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

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Title:

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

URL:

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 2, Topic A begins a sequential study of multiplication that culminates in Topic D. In order to link prior learning from Grade 4 Module 1 and Grade 5 Module 1 and to set the stage for solidifying the standard multiplication algorithm, students begin at the concretepictorial level. They use place value disks to model multi-digit multiplication of place value units, for example, 42 × 10, 42 × 100, 42 × 1,000, leading quickly to problems such as 42 × 30, 42 × 300, and 42 × 3,000 (5.NBT.1, 5.NBT.2). Students then round factors in Lesson 2 and discuss the reasonableness of their products. Throughout Topic A, students evaluate and write simple expressions to record their calculations using the associative property and parentheses to record the relevant order of calculations (5.OA.1).

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
1. Write, explain, and evaluate simple numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving parentheses, brackets, or braces, using commutative, associative, and distributive properties.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given a mathematical expression in words, will
  • Write numerical expressions to represent the context and evaluate the expression.
  • Explain their thinking as they use the order of operations to evaluate a variety of problems.
Given a numerical expression involving multiple operations and up to two sets of grouping symbols, will
  • Evaluate the expression.
  • Explain the meaning of the expression without evaluating the expression.
Note: Expressions should not contain nested grouping symbols, should be limited to expressions found in application of associative or distributive properties, and not always limited to whole numbers.
Teacher Vocabulary:
  • Expression
  • Calculate
  • Interpret
  • Evaluate
  • Compare
  • Reasoning
  • Grouping symbol
  • Parentheses
  • Braces
  • Brackets
  • Commutative property
  • Associative property
  • Distributive property
Knowledge:
Students know:
  • Vocabulary associated with the four operations to write the symbolic notation of the mathematical expression.
    Example: The phrase, "the product of 4 and 3" is written as "4 x 3."
  • Strategies for evaluating a numerical expression and replace it with an equivalent form.
    Example: Given (22 + 16) + 43 can be replaced with 38 + 43 and then further simplified.
Skills:
Students are able to:
  • Write, explain, and evaluate numerical expressions representing two-step problems in context.
  • Evaluate numerical expressions with grouping symbols.
  • Translate a numerical expression into words.
  • Write a numerical expression given a mathematical expression in words.
Understanding:
Students understand that:
  • multi-step word problems can be represented by numerical expressions using operations and grouping symbols to indicate order of evaluating them.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.1.1: Define parentheses, braces, and brackets.
M.5.1.2: Distinguish between non-numerical and numerical expression.
M.5.1.3: Recognize expressions.
M.5.1.4: Apply properties of operations as strategies to add and subtract.
M.5.1.5: Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.

Prior Knowledge Skills:
  • Write, explain, and evaluate numerical expressions representing two-step problems in context.
  • Evaluate numerical expressions with grouping symbols.
  • Translate a numerical expression into words.
  • Write a numerical expression given a mathematical expression in words.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.1 Evaluate simple numerical expressions involving the four operations.


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
  • Product
Knowledge:
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 (<, >, =).


Tags: braces, brackets, decimal, expressions, multidigit, parentheses, patterns, powers of 10, zeros
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There are two lessons in this topic.

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Author: Hannah Bradley