3.OA.9 - About the Math, Learning Targets, and Rigor

Grade 3 Whole Numbers

3.OA.D.9

About the Math

Full Standard

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

 

Measurement Topic

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

3rd Grade Students Learning 3rd Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of addition and subtraction.

 

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Learning Targets

  • Describe patterns in addition and multiplication charts.
  • Explain patterns when adjusting addends. (i.e. 56 + 98 is the same as 54 + 100)
  • Explain that doubling a factor doubles the product.
  • Explain that a factor can be decomposed and the partial products can be put back together.
  • Explain patterns in addition for example (even + even = even, odd + odd = even, and odd + even = odd, two addends less than 50 have a sum less than 100, a difference of numbers is unchanged when both numbers are adjusted by the same amount)
  • Explain patterns in multiplication for example (even x even = even, odd x odd = odd, and odd x even = even)

 

About the Math

We can use patterns to solve problems, make calculations, or recall basic facts. It is important that we record equations intentionally so that patterns can be observed.

  • Describe patterns in addition and multiplication charts.

Addition chart patterns to examine include patterns within sums of even/odd, odd/odd, or even/even addends. Other patterns include those of using ten (e.g. 9 + 7 = 16). These patterns can be extended to other numbers. For example, we can use ten with two and three-digit numbers (e.g. 249 + 7 is 256 as we make a new ten 250 and add on).

The multiplication chart is full of patterns. Connecting these patterns helps students learn the basic facts. For instance, doubling the products of four gives you the eights tables. Similarly, numbers with a factor of six can be found by doubling the three products. 

  • Explain patterns when adjusting addends. (i.e. 56 + 98 is the same as 54 + 100)

Adjusting can improve efficiency. We can adjust addends in any way to use friendly, compatible numbers. The example above is just one of an infinite number of possible adjustments we can use when adding. Another form of adjusting is a constant difference or shifting the difference. For example, you can shift the difference (50 - 27 is the same as 49 - 26).

  • Explain that doubling a factor doubles the product.

When one factor is doubled, the product is doubled. This is useful for recalling basic facts and for other multiplication situations in later grades. For example, 4 x 3 = 12 so 4 x 6 = 24. The product of 24 is double 12 because the factor of 6 is double 3.

  • Explain that a factor can be decomposed and the partial products can be put back together.

We can decompose a factor and add the partial products. This is especially useful as the number of digits in a number changes. It is also helpful for recalling basic facts. For example, 7 x 6 can be thought of as 7 x 5 + 7 x 1 or 35 + 7.

  • Explain patterns in addition for example (even + even = even, odd + odd = even, and odd + even = odd, two addends less than 50 have a sum less than 100, a difference of numbers is unchanged when both numbers are adjusted by the same amount)

These patterns help students determine if their calculations are accurate. These patterns should be discovered through investigation. They should be explored to see if they are always true. These are not "rules" for students to memorize.

  • Explain patterns in multiplication for example (even x even = even, odd x odd = odd, and odd x even = even)

Like patterns with addition, patterns in multiplication help students determine if their calculations are reasonable. Other patterns to know in 3rd grade include products of 5 have a 0 or 5 in the ones place and the products of 10 have a 0 in the ones place.

 

Progression of Standard within Grade 3

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
  • Describe patterns in addition and multiplication charts.
  • Explain patterns when adjusting addends. (i.e. 56 + 98 is the same as 54 + 100)
  • Explain that doubling a factor doubles the product.
  • Explain patterns in addition for example (even + even = even, odd + odd = even, and odd + even = odd, two addends less than 50 have a sum less than 100, a difference of numbers is unchanged when both numbers are adjusted by the same amount)
  • Explain that a factor can be decomposed and the partial products can be put back together.
  • Explain patterns in multiplication for example (even x even = even, odd x odd = odd, and odd x even = even)
  • Explain patterns in multiplication for example (even x even = even, odd x odd = odd, and odd x even = even)

 

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 2 Grade 4
Determine whether a group of objects (up to 20) has an odd or even number of members (2.OA.3) Generate shape and number patterns ( 4.OA.5)

 

 

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Instructional Tasks

TASKS

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

  • What patterns do you notice on an addition table?
  • What patterns do you notice on a multiplication table?
  • Describe the relationship between multiplying by 2 and multiplying by 4.
  • John says that when you multiply any number by an an even number, you will always get an even product. Explain why John is or is not correct.
  • Malik said when you multiply two odd numbers, the product is always odd. He used 3 x 7 and 7 x 7 to support his statement. Is he correct?
  • 6 x 4, 6 x 5, 6 x 6...explain the pattern with the products of these problems.
  • Show what you understand about patterns to explain why 6 x 3 is the same as 6 + 6 + 6  and 3 + 3 + 3 + 3 + 3 + 3 
  • Why does any number ending in a 5 or a 0 always have 5 as one of it's factor?  Prove your explanation with examples. 

 

 

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.

Module •

Panel Content

 

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

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 K-3  

57 (Patterns on the Hundreds Chart, Activity 2.29)
58 (Missing Numbers, Activity 2.30)
285 (What's Next and Why?, Activity 10.8)
288 (Fractured Chart Pieces, Activity 10.12)
290 (One Up and One Down: Multiplication, Activity 10.15)
298 (Number Tricks, Activity 10.19) 

  Nimble With Numbers

1-2

3-4

58

115-128 
  Hands On Standards

1-2

3-4

90-91 (Skip Counting Patterns)

92-93 (Skip Counting by 5's)

104, (Commutative Property)

108, (Associative Property)
  Groundworks Reasoning with Numbers 3 32-39 (Flags) 
  Fundamentals 3-4

48-51 (Four of a Kind) 

56-59 (Double Barrel)
  Developing Mathematics with Unifix

 

42-43 (Number Patterns)

74-75 (Discovering 1 to 100 on a 100 Tack)
  Roads to Reasoning 2

12 (Number Pattern)

26 (Skip-Counting) 
  Developing Mathematics with Base Ten   2-3
  NumberSense 4-6 176-178 
  Brain-Compatible Activities
for Mathematics		 2-3 48-50

 

 

 

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Independent Work

Centers

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

 

 

 

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.

 

 

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Assessment

Learning Targets

  • Describe patterns in addition and multiplication charts.
  • Explain patterns when adjusting addends. (i.e. 56 + 98 is the same as 54 + 100)
  • Explain that doubling a factor doubles the product.
  • Explain that a factor can be decomposed and the partial products can be put back together.
  • Explain patterns in addition for example (even + even = even, odd + odd = even, and odd + even = odd, two addends less than 50 have a sum less than 100, a difference of numbers is unchanged when both numbers are adjusted by the same amount)
  • Explain patterns in multiplication for example (even x even = even, odd x odd = odd, and odd x even = even)

 

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

Download Rubric for Tasks

(pdf)

 

 

 

 

 

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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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.