Topic Four: Meanings of Multiplication

Pacing (Duration of Unit):

Desired Results

Transfer:

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.
Established Goals:
3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.5 Apply properties of operations as strategies to multiply and divide.
Examples:
  • If 6 X 4 is known, then 4 X 6=24 is also known. (Commutative property of multiplication.)
  • 3 X 5 X 2 can be found by 3 X 5=15, then 15 X 2=30, or by 5 X 2 =10 then 3 X 10 =30. (Associative property of multiplication.)
  • Knowing that 8 X 5=40 and 8 X 2=16, one can find 8 X 7 as 8 X (5 + 2)= (8 X 5) + (8 X 2)= 40 +16=56. (Distributive property.)

Student I Can Statements:
  • I can determine when to multiply in word problems.
  • I can represent multiplication word problems using drawings, and equations with unknowns in all positions.
  • I can explain the commutative, associative, and distributive property of multiplication.
  • I can apply the commutative, associative, and distributive properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.

Prerequisite Standards:
2.OA.3 Determine whether a group of objects (up to 20) has an add or even numbers of members, e.g., by pairing objects or counting them by 2s,

2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Big Ideas:

Operation Meanings and Relationships
There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.

Properties
For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • What are the different meanings of multiplication?
  • How are addition and multiplication related?
  • How are properties of operations helpful for computing numbers?
  • How can different strategies be helpful when solving a problem?
Students will know...
  • Repeated addition involves joining equal groups and is one way to think about multiplication.
  • An array involves equal groups and is one way to think about multiplication.
  • Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication.
  • Two numbers can be multiplied in any order and the product remains the same.
  • Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete and easy to understand.


Vocabulary:
multiplication
factors
product
array
Commutative (Order) Property of Multiplication

Students will be skilled at...
  • writing multiplication number sentences for given equal group situations, using the X symbol.
  • writing multiplication sentences for arrays and using arrays to find products.
  • applying the Commutative Property of Multiplication to solve multiplication number sentences.
  • writing math stories for given multiplication facts.
  • explaining to reflect their math understanding by using objects, words, pictures, numbers, and technology.

Assessment Evidence

Performance Assessment:




Tasks Adapted from Smarter Balance and/or PARCC Assessment Sample Tasks
These tasks are adapted from authentic Smarter Balance/PARCC Sample Tasks.

Other Evidence:


Learning Plan

Learning Activities:

4-1 Repeated addition involves joining equal groups and is one way to think about multiplication.

4-2 An array involves equal groups and is one way to think about multiplication.

4-3 Two numbers can be multiplied in any order and the product remains the same

4-4 Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication.

4-5 Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete and easy to understand.
Resources:

Home School Connection


Centers:



The Product Game
Illuminations Concentration

Student Video:
Thinking Blocks Multiplication
Learn Zillion Video: Problem Solving

Teacher Video: