Topic Six: Multiplication Facts: Use Known Facts

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.

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
3.OA.1 Interpret products of whole numbers, e.g., interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 X 7.

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.)
Big Ideas:

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.

Basic Facts and Algorithms
There is more that one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.

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

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • How can unknown multiplication facts be found using known facts?
Students will know that...
  • the distributive property can be used to break a large array into smaller arrays.
  • three or more numbers can be grouped and multiplied in any order.
  • basic multiplication facts with 3, 4, 6, 7, and 8 as a factor can be found by breaking apart the unknown fact into known facts. The answer to the known facts are added to get the final product.
  • patterns and known facts can be used to find unknown multiplication facts.
  • finding the number of combinations that are possible between the members of one group and the members of another group is one meaning of multiplication.
  • some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem.

Vocabulary:
distributive property
associative (grouping) property of multiplication

Students will be skilled at...
  • applying the distributive property to simply multiplication problems by breaking apart large arrays that represent multiplication facts into smaller arrays that represent other multiplication facts.
  • applying known facts to compute products with 3 as a factor.
  • applying known facts to compute products with 4 as a factor.
  • applying known facts to compute products with 6 and 7 as a factor.
  • applying known facts to compute products with 8 as a factor.
  • multiplying three numbers and applying the associative property of multiplication.
  • applying known facts and patterns to compute products.
  • solving the number of possible combinations of data or objects in a problem using objects, pictures, and multiplication.

Assessment Evidence

Performance Assessment:
Other Evidence:

Learning Plan

Learning Activities:

6-1 The distributive property can be used to break a large array into smaller arrays.

6-2 Basic multiplication facts with 3 as a factor can be found by breaking apart the unknown fact into known facts. The answer to the known facts are added to get the final product.

6-3 Basic multiplication facts with 4 as a factor can be found by breaking apart the unknown fact into known facts. The answer to the known facts are added to get the final product.

6-4 Basic multiplication facts with 6 or 7 as a factor can be found by breaking apart the unknown fact into known facts. The answer to the known facts are added to get the final product.

6-5 Basic multiplication facts with 8 as a factor can be found by breaking apart the unknown fact into known facts. The answer to the known facts are added to get the final product.

6-6 Three or more numbers can be grouped and multiplied in any order.

6-7 Patterns and known facts can be used to find unknown multiplication facts.

6-8 Finding the number of combinations that are possible between the members of one group and the members of another group is one meaning of multiplication.

6-9 Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem.
Resources:

Home School Connection:

Centers:

The Product Game