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# 3.OA.D.9

**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.*

__Summary:__

Identifying a particular arithmetic pattern is critical to understanding the complex and dynamic relationships between numbers. While it is important to verbally explain such things, expressing them as a numeric equation is also important.

__Understanding the Standard:__

__Understanding the Standard:__

- The use of manipulatives is useful for practice with this skill. Such activities allow students to create their own patterns and then express their creations with a numeric sentence. For example, students can highlight all of the even numbers on a 100s chart. They can then express the pattern as "plus 2" to go from one highlighted number to the next. 2 + 2 = 4, and 4 + 2 = 6, etc. Similarly, students can highlight all of the multiples of 10, and express these as a "plus 10" rule. They could show that 10 + 10 = 20, and 20 + 10 = 30, and all extensions of these equations will correspond with the highlighted numbers on the 100s chart.
- Using a multiplication table, students can look for all of the occurrences of a given number, say 24, and then express 24 as multiplication expressions that are all equivalent. 24 = 6 x 4 = 4 x 6 = 8 x 3 = 3 x 8.
- Teachers need to guide students’ interpretation of patterns they encounter into numeric sentences.

__Questions to Focus Instruction:__

- Are students able to express numeric patterns using a numeric sentence?
- Are students able to extend numeric patterns?

__Skills__

**Prior to:**Students have had a variety of experiences using addition and multiplication tables. Go to 2.NBT.B.9. to see previous skills in this progression.

**Students can identify a variety of number patterns and use numeric expressions to represent their findings. Further, students are able to extend those patterns beyond their representation on a chart.**

At Grade Level:

At Grade Level: