4.OA.4 - About the Math, Learning Targets, and Rigor

Full Standard 

Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. 

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

4th Grade Students Learning 4th Grade Standards

Quarter 1	Quarter 2	Quarter 3	Quarter 4
	Report Card Measurement Topic: Demonstrates understanding of multiplication.

3rd Grade Students Learning 4th Grade Standards

Quarter 1	Quarter 2	Quarter 3	Quarter 4
	Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Learning Targets

• Find factor pairs of any number between 1 and 100.
• Find multiples of a number (multiples up to 100).
• Determine if a number is prime or composite.

 

About the Math

A factor is a number that is multiplied by another number to yield a product. Two and eight are factors of sixteen. A multiple is the product of a whole number and any other whole number. Sixteen is a multiple of eight

• Find factor pairs of any number between 1 and 100.

1, 3, 7, and 21 are factor pairs of 21. Students find factor pairs of numbers to 100. Students should use basic fact recall and number sense to identify factor pairs. Factoring procedures should be avoided. Explicit instruction of divisibility rules is not appropriate, however student discovery of these rules could be an enrichment within this standard for students who show proficiency with factors, multiples, and prime/composite numbers. 

• Find multiples of a number (multiples up to 100).

24 is a multiple of 1, 2, 3, 4, 6, 8, 12, and 24. Students determine if a number is a multiple of another number. 

• Determine if a number is prime or composite.

Sixteen is a multiple of eight. A prime number has two unique factors. The number one is considered to be neither prime nor composite. A composite number has more than 2 factors; composite numbers can be represented by at least two unique rectangular arrays.  

Essential vocabulary for this standard includes factor, factor pairs, multiple, prime number, and composite number.

 

 

 

Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year

Quarter 1	Quarter 2	Quarter 3	Quarter 4
	Find factor pairs of any number between 1 and 100. Find multiples of a number (multiples up to 100). Determine if a number is prime or composite.	Revisit through routines.	Revisit through routines.

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades

Grade 3	Grade 6
Fluently multiply and divide (3.OA.7)	Find GCF and LCM (6.NS.4) Write and evaluate numerical expressions with exponents (6.EE.1)

 

 

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TASKS

These tasks can be used with small group or whole group instruction. 

• Using the hundreds chart from the resources page, students will investigate multiples and see what patterns they notice. On the hundreds chart, shade in all of the multiples of 2 that are less than 50. Students can continue this process with the other hundreds charts using multiples of 3, 4, 5 and 6. As students work, look for accurately identified patterns that are made about the chosen number and its multiples. Determine if the students can provide mathematical support for their statements, using the hundreds chart or their own number sense as evidence. Have teams share their insights with the whole group.
• After defining important vocabulary for the lesson (prime, composite, array, factor), students will use colored tiles to create arrays for numbers 1-20 to determine if they are prime or composite. Students should build arrays and record the factors (or the dimensions) used to create the array. Consider using 1-inch graph paper for students to use as a recording sheet.
• What are possible multiples that could go in the Venn Diagram? Place at least three numbers in each section of the Venn.
• Jacob said that all prime numbers have to be odd? Do you agree with him? Justify your answer.
• How are the terms “factors” and “multiples” related? Use examples to support your answer.
• Linda says that 33 is prime because it is odd. Is she correct? Explain why or why not.
• What products could have a factor of 4? How many of those products exist in the numbers 1-100? What are they?
• Name three prime numbers greater than 12? What is the greatest prime number in the number set 1-100?
• Use the digits 0-9 to form five prime numbers.

 

SLIDE-BASED TASKS 

  These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

 

 

Additional Tasks

  These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.] 

• The Locker Game Links to an external site. (Illustrative Math)
• Identifying Multiples Links to an external site. (Illustrative Math)
• Numbers in a Multiplication Table Links to an external site. (Illustrative Math)
• Multiples of 3, 6, and 7 Links to an external site. (Illustrative Math)
• Geared Up Links to an external site. (3 Act Task, G.Fletcher)
• Factor Track Links to an external site. (Nrich lesson seed)
• Factor Lines Links to an external site. (Nrich lesson seed)
• Factors and Multiples Links to an external site. (Nrich lesson seed)
• Chocolate Factory Links to an external site. (NCTM Illuminations Lesson)
• Number Riddles Links to an external site.(Georgia Department of Education, pg. 103-106)
• The Sieve of Eratosthenes Links to an external site. (Georgia Department of Education, pg. 40-45)
• Prime vs. Composite Links to an external site. (Georgia Department of Education, pg. 27-30)
• Investigating Prime and Composite Numbers Links to an external site. (Georgia Department of Education, pg. 24-26)
• Finding Multiples Links to an external site.(Georgia Department of Education, pg. 56-59)
• Factor Trail Game Links to an external site.(Georgia Department of Education, pg. 31-34)
• Cicadas, Brood X Links to an external site. (Georgia Department of Education, pg. 51-55)
• Finding Products Links to an external site.(Georgia Department of Education, pg. 60-63 )
• Hot Salsa Download Hot Salsa
  (Utah Core Academy Lesson)
• Bake Sale Download Bake Sale
  (Utah Core Academy Lesson)
• Program Seating Download Program Seating
  (Utah Core Academy Lesson)
• School Supply Shopping Download School Supply Shopping
  (Utah Core Academy Lesson)
• Animal Crackers Download Animal Crackers
  (Utah Core Academy Lesson)

 

Tasks From Print Resources

  These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	3-5	Finding Factors, Activity 2.22, Page 63 Factor Patterns, Activity 2.23, Page 64 Expanded Lesson Area Model for Multiplication, Page 129
	Groundworks Reasoning with Numbers	4 5	48-55 48-55, 60-61
	Nimble with Numbers	6-7	30-31, 41,
	Navigating Through Algebra	3-5	15-17
	Ten Minute Math		12-15
	Math Intervention: Building Number Power	3-5	144-146
	NumberSense	4-6 3-4	104-106, 176-177
	Math In Practice Teaching Fourth-Grade Math	4	Module 2

 

 

 

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Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

• Building Prime and Composite Numbers Download Building Prime and Composite Numbers
  (HCPSS-adapted print resource)
• Coloring Common Multiples Download Coloring Common Multiples
  (HCPSS-adapted print resource)
• Missing Factor Download Missing Factor
  (HCPSS-adapted print resource)
• Finding Common Multiples Download Finding Common Multiples
  (HCPSS-adapted print resource)
• Prime or Composite Download Prime or Composite
  (HCPSS-adapted print resource)
• Factor Trail Game Links to an external site. (NCTM Illuminations, print resource)
• Play Two-Minute Multiples Links to an external site. (print resource)

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

Factors and multiples/prime and composite:

• Practice A Links to an external site.
• Practice B Links to an external site.
• Practice C Links to an external site.
• Practice D Links to an external site..

• Factors and Multiples a Links to an external site.
• Factors and Multiples b Links to an external site.

 

• Solve Problems Involving Multiples Links to an external site.
• Solve Problems Involving Multiples_2 Links to an external site.
• Solve Problems Involving Multiples_3 Links to an external site.
• Solve Problems Involving Factors and Multiples Links to an external site.
• Solve Problems Involving Factors and Multiples_2 Links to an external site.
• Identify Prime Numbers Links to an external site.
• Identify Prime and Composite Numbers Links to an external site.
• Reason About Prime and Composite Numbers Links to an external site.

 

 

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Learning Targets

• Find factor pairs of any number between 1 and 100.
• Find multiples of a number (multiples up to 100).
• Determine if a number is prime or composite.

Learning targets identify what students should be able to do.  This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.

 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

 

 

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