 gal 1 qt. 5 ft 5 in. 11 min 20 sec. 20 lb 14 oz. 6 4.OA.1 4.OA.2 4.OA.3 4.MD.1 4.MD.2 The student answers fewer than three parts correctly. The student correctly answers three of the five parts. The student correctly answers all parts but does not provide solid reasoning or evidence of showing work in two of the five parts. Or, the student correctly answers four of the five parts. The student correctly: Completes the table: 36, 72, 108, 144, 180, 360 inches. Describes the rule, such as multiply the number of yards times 36. Solves for 540 inches in 15 yards. Answers yes, and provides an accurate explanation such as 15 yards is 3 times as much as 5 yards, so 3 × 180 inches = 540 inches. Answers 14 feet 7 inches using RDW.
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 5.NBT.1 5.NBT.2 The student is unable to provide a correct response. The student attempts but is not able to accurately draw the place value chart or explain reasoning fully. The student correctly draws place chart but does not show full reasoning, or explains reasoning fully but the place value chart does not match the reasoning. The student correctly: Draws place value chart showing movement of digits. Explains movement of units to the left for multiplication and movement of units to the right for division. 2 5.NBT.7 The student is unable to use the area model to find the product. The student attempts using an area model to multiply but does so inaccurately. Student attempts to write either word or expanded form of inaccurate product. The student uses the area model to multiply but does not find the correct product. Student accurately produces word and expanded form of inaccurate product. The student correctly: Draws an area model. Shows work to find product 13.8. Accurately expresses product in both word and expanded form. 3 5.NBT.3a 5.NBT.3b The student answers none or one part correctly. The student answers two or three answers correctly. The student answers four or five answers correctly. The student correctly answers all six parts. a. > d. > b. = e. < c. > f. <
4 5.NBT.1 5.NBT.2 5.NBT.3a 5.NBT.3b 5.NBT.4 5.NBT.7 5.MD.1 The student answers none or one part correctly. The student answers two parts correctly. The student is able to find all answers correctly but is unable to explain strategy in Part(c), or answers three of the four parts correctly. The student correctly: Estimates 10.357 g to 10.4 g, 12.062 g to 12.1 g, and 7.506 g as 7.5 g; finds sum 30 g; shows work or model. Finds sum 29.925 g and difference 0.075 g. Finds the quotient 5.985 g and explains accurately the strategy used. Rounds 5.985 g to 6 g.
(1 Point) (2 Points) (3 Points) (4 Points) 1 5.NBT.3a 5.NBT.3b The student answers none or one part correctly. The student answers two or three parts correctly. The student answers four or five parts correctly. The student correctly answers all six parts: a. > d. < b. > e. = c. < f. < 2 5.NBT.1 5.NBT.2 The student answers none or one part correctly. The student answers two parts correctly. The student is able to answers all parts correctly but is unable to explain his strategy in Part (a), (b), or (c), or answers three of the four parts correctly. The student accurately models 8.88 on the place value chart and correctly: Uses words, numbers, and model to explain why each digit has a different value. Finds product of 88,800 and explains. Finds quotient of 888 and explains. 3 5.NBT.4 5.MD.1 The student is unable to identify any answers for Part (a) or answer Part (b) correctly. The student identifies one or two answers correctly for Part (a) and makes an attempt to convert but gets an incorrect solution for Part (b). The student identifies two answers correctly for Part (a) and converts correctly for Part (b), or the student identifies three answers correctly for Part (a) and converts with a small error for Part (b). The student identifies all three answers correctly for Part (a) and answers Part (b) correctly: 2.251 cm, 2.349 cm, 2.295 cm. 2.3 102 = 0.023 4 5.NBT.1 5.NBT.2 5.NBT.3 5.NBT.4 The student answers none or one part correctly. The student answers two problems correctly. The student is able to answer all parts correctly but is unable to explain strategy in Part (d), or the student answers three of the four problems correctly. The student correctly responds: 0.947 m, 0.97 m, 1.268 m, 1.5 m. Nine hundred forty-seven thousandths meters. 0.9 + 0.04 +
5.NBT.7 division necessary to show non-equivalence of quotients. necessary to produce the whole number portion of the quotient, but is unable to continue dividing the decimal places to show non-equivalence of quotients. of the quotients, but with errors in the division calculation. the non-equivalence of the quotients. 26 ÷ 8 = 3.25 14 ÷ 4 = 3.5 5 5.NBT.6 The student does not divide to find the length of the playground. The student makes two errors in division that lead to incorrect length of the playground. The student makes one error in division that leads to an incorrect length of the playground. The student correctly divides, and finds the length of the rectangle to be 106 m. 6 5.OA.1 5.OA.2 5.NBT.1 5.NBT.2 5.NBT.5 5.NBT.6 5.NBT.7 5.MD.1 The student uses incorrect reasoning for all parts of the task. The student uses correct reasoning for at least two parts of the task, but makes errors in calculation. The student uses correct reasoning for all parts of the task, but makes errors in calculation. The student describes correct reasoning using words, numbers or pictures, and correctly calculates for all parts of the task. 1,232 oz 102 loaves 7 boxes (20 × 0.80) + (6 × $1.25) $8.00
Lesson 8 Objective: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product. Suggested Lesson Structure Practice (7 minutes) Application Problem (10 minutes) Development (33 minutes) Student Debrief (10 minutes) Total Time (60 minutes) Fluency Practice (7 minutes) State in Exponential Form Name 5.NBT.2 (3 minutes) Multiply Using the Area Model with a Zero in One Factor 5.NBT.6 (4 minutes) State in Exponential Form Name (3 minutes) Materials: (S) Personal white board Note: This fluency activity maintains earlier skills and encourages insights into the place value structure of multi-digit multiplication’s partial products. A quick review of relevant vocabulary (base, exponent, power) may be in order. T: (Write 102 = .) Say the base. S: 10. T: Say the exponent. S: 2. T: Say 10 squared as a multiplication sentence starting with 10. S: 10 × 10 = 100. T: Say it as a number sentence without using a multiplication sentence. S: 10 squared equals 100. Repeat the process with 103, 104, 105, and 107.
necessary. Ask students to discuss how putting the single-digit numeral (3 tenths) as the top number affects the recording of partial products? (It does not. The process is the same. The order is different.) Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Name Date Estimate the product. Solve using an area model and the standard algorithm. Remember to express your products in standard form. 22 × 2.4 ≈ _______ × _______ = _______ 3.1 × 33 _______ × _______ = _______
2(a) 5.NF.1 5.NF.2 The solution is incorrect and shows little evidence of understanding of the need for like units. The student shows evidence of beginning to understand addition fractions with unlike denominators, but cannot apply that knowledge to this part–whole comparison. The student calculates correctly and sets up the part–whole situation correctly, but fails to write a complete statement. Or, the student fully answers the question but makes one small calculation error that is clearly careless, such as copying a number wrong. The student is able to apply part–whole thinking to correctly answer and explains the answer using words, pictures, or numbers. 2(b) 5.NF.1 5.NF.2 The solution is incorrect and shows no evidence of being able to work with decimal fractions and fifths simultaneously. The student shows evidence of recognizing how to convert fractions to decimals or decimals to fractions, but fails to do so correctly. The student calculates correctly, but may be less than perfectly clear in stating his or her solution. For example, “The answer is ,” is not a clearly stated solution. The student gives a correct equation and correct answer of kg or kg and explains the answer using words, pictures, or numbers. 2(c) 5.NF.1 5.NF.2 The solution is incorrect and shows little evidence of understanding of fraction comparison. The student may have compared correctly but calculated incorrectly and/or does not explain the meaning of his or her numerical solution in the context of the story. The student may have compared correctly, but calculated incorrectly and/or does not explain the meaning of his or her numerical solution in the context of the story. The student correctly: Responds that the garden produced more strawberries. Responds that there were kg or 2.1 kg more strawberries. Gives equation such as .
