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MISD Scope and Sequence Specificity 5th Grade Mathematics FIRST SIX WEEKS Reporting Category 1: Numbers, Operations, and Quantitative Reasoning Topic/TEKS Place Value The student uses place value to represent whole numbers and decimals. Recommended Time Frame: 1 week Content Skills (5.1A) The student is expected to use place value to read, write, compare, and order whole numbers through 999,999,999,999. Supporting Standard (Assessed once in 2012 with no integrated process skill) Including, but not limited to: Distinguish the difference between a digit and a number Identify the word form of a number given in standard form (digits to words) Write the standard form of a number given in word form (words to digits) Determine the value of a given digit when given a number in standard form Identify a number with a given digit in an indicated place Convert between a number and its expanded form Describe place and value (example: 97,465,831,206 Seven is in the trillions place and its value is 7,000,000,000) Compare and order a list of numbers using symbols and words “greater than” (>), “less than” (>), and “equal” (=) Represent place value concepts using whole numbers through 999,999,999,999 with numerals, words, expanded notation, and concrete objects Process Skills The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (5.14A) identify the mathematics in everyday situations; (5.14B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (5.14C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; (5.14D) use tools such as real objects, manipulatives, and technology to solve problems. The student communicates about Grade 5 mathematics using informal language. The student is expected to: (5.15A) explain and record observations using objects, words, pictures, numbers, and technology; (5.15B) relate informal language to mathematical language and symbols. The student uses logical reasoning. The student is expected to: (5.16A) make generalizations from patterns or sets of examples and nonexamples; (5.16B) justify why an answer is reasonable and explain the solution process. (5.1B) The student is expected to use place value to read, write, compare, and order decimals through the thousandths place. Supporting Standard (Not assessed in 2012) 24-Jun-17 1 MISD Scope and Sequence Specificity 5th Grade Mathematics Including: Use place value to read, write, compare, and order decimals involving thousandths, including money, using concrete objects Use place value to read, write, compare, and order decimals involving thousandths, including money, using pictorial models Distinguish between place and value such as 2.745, 5 is in the thousandths place and the value is .005 or 5 thousandths Compare and order decimal numbers using symbols and words Round and write place value without unnecessary trailing zeros NOTE: 5th grade decimals (through thousandths) 24-Jun-17 2 MISD Scope and Sequence Specificity 5th Grade Mathematics FIRST SIX WEEKS Reporting Category Topic/TEKS 1: Numbers, Operations, and Quantitative Reasoning Addition, Subtraction Problem Solving The student adds, subtracts, multiplies, and divides to solve meaningful problems. Rounding and Estimating Solutions to Problems The student estimates to determine reasonable results. Recommended Time Frame: 1 week Content Skills (5.3A)The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals; Readiness Standard (Assessed three times in 2012 with integrated process skills) Including: Extract necessary information needed to solve the problem (ignoring extraneous information) and recognizes the operation(s) needed to solve Justify answer by solving the problem using a different strategy or estimation of solution and checking for reasonableness Recognize that addition and subtraction are inverse operations Solve problems using addition and subtraction of whole numbers in flexible ways by composing and decomposing numbers Analyze different problem situation to determine the operation(s) needed to solve problems Solve multi-step problems that use terminology such as less than, more than, greater than, fewer than (Ex: Robb is 2.5 feet less than Juan) Use addition and subtraction of whole numbers given information in a table Note: Grade 4 models addition and subtraction of decimals through hundredths using concrete object and pictorial models (5.4A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. 24-Jun-17 Process Skills The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (5.14A) identify the mathematics in everyday situations; (Assessed once with 5.3A in 2012) (5.14B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (Assessed once with 5.4A in 2012) (5.14C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; (Assessed once with 5.3A in 2012) (5.14D) use tools such as real objects, manipulatives, and technology to solve problems. The student communicates about Grade 5 mathematics using informal language. The student is expected to: (5.15A) explain and record observations using objects, words, pictures, numbers, and technology; (5.15B) relate informal language to mathematical language and symbols. The student uses logical reasoning. The student is expected to: (5.16A) make generalizations from patterns or sets of examples and nonexamples; (Assessed once with 5.3A in 2012) (5.16B) justify why an answer is reasonable and explain the solution process. 3 MISD Scope and Sequence Specificity 5th Grade Mathematics Supporting Standard (Assessed once in 2012 with integrated process skill) Including: Using numbers found in a table to estimate a solution Estimate a solution to a multi-step problem Emphasize estimating before solving problem situations Estimate solutions by using rounding in multiplication and division o to round to the largest place value for each number (do not round single digit numbers) Ex: 56 x 82 = 60 x 80 Ex: 84 x 7 = 80 x 7 Ex: 362 ÷ 8 = 400 ÷ 8 Estimate solutions by using compatible numbers in multiplication and division o numbers that are easy to compute mentally (do not always end in 0) Ex. 92 x 12 could be 92 x 10 or 90 x 10 or 90 x 12 Ex. 285 ÷ 9 could be 270 ÷ 10 Round to the nearest dime and dollar is included Relate answers to a range of numbers or a number less than or greater than a given value Ex: Tamara sold cookies. She sold 34 boxes on Tuesday and twice as many boxes on Wednesday. About how many cookies did she sell? (Ex ans: greater than 50, between 30 and 50, or less than 30, etc. Note: Students should round and write numbers to the indicated place value omitting any trailing zeros. 