Curriculum Guide
Grade 3 – Math Standard 1.3
Math.1.3 - Multiplication and division are inverse operations and can be modeled in a variety of ways.
Related Colorado Department of Education Sample Units:
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Multiply, Divide & Conquer (Concepts: Multiplication, division, equal groups, arrays, combinations, fair share, rate, scaling, area, unit
conversions, addition, subtraction, rows, columns, times as many, times fewer, unknown factor, inverse operations, substitution, models,
properties of operations (commutative property, associative property, distributive property, identity property, zero property), equations,
arithmetic patterns)
Essential Questions - 21st Century Skills and Readiness Competencies (District):
1. What does "product" mean?
2. What does "quotient" mean?
3. How do you use multiplication and division to solve word problems?
4. How can you find the missing number in a multiplication or division equation?
5. How can you use arithmetic to help achieve a goal involving money?
6. How can understanding the properties of operations help when you multiply and
divide?
7. How are multiplication and division related?
8. How can understanding the properties of operations help you to learn basic
multiplication and division facts?
9. Why is it important to memorize multiplication facts?
10. How do you use adding, subtracting, multiplying, or dividing to solve word
problems?
11. How do you solve two-step word problems?
*12. Why do you use letters when writing equations for two-step word problems?
13. Why is it important to estimate before solving a problem?
14. How can you explain patterns using the properties of operations?
*Meets embedded requirement for Standard 2
Academic Vocabulary (District):
repeated addition
repeated subtraction
arrays
factor
product
quotient
zero property of multiplication
identity property of multiplication
commutative property of multiplication
Evidence Outcomes (District):
1. Interpret products of whole numbers.
2. Interpret whole-number quotients of whole numbers.
3. Use multiplication and division within 100 to solve word problems in situations
involving equal groups, arrays, and measurement quantities.
4. Determine the unknown whole number in a multiplication or division equation
relating three whole numbers.
5. Model strategies to achieve a personal financial goal using arithmetic operations.
6. Apply properties of operations as strategies to multiply and divide.
7. Interpret division as an unknown-factor problem.
8. Fluently multiply and divide within 100, using strategies such as the relationship
between multiplication and division or properties of operations.
9. Recall from memory all products of two one-digit numbers.
10. Solve problems involving the four operations, and identify and explain patterns in
arithmetic.
11. Solve two-step word problems using the four operations.
12. Represent two-step word problems using equations with a letter standing for the
unknown quantity.
13. Assess the reasonableness of answers using mental computation and estimation
strategies including rounding.
14. Identify arithmetic patterns (including patterns in the addition table or multiplication
table) and explain them using properties of operations.
Assessment (District):
1. Use the Identifying Factors and Products.
 See: http://www.free-math-handwriting-and-readingworksheets.com/multiplication-factors.html
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Identifying Factors and Products
2. Given a set of division problems written in a variety of formats, students will circle
the quotient of each problem.
associative property of multiplication
distributive property of multiplication
equation
*variable
rounding
estimate
estimation
interpret
quantity
computation
solve
operations
division
multiplication
divisor
dividend
*Meets embedded requirement for Standard 2
3a. Use the Rubric for "Pedal Power" Performance Task.
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3a. Rubric for Pedal Power
3b. Use this site to create an assessment for multiplication word problems.
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3b. Multiplication Word Problems
3b. Create Division Word Problems Assessment
3c. Use this site to create an assessment for division word problems.
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3c. Practice Sheets for Assessing Division Word Problems
4. Use these assessments for finding missing numbers in multiplication and division
equations.
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4. Missing Numbers in a Multiplication Sentence
4. Missing Number in a Division Equation
5a-b. Use the rubric to assess the "Skip the Movie" Performance Task.
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5a-b. Rubric for Assessing the "Skip the Movie" Performance Task
5c. Use this site for a generic Performance Task Rubric.
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5c. General Task Rubric
6a. Use the link to assessment for addition properties.
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6a. Properties of Addition Worksheet
6b. Use the link to assessment for multiplication properties.
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6b. Practice Sheet for Properties of Multiplication
7a. Use the link to missing factor assessment.
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7a. Create Missing Factor Assessments
7b. Use the assessment for division as an unknown factor.
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7b. Practice Sheet Relating Division as an Unknown Factor
8. Use the link to multiplication facts assessment.
 See: http://www.superteacherworksheets.com/multiplication.html
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8. Multiplication Facts Assessment
9. Use the link to multiplication facts.
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9. Multiplication Facts
10. Create a custom assessment with a variety of operations.
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10. Word Problems
11. Use the link to the two-step word problem assessment.
 See: http://www.kutasoftware.com/freemain.html
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11. Assessment for Two-step Word Problems
12. This is the same assessment as used on #11. However, this time have the
students write an equation using a letter to stand for the unknown quantity.
