Unit of Study 13: Fluently Multiply with Products up to
Projected Time Allotment: 6 days
100
Global Concept Guides: Strategies for Multiplying by 3, 4, and 6; Strategies for Multiplying by 9, 8, and 7.
Prior Learning: MA.3.A.1.1 , MA.3.A.1.2, MA.3.A.1.3
Progressions Document Link
Show What You Know Task: Factor Power
3rd
Common Core State Standards for Mathematical Content:
Comments:
DO NOT subject any student to fact
3.OA.7: Fluently multiply and divide within 100, using strategies such as drills unless the student has
the relationship between multiplication and division (e.g., knowing that developed an efficient strategy for
8 ×5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end the facts included in drill.
of Grade 3, know from memory all products of two one-digit numbers.
(Van de Walle 2006, p. 94)
Notes on Assessment:
Utilize Fastt Math to assess
students’ focus facts and mastered
facts only.
Math Fact Automaticity Interview
See Common Performance Task link
below.
Unpacking the Standards for this Unit: In fourth grade, the standard uses the word fluently, which means
accuracy, efficiency (using a reasonable amount of steps and time), and flexibility (using strategies such as the
distributive property). “Know from memory” should not focus only on timed tests and repetitive practice, but
ample experiences working with manipulatives, pictures, arrays, word problems, and numbers to internalize
the basic facts (up to 10 x 10). By studying patterns and relationships in multiplication facts and relating
multiplication and division, students build a foundation for fluency with multiplication and division facts.
Students demonstrate fluency with multiplication facts through 10 and the related division facts. Multiplying
and dividing fluently refers to knowledge of procedures, knowledge of when and how to use them
appropriately and skill in performing them flexibly, accurately and efficiently. Students should have exposure
to multiplication and division problems presented in both vertical and horizontal forms. NCDPI, p. 12
Page
Future learning: Developing understanding and fluency with multi-digit multiplication and developing
understanding of dividing to find quotients involving multi-digit dividends - Students generalize their
understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They
apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value,
and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient,
accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the
numbers and the context, they select and accurately apply appropriate methods to estimate or mentally
calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand
and explain why the procedures work based on place value and properties of operations; and use them to
solve problems. Students apply their understanding of models for division, place value, properties of
operations and the relationship of division to multiplication as they develop, discuss, and use efficient,
accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and
accurately apply appropriate methods to estimate and mentally calculate quotients and interpret remainders
based upon the context.
1
Common Performance Task with Rubric for this Unit: Number Bonds - In this performance task, students
explain strategies used to complete related facts. Click here for the performance task and rubric.
3rd
Global Concept 1 of 2 for this Unit of Study: Fluently Multiply with Products up to
100 - Strategies for Multiplying by 3, 4, and 6
Projected Time
Allotment: 3 days
Sample Essential Questions:
Day 1: How can you use your doubles facts to help you multiply by 3?
Day 2: What strategies can you use to multiply by 4? Explain.
Day 3: How are the 6 facts like the 5 facts? Explain.
Instructional Resources
Manipulatives:
Students should use these tools as needed to
 Unit cubes
explore the relationships between the x2, x3,
 Two color counters
x4, x5, and x6 facts.
 Snap cubes
 Color tiles
 Number line - Students will use jumps to represent equal groups and the intervals to represent the number in each
group.
Lesson Ideas:
 Fruit Baskets - This can be used to connect the relationship between the x2 and x3 facts.
 X3 Corners - This is a game that can be used to reinforce strategies learned for multiplying by 3.
 1-40 Charts - Explore patterns by having students chart multiples of 2 and 4 on a 1 – 40 chart.
 Multi-Models - Students draw arrays on large grids to practice their x4 facts.
 Capture - A game that can be used to reinforce strategies learned for multiplying by 4.
 Circles of Dots - Students select a fact card and represent the fact by circling rows and dots in each row. Then, they
use the array to write an equation and find the product.
 Rio - This is a game that can be used to reinforce strategies learned for multiplying by 6.
 I have Who Has Cards - This is a game that can be used to reinforce strategies learned for multiplying.
For more info on SMP’s click here.
Because as teachers we…
 Provide varied opportunities for students to explore
basic math facts rather than simply asking them to
memorize. (SMP 7, 8)
 Allow students to investigate the meaning of facts
through hands-on activities. (SMP 1)
 Facilitate thoughtful discussions where multiple
strategies used to arrive at an answer are shared and
evaluated. (SMP 1, 3)
 Engage students in meaningful and varied practice
activities. (SMP 7, 8)
Page
Our students are able to…
 Use known facts to find products of unknown facts.
(SMP 7, 8)
 Explain strategies used to find unknown facts. (SMP
3)
 Make generalizations based on the predictability of
math facts. (SMP 7, 8)
 Connect operations to problem types and real
world examples. (SMP 2)
2
Interactive Online Resources:
 Fastt Math - Utilize this program for targeted fact practice and to generate fact practice printouts tailored to
students’ individual needs. See the Fastt Math icon on the math bulletin board for instructions.
For more information about integrating the content within this GCG, click here for the PowerPoint.
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1, 3)
 What patterns do you notice in the products?
 Does the order of the factors affect the product? Give examples to justify your thinking.
 What does it mean to triple a number? How is it different from doubling a number?
 How can you use your x2 facts to find x4 facts?
 How do the x5 facts compare to the x6 facts?
 How are the x1, x2, x3 facts alike? How are they different?
3rd
Global Concept 2 of 2 for this Unit of Study: Fluently Multiply with products up to
100 - Strategies for Multiplying by 7, 8, and 9
Projected Time
Allotment: 3 days
For more info on SMP’s click here.
Because as teachers we…
 Provide varied opportunities for students to
explore basic math facts rather than simply asking
them to memorize. (SMP 7, 8)
 Allow students to investigate the meaning of facts
through hands-on activities. (SMP 1)
 Facilitate thoughtful discussions where multiple
strategies used to arrive at an answer are shared
and evaluated. (SMP 1, 3)
 Engage students in meaningful and varied practice
activities. (SMP 7, 8)
Page
Our students are able to…
 Use known facts to find products of unknown
facts. (SMP 7, 8)
 Explain strategies used to find unknown facts.
(SMP 3)
 Make generalizations based on the predictability
of math facts. (SMP 7, 8)
 Connect operations to problem types and real
world examples. (SMP 2)
3
Sample Essential Questions:
Day 1: How can you use your tens facts to help you multiply by 9?
Day 2: How can you use doubling to help you multiply by 8? Explain.
Day 3: How does the commutative property make it more manageable to multiply by 7?
Instructional Resources
Manipulatives:
 Unit cubes
Students should use these tools as needed
 Two color counters
to explore the relationships between the x9,
 Snap cubes
x8, and x7 facts.
 Color tiles
 Number line - Students will use jumps to represent equal groups and the intervals to represent the number in
each group.
Lesson Ideas:
 Plates of Meatballs - This can be used to connect the relationship between the x9 and x10 facts.
 Nine Cross - This is a game that can be used to reinforce strategies learned for multiplying by 9.
 Crazy Eight - This is a game that can be used to reinforce strategies learned for multiplying by 8.
 Thunder Cake - This can be used as an engage to introduce strategies for multiplying by 7.
 Target 70 - This is a game that can be used to reinforce strategies learned for multiplying by 7. Click here for the
spinner.
Interactive Online Resources: (Must be interactive to be considered)
 Fastt Math - Utilize this program for targeted fact practice and to generate fact practice printouts tailored to
students’ individual needs. See the Fastt Math icon on the math bulletin board for instructions.
For more information about integrating the content within this GCG, click here for the PowerPoint.
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1, 3)
 What patterns do you notice in the products?
 Does the order of the factors affect the product? Give examples to justify your thinking.
 What does it mean to double a number? How can you use doubling to find x8 facts?
 How can you use your x10 facts to find x9 facts?
 How can the distributive property help you multiply by 7?
 How do turn around facts make multiplying by 7 more manageable?