24-Jun-17 4 MISD Scope and Sequence Specificity 5th Grade Mathematics FIRST SIX WEEKS Reporting Category 1: Numbers, Operations, and Quantitative Reasoning Topic/TEKS Multiplication Problem Solving The student adds, subtracts, multiplies, and divides to solve meaningful problems. Rounding and Estimating Solutions to Problems The student estimates to determine reasonable results. Recommended Time Frame: 1 week Content Skills (5.3B)The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology); Readiness Standard (Assessed three times in 2012 with integrated process skills twice and no process skill once) Including but not limited to: Apply multiplication (up to 3 digits by 2 digits) to problem situations Extract necessary information needed to solve the problem (ignoring extraneous information) and recognizes the operation(s) needed to solve Justify answer by solving the problem using a different strategy or estimation of solution and checking for reasonableness Demonstrate multiplication problem solving methods Convert words such as dozen, week, half dozen to their numerical values 12, 7, 6 Divisibility rules for 2, 5, 10 (5.4A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. Supporting Standard Process Skills The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (5.14A) identify the mathematics in everyday situations; (Assessed once with 5.3B in 2012) (5.14B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (Assessed once with 5.3B and once with 5.4A in 2012) (5.14C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; (5.14D) use tools such as real objects, manipulatives, and technology to solve problems. The student communicates about Grade 5 mathematics using informal language. The student is expected to: (5.15A) explain and record observations using objects, words, pictures, numbers, and technology; (5.15B) relate informal language to mathematical language and symbols. The student uses logical reasoning. The student is expected to: (5.16A) make generalizations from patterns or sets of examples and nonexamples; (5.16B) justify why an answer is reasonable and explain the solution process. (Assessed once in 2012 with integrated process skill) 24-Jun-17 5 MISD Scope and Sequence Specificity 5th Grade Mathematics Including but not limited to: Using numbers found in a table to estimate a solution Estimate a solution to a multi-step problem Emphasize estimating before solving problem situations Estimate solutions by using rounding in multiplication and division o to round to the largest place value for each number (do not round single digit numbers) Ex: 56 x 82 = 60 x 80 Ex: 84 x 7 = 80 x 7 Ex: 362 ÷ 8 = 400 ÷ 8 Estimate solutions by using compatible numbers in multiplication and division o numbers that are easy to compute mentally (do not always end in 0) Ex. 92 x 12 could be 92 x 10 or 90 x 10 or 90 x 12 Ex. 285 ÷ 9 could be 270 ÷ 10 Round to the nearest dime and dollar is included Relate answers to a range of numbers or a number less than or greater than a given value Ex: Tamara sold cookies. She sold 34 boxes on Tuesday and twice as many boxes on Wednesday. About how many cookies did she sell? (Ex ans: greater than 50, between 30 and 50, or less than 30, etc. Note: Students should round and write numbers to the indicated place value omitting any trailing zeros. 24-Jun-17 6 MISD Scope and Sequence Specificity 5th Grade Mathematics FIRST SIX WEEKS Reporting Category Topic/TEKS 1: Numbers, Operations, and Quantitative Reasoning Division Problem Solving The student adds, subtracts, multiplies, and divides to solve meaningful problems. Rounding and Estimating Solutions to Problems The student estimates to determine reasonable results. Recommended Time Frame: 2 weeks Content Skills (5.3C)The student is expected to use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology), including interpreting the remainder within a given context; Readiness Standard (Assessed three times in 2012 with integrated process skills) Including: Extract necessary information needed to solve the problem (ignoring extraneous information) and recognizes the operation(s) needed to solve Justify answer by solving the problem using a different strategy or estimation of solution and checking for reasonableness Use various strategies to solve problems involving division:(two-digit divisor and three digit dividends) Interpret the remainder dependent upon the contextual situation Remainder is written as a fraction or decimal Ex: dividing money among 4 people) Quotient is always rounded up regardless size of remainder (Ex: number of cars needed to transport people) Remainder dropped and the quotient remains the same (Ex: sharing footballs among 6 people Teach division rules 2, 5, 10 (others are optional) Process Skills The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (5.14A) identify the mathematics in everyday situations; (Assessed once with 5.3C in 2012) (5.14B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (Assessed once with 5.3C and once with 5.4A in 2012) (5.14C) select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; (5.14D) use tools such as real objects, manipulatives, and technology to solve problems. The student communicates about Grade 5 mathematics using informal language. The student is expected to: (5.15A) explain and record observations using objects, words, pictures, numbers, and technology; (5.15B) relate informal language to mathematical language and symbols. The student uses logical reasoning. The student is expected to: (5.16A) make generalizations from patterns or sets of examples and nonexamples; (Assessed once with 5.3C in 2012) (5.16B) justify why an answer is reasonable and explain the solution process. NOTE: 5.3 (C) is the first time mentioned in TEKS for interpretation of remainders 24-Jun-17 7 MISD Scope and Sequence Specificity 5th Grade Mathematics (5.4A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. Supporting Standard (Assessed once in 2012 with integrated process skill) Including: Using numbers found in a table to estimate a solution Estimate a solution to a multi-step problem Emphasize estimating before solving problem situations Estimate solutions by using rounding in multiplication and division o to round to the largest place value for each number (do not round single digit numbers) Ex: 56 x 82 = 60 x 80 Ex: 84 x 7 = 80 x 7 Ex: 362 ÷ 8 = 400 ÷ 8 Estimate solutions by using compatible numbers in multiplication and division o numbers that are easy to compute mentally (do not always end in 0) Ex. 92 x 12 could be 92 x 10 or 90 x 10 or 90 x 12 Ex. 285 ÷ 9 could be 270 ÷ 10 Round to the nearest dime and dollar is included Relate answers to a range of numbers or a number less than or greater than a given value Ex: Tamara sold cookies. She sold 34 boxes on Tuesday and twice as many boxes on Wednesday. About how many cookies did she sell? (Ex ans: greater than 50, between 30 and 50, or less than 30, etc. Note: Students should round and write numbers to the indicated place value omitting any trailing zeros. 24-Jun-17 8