B01 = B + nby2; B10 = B + nby2*N; B11 = B + nby2*N + nby2; left_half_lower_solve(B00, B10, LU, nby2, N); right_half_lower_solve(B01, B11, LU, nby2, N); } else if (n == min_block_size) { lower_solve_serial(B, LU, n, N); } else { printf("Error : [upper_solve] : n <= 0"); } } void left_half_lower_solve(double *B00, double *B10, double *LU, int n, int N) { double *L00, *L10, *L11; L00 = LU; L10 = LU + n*N; L11 = LU + n*N + n; lower_solve(B00, L00, n, N); schur(B10, B00, L10, n, N); lower_solve(B10, L11, n, N); } void right_half_lower_solve(double *B01, double *B11, double *L, int n, int N) { double *L00, *L10, *L11; L00 = L; L10 = L + n*N; L11 = L + n*N + n; lower_solve(B01, L00, n, N); schur(B11, B01, L10, n, N); lower_solve(B11, L11, n, N); } int main(int argc, char** argv) { int n = 16; int nby2 = n / 2; int i, j, k; int errorFlag; double sum; double *M1, *M2, *L, *U; double *M00, *M01, *M10, *M11; if(argc==2) { n = atoi(argv[1]); nby2 = n / 2; }
for (k = 0; k < j; k++) sum += LU[j*N + k] * B[k*N + i]; B[j*N + i] = (B[j*N + i] - sum); } } } void upper_solve(double *B, double* LU, int n, int N) { /* Solve B'*U=B */ /* U - given */ /* B - given */ /* solve for B' */ double *B00, *B01, *B10, *B11; if (n > min_block_size) { int nby2 = n / 2; B00 = B; B01 = B + nby2; B10 = B + nby2*N; B11 = B + nby2*N + nby2; cilk_spawn top_upper_half_solve(B00, B01, LU, nby2, N); bottom_upper_half_solve(B10, B11, LU, nby2, N); } else if (n == min_block_size) { upper_solve_serial(B, LU, n, N); }
Problem 5 Leonard spent of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had of his money left. What fraction of his money did he spend on the comic books? Student Debrief (10 minutes) Lesson Objective: Solve two-step word problems. 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. T: Bring your Problem Set to the Debrief. Share, check, and/or explain your answers to your partner. S: (Work together for 2 minutes.) T: (Circulate and listen to students’ explanations while they work, and then review answers.) T: Let’s take a look at two different strategies for solving Problem 4.
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 5. NF.4 5. NF.7 The student draws valid models and/or arrives at the correct answer for two or more items. The student draws valid models and/or arrives at the correct answer for three or more items. The student draws valid models and/or arrives at the correct answer for four or more items. The student correctly answers all eight items, and draws valid models: 12 20 2 5.NBT.7 The student has two or fewer correct answers. The student has three correct answers. The student has four correct answers. The student correctly answers all six items: 48 0.48 400 4 9.6 or or any equivalent fraction 32 3 5.OA.2 The student has no correct answers. The student has one correct answer. The student has two correct answers. The student correctly answers all three items: (9 + 12) or 2 × (9 + 12)
4 5.NF.3 5.NF.6 5.MD.1 The student has no correct answers. The student has one correct answer. The student has two correct answers. The student correctly answers all three items: 4.8 hours 4 hours, 48 minutes 288 minutes 5 5.NF.6 5.NF.7 The student gives one or fewer correct responses among Parts (a), (b), (c), and (d). The student gives at least two correct responses among Parts (a), (b), (c), and (d). The student gives at least three correct responses among Parts (a), (b), (c), and (d). The student correctly answers all four items: 5 ÷ 2 5 ÷ Draws a correct diagram for both expressions and solves. Correctly identifies 5 ÷ 2, and offers solid reasoning. 6 5.NF.5 The student gives both a faulty example and faulty explanation. The student gives either a faulty example or explanation. The student gives a valid example or clear explanation. The student is able to give a correct example and clear explanation. A Progression Toward Mastery 7 5.NF.3 5.NF.4 5.NF.6 5.NF.7 5.MD.1 5.MD.2 The student has two or fewer correct answers. The student has three correct answers. The student has five correct answers. The student correctly answers all seven items: a. 0 gal, 3 qt, 0 pt 1 gal, 2 qt, 0 pt 2 gal, 0 qt, 1 pt 2 gal, 2 qt, 1 pt b. 13 gal, 1 pt c. gal d. gal e. gal f. 6 c
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 5.NF.4a 5.MD.1 The student draws valid models and/or arrives at the correct product for two or more items. The student draws valid models and/or arrives at the correct product for at least four or more items. The student draws valid models and/or arrives at the correct product for at least six or more items. The student correctly answers all eight items, and draws valid models: 3 9 12 8 inches feet 49 2 5.NF.4a 5.NF.3 The student’s work shows no evidence of being able to express the length of the shaded area. The student approximates the length of the shaded bar, but does not write a multiplication equation. The student is able to write the correct multiplication equation for the diagram, but incorrectly states the length of the shaded part of the bar. The student correctly: Writes a multiplication equation: × 3. Finds the length of the shaded part of the bar as or . 3 5.OA.1 The student is unable to identify any equal expressions. The student correctly identifies one correct expression. The student correctly identifies two equal expressions. The student correctly: Identifies (a), (c), and (d) as equal to × 6. Explains why (b) is not equal.
