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# The Stamp Collection

Alignments to Content Standards: 3.OA.D.8

Masha had $120$ stamps. First, she gave her sister half of the stamps and then she used three to mail letters. How many stamps does Masha have left?

## IM Commentary

This task uses language, "half of the stamps," that students in Grade 5 will come to associate with multiplication by the fraction $\frac12$. In Grade 3, many students will understand half of 120 to mean the number obtained by dividing 120 by 2. For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

## Solution

We can visualize the problem with a bar diagram:

2 units = 120

1 unit = 60

60 - 3 = 57

#### kassymov says:

over 4 years

Would division of a number above 100 included in 3rd grade?

#### Cam says:

over 4 years

My personal opinion is that the division of 120 by 2 is certainly developmentally appropriate for third grade. It seems a notch below the 4th grade standard 4.NBT.6: "Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." But I'd agree that it's more borderline whether or not it would be appropriate for assessment purposes.

#### cassienorvell says:

over 6 years

[Editor's note: this comment applies to an earlier misclassification of the task under 4.NF] This is great! But could you please provide an illustration or further explanation for Grade 4 NF 3C. Specifically, are the equivalent fractions for the mixed numbers the old "improper fractions"?

#### Kristin says:

over 6 years

I will put a call out for our item writers to work on this!