Understanding Contributions and Additive Decomposition

The video tutorial explains how to decompose numbers additively by breaking them into groups that sum to the original number. It provides two examples: one with Jen and Dan contributing to a total of $16, and another with Jen, Dan, and Paul contributing to a total of $21. Each example explores different possible contributions while adhering to specific conditions, such as each person contributing at least $2 and having different amounts. The tutorial emphasizes understanding the concept of additive decomposition through practical examples.

What does it mean to decompose a number additively?

• To break a number into smaller groups

• To multiply a number by two

• To divide a number by its factors

• To subtract a number from itself

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CCSS.1.OA.A.1

In the first example, what is one possible contribution from Jen if Dan contributes $12?

• $4

• $8

• $10

• $6

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CCSS.2.OA.A.1

If Jen contributes $11, how much does Dan contribute to make a total of $16?

• $7

• $9

• $5

• $3

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In the first example, why can't both Jen and Dan contribute $8?

• Because they must contribute different amounts

• Because $8 is not allowed

• Because $8 is too little for one person

• Because $8 is too much for one person

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CCSS.2.OA.A.1

In the second example, if Jen contributes $5 and Dan contributes $6, how much does Paul contribute?

• $10

• $9

• $11

• $8

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CCSS.2.OA.A.1

What is the total amount pooled by Jen, Dan, and Paul in the second example?

• $19

• $21

• $20

• $18

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CCSS.2.OA.A.1

If Jen contributes $3 and Dan contributes $5, how much does Paul contribute to make a total of $21?

• $11

• $14

• $12

• $13

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CCSS.1.OA.A.1

In the second example, what is one possible contribution from Jen if Paul contributes $4?

• $12

• $14

• $16

• $18

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Why can't Dan and Paul both contribute $3 in the second example?

• Because Jen must contribute $3

• Because each contribution must be different

• Because each must contribute at least $5

• Because the total would exceed $21

What is the minimum contribution each person must make in both examples?

• $4

• $3

• $2

• $1