Using Benchmark Decimals on a Number Line

Getting Started

The student uses only the numerators to locate the fractions on the number line.

The student does not have an appropriate strategy to locate fractions on the number line.

The student places and before the 0.25 because six and eight come before 25 and places the 12 and 47 after the 0.5 because they come after five.

What is your strategy for locating the fractions on the number line?

What do you know about the benchmark decimals on the number line? What are the fraction equivalents? How might thinking of these decimals as fractions help you?

Do all of the fractions and decimals refer to the same size whole? Why is that important?

Some of the numbers are given as decimals and some are given as fractions. How can you make the numbers easier to work with?

Can you read 0.17 aloud? Can you write that as a fraction? Where is 0.17 located on the number line?

What does the numerator of each fraction tell you? What does the denominator tell you?

Do all of the fractions and all of the decimals refer to the same size whole? Why is that important?

How many hundredths is equivalent to? How does that help you locate on the number line?

Encourage the student to express all of the numbers in a common form. Model for the student how to read decimals and write them as fractions. Guide the student to understand that the number of digits to the right of the decimal indicates the number of zeros in the denominator of the fraction. Begin with decimals such as 0.6 and 0.93. Next, introduce decimals with zeros in the tenths or hundredths place such as 0.40 and 0.07. Model for the student how to express a fraction with denominator 10 as an equivalent fraction with denominator 100. Use place value blocks, 10 by 10 grids, and money to model the equivalence of decimals such as 0.8 and 0.80 and the corresponding fractions of and . Provide opportunities for the student to use base ten models (e.g., blocks, number lines) to explore the relative sizes of decimals and fractions.

Provide additional opportunities for the student to locate decimal numbers given in tenths and hundredths on a number line when benchmark decimals or fractions are given. Guide the student to observe that every number is located at an exact spot on the number line, and equivalent numbers expressed in different forms share the same location (e.g., , and 0.50). Remind the student to consider the size of the whole when locating fractions/decimals on the number line.

Consider implementing the MFAS tasks Fractions to Decimals or Using Benchmark Fractions on a Number Line.

Making Progress

The student does not accurately locate numbers within the benchmark intervals.

The student does not recognize the number line consists of equal size intervals (in this case, hundredths).

The student places the fractions between the appropriate benchmarks without regard for the relative values.

How many hundredths are between each benchmark? How can you use that knowledge to help you locate the fractions on the number line?

How can you show on the number line that is about half of ?

What was your strategy for placing the decimals on the number line?

Provide additional opportunities for the student to locate fractions given in tenths and hundredths on a number line when benchmark decimals or fractions are shown. Remind the student the number line is divided into equal intervals. It is important to note that minor errors in proportionality are acceptable; however, the student should be able to reason about the size of each fraction and compare it to the benchmarks. For example, the student should be expected to understand that  should be placed almost equidistant from 0 and 0.25.

Consider implementing the MFAS task Using Benchmark Fractions on a Number Line (4.NF.3.6).

Got It

The student provides complete and correct responses to all components of the task.

The student accurately uses the benchmark decimals to locate each of the four fractions on the number line. The student places the about halfway in between 0 and 0.25, directly before 0.5, a bit less than the midpoint of 0.5 and 0.75, and directly to the right of 0.75.

Where would be located on the number line? Why is it in the same location as ? Do you know any other numbers that would be in the same location?

Another student placed near the zero. Why do you think that is?

If the number line were anchored with zero and two, where would you place 1?

How would you convince others that you placed the fractions correctly on the number line?

How would you compare 0.4 and 0.04?

Provide practice comparing two fractions to hundredths by reasoning about their size. Remind the student that comparisons are valid only when the two fractions refer to the same size whole. Challenge the student with numbers given in varying formats (e.g., compare to 0.77). Consider implementing the MFAS tasks from standard 4.NF.3.7.

Encourage the student to think of other equivalent forms of the benchmark decimals.

Extend the number line and challenge the student to locate decimals and fractions greater than one.