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Math DesCartes: Numbers and Operations Skills: Computation Strategies – Multiplication and Division Students: DesCartes Skills: • Solves problems involving percents (Highlight the skills related to your chosen • Solves problems involving percents standard/concept) (analysis) RIT 251-260: • Solves problems involving simple percent • Solves problems involving complex percent discounts (e.g., finding sale price) discounts (e.g., finding percent discount, • Solves problems involving percent increase regular price) and decrease • Performs basic operations on matrices • Solves problems involving tax and tips RIT 241-250: • Calculates commission/deductions and total • Solves real-world problems involving pay multiplication and division of integers • Performs basic operations on matrices (analysis) RIT 221-230: • Calculates the percent one number is of • Uses multiplication strategies to explain another (e.g., 20 is what % of 90) computation (e.g., doubles, 9-patterns, • Calculates a percent of a rational number decomposing, partial products) (e.g., 6% of 0.78) • Multiplies multiple-digit numbers • Solves problems involving percents • Divides a 4-digit number by a 2-digit (analysis) number • Solves problems involving simple percent • Divides multiple-digit numbers discounts (e.g., finding sale price) • Divides numbers by powers of 10 • Solves problems involving complex percent • Solves complex word problems involving discounts (e.g., finding percent discount, whole number division with remainder (e.g., regular price) 2-step, 2-digit divisor) • Calculates commission/deductions and total • Uses division for multiple-step real-world pay problems (whole numbers) • Solves problems involving simple interest • Multiplies a fraction by a fraction without rates without the formula reducing to simplest form (complex problem) • Performs basic operations on matrices • Multiplies a fraction by a fraction where RIT 231-240: reducing to simplest form is necessary • Divides multiple-digit numbers • Multiplies a fraction by a whole number • Uses appropriate algorithms to represent • Multiplies mixed fractions multiplication or division with whole numbers • Divides a fraction by a fraction • Multiplies mixed fractions • Divides a mixed fraction by a fraction • Divides a fraction by a fraction • Solves 1-step real-world problems involving • Divides a fraction by a whole number fractions with multiplication and division • Divides a whole number by a fraction • Solves 2- or more step real-world problems • Divides a mixed fraction by a whole involving fractions with multiplication and number division • Divides a whole number by a mixed • Solves problems involving fractions (e.g., fraction multiple operations, conversions) • Divides a mixed fraction by a fraction • Multiplies a decimal by a decimal, vertical • Divides a fraction by a mixed fraction form (factors to tenths or hundredths) • Divides a mixed fraction by a mixed fraction • Multiplies a decimal by a decimal (factors to • Solves 2- or more step real-world problems hundredths) involving fractions with multiplication and • Multiplies a decimal by 10, 100, 1000 division • Multiplies a decimal by a decimal (factors to • Solves problems involving fractions (e.g., thousandths) multiple operations, conversions) • Solves real-world problems involving rate of • Multiplies a decimal by 10, 100, 1000 pay • Solves real-world problems involving rate of • Divides a decimal by 10, 100, 1000 pay • Divides a decimal by a decimal • Solves real-world problems involving rate of • Computes with dollars and cents over pay with time and a half $5.00 and converts to decimals • Divides a whole number by a decimal (multiplication/division) • Divides a decimal by 10, 100, 1000 • Computes the value of multiple bills and • Divides a decimal by a decimal coins (multiplication/division) • Solves difficult real-world problems • Solves difficult real-world problems involving decimals (e.g., multiple involving decimals (e.g., multiple multiplications, conversions) multiplications, conversions) • Multiplies integers with like signs • Multiplies integers with unlike signs • Divides integers with like signs • Divides integers with unlike signs • Solves real-world problems involving • Solves real-world problems involving multiplication and division of integers multiplication and division of integers (analysis) • Calculates basic percents of a number • Multiplies rational expressions (e.g., 10%, 20%, 25%, 50%, 100%) • Divides rational expressions in a/b form • Calculates a percent of a number (e.g., 6% • Calculates sums combining fractions, of 30) decimals, and percents • Calculates a number from a percent (e.g., 4 • Calculates a percent of a number (e.g., 6% is 9% of what) of 30) • Adds and subtracts percent • Calculates the percent one number is of • Solves problems involving percents another (e.g., 20 is what % of 90) • Solves problems involving tax and tips Math Numbers & Operations – Computation Strategies – Multiplication and Division Page 1 of 3 Info taken from NWEA DesCartes – HI Alignment 3.2.1 Math DesCartes: Numbers and Operations Skills: Computation Strategies – Multiplication and Division • Solves problems involving simple interest RIT 201-210: rates with the formula • Instantly recalls basic multiplication facts • Solves problems comparing percents, where one factor is 6-12 and the other factor fractions, and decimals is 0-12 RIT 211-220: • Instantly recalls basic multiplication and • Instantly recalls basic multiplication and division facts in a table division facts in a table • Multiplies a 2-digit number by a 1-digit • Multiplies a 2-digit number by a 2-digit number with regrouping number with regrouping • Multiplies a 3- or 4-digit number by a 1- • Multiplies a 3-digit number by a 2-digit digit number number with regrouping • Multiplies multiple 1-digit numbers • Performs mental computation with • Multiplies a 2-digit number by a 2-digit multiplication number with no regrouping • Multiplies a 3-digit number by a 3-digit • Multiplies a 2-digit number by a 2-digit number number with regrouping • Multiplies a 4- or more digit number by • Multiplies a 3-digit number by a 2-digit multiples of 100 or 1000 number with regrouping • Multiplies multiple-digit numbers • Performs mental computation with • Divides a 2-digit number or a 3-digit multiplication number by a 1-digit number with a • Multiplies a 2- or 3-digit number by remainder multiples of 10 or 100 • Performs mental computation with division • Multiplies a 3-digit number by a 3-digit • Divides a 4-digit number by a 1-digit number number with no remainder • Solves word problems involving whole • Divides a 4-digit number by a 1-digit number multiplication with numbers greater number with a remainder than 10 x 10 • Divides a 3-digit number by a 2-digit • Instantly recalls division facts with dividend number and divisors less than 13 • Divides a 4-digit number by a 2-digit • Divides a 1-digit number by a 1-digit number number with a remainder • Solves problems using the inverse • Divides a 2-digit number by a 1-digit relationship between multiplication and number with no remainder division • Divides a 2-digit number or a 3-digit • Divides a whole number by a whole number by a 1-digit number with a number and expresses the remainder as a remainder decimal • Performs mental computation with division • Divides multiple-digit numbers • Divides a 3-digit number by a 1-digit • Uses strategies to determine 2 or more number with no remainder missing digits (multiplication/division only) • Divides a 4-digit number by a 1-digit • Solves whole number word problems with number with no remainder division over 10 x 10 • Divides a 4-digit number by a 1-digit • Solves complex word problems involving number with a remainder whole number division with remainder (e.g., • Divides a 2-digit number by a 2-digit 2-step, 2-digit divisor) number with a remainder • Multiplies a fraction by a fraction where • Divides 3-digit number by multiple of 10 reducing to simplest form is necessary • Divides a 4-digit number by a 2-digit • Multiplies a fraction by a whole number number • Solves 1-step real-world problems involving • Solves word problems with whole number fractions with multiplication and division division facts with dividend and divisors less • Multiplies a decimal by a decimal, vertical than 11 form (factors to tenths or hundredths) • Solves simple word problems involving • Multiplies a decimal by a decimal (factors to whole number division with remainder (e.g., hundredths) 1-step, 1-digit divisor) • Solves real-world problems involving • Solves whole number word problems with decimals (not money) using multiplication division over 10 x 10 • Divides decimal by a whole number • Multiplies a fraction by a fraction without • Analyzes and computes 1 operation on reducing to simplest form (simple problem) real-world problems involving money over • Multiplies a decimal by whole number $5.00 (multiplication/division) • Divides decimal by a whole number • Computes with dollars and cents over • Computes with dollars and cents up to and $5.00 and converts to decimals including $5.00 and converts to decimals (multiplication/division) (multiplication/division) • Computes addition, subtraction, • Computes money problems with multiple multiplication, and division on multiple-step, operations (addition/subtraction only) real-world problems involving money • Computes addition, subtraction, • Multiplies integers with unlike signs multiplication, and division on multiple-step, • Divides integers with unlike signs real-world problems involving money • Solves real-world problems involving RIT 191-200: multiplication and division of integers • Instantly recalls basic multiplication facts • Calculates basic percents of a number where one factor is 6-12 and the other factor (e.g., 10%, 20%, 25%, 50%, 100%) is 0-12 • Multiplies a 2- or 3-digit number by a 1- Math Numbers & Operations – Computation Strategies – Multiplication and Division Page 2 of 3 Info taken from NWEA DesCartes – HI Alignment 3.2.1 Math DesCartes: Numbers and Operations Skills: Computation Strategies – Multiplication and Division digit number with no regrouping Lesson Title: • Multiplies a 2-digit number by a 1-digit number with regrouping Standard/Concept for All: • Multiplies a 3- or 4-digit number by a 1- digit number • Multiplies a 2-digit number by a 2-digit number with no regrouping • Multiplies a 3-digit number by a 2-digit number with no regrouping Introduction: (Get Attention; Connect to Prior Knowledge) • Performs mental computation with multiplication • Solves word problems involving basic whole number multiplication facts to 10 x 10 • Solves word problems involving whole For Students Ready for a Challenge: number multiplication with numbers greater than 10 x 10 • Instantly recalls division facts with dividend Lesson/Activity: and divisors less than 10 • Instantly recalls division facts with dividend and divisors less than 13 • Divides a 2-digit number by a 1-digit number with no remainder Resources: • Uses strategies to determine 1 missing digit (multiplication/division only) • Solves word problems with whole number division facts with dividend and divisors less than 11 Means of Assessment: • Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) • Solves real-world 1-step problems involving For Most Students: multiplication or division of a whole number by a fraction • Multiplies a decimal by whole number Lesson/Activity: • Computes half price (multiplication/division) • Computes with dollars and cents up to and including $5.00 and converts to decimals (multiplication/division) Resources: • Computes 1 operation on real-world problems involving money over $5.00 (multiplication/division) • Solves problems involving basic percent concepts (e.g., 10%, 50%, 100%) RIT 181-190: Means of Assessment: • Multiplies basic facts to 10 x 10 vertically • Multiplies a 2-digit number by a 1-digit number with regrouping • Solves word problems involving basic whole For Students Needing Extra Support: number multiplication facts to 10 x 10 • Instantly recalls division facts with dividend Lesson/Activity: and divisors less than 10 • Solves word problems with whole number division facts with dividend and divisors less that 11 involving money RIT 171-180: Resources: • Instantly recalls basic multiplication facts where one factor is 0-5 and the other factor is 0-12 • Multiplies basic facts to 10 x 10 vertically RIT 161-170: • Instantly recalls basic multiplication facts Means of Assessment: where one factor is 0-5 and the other factor is 0-12 Closure/Summary for All: Math Numbers & Operations – Computation Strategies – Multiplication and Division Page 3 of 3 Info taken from NWEA DesCartes – HI Alignment 3.2.1