4 5.OA.2 The student is unable to write expressions for (a), (b), or (c). The student correctly writes one expression. The student correctly writes two expressions. The student correctly writes three expressions: × (6 + 3) 4 × (3 ÷ 4) or 4 × 5 5.NF.4a 5.NF.6 5.MD.2 The student is neither able to produce a multiplication expression that identifies the data from the line plot nor find the total gallons of water collected. The student is either able to write a multiplication expression that accounts for all data points on the line plot or find the total gallons of water collected. The student’s multiplication expression correctly accounts for all the data points on the line plot when finding the total gallons of water collected, but makes a calculation error. The student correctly: Accounts for all data points in the line plot in the multiplication expression. Finds the total gallons of water collected as gallons or gallons. 6 5.NF.4a 5.NF.6 5.MD.1 The student correctly calculates two correct answers. The student is able to correctly calculate three correct answers. The student is able to correctly calculate four correct answers. The student correctly: Calculates c butter, 16 oz of marshmallows, c of cereal. Converts c butter to fluid ounces. Uses an equation or model and finds the number of treats taken to school as 18 treats.
109 221–22 217–18 Practice addition and subtraction facts Practice math concepts Subtract 3-digit numbers with renaming Solve a multi-step word problem and interpret the solution Connect math to the biblical worldview truth that the whole world was designed by God 110 223–24 219–20 Review subtracting 3-digit numbers with and without renaming Review checking subtraction with addition Review solving a word problem and interpreting the solution Review the biblical worldview truth that the whole world was designed by God 111 221–22 Concept Review Chapter 14 • Multiplication Facts 112 225–28 223–24 Practice addition and subtraction facts Determine the greatest and the least possible numbers from 3 given digits Write a multiplication equation for equal sets of pictures Use multiplication to read and interpret the data given in a picture graph 113 229–30 225–26 Practice addition and subtraction facts Write a 3-digit number in expanded form Interpret the function of each factor by picturing a multiplication equation Complete a multiplication equation with 2 as a factor, using skip counting and the doubles strategy Solve a multiplication word problem and interpret the solution Connect math to the biblical worldview truth that people are important Lesson Worktext Pages Reviews Pages Practice and Review Objectives Lesson Objectives 114 231–32 227–28 Practice addition and subtraction facts Count on by 100 Skip count by 5s to complete a multiplication fact with 5 as a factor Use a number line to solve a multiplication equation Solve a multiplication word problem and interpret the solution 115 233–34 229–30 Practice addition and subtraction facts Skip count by 3s to 30 Skip count by 10s to solve a multiplication equation Picture a multiplication equation when 10 is a factor Solve a multiplication word problem and interpret the solution 116 235–36 231–32 Practice addition and subtraction facts Determine whether a number is even or odd Complete a multiplication fact with 1 as a factor Complete a multiplication fact with 0 as a factor 117 237–38 233–34 Practice addition and subtraction facts Subtract 2-digit numbers Use a number line to solve a multiplication problem with 3 as a factor Use an array to solve a multiplication problem with 3 as a factor Solve a multiplication word problem and interpret the solution Connect math to the biblical worldview truth that people are important
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths . . . . . . . . . . __________________________ millions through thousandths place value chart
