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3rd Unit of Study 13: Fluently Multiply with Products up to 100

Projected Time Allotment: 6 days

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.1.3Progressions Document LinkShow What You Know Task: Factor Power

Common Core State Standards for Mathematical Content:

3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 ×5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Comments:DO NOT subject any student to fact drills unless the student has developed an efficient strategy for the facts included in drill. (Van de Walle 2006, p. 94)

Notes on Assessment: Utilize Fastt Math to assess students’ focus facts and mastered facts only.

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

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.

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.

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3rdGlobal 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 ResourcesManipulatives:

Unit cubes Two color counters 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:

Jaleah's Friends - This can be used to connect the relationship between the x2 and x3 facts. X3 Memory - This is a game that can be used to reinforce strategies learned for multiplying by 3. Multiple Round Up - Explore patterns by having students chart multiples of 2 and 4 on a 100 chart. Quilt Cover Up - Students draw arrays on large grids to practice their x4 facts. Go Fish - A game that can be used to reinforce strategies learned for multiplying by 4. x6 Arrays - Students select a fact card and represent the fact by tracing rows and squares in each row. Then, they use

the array to find the product. Rio - This is a game that can be used to reinforce strategies learned for multiplying by 6. I have Who Has Directions - This are the directions that go with the game below. I have Who Has Cards - This is a game that can be used to reinforce strategies learned for multiplying by 4 and 6.

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?

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)

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)

Students should use these tools as needed to explore the relationships between the x2, x3, x4, x5, and x6 facts.

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3rdGlobal 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

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 ResourcesManipulatives:

Unit cubes Two color counters 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:

Delicious Dots - This can be used to connect the relationship between the x9 and x10 facts. Nifty Nines - This is a game that can be used to reinforce strategies learned for multiplying by 9. Super Starburst - This can be used to reinforce the strategy of Double-Double when multiplying by 8. Easy Eights - This is a game that can be used to reinforce strategies learned for multiplying by 8. Party Favors - This can be used as an engage to introduce strategies for multiplying by 7. Super Sevens - This is a game that can be used to reinforce strategies learned for multiplying by 7.

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?

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)

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)

Students should use these tools as needed to explore the relationships between the x9, x8, and x7 facts.