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

Grade 3 Whole Numbers

3.OA.D.9

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:

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

Not reported on report card but taught concurrently with other standards.

Not reported on report card but taught concurrently with other standards.

Not reported on report card but taught concurrently with other standards.

Not reported on report card but taught concurrently with other standards.

 

About the Math

Skills and concepts below are learning goals for this standard.

  • 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)

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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