S: Yards. T: Compare this problem with the conversions we worked on yesterday. What do you notice about the units? Turn and talk. S: This is starting with larger units and converting to smaller ones. Yesterday every conversion we did was small units to large units. This is large to small conversion. T: Let’s draw a tape diagram to model this problem. We want to name yards using feet. (Draw a bar and label it yd.) Let’s partition the bar into 4 equal units to represent the 4 whole yards and 1 smaller unit to represent of a yard. yards is the same as × 1 yard. (Write on the board.) How many feet are in 1 yard? S: 3 feet. T: On your personal white board, draw a tape diagram to explain your thinking. S: (Draw.) T: (Show 1 yard equal to 3 feet below the tape diagram.) Write a new expression to rename the yard in feet. S: (Write × 3 ft.) T: Before we multiply, let’s express as an improper fraction. How many thirds are in 1 whole? S: 3 thirds. T: So how many thirds are in 4 wholes? S: 12 thirds. T: How many thirds are in 4 and 1 third? S: 13 thirds. T: Write a new multiplication expression that uses the improper fraction we just found. S: (Write × 3 ft.) T: Work with a partner to find the product of 13 thirds and 3. S: (Work.) T: (Point to the original problem.) Fill in the blank using a complete sentence. S: yd is equal to 13 ft. As necessary, repeat the same process with the following problems. ft = ____ in
You may choose to use any combination of the questions below to lead the discussion. Share your solutions and explain your thought process for solving Problem 1 to a partner. How did you decide which number goes into which expression? Compare your solutions for Problem 2 with a partner. Did you have different answers? If so, explain your thinking behind each sorting. What was your strategy for solving Problem 3? Share it with a partner. How did you solve Problem 4? Did you make a drawing or tape diagram to compare the sprouts? Share it with and explain it to a partner. Share your decimal examples for Problem 5 with a partner. Did you have the same or different examples? Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students.
units (square feet). Finds the cost of the sod. of the yard with the correct units (square feet). Finds the cost of the sod. Calculates the area of the yard using appropriate units as 313 ft2 or 313 ft2. Finds the cost of the sod to be $203.84. 3 5.MD.3 5.MD.5 The student is unable to find the volume of the water that has overflowed and is unable to explain the reasoning used. The student finds the volume of the water that has overflowed but is unable to explain the reasoning used. The student makes a calculation error in finding the volume of the water that has overflowed but is able to clearly explain the reasoning used. The student finds the volume of the water that has overflowed to be 1.1 L and uses words, numbers, and pictures to clearly explain the reasoning used. A Progression Toward Mastery 4 5.NF.4b 5.NF.6 The student is not able to draw an area model, provide an explanation of Jim’s error, or give the correct area. The student does one of the following: Accurately partitions the area model in both dimensions. Provides a clear explanation of Jim’s error. Calculates the correct area of the rectangle. The student does two of the following: Accurately partitions the area model in both dimensions. Provides a clear explanation of Jim’s error. Calculates the correct area of the rectangle. The student does the following: Accurately partitions the area model in both dimensions. Provides a clear explanation of Jim’s error. Calculates the correct area of the rectangle as 8 1/8 in2. 5 5.MD.5 The student is neither able to find the heights of the towers nor able to answer which tower is taller. The student makes an attempt to calculate the towers’ heights but makes errors in both calculations. Explanation of reasoning used is unclear. The student calculates the heights of towers but makes a calculation error that causes an error in the determination of the taller tower. However, the explanation of the reasoning used is clear. The student does the following: Accurately calculates the heights of both towers (8 inches). Explains clearly that the towers are equal in height.
