# ALEX Classroom Resource

## Grade 5 Mathematics Module 2, Topic E: Mental Strategies for Multi-Digit Whole Number Division

Classroom Resource Information

Title:

Grade 5 Mathematics Module 2, Topic E: Mental Strategies for Multi-Digit Whole Number Division

URL:

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 2, Topics E through H provide a parallel sequence for division to that offered in Topics A to D for multiplication. Topic E begins concretely with place value disks as an introduction to division with multi-digit whole numbers (5.NBT.6). In Lesson 17, 420 ÷ 60 is interpreted as 420 ÷ 10 ÷ 6. Next, students round dividends and 2-digit divisors to nearby multiples of ten in order to estimate single-digit quotients (e.g., 431 ÷ 58  420 ÷ 60 = 7) and then multi-digit quotients. This work is done horizontally, outside the context of the written vertical method.

Content Standard(s):
 Mathematics MA2015 (2016) Grade: 5 5 ) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. [5-NBT2] NAEP Framework NAEP Statement:: 4A1b: Given a pattern or sequence, construct or explain a rule that can generate the terms of the pattern or sequence. NAEP Statement:: 4NPO3d: Describe the effect of operations on size (whole numbers). NAEP Statement:: 4NPO6a: Explain or justify a mathematical concept or relationship (e.g., explain why 15 is an odd number or why 7-3 is not the same as 3-7). NAEP Statement:: 8NPO1a: Use place value to model and describe integers and decimals. Mathematics MA2019 (2019) Grade: 5 3. Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left. a. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.b. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10. Unpacked Content Evidence Of Student Attainment:Students: Use models to illustrate the relationship between two successive place values in whole numbers and decimals. Explain that a digit in one place represents 1/10 of what it represents to its left or the place value is 10 times the place value on the right. Use strategies to find products and explain patterns when multiplying by powers of 10. Example: The product of 420 x 200 = 42 x 10 x 2 x 100 is the same as (42 x 2) x (10 x 100) = 84 x 1000 = 84,000 shows multiplying by three powers of 10 shifts the digits in the product three place values greater (to the left.) Use strategies to find products and quotients and use place value understanding to explain patterns in the placement of the decimal point when involving a power of 10. Write powers of 10 in standard form and using exponential notation.Teacher Vocabulary:Digit Decimal Decimal point Thousandths Hundredths Tenths Base-ten Expanded form Place value Power of 10 Factor Base Exponent ProductKnowledge:Students know: Each place value position represents 10 times what it represents in the place to its right. Example: In 433, the underlined 3 represents 3 tens and has a value of 30 which is ten times the value of the 3 ones to its right. Place value understanding is extended to apply reasoning that a place value position represents 1/10 of what it represents in the place value to its left. Example: In 433, the underlined 3 represents 3 ones and has a value of 3 which is one-tenth of the value of the 3 tens or 30 to its left. A given number multiplied by a power of 10 shifts the digits in the given number one place value greater (to the left) for each factor of 10. -A given number divided by a power of 10 shifts the digits in the given number one-tenth of the value (to the right) for each factor of 10.Skills:Students are able to: Reason and explain the relationship between two successive place values. Explain patterns of zeros of the product when multiplying by powers of 10. Explain patterns in placement of decimals when multiplying or dividing by power of 10. Write powers of 10 using exponential notation.Understanding:Students understand that: The relationship of adjacent places values in the base ten system extend beyond whole numbers to decimal values. Multiplying or dividing by a power of 10 shifts the digits in a whole number or decimal that many places to the left or right respectively.Diverse Learning Needs: Essential Skills:Learning Objectives: M.5.3.1: Use place value understanding to round whole numbers to the nearest 10 or 100. M.5.3.2: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons. M.5.3.3: Identify that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Prior Knowledge Skills:Reason and explain the relationship between two successive place values. Explain patterns of zeros of the product when multiplying by powers of 10. Explain patterns in placement of decimals when multiplying or dividing by power of 10. Write powers of 10 using exponential notation. Alabama Alternate Achievement Standards AAS Standard: M.AAS.5.3 Compare base-10 models up to 99 and whole numbers up to 100 to determine symbols (<, >, =). Mathematics MA2019 (2019) Grade: 5 7. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Unpacked Content Evidence Of Student Attainment:Students: Choose strategies based on place value, partial quotients, properties of operations, or the relationship between multiplication and division to find whole number quotients and remainders. Solve word problem situations involving division. Justify solution path for quotients using equations, arrays or area models. Note: Standard algorithm for division is not an expectation at grade 5.Teacher Vocabulary:Quotient Dividend Divisor Divide Multiply Equation Remainder Multiple Area model Decompose Partial quotient EquationKnowledge:Students know: Efficient strategies to find a whole number quotient when a multi-digit number (up to 4-digit dividend) is divided by a single-digit divisor. How to justify quotients using an illustration or the relationship between multiplication and division.Skills:Students are able to: Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations. Illustrate and explain the calculation using equations, arrays, and area models.Understanding:Students understand that: Strategies for division by a one-digit divisor are extended to two-digit divisors. Visual models are used to illustrate division. Remainders may be written as a fraction or decimal and interpreted based on context of the problem situation. Diverse Learning Needs: Essential Skills:Learning Objectives: M.5.7.1: Construct a division equation with an example of the division algorithm. M.5.7.2: Illustrate the division algorithm using a one-digit divisor and a 2-digit dividend. M.5.7.3: Identify the place value of a division problem. M.5.7.4: Restate the inverse process of division as multiplication. M.5.7.5: Recall basic multiplication facts. Prior Knowledge Skills:Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals. Relate strategies for operations with decimals to a written method and explain reasoning used. Solve real-world context problems involving decimals. Alabama Alternate Achievement Standards AAS Standard: M.AAS.5.6 Model multiplication with two digit whole numbers by one digit whole numbers with regrouping using strategies such as arrays, decomposition, and manipulatives.
Tags: arrays, decimal, divide, dividend, divisors, equations, exponents, multidigit, multiply, operations, patterns, place value, powers of 10, quotient, zeros