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Grade 5 Mathematics Module 2, Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication

  Classroom Resource Information  

Title:

 Grade 5 Mathematics Module 2, Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication

URL:

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

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 2, Topic B, place value understanding moves toward understanding the distributive property by using area models to generate and record partial products (5.OA.1, 5.OA.2), which are combined within the standard algorithm (5.NBT.5). Writing and interpreting numerical expressions in Lessons 1 and 2 and comparing those expressions using visual models, lay the necessary foundation for students to make connections between the distributive property, as depicted in area models, and the partial products within the standard multiplication algorithm. The algorithm is built over a period of days, increasing in complexity as the number of digits in both factors increases. Reasoning about zeros in the multiplier, along with considerations about the reasonableness of products, also provides opportunities to deepen understanding of the standard algorithm. Although word problems provide context throughout Topic B, the final lesson offers a concentration of multi-step problems that allows students to apply this new knowledge.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 5
2 ) Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5-OA2]

Examples: Express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.2- Select the expression that represents a given calculation (include parentheses).
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
6. Fluently multiply multi-digit whole numbers using the standard algorithm.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given a context for multiplication of two whole numbers,
  • Choose the most appropriate strategy to find the product.
  • Accurately use standard algorithm when appropriate.
Teacher Vocabulary:
  • Multiply
  • Multi-digit
  • Standard algorithm
  • Distributive property
  • Partial product
  • Area model
Knowledge:
Students know:
  • Strategies based on place value and properties of operations for finding products of two factors including a one-digit and up to a four-digit factor and two two-digit factors.
  • Decomposition of a given number into base ten units.
  • How to illustrate a product of two factors using an area model.
  • Connections between an area model and finding partial products when multiplying.
Skills:
Students are able to:
  • Use the standard algorithm to find a product.
Understanding:
Students understand that:
  • properties of operations and the base ten system are foundational to the computation of products using the standard algorithm.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.6.1: Demonstrate steps in setting up a long multiplication problem.
M.5.6.2: Multiply 2-digit numbers by 1-digit multiplier.
M.5.6.3: Multiply 1-digit numbers by 1-digit multiplier.
M.5.6.4: Recall basic multiplication facts.
M.5.6.5: Recall repeated addition facts.

Prior Knowledge Skills:
  • 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 mode.
  • 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: algorithm, braces, brackets, expressions, multidigit, multiply, parentheses
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Comments

There are seven lessons in this topic.

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Author: Hannah Bradley
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