6 5.G.3 5.G.4 The student provides a combination of at least three correct true or false responses and/or explanations. The student provides a combination of at least six correct true or false responses and/or explanations. The student provides a combination of at least seven correct true or false responses and/or explanations. The student provides seven correct true or false responses and clear explanations for all seven items. True True False True False False False
(1 Point) (2 Points) (3 Points) (4 Points) 1 5.MD.3 5.MD.4 The student has neither the correct volume nor the correct unit of measure for either figure. The student calculates the volume incorrectly for both figures but uses the correct unit of measure. The student calculates the volume for one figure correctly and uses the correct unit of measure for both. The student correctly calculates the volume and uses the correct unit of measure for both: a. 12 in3 b. 8 in3 2 5.MD.5a 5.MD.5b The student is unable to explain the equivalence of the two approaches and is unable to find the volume of the prism in Part (b) using Jack’s method. The student makes an attempt to explain the equivalence of the two approaches but uses faulty logic and is unable to find the volume of the prism in Part (b) using Jack’s method. The student explains the equivalence between the two approaches by explaining that the sides may be multiplied in any order because any face can be used as the base of the figure but is unable to use Jack’s method to calculate the volume of the prism in Part (b). The student may not score more than 3 points if the student does not label Part (b) as cubic feet (ft3). The student correctly explains the equivalence between the two approaches by explaining the sides may be multiplied in any order because any face can be used as the base of the figure. The student also uses Jack’s method to correctly calculate the area of the prism in Part (b) as (3 × 2) × 5 = 30 ft3. A Progression Toward Mastery 3 5.MD.5a The student is neither able to calculate the volume of the figure nor explain the reasoning used. The student uses a correct method for finding the volume of the cube but does not consider the size of the cubes (2 cm side lengths) and does not The student uses a correct method for finding the volume of the cube and is able to explain the reasoning used but does not consider the size of the The student correctly answers 1,440 cm3 and is able to explain the reasoning used.
Name Date Sketch the rectangles and your tiling. Write the dimensions and the units you counted in the blanks. Then, use multiplication to confirm the area. Show your work. We will do Rectangles A and B together. 2. Rectangle B: 3. Rectangle C: 4. Rectangle D: 5. Rectangle E:
Assessed (1 Point) (2 Points) evidence of solid reasoning with an incorrect answer. (3 Points) (4 Points) 1 5.G.1 The student gives the coordinates for one point on the plane and uses correct notation, including parentheses and a comma. The student gives the coordinates for two points on the plane and uses correct notation, including parentheses and a comma. The student gives the coordinates for three points on the plane and uses correct notation, including parentheses and a comma. The student correctly gives the coordinates for four or five points using correct notation as: A (3, 4) B (4, 2) C (, ) D (1, 2) E (, ) 2 5.G.1 The student plots one point, but does not label it. The student plots one point with label or two points without labels. The student is able to correctly plot three points, but does not label them. The student correctly: Plots three points Labels the points on the grid. 3 5.G.1 5.OA.3 The student is unable to give coordinates for points on the same vertical line or horizontal line. The student gives coordinates for two points on the same vertical line or horizontal line. The student gives two coordinates on the same vertical line and two coordinates on the same horizontal line. The student: Gives three collinear points on a vertical line (all three points have the same Gives three collinear points on a horizontal line (all three points have the same 4 5.G.1 The student is neither able to identify Garrett’s placement as correct nor able to explain the reasoning used. The student is unable to identify Garrett’s placement as correct, but does explain the reasoning used. The student identifies Garrett’s placement as correct, but the explanation lacks clarity. The student: Identifies Garrett’s placement as correct. Clearly explains the reasoning used.
A quadrilateral with two pairs of equal sides that are also adjacent. An angle that turns through of a circle. A quadrilateral with at least one pair of parallel lines. A closed figure made up of line segments. Measurement of space or capacity. A quadrilateral with opposite sides that are parallel. An angle measuring 90 degrees. The union of two different rays sharing a common vertex. The number of square units that covers a shape. Two lines in a plane that do not intersect. The number of adjacent layers of the base that form a rectangular prism. A three-dimensional figure with six square sides. A quadrilateral with four 90-degree angles. A polygon with 4 sides and 4 angles. A parallelogram with all equal sides. Cubes of the same size used for measuring. Two intersecting lines that form 90-degree angles. A three-dimensional figure with six rectangular sides. A three-dimensional figure. Any flat surface of a 3-D figure. A line that cuts a line segment into two equal parts at 90 degrees. Squares of the same size, used for measuring. A rectangular prism with only 90-degree angles. One face of a 3-D solid, often thought of as the surface upon which the solid rests.
