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Using Place Value


Alignments to Content Standards: 4.NF.C.7

Task

  1. Fill in the following blanks to:

    0.17, 0.27, ______, ______, ______, ______, ______, _____

    ______, ______, 0.56, 0.66, ______, ______, ______, ______

    ______, ______, ______, 103.12, ______, 103.32, ______, ______

    ______, ______, ______, 103.12, ______, ______, ______, 103.16

    ______, ______, ______, 103.12, 113.12, ______, ______, ______

    • Count by tenths:

    • Count by tenths:

    • Count by tenths:

    • Count by hundredths

    • Count by tens:

  2. Fill in the blank with $\lt$, $=$ , or $\gt$ to make the correct comparison.

    • $4$ tenths + $3$ hundredths _____ $2$ tenths + $12$ hundredths
    • $3$ hundredths + $4$ tenths _____ $2$ tenths + $22$ hundredths
    • $5$ hundredths + $1$ tenth _____ $11$ tenths + $4$ hundredths
    • $5$ hundredths + $1$ tenth _____ $15$ hundredths + $0$ tenths
    • $5$ hundredths + $1$ tenth _____ $0$ tenths + $15$ hundredths
  3. Fill in the blank with $\lt$, $=$ , or $\gt$ to complete the equation.

    • $0.01$ _____ $0.11$

    • $0.2$ _____ $0.20$

    • $0.6$ _____ $0.41$

    • $0.07$ _____ $0.70$

    • $0.57$ _____ $0.75$

IM Commentary

Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

Part a requires students to use what they know about place value to count forward and backward from a given number by tens, tenths, and hundredths. It makes explicit the connections between place value, counting, and, with the help of some classroom discussion, makes a connection to addition and subtraction.

Part b illustrates the cluster heading, “Understand decimal notation for fractions, and compare decimal fractions.” Students can justify with an explanation or a visual model, such as a number line diagram. Whatever method the student chooses, it must be clear that comparisons are only valid when based on the same whole.

If needed students may be asked to provide a model to justify their response in part c. Acceptable models could include a number line, an area model, money, etc.

Solutions

Solution: Solution to Part a

  • Count by tenths:
  • 0.17, 0.27, 0.37, 0.47, 0.57, 0.67, 0.77, 0.87,

  • Count by tenths:
  • 0.36, 0.46, 0.56, 0.66, 0.76, 0.86, 0.96 , 1.06

  • Count by tenths:
  • 102.82, 102.92, 103.02, 103.12, 103.22, 103.32, 103.42, 103.52

  • Count by hundredths:
  • 103.09, 103.10, 103.11, 103.12, 103.13, 103.14, 103.15, 103.16

  • Count by tens:
  • 73.12, 83.12, 93.12, 103.12, 113.12, 123.12, 133.12, 143.12

Solution: Solution to Part b

  • $4$ tenths + $3$ hundredths $\gt$ $2$ tenths + $12$ hundredths
  • $3$ hundredths + $4$ tenths $\gt$ $2$ tenths + $22$ hundredths
  • $5$ hundredths + $1$ tenth $\lt$ $11$ tenths + $4$ hundredths
  • $5$ hundredths + $1$ tenth = $15$ hundredths + $0$ tenths
  • $5$ hundredths + $1$ tenth = $0$ tenths + $15$ hundredths

Solution: Solution to Part c

  • $0.01 \lt 0.11$
  • $0.2 = 0.20$
  • $0.6 \gt 0.41$
  • $0.07 \lt 0.70$
  • $0.57 \lt 0.75$

Shelah Feldstein says:

over 3 years

The plurals part b. need to be revised... 3rd bullet- "5 hundredths + 1 tenths _____ 11 tenths + 4 hundredths"

Cam says:

over 3 years

Fixed, thanks!

John says:

about 4 years

Am I incorrect in my interpretation of the standards (4.NF.C, 4.NBT.2 and 5.NBT.3a in particular) that students are not required to read decimals in written form (as in part b here) until grade 5? I see this skill appearing in a few different 4.NF tasks, and it seems not yet explicit in the standards. In grade 2, fraction words half, third, fourth and quarter are explicitly included. Am I splitting hairs because of the overlap with NBT when talking about decimal fractions?

Kristin says:

over 3 years

Dear johnrmead,

Sorry for the long-delayed response; this comment slipped past us. If you look at page 12 of the NBT progression, I think you can interpret it to say that part (b) of this task is appropriate:

http://commoncoretools.me/wp-content/uploads/2011/04/ccss_progression_nbt_2011_04_073_corrected2.pdf

In any case, I don't think you'd want something like that on a high-stakes assessment, but it seems very useful in instructional settings.