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Two important building blocks for understanding relationships between fraction and decimal notation occur in Grades 4 and 5. In Grade 4, students’ understanding of decimal notation for fractions includes using decimal notation for fractions with denominators 10 and 100 (4.NF.5; 4.NF.6). In Grade 5, students’ understanding of fraction notation for decimals includes using fraction notation for decimals to thousandths (5.NBT.3a).
Students identify correspondences between different approaches to the same problem (MP.1). In Grade 4, when solving word problems that involve computations with simple fractions or decimals (e.g., 4.MD.2), one student might compute 1/5 + 12/10 as .2 + 1.2 = 1.4, another as 1/5 + 6/5 = 7/5; and yet another as 2/10 + 12/10 = 14/10. Explanations of correspondences between 1/5 + 12/10, .2 + 1.2, 1/5 + 6/5, and 2/10 + 12/10 draw on understanding of equivalent fractions (3.NF.3 is one building block) and conversion from fractions to decimals (4.NF.5; 4.NF.6). This is revisited and augmented in Grade 7 when students use numerical and algebraic expressions to solve problems posed with rational numbers expressed in different forms, converting between forms as appropriate (7.EE.3).
Would you say that students should be able to convert fractions to decimals by the end of Gr.4 or the end of Gr. 5?
It depends which fractions and decimals. First, let me reiterate that the standards do not regard fractions and decimals as different kinds of numbers, but rather different ways of writing the same number. Thus, rather than talking about converting fractions to decimals, I would talk about writing fractions in decimal notation (and vice versa). And this is indeed the language used in the standards:
4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
So, in Grade 4, students deal with decimals that have one or two digits after the decimal point.
I would like a clarification of which grade level is the first grade level to introduce and work with decimals. It is my understanding that it is in 4th grade. As a person that provides professional development to teachers, the Progressions, Illustrative Mathematics, and this Forum are where I refer teachers to clarify their understanding of what the Standards are asking the students to learn and what it might look like. There are two Illustrative Tasks for 2nd grade that I am concerned send the message to teachers that they are to add $1.35 + $1.25, “Pet Shop” and “Choices, Choices, Choices”. I would like to teach the teachers the correct expectations for money and the use of decimals in 2nd Grade. Thank you!
I just looked at the Pet Shop task and this was just added to the comments:
- Mathematics Specialist wrote this public comment about 8 hours ago
Is the decimal point in the money notation appropriate for 2nd grade? Decimals in place value are not introduced until 4th grade. In referring to the Progressions and to the comments in the Forum, it seems as if the intent of this standard is to use the dollar sign and cent sign appropriately, not to work with decimal numbers.
- Kristin Umland wrote this public reply about 3 hours ago
You are so right–thank you for catching that! The task and solution are fixed now.
It looks like Choices, Choices, Choices was fixed as well.
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