 See: http://www.kutasoftware.com/freemain.html
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12. Writing Equations for Two-step Problems Using Variables
13. Choose from a variety of word problem activities. Have students estimate the
answer first, then solve, and check for the reasonableness of their answer.
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13. Word Problems
14. Use the link to the Performance Task Rubric.
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1-14. Cookie Dough Unit (Rubric Included)
14. Performance Task - General Rubric
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Suggested Activities/Strategies (District):
1. Teach the terms "factor" and "product." Display the poster identifying each.
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1. Factors and Products Poster and Activities
Posters Displaying Factors and Products
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2. Teach the terms "quotient," "dividend," and "divisor." Display the poster identifying
each.
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3. Use the "Pedal" Performance Task. Students use problem solving skills to determine
the number of gears on a bike.
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3b. Use the videos and practice with word problems.
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4. Use the Missing Factor PowerPoint.
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5. Distribute copies of the "Josh wants.." story and read together. Have the students
work in small groups to decide what Josh should do and why. Afterwards, have
students set a goal for something they would like to purchase in the future. They
should then explain how they will work/save for the item and demonstrate, using a
chart or diagram to illustrate how they will achieve this goal.
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2. Division Poster
3a. Pedal Power Performance Task
3b. Word Problems with Katie Video
4. Missing Factor PowerPoint
5. Story
5a. Use the Teacher Directions for "Skip the Movie" Performance Task.
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5a. Teacher Instructions for "Skip the Movie" Performance Task
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5b. Use the "Skip the Movie" Performance Task. Students must solve a problem
involving making a financial choice.
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6a. Watch video explaining the commutative property of multiplication in word
problems.
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6b. Play Basketball Multiplication to practice with the properties of multiplication.
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6c. Watch the video explaining the associative and commutative properties of
multiplication.
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5b. "Skip the Movie" Performance Task
6a. Commutative Property of Multiplication Video
6b. Basketball Multiplication - Practice with the Properties
6c. Associative and Commutative Properties Video
7a. Watch the video explaining how division is an unknown factor problem.
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7a. Division as an Unknown Factor Tutorial Video
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7b. Watch the video explaining how multiplication and division are related.
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7c. View the video with multiplication/division input/output boxes.
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8. Play the Basketball Game to practice properties of multiplication.
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7b. Relationship Between Multiplication and Division Video
7c, 14. Input/Output Boxes Video
8. Basketball Game - Properties of Multiplication
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9a. Play Baseball Multiplication to practice facts.
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9b. Play the "I Have, Who Has?" Game.
 See: http://www.mathwire.com/whohas/whohas.html
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9a. Baseball Multiplication
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9b. I Have, Who Has Cards
Resources/Technology (District):
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Math Games
Everyday Math Games
Performance Task Bank
I Have, Who Has Cards
A Variety of Practice Activities
Multiplication Tables
Funbrain Practice with Basic Skills
Practice Sheets for Properties of Multiplication
Practice with a Variety of Word Problems
Word Problems
Basic Fact Practice Sheets
Teaching Word Problems
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10. Students create a Frayer Model with key words/tips to help them solve word
problems. "Key words" or "Problem Solving Hints" can be put in the center of the
Frayer Model. Use the sites listed under "Resources" to create a variety of practice
word problems. Have students use their Frayer Models to help them highlight the key
words. (See resources for an explanation of Frayer Models.)
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11a. View the video introducing solving two-step problems.
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11b. Practice with two-step word problems.
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12. Practice choosing the correct algebraic expression.
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13a. View the video explaining estimation.
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13b. Students play the "Golden Path" Game in which they move from space to space
by choosing the space with the largest answer.
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14a. Use the Betty's Birdhouse Performance Task. Students analyze patterns and use
multiplication to solve the problem.
 See: http://rda.aps.edu/MathTaskBank/start.htm
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14b. Use the "Meddling with Medals" Performance Task.
 See: http://rda.aps.edu/MathTaskBank/start.htm
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10. Tips for Teaching Word Problems
11a. Demonstrating Two-step Word Problems Video
11b. Two-step Word Problems Practice
12. Algebraic Expressions
13a. Explaining Estimation Video
13b. "Golden Path" Game
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14a. Betty's Birdhouse Performance Tasks
14b. Meddling with Medals Performance Task
14c. Use the Multiplication Grid Activity. Students click and drag numbers into the grid.
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14c. Multiplication Grid
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14d. Complete the Patterns in Multiplication "Hotel 6" Activity. Students use patterns to
help them solve larger multiplication problems.
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14e. Use the activity involving finding patterns in numerical sequences.
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1-14. This "Cookie Dough" unit encompasses numerous skills with multiplication and
division. Performance tasks and assessments are included.
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14d. Hotel 6 Activity
14e. Number Patterns Activity
1-14. Cookie Dough Unit