Topic Eight: Division 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 unknown number to represent the problem.

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 X 5=40, one knows that 40 ÷ 5=8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. \
Student I Can Statements:
  • I can determine when to multiply and divide in word problems.
  • I can represent multiplication and division word problems using drawings, and equations with unknowns in all positions.
  • I can multiply any two numbers with a product within 100 with ease by picking and using strategies that will get to the answer fairly quickly.
  • I can divide whole numbers with a divisor within 100 and with a whole number quotient with ease by picking and using strategies that will get to the answer fairly quickly.
  • I can instantly recall from memory the product of any two one-digit numbers.
Prerequisite Standards:
3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 X ?=48, 5 =?÷ 3, 6 X 6=?

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.)

3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷8 by finding the number that makes 32 when multiplied by 8.
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 the 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.

Equivalence
Any number, measure, numerical expression, algebraic expression, or equation can be represented in infinite number of ways that have the same value.

Variable
Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
How can an unknown division fact be found by thinking of a related multiplication fact?
Students will know...
  • Multiplication and division have an inverse relationship.
  • The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.
  • Patterns and known facts can be used to find unknown multiplication facts. Division facts can be found by thinking of a related multiplication fact.
  • Any number (except 0) divided by itself equal to 1. Any number divided by 1 is that number. Zero divided by an number (except 0) is zero. Zero cannot be a divisor.
  • Different numerical expressions can have the same value. Or, the value of one expression can be less than (or greater than) the value of the other expression.
  • An equation shows a balance between what is on the right side and what is on the left side of the equal sign.
  • Some problems can be solved by first finding and solving one or more sub-problems and then using the answer(s) to solve the original problem.
  • Information in a problem can often be shown by using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation.

Vocabulary:
dividend
divisor
quotient

Students will be skilled at...
  • relating a multiplication fact to its related division fact and vice versa.
  • computing quotients for division facts with divisors of 2, 3, 4, and 5.
  • computing quotients for division facts with divisors of 6 and 7.
  • computing quotients for division facts with divisors of 8 and 9.
  • solving multi-step problems.
  • comparing the equations on two sides of an equal sign to determine if they are equal.
  • computing the value of an unknown number in an equation.
  • generalizing using patterns and fact families to find answers to division facts with 0 and 1.
  • solving problems using multiplication and division facts.
  • solving division problems involving sharing and repeated subtraction by drawing a picture and writing a number sentence.

Assessment Evidence

Performance Assessment:
Other Evidence:
Writing Tasks:


Formative Assessment Tasks:



Learning Plan

Learning Activities:
8-1 Multiplication and division have an inverse relationship.

8-2 The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.
Different numerical expressions can have the same value. Or, the value of one expression can be less than (or greater than) the value of the other expression.

8-3 The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.

8-4 The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.

8-5 Some problems can be solved by first finding and solving one or more sub-problems and then using the answer(s) to solve the original problem.

8-6 An equation shows a balance between what is on the right side and what is on the left side of the equal sign.

8-7 Any number (except 0) divided by itself equal to 1. Any number divided by 1 is that number. Zero divided by an number (except 0) is zero. Zero cannot be a divisor.

8-8 Patterns and known facts can be used to find unknown multiplication facts. Division facts can be found by thinking of a related multiplication fact.

8-9 Information in a problem can often be shown by using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation.
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