Unit 2

Multi-Digit Multiplication and Division

Math

Unit Length and Description:

46 days

In fourth-grade, students develop an initial understanding of multiplication of whole numbers by modeling situations in which there are a specific number of groups with the same number of items in each group. Students extend previous experiences to multiplying a single-digit factor times a multi-digit factor. Students may use strategies such as the standard algorithm, arrays, area models, mental strategies as well as properties of multiplication to multiply. Students will also model, write and explain division by one-digit divisors. Students should continue to become fluent with extending basic facts to efficient recall of situations with remainders.

Accurate units of measure are used to solve problems. Fourth-grade students use quantitative reasoning to solve multi-step problems. They begin to solve multiplication and division comparison problems. Students also look for and extend mathematical patterns to understand the structure of the four operations.

Standards:

 Number and Operations in Base Ten Use place value understanding to perform multi-digit arithmetic. 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Operations and Algebraic Thinking Gain familiarity with factors and multiples. 4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Operations and Algebraic Thinking Generate and analyze patterns. 4.OA.5 Generate a number or shape pattern that follows a given rule.  Identify apparent features of the pattern that were not explicit in the rule itself.  For example, given the rule, “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.  Explain informally why the numbers will continue to alternate in this way. Standards for Mathematical Practices 1.   Make sense of problems and persevere in solving them. 2.   Reason abstractly and quantitatively. 3.   Construct viable arguments and critique the reasoning of others. 4.   Model with mathematics. 5.   Use appropriate tools strategically. 6.   Attend to precision. 7.   Look for and make use of structure. 8.   Look for and express regularity in repeated reasoning. Instructional Outcomes 4.NBT.5 ·         I can multiply 4 digit by one digit numbers without a calculator. ·         I can multiply 2 digit by 2 digit numbers without a calculator. ·         I can use 2 or more different strategies to multiply numbers. ·         I can use words, drawings, and equations to explain multiplication with arrays. ·         I can use words, drawings, and equations to explain multiplication with area models. 4.NBT.6 ·         I can divide a 4 digit number by a one digit number. ·         I can show the relationship between multiplication and division. ·         I can use an array to show a multiplication problem. ·         I can use an array to explain a division problem. ·         I can find the area of a space using multiplication. 4.OA.1 ·         I can identify that multiplication represents grouping of numbers, and identify the first factor represents number of groups and the second factor represents how many within each group. ·         I can illustrate that 5 groups of 7 has the same product as 7 groups of 5. ·         I can write a multiplication equation based on given data. 4.OA.2 ·         I can use multiplication in 2 or more ways to solve the same problem ·         I can use division in 2 or more ways to solve the same problem. ·         I can multiply or divide to solve word problems by using drawings or writing equations and solving for a missing number. 4.OA.3 ·         I can divide whole numbers including division with remainders. ·         I can use what I know about addition, subtraction, multiplication and division to solve multi-step work problems involving whole numbers. ·         I can choose the correct operation to solve a word problem. ·         I can interpret the meanings of remainders. ·         I can determine whether my answer is reasonable to a word problem by using estimation, mental math, and rounding. 4.OA.4 I can determine whether a given whole number up to 100 is a prime or composite number. I can find all the factors (factor pairs) of each number from 1 to 100. I can show that a whole number is a multiple of each of its factors I can check to see if a given whole number is a multiple of numbers one through nine. 4.OA.5 I can continue a given number or shape pattern. I can make a number or shape pattern that follows a given rule. I can explain how different patterns are built and relate the pattern to one or more of the four operations. I can analyze a pattern to determine parts not stated in the rule.

Enduring Understandings:

·         Place value understanding and visual representations help me solve multiplication and division problems with multi-digit numbers.

·         Understanding the properties of numbers helps me find factors, multiples, products and quotients.

·         Proficiency with basic facts aids estimation and computation of larger and smaller numbers.

·         Decomposing numbers into base ten units help me find products of single-digit by multi-digit numbers.

·         Computation involves taking and combining numbers using variety of approaches.

·         Flexible methods of computation involve grouping numbers in strategic ways.

·         When solving word problems, I must understand what needs to be done, different strategies to solve the problem, and the reasonableness of the solution.

Essential Questions:

·         How does place value understanding and visual representation help me solve multiplication and division problems?

·         What are efficient methods for finding products and quotients?

·         In what ways can numbers be composed and decomposed?

·         How do the four operations related to one another?

·         What are different models of and models for multiplication and division?

·         What questions can be answered using multiplication and division?

·         What must I need to solve word problem?

·         How can understanding patterns help me solve problems?