Multiplicative Comparison Word Problems
Lesson 1: Investigate and use the formulas for area and perimeter of rectangles.
Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas.
Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi-step real world problems.
Multiplication by 10, 100, and 1,000
Lesson 4: Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically.
Lesson 5: Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns.
Lesson 6: Multiply two-digit multiples of 10 by two-digit multiples of 10 with the area model.
Multiplication of up to Four Digits by Single-Digit Numbers
Lesson 7: Use place value disks to represent two-digit by one-digit multiplication.
Lesson 8: Extend the use of place value disks to represent three- and four-digit by one-digit multiplication.
Lessons 9–10: Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm.
Lesson 11: Connect the area model and the partial products method to the standard algorithm.
Multiplication Word Problems
Lesson 12: Solve two-step word problems, including multiplicative comparison.
Lesson 13: Use multiplication, addition, or subtraction to solve multi-step word problems.
Division of Tens and Ones with Successive Remainders
Lesson 14: Solve division word problems with remainders.
Lesson 15: Understand and solve division problems with a remainder using the array and area models.
Lesson 16: Understand and solve two-digit dividend division problems with a remainder in the ones place by using place value disks.
Lesson 17: Represent and solve division problems requiring decomposing a remainder in the tens.
Lesson 18: Find whole number quotients and remainders.
Lesson 19: Explain remainders by using place value understanding and models.
Lesson 20: Solve division problems without remainders using the area model.
Lesson 21: Solve division problems with remainders using the area model.
Reasoning with Divisibility
Lesson 22: Find factor pairs for numbers to 100, and use understanding of factors to define prime and composite.
Lesson 23: Use division and the associative property to test for factors and observe patterns.
Lesson 24: Determine if a whole number is a multiple of another number.
Lesson 25: Explore properties of prime and composite numbers to 100 by using multiples.
Division of Thousands, Hundreds, Tens, and Ones
Lesson 26: Divide multiples of 10, 100, and 1,000 by single-digit numbers.
Lesson 27: Represent and solve division problems with up to a three-digit dividend numerically and with place value disks requiring decomposing a remainder in the hundreds place.
Lesson 28: Represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5 numerically.
Lesson 29: Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times.
Lesson 30: Solve division problems with a zero in the dividend or with a zero in the quotient.
Lesson 31: Interpret division word problems as either number of groups unknown or group size unknown.
Lesson 32: Interpret and find whole number quotients and remainders to solve one-step division word problems with larger divisors of 6, 7, 8, and 9.
Lesson 33: Explain the connection of the area model of division to the long division algorithm for three- and four-digit dividends
Multiplication of Two-Digit by Two-Digit Numbers
Lesson 34: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart.
Lesson 35: Multiply two-digit multiples of 10 by two-digit numbers using the area model.
Lesson 36: Multiply two-digit by two-digit numbers using four partial products.
Lessons 37–38: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication.
New or Recently Introduced Terms
? Associative property (e.g., 96 = 3 × (4 × 8) = (3 × 4) × 8)
? Composite number (positive integer having three or more whole number factors)
? Distributive property (e.g., 64 × 27 = (60 × 20) + (60 × 7) + (4 × 20) + (4 × 7))
? Divisor (the number by which another number is divided)
? Formula (a mathematical rule expressed as an equation with numbers and/or variables)
? Long division (process of dividing a large dividend using several recorded steps) This work is licensed under a
? Partial product (e.g., 24 × 6 = (20 × 6) + (4 × 6) = 120 + 24)
? Prime number (positive integer greater than 1 having whole number factors of only 1 and itself)
? Remainder (the number left over when one integer is divided by another)
Familiar Terms and Symbols
? Algorithm (steps for base ten computations with the four operations)
? Area (the amount of two-dimensional space in a bounded region)
? Area model (a model for multiplication and division problems that relates rectangular arrays to area, in which the length and width of a rectangle represent the factors for multiplication, and for division, the width represents the divisor and the length represents the quotient)
? Array (a set of numbers or objects that follow a specific pattern, a matrix)
? Bundling, grouping, renaming, changing (compose or decompose a 10, 100, etc.)
? Compare (to find the similarity or dissimilarity between)
? Distribute (decompose an unknown product in terms of two known products to solve)
? Divide, division (e.g., 15 ÷ 5 = 3)
? Equation (a statement that the values of two mathematical expressions are equal using the = sign)
? Factors (numbers that can be multiplied together to get other numbers)
? Mixed units (e.g., 1 ft 3 in, 4 lb 13 oz)
? Multiple (product of a given number and any other whole number)
? Multiply, multiplication (e.g., 5 × 3 = 15)
? Perimeter (length of a continuous line forming the boundary of a closed geometric figure)
? Place value (the numerical value that a digit has by virtue of its position in a number)
? Product (the result of multiplication)
? Quotient (the result of division)
? Rectangular array (an arrangement of a set of objects into rows and columns)
? Rows, columns (e.g., in reference to rectangular arrays)
? ___ times as many ___ as ___ (multiplicative comparative sentence frame)