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The Stamp Collection


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

Task

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:

Fractions_3_786faf7b6d3c295b4562b5f552233984

2 units = 120

1 unit = 60

60 - 3 = 57

Masha had 57 stamps left.

kassymov says:

over 3 years

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

Cam says:

over 3 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 5 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 5 years

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