Base Volume of a Solid Cubic Units Kite Height One-Degree Angle Face Trapezoid Right Rectangular Prism Perpendicular Bisector Cube Area Perpendicular Lines Rhombus Parallel Lines Angle Polygon Rectangular Prism Parallelogram Rectangle Right Angle Quadrilateral Solid Figure Square Units
b 6.G.A.3 Student does not calculate the area. Student counts the squares inside the shape by estimating the parts of squares that are part of the area. Student uses the area of rectangles and/or triangles to calculate the area of the shape but does so incorrectly. Student uses the area of rectangles and/or triangles to calculate the area of the shape and correctly calculates square units as the area. 6 a 6.G.A.1 Student does not calculate the area. Student calculates the area incorrectly, perhaps using the wrong dimensions. Student calculates the area correctly but does not label the answer. Student calculates the area correctly and labels accurately . b 6.G.A.1 Student does not calculate the area. Student calculates the area of the new garden but does not divide by . Student calculates the area of both shapes correctly but does not answer the question. Student calculates the area of both shapes correctly and explains that the original garden has a larger area because is larger than ; therefore, students can plant more vegetables in the original garden. Name Date The juice box pictured below is high, long, and wide.
Find the difference by aligning the expressions vertically. Subtraction as adding the opposite Align like terms vertically and combine by addition Adding the opposite is equivalent to subtraction Students should recognize that the subtracted expression in Example 1(b) did not include a term containing the variable , so the from the first grouped expression remains unchanged in the answer. Example 3 (3 minutes): Using Expressions to Solve Problems Students write an expression representing an unknown real-world value, rewrite as an equivalent expression, and use the equivalent expression to find the unknown value. Example 3: Using Expressions to Solve Problems A stick is meters long. A string is times as long as the stick. Express the length of the string in terms of . The length of the stick in meters is meters, so the string is , or , meters long. If the total length of the string and the stick is meters long, how long is the string? The length of the stick and the string together in meters can be represented by , or . If the length of the stick and string together is meters, the length of the stick is meters, and the length of the string is meters. Example 4 (4 minutes): Expressions from Word Problems Students write expressions described by word problems and rewrite the expressions in standard form. Example 4: Expressions from Word Problems It costs Margo a processing fee of to rent a storage unit, plus per month to keep her belongings in the unit. Her friend Carissa wants to store a box of her belongings in Margo’s storage unit and tells her that she will pay her toward the processing fee and for every month that she keeps the box in storage. Write an expression in standard form that represents how much Margo will have to pay for the storage unit if Carissa contributes. Then, determine how much Margo will pay if she uses the storage unit for months. Let represent the number of months that the storage unit is rented. Original expression Subtraction as adding the opposite Opposite of the sum is the sum of its opposites Any order, any grouping Combined like terms This means that Margo will have to pay only of the processing fee and per month that the storage unit is used.
The breakdown of the grades is as follows: Your final grade will be based on the overall breakdown: A: 90-100% B: 80-89.9% C: 70-79.9% D: 60-69.9% F: Below 60% Academic Integrity: Integrity is an essential component of the student academic experience. The integrity students learn and exhibit at Chaffey College will be a model for the professional integrity they practice when they complete their college work. Students are expected at all times to act in a manner consistent with Chaffey College’s Student Academic Integrity Code and Student Behavior Code. A student’s failure to act in a manner consistent with Chaffey College’s Student Academic Integrity Code and its Student Behavior Code shall constitute good cause for discipline, including but not limited to removal, suspension or expulsion. You can access the student handbook here: http://www.chaffey.edu/fac-handbook/c/pdf/Student_Behavior_CodeSH14-15.pdf Path to Success! Important Dates
marks as evidence of your work, and label all side and angle measurements. Under what condition is drawn? Compare the triangle you drew to two of your peers’ triangles. Are the triangles identical? Did the condition determine a unique triangle? Use your construction to explain why. A triangle has angles and and side cm. Draw triangle under the same condition. Leave all construction marks as evidence of your work, and label all side and angle measurements. Under what condition is drawn? Compare the triangle you drew to two of your peers’ triangles. Are the triangles identical? Did the condition determine a unique triangle? Use your construction to explain why. A triangle has angles and and side cm. Draw triangle under the same condition. Leave all construction marks as evidence of your work, and label all side